Noise in AlGaN/GaN HEMTs and Oscillators - Microwave Electronics ...
Noise in AlGaN/GaN HEMTs and Oscillators - Microwave Electronics ...
Noise in AlGaN/GaN HEMTs and Oscillators - Microwave Electronics ...
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Committee <strong>in</strong> charge:<br />
UNIVERSITY of CALIFORNIA<br />
Santa Barbara<br />
<strong>Noise</strong> of <strong>Al<strong>GaN</strong></strong>/<strong>GaN</strong> <strong>HEMTs</strong> <strong>and</strong> <strong>Oscillators</strong><br />
A dissertation submitted <strong>in</strong> partial satisfaction of the<br />
requirements for the degree of<br />
Professor Robert A. York, Chair<br />
Professor Umesh K. Mishra<br />
Professor Mark J. Rodwell<br />
Dr. Yifeng Wu<br />
Doctor of Philosophy<br />
<strong>in</strong><br />
Electrical <strong>and</strong> Computer Eng<strong>in</strong>eer<strong>in</strong>g<br />
by<br />
Christopher Sanabria<br />
June 2006
The dissertation of Christopher Sanabria is approved:<br />
Chair<br />
June 2006
<strong>Noise</strong> of <strong>Al<strong>GaN</strong></strong>/<strong>GaN</strong> <strong>HEMTs</strong> <strong>and</strong> <strong>Oscillators</strong><br />
Copyright c○ 2006<br />
by<br />
Christopher Sanabria<br />
iii
EDUCATION<br />
Curriculum Vitæ<br />
Christopher Sanabria<br />
Bachelor of Science <strong>in</strong> Electrical Eng<strong>in</strong>eer<strong>in</strong>g, Magna Cum Laude, University of<br />
Notre Dame, May 2001.<br />
Master of Science <strong>in</strong> Electrical <strong>and</strong> Computer Eng<strong>in</strong>eer<strong>in</strong>g, University of California,<br />
Santa Barbara, December 2002.<br />
Doctor of Philosophy <strong>in</strong> Electrical Eng<strong>in</strong>eer<strong>in</strong>g, University of California, Santa Barbara,<br />
June 2006.<br />
PROFESSIONAL EMPLOYMENT<br />
May 1998 - August 1998, Intern, Delphi-Delco <strong>Electronics</strong>, Kokomo, IN.<br />
May 1999 - August 1999, Intern, Delphi-Delco <strong>Electronics</strong>, Kokomo, IN.<br />
May 2000 - August 2000, Intern, Texas Instruments, Houston, TX.<br />
September 2001 - March 2002, Teach<strong>in</strong>g Assistant, Department of Electrical <strong>and</strong><br />
Computer Eng<strong>in</strong>eer<strong>in</strong>g, University of California, Santa Barbara.<br />
June 2003 - September 2003, Intern, Agilent Labs, Agilent Technologies, Palo Alto,<br />
CA.<br />
March 2002 - May 2006, Research assistant, Department of Electrical <strong>and</strong> Computer<br />
Eng<strong>in</strong>eer<strong>in</strong>g, University of California, Santa Barbara.<br />
iv
PUBLICATIONS<br />
S. Gao, C. Sanabria, H. Xu, S. Heikman, U. K. Mishra <strong>and</strong> R. A. York, MMIC Class-<br />
F Power Amplifiers us<strong>in</strong>g Field-Plated <strong>GaN</strong> <strong>HEMTs</strong>, accepted IEEE Proceed<strong>in</strong>gs on<br />
<strong>Microwave</strong>, Antennas <strong>and</strong> Propagation, 2006.<br />
C. Sanabria, A. Chakraborty, H. Xu, M. J. Rodwell, U. K. Mishra, <strong>and</strong> R. A. York,<br />
The Effect of Gate Leakage on the <strong>Noise</strong> Figure of <strong>Al<strong>GaN</strong></strong>/<strong>GaN</strong> <strong>HEMTs</strong>, IEEE Electron<br />
Device Letters, January 2006, pp. 19-21.<br />
C. Sanabria, H. Xu, A. Chakraborty, M. J. Rodwell, U. K. Mishra, <strong>and</strong> R. A. York,<br />
<strong>Noise</strong> Figure Measurements <strong>and</strong> Model<strong>in</strong>g of Field-Plated <strong>Al<strong>GaN</strong></strong>/<strong>GaN</strong> <strong>HEMTs</strong>, International<br />
Conference on Nitride Semiconductors, Bremen, Germany, August 2005.<br />
C. Sanabria, H. Xu, S. Heikman, U. K. Mishra, R. A. York, A <strong>GaN</strong> Differential Oscillator<br />
with Improved Harmonic Performance, IEEE <strong>Microwave</strong> <strong>and</strong> Wireless Components<br />
Letters, July 2005, pp. 463-465.<br />
H. Xu, C. Sanabria, S. Heikman, S. Keller, U. K. Mishra, <strong>and</strong> R. A. York, High<br />
Power <strong>GaN</strong> <strong>Oscillators</strong> us<strong>in</strong>g Field-Plated HEMT Structure, IEEE <strong>Microwave</strong> Theory<br />
<strong>and</strong> Technique International <strong>Microwave</strong> Symposium, June 2005.<br />
C. Sanabria, H. Xu, T. Palacios, A. Chakraborty, S. Heikman, U. K. Mishra, R. A.<br />
York, Influence of Epitaxial Structure <strong>in</strong> the <strong>Noise</strong> Figure of <strong>Al<strong>GaN</strong></strong>/<strong>GaN</strong> <strong>HEMTs</strong>,<br />
IEEE <strong>Microwave</strong> Theory <strong>and</strong> Technique Transactions, Vol. 53, February 2005, pp.<br />
762-769.<br />
H. Xu, C. Sanabria, Y. Wei, S. Heikman, S. Keller, U. K. Mishra, <strong>and</strong> R. A. York,<br />
Characterization of two field-plated <strong>GaN</strong> HEMT structures, IEEE Topical Workshop<br />
on Power Amplifiers for Wireless Communications, September 2004.<br />
H. Xu, C. Sanabria, A. Ch<strong>in</strong>i, Y. Wei, S. Heikman, S. Keller, U. K. Mishra <strong>and</strong> R. A.<br />
York, A new field-plated <strong>GaN</strong> HEMT structure with improved power <strong>and</strong> noise performance,<br />
IEEE Lester Eastman Conference on High Performance Devices, August<br />
2004.<br />
H. Xu, C. Sanabria, A. Ch<strong>in</strong>i, S. Keller, U. K. Mishra, <strong>and</strong> R. A. York, A C-b<strong>and</strong><br />
high-dynamic range <strong>GaN</strong> HEMT low-noise amplifier, IEEE <strong>Microwave</strong> <strong>and</strong> Wireless<br />
Components Letters, Vol. 14, June 2004, pp. 262 264.<br />
v
C. Sanabria, H. Xu, T. Palacios, A. Chakraborty, S. Heikman, U. K. Mishra, R. A.<br />
York, Influence of the Heterostructure Design on <strong>Noise</strong> Figure of <strong>Al<strong>GaN</strong></strong>/<strong>GaN</strong> <strong>HEMTs</strong>,<br />
Device Research Conference, June 2004.<br />
H. Xu, C. Sanabria, A. Ch<strong>in</strong>i, S. Keller, U. K. Mishra, <strong>and</strong> R. A. York, Robust Cb<strong>and</strong><br />
MMIC Low <strong>Noise</strong> Amplifier us<strong>in</strong>g <strong>Al<strong>GaN</strong></strong>/<strong>GaN</strong> HEMT Power Devices, 8th Wide-<br />
B<strong>and</strong>gap III-Nitride Workshop, September 2003.<br />
vi
Abstract<br />
<strong>Noise</strong> of <strong>Al<strong>GaN</strong></strong>/<strong>GaN</strong> <strong>HEMTs</strong> <strong>and</strong> <strong>Oscillators</strong><br />
by<br />
Christopher Sanabria<br />
<strong>GaN</strong> <strong>HEMTs</strong> will likely become the solid-state device of choice for power <strong>in</strong> mi-<br />
crowave <strong>and</strong> millimeter-wave circuits. These products, such as base stations <strong>and</strong> other<br />
communication systems, tend to be space-constra<strong>in</strong>ed. Hence solutions cont<strong>in</strong>uously<br />
move from a hybrid (circuit board plus components) approach to a microwave mono-<br />
lithic <strong>in</strong>tegrated circuit (MMIC). To be successful <strong>in</strong> a MMIC design, <strong>GaN</strong> will have<br />
to perform well <strong>in</strong> other areas besides power. One of the most crucial metrics of a<br />
system is its noise. The noise of <strong>GaN</strong> devices <strong>and</strong> circuits has only been critically<br />
exam<strong>in</strong>ed <strong>in</strong> the last five years.<br />
This work will <strong>in</strong>vestigate several aspects of the noise performance of <strong>GaN</strong> <strong>HEMTs</strong>.<br />
Measurements of noise figure (NF) <strong>and</strong> low-frequency noise (LFN) are used to char-<br />
acterize devices. Model<strong>in</strong>g useful for calculations <strong>and</strong> circuit simulation are applied,<br />
with some <strong>in</strong>troduced. Several studies of NF <strong>and</strong> LFN are presented. Some confirm<br />
or challenge previous publications while others are new observations. Two differen-<br />
tial oscillators were built to characterize the phase noise. As it is believed that <strong>GaN</strong><br />
vii
<strong>HEMTs</strong> will replace GaAs <strong>HEMTs</strong> <strong>in</strong> various applications, the NF, LFN, <strong>and</strong> phase<br />
noise of the two are compared.<br />
viii
Contents<br />
List of Figures xii<br />
List of Tables xvi<br />
1 Introduction 1<br />
1.1 Motivation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1<br />
1.2 Literature Review of <strong>Noise</strong> <strong>in</strong> <strong>GaN</strong> <strong>HEMTs</strong> . . . . . . . . . . . . . . 5<br />
1.3 Thesis Outl<strong>in</strong>e . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8<br />
References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9<br />
2 <strong>Noise</strong> Figure Model<strong>in</strong>g of <strong>Al<strong>GaN</strong></strong>/<strong>GaN</strong> <strong>HEMTs</strong> 12<br />
2.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12<br />
2.2 <strong>Noise</strong> Sources . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13<br />
2.2.1 Thermal <strong>Noise</strong> . . . . . . . . . . . . . . . . . . . . . . . . . 13<br />
2.2.2 Shot<strong>Noise</strong> . . . . . . . . . . . . . . . . . . . . . . . . . . . 15<br />
2.2.3 Other Sources of <strong>Noise</strong> . . . . . . . . . . . . . . . . . . . . . 16<br />
2.3 Equivalent Circuit Model . . . . . . . . . . . . . . . . . . . . . . . . 17<br />
2.4 <strong>Noise</strong> Figure <strong>and</strong> <strong>Noise</strong> Parameters . . . . . . . . . . . . . . . . . . . 21<br />
2.5 HEMT <strong>Noise</strong> Figure Models . . . . . . . . . . . . . . . . . . . . . . 25<br />
2.5.1 van der Ziel <strong>and</strong> Pucel Models . . . . . . . . . . . . . . . . . 25<br />
2.5.2 Fukui Model . . . . . . . . . . . . . . . . . . . . . . . . . . 28<br />
2.5.3 Pospieszalski Model . . . . . . . . . . . . . . . . . . . . . . 29<br />
2.5.4 Pospieszalski <strong>and</strong> Correlated <strong>Noise</strong> Models Applied to Al-<br />
<strong>GaN</strong>/<strong>GaN</strong> <strong>HEMTs</strong> . . . . . . . . . . . . . . . . . . . . . . . 31<br />
2.6 A Proposed <strong>Noise</strong> Figure Model . . . . . . . . . . . . . . . . . . . . 35<br />
2.6.1 Setup Details . . . . . . . . . . . . . . . . . . . . . . . . . . 36<br />
2.6.2 Derivation of <strong>Noise</strong> Parameters . . . . . . . . . . . . . . . . 39<br />
2.6.3 Derivation of Dra<strong>in</strong> <strong>Noise</strong> Source . . . . . . . . . . . . . . . 44<br />
2.6.4 <strong>Noise</strong> Parameter Scal<strong>in</strong>g . . . . . . . . . . . . . . . . . . . . 49<br />
2.6.5 Discussion of the Model . . . . . . . . . . . . . . . . . . . . 53<br />
2.7 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 57<br />
ix
References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 57<br />
3 <strong>Noise</strong> Figure Measurements <strong>and</strong> Studies 60<br />
3.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 60<br />
3.2 Device Details . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 61<br />
3.3 <strong>Noise</strong> Figure Measurement Setup <strong>and</strong> Method . . . . . . . . . . . . . 62<br />
3.4 Bias Dependence . . . . . . . . . . . . . . . . . . . . . . . . . . . . 68<br />
3.5 <strong>GaN</strong> HEMT <strong>Noise</strong> Figure Studies . . . . . . . . . . . . . . . . . . . 75<br />
3.5.1 Substrate . . . . . . . . . . . . . . . . . . . . . . . . . . . . 75<br />
3.5.2 Al Composition <strong>in</strong> the Barrier . . . . . . . . . . . . . . . . . 76<br />
3.5.3 AlN Interlayer . . . . . . . . . . . . . . . . . . . . . . . . . 78<br />
3.5.4 Gate Leakage . . . . . . . . . . . . . . . . . . . . . . . . . . 81<br />
3.5.5 Field-Plated Devices . . . . . . . . . . . . . . . . . . . . . . 84<br />
3.5.6 Thick-Epitaxial Cap Devices . . . . . . . . . . . . . . . . . . 91<br />
3.6 Comparison of High-Performance <strong>GaN</strong> <strong>HEMTs</strong> to Other Material Systems<br />
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 93<br />
3.7 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 95<br />
References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 96<br />
4 Low-Frequency <strong>Noise</strong> of <strong>GaN</strong> <strong>HEMTs</strong> 101<br />
4.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 101<br />
4.2 Review of Low-Frequency <strong>Noise</strong> . . . . . . . . . . . . . . . . . . . . 102<br />
4.3 Low-Frequency <strong>Noise</strong> Setup . . . . . . . . . . . . . . . . . . . . . . 107<br />
4.4 <strong>GaN</strong> HEMT Low-Frequency <strong>Noise</strong> Model<strong>in</strong>g . . . . . . . . . . . . . 113<br />
4.5 <strong>GaN</strong> HEMT Low-Frequency <strong>Noise</strong> Studies . . . . . . . . . . . . . . 119<br />
4.5.1 Substrate . . . . . . . . . . . . . . . . . . . . . . . . . . . . 119<br />
4.5.2 Passivation . . . . . . . . . . . . . . . . . . . . . . . . . . . 119<br />
4.5.3 Thick-Epitaxial Cap Devices . . . . . . . . . . . . . . . . . . 121<br />
4.5.4 Field-Plated Devices . . . . . . . . . . . . . . . . . . . . . . 122<br />
4.6 Comparison to GaAs <strong>HEMTs</strong> . . . . . . . . . . . . . . . . . . . . . . 123<br />
4.7 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 125<br />
References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 126<br />
5 <strong>GaN</strong> HEMT Based <strong>Oscillators</strong> 128<br />
5.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 128<br />
5.2 Concern<strong>in</strong>g Phase <strong>Noise</strong> . . . . . . . . . . . . . . . . . . . . . . . . 129<br />
5.3 MMIC Process Description . . . . . . . . . . . . . . . . . . . . . . . 134<br />
5.4 Differential <strong>Oscillators</strong> . . . . . . . . . . . . . . . . . . . . . . . . . 135<br />
5.4.1 High L<strong>in</strong>earity Oscillator . . . . . . . . . . . . . . . . . . . . 135<br />
5.4.2 Low-Phase <strong>Noise</strong> Oscillator . . . . . . . . . . . . . . . . . . 140<br />
5.5 Comparison to Other <strong>Oscillators</strong> . . . . . . . . . . . . . . . . . . . . 143<br />
x
5.6 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 146<br />
References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 147<br />
6 Summary, Conclusions, <strong>and</strong> Future Directions 149<br />
6.1 Summary <strong>and</strong> Conclusions . . . . . . . . . . . . . . . . . . . . . . . 149<br />
6.2 FuturePaths . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 151<br />
A ADS Files 154<br />
A.1 Small-Signal Extraction . . . . . . . . . . . . . . . . . . . . . . . . . 155<br />
A.2 <strong>Noise</strong> Figure Simulation . . . . . . . . . . . . . . . . . . . . . . . . 158<br />
A.3 Correlated <strong>Noise</strong> Model Extraction . . . . . . . . . . . . . . . . . . . 160<br />
B Matlab Code for <strong>Noise</strong> Parameter Model<strong>in</strong>g 163<br />
C Matlab Code for Pospieszalski <strong>Noise</strong> Parameter Model<strong>in</strong>g 166<br />
xi
List of Figures<br />
1.1 Cartoon of a very simple transmitter. . . . . . . . . . . . . . . . . . . 2<br />
1.2 Cartoon of a CDMA-like spectrum with four channels. . . . . . . . . 3<br />
2.1 Cartoon show<strong>in</strong>g the device small-signal model on a cross section of<br />
a HEMT. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 18<br />
2.2 Equivalent model of a transistor driven by a noisy source of impedance<br />
Zsource. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 22<br />
2.3 <strong>Noise</strong> <strong>and</strong> ga<strong>in</strong> circles on a Smith Chart. . . . . . . . . . . . . . . . . 24<br />
2.4 Pucel noise model <strong>in</strong> a small-signal circuit. . . . . . . . . . . . . . . 27<br />
2.5 Pospieszalski noise model <strong>in</strong> a small-signal circuit. . . . . . . . . . . 29<br />
2.6 Comparison of Correlated <strong>Noise</strong> <strong>and</strong> Pospieszalski models to measured<br />
noise parameters versus frequency. . . . . . . . . . . . . . . . . 34<br />
2.7 A simplified HEMT circuit model <strong>in</strong>clud<strong>in</strong>g noise sources. . . . . . . 36<br />
2.8 Cartoon show<strong>in</strong>g the effect of source degeneration. . . . . . . . . . . 38<br />
2.9 Circuit model used for deriv<strong>in</strong>g noise figure. . . . . . . . . . . . . . . 39<br />
2.10 Cartoon used for deriv<strong>in</strong>g the channel noise. . . . . . . . . . . . . . . 47<br />
2.11 Variation <strong>in</strong> Γ for different dra<strong>in</strong> <strong>and</strong> gate voltages. . . . . . . . . . . 49<br />
2.12 <strong>Noise</strong> parameters versus total gate width. . . . . . . . . . . . . . . . 51<br />
2.13 <strong>Noise</strong> parameters versus number of gate f<strong>in</strong>gers for a constant total<br />
gatewidth. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 52<br />
2.14 <strong>Noise</strong> parameters predicted with the proposed model <strong>and</strong> compared to<br />
measurements. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 53<br />
2.15 Relative contributions of different noise sources to the overall noise<br />
figure. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 55<br />
3.1 Typical epitaxial structures for the devices <strong>in</strong> this work. . . . . . . . . 61<br />
3.2 Schematic of the source-pull noise figure setup. . . . . . . . . . . . . 63<br />
3.3 Coplanar waveguide attenuator. . . . . . . . . . . . . . . . . . . . . . 65<br />
3.4 <strong>Noise</strong> factor, fτ <strong>and</strong> fmax for devices from different samples versus<br />
current. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 65<br />
xii
3.5 Variation <strong>in</strong> expected m<strong>in</strong>imum noise figure with changes <strong>in</strong> three<br />
small-signal parameters. . . . . . . . . . . . . . . . . . . . . . . . . 68<br />
3.6 Change <strong>in</strong> noise parameters with dra<strong>in</strong>-source voltage. . . . . . . . . 69<br />
3.7 Typical plots of the noise parameters versus dra<strong>in</strong> source current with<br />
Correlated <strong>Noise</strong> <strong>and</strong> Pospieszalski models. . . . . . . . . . . . . . . 71<br />
3.8 <strong>Noise</strong> variables for the Pospieszalski <strong>and</strong> a CN noise model versus<br />
dra<strong>in</strong>-source current. . . . . . . . . . . . . . . . . . . . . . . . . . . 73<br />
3.9 M<strong>in</strong>imum noise figure, small signal associated <strong>and</strong> maximum ga<strong>in</strong> for<br />
devices on sapphire <strong>and</strong> SiC substrates. . . . . . . . . . . . . . . . . 75<br />
3.10 <strong>Noise</strong> parameters versus frequency for devices of different alum<strong>in</strong>um<br />
composition <strong>in</strong> the barrier. . . . . . . . . . . . . . . . . . . . . . . . 77<br />
3.11 M<strong>in</strong>imum noise figure of samples with different alum<strong>in</strong>um composition<br />
<strong>in</strong> the barrier at vary<strong>in</strong>g dra<strong>in</strong>-source current. . . . . . . . . . . . 78<br />
3.12 M<strong>in</strong>imum noise figure, fτ, <strong>and</strong> fmax versus dra<strong>in</strong>-source current for a<br />
sample with <strong>and</strong> without an AlN <strong>in</strong>terlayer. . . . . . . . . . . . . . . 79<br />
3.13 (a) Associated <strong>and</strong> maximum ga<strong>in</strong> <strong>and</strong> (b) source resistance for devices<br />
with <strong>and</strong> without an AlN <strong>in</strong>terlayer at different applied currents. 80<br />
3.14 (a) M<strong>in</strong>imum noise figure, (b) device associated ga<strong>in</strong>, <strong>and</strong> maximum<br />
ga<strong>in</strong> versus frequency for devices with different gate leakage currents 82<br />
3.15 Simulated (l<strong>in</strong>e) <strong>and</strong> measured (crosses) noise parameters for devices<br />
with different gate leakage currents. . . . . . . . . . . . . . . . . . . 83<br />
3.16 fτ <strong>and</strong> fmax of devices with different field-plate lengths. . . . . . . . . 84<br />
3.17 <strong>Noise</strong> parameters versus frequency for devices with field plates of differentlength.<br />
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 85<br />
3.18 Typical change <strong>in</strong> gate leakage for devices of <strong>in</strong>creas<strong>in</strong>g field-plate<br />
length. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 87<br />
3.19 Electric field profile for a device with <strong>and</strong> without a field plate. . . . . 87<br />
3.20 Small-signal parameters that change with a field plate. . . . . . . . . 89<br />
3.21 M<strong>in</strong>imum noise figure versus gate width for devices with <strong>and</strong> without<br />
a longfieldplate. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 90<br />
3.22 M<strong>in</strong>imum noise figure of the field-plated devices at different measurement<br />
frequencies. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 90<br />
3.23 <strong>Noise</strong> parameters versus dra<strong>in</strong>-source current of a thick cap device<br />
(triangles) <strong>and</strong> a st<strong>and</strong>ard HEMT (squares). . . . . . . . . . . . . . . 92<br />
3.24 M<strong>in</strong>imum noise figure of two 0.15 µm gate length transistors provided<br />
by Tomás Palacios. . . . . . . . . . . . . . . . . . . . . . . . . . . . 95<br />
4.1 Sketch of the key features of low-frequency noise. . . . . . . . . . . . 103<br />
4.2 Variation of α with (a) dra<strong>in</strong>-source voltage bias <strong>and</strong> (b) frequency of<br />
extraction for two devices on the same sample. . . . . . . . . . . . . 106<br />
xiii
4.3 Measured noise floor of the HP 3561A DSA only <strong>and</strong> with the SRS<br />
SR560 LNA (short-circuited <strong>in</strong>put). . . . . . . . . . . . . . . . . . . 109<br />
4.4 Schematic of the setup used for device dra<strong>in</strong>-side low-frequency noise<br />
measurements. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 110<br />
4.5 A typical low-frequency plot. . . . . . . . . . . . . . . . . . . . . . . 112<br />
4.6 Plots of the measured dra<strong>in</strong> low-frequency noise with (a) change <strong>in</strong><br />
dra<strong>in</strong>-source current <strong>and</strong> (b) voltage. . . . . . . . . . . . . . . . . . . 114<br />
4.7 Measured gate low-frequency noise versus gate-source voltage (<strong>and</strong><br />
current). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 115<br />
4.8 Change <strong>in</strong> low-frequency noise with gate width at various decade frequencies<br />
for three devices. . . . . . . . . . . . . . . . . . . . . . . . 116<br />
4.9 Change <strong>in</strong> low-frequency noise with gate length. . . . . . . . . . . . . 116<br />
4.10 Proposed low-frequency noise model<strong>in</strong>g of the HEMT with a gate <strong>and</strong><br />
dra<strong>in</strong> noise source. . . . . . . . . . . . . . . . . . . . . . . . . . . . 117<br />
4.11 Measurement of devices on a sapphire <strong>and</strong> SiC substrate at a bias of<br />
Vds 5V,Ids 30mA . . . . . . . . . . . . . . . . . . . . . . . . . . . 120<br />
4.12 (a) Low-frequency noise of a device before <strong>and</strong> after passivation. (b)<br />
Low-frequency noise at 10 Hz <strong>and</strong> 1 kHz of a device before <strong>and</strong> after<br />
passivation at different Vgs . . . . . . . . . . . . . . . . . . . . . . . . 120<br />
4.13 Comparison of st<strong>and</strong>ard passivated <strong>HEMTs</strong> to an unpassivated thick<br />
cap <strong>HEMTs</strong>. Bias is Vds =5V<strong>and</strong>Ids = 30 mA. . . . . . . . . . . . . 122<br />
4.14 Low-frequency noise of field-plated devices. . . . . . . . . . . . . . . 123<br />
4.15 Low-frequency noise comparison of <strong>GaN</strong> <strong>and</strong> GaAs <strong>HEMTs</strong>. . . . . . 124<br />
5.1 Examples of typical phase noise plots. . . . . . . . . . . . . . . . . . 131<br />
5.2 Circuit schematic of the oscillator (bias<strong>in</strong>g not shown). . . . . . . . . 136<br />
5.3 Photograph of the high l<strong>in</strong>earity oscillator. . . . . . . . . . . . . . . . 136<br />
5.4 Measurements of the oscillator: (a) power spectrum (b) frequency<br />
pull<strong>in</strong>g. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 138<br />
5.5 Output power, second harmonic power, <strong>and</strong> efficiency of the highl<strong>in</strong>earity<br />
oscillator. . . . . . . . . . . . . . . . . . . . . . . . . . . . 138<br />
5.6 Circuit schematic of the low-phase noise oscillator (bias<strong>in</strong>g not shown). 140<br />
5.7 Photograph of the low-phase noise oscillator. . . . . . . . . . . . . . 141<br />
5.8 Measured phase noise of the oscillator. . . . . . . . . . . . . . . . . . 142<br />
5.9 Phase noise at 100 kHz <strong>and</strong> 1 MHz offsets versus dra<strong>in</strong>-source bias<br />
for a few oscillators. . . . . . . . . . . . . . . . . . . . . . . . . . . . 142<br />
5.10 Relative comparison of <strong>GaN</strong> oscillator to a typical oscillator with low<br />
phase noise. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 146<br />
A.1 First page of template small signal parameter extraction.dds. . . . . 156<br />
xiv
A.2 Schematic used for simulat<strong>in</strong>g S-parameters of the small-signal circuit<br />
<strong>and</strong> for optimization. . . . . . . . . . . . . . . . . . . . . . . . . . . 158<br />
A.3 Schematic used for simulat<strong>in</strong>g noise parameters. . . . . . . . . . . . . 159<br />
A.4 Schematic used for extract<strong>in</strong>g correlated noise model noise variables. 162<br />
A.5 Data display used for extract<strong>in</strong>g correlated noise model noise variables. 162<br />
xv
List of Tables<br />
2.1 Extracted small-signal parameters for various samples. Devices have<br />
a gate geometry of 0.7 × 150 µm. . . . . . . . . . . . . . . . . . . . 21<br />
2.2 Comparison of Pospieszalski <strong>and</strong> Correlated <strong>Noise</strong> models to measured<br />
data. Devices have a gate geometry of 0.7 × 150 µm . . . . . . 33<br />
2.3 Comparison of the various noise models’ <strong>in</strong>put <strong>and</strong> output noise currents. 56<br />
3.1 M<strong>in</strong>imum noise figure for devices <strong>in</strong> many technologies. . . . . . . . 94<br />
5.1 Comparison of <strong>GaN</strong> oscillators from this <strong>and</strong> other works to oscillators<br />
<strong>in</strong> other materials (FET, MMICs, only). . . . . . . . . . . . . . . 144<br />
xvi
Acknowledgements<br />
BEHIND the c<strong>and</strong>y Santa Barbara exterior of sun, perfect weather, surf<strong>in</strong>g, <strong>and</strong><br />
tourists is a university that is a powerhouse of research that I didn’t have the<br />
foggiest idea existed until I decided to come to graduate school. I’ve been impressed<br />
with the faculty, facilities, labs, peers, <strong>and</strong> the graduate sciences <strong>and</strong> eng<strong>in</strong>eer<strong>in</strong>g programs<br />
at UCSB. It has made for a great research experience <strong>and</strong> I want to thank <strong>and</strong><br />
acknowledge all those who have helped me along the way toward gett<strong>in</strong>g my Ph.D.<br />
I would first like to thank my advisor Professor Robert York. Not only did he<br />
take me <strong>in</strong>, he has provided (along with my co-advisor) five years of constant, un<strong>in</strong>terrupted,<br />
f<strong>in</strong>ancial support. Watch<strong>in</strong>g peers struggle with fund<strong>in</strong>g shortfalls <strong>and</strong><br />
chang<strong>in</strong>g projects has made me realize what a bless<strong>in</strong>g fund<strong>in</strong>g is. I would also like<br />
to thank him for giv<strong>in</strong>g me a great deal of freedom. This was frighten<strong>in</strong>g for me at<br />
first as I thought I would become lost, but later I realized what research I wanted to do<br />
<strong>and</strong> was able to do it without restra<strong>in</strong>t. Professor York has always steered me <strong>in</strong> the<br />
right direction on important matters of publications, research, <strong>and</strong> th<strong>in</strong>gs <strong>in</strong> general.<br />
We had many good, frank, talks that I enjoyed.<br />
I thank my co-advisor Professor Umesh Mishra for many th<strong>in</strong>gs. The first is the<br />
amusement of watch<strong>in</strong>g someone juggle the work of five men like some god with 10<br />
arms. Yet, when I needed to discuss work, we always got a few m<strong>in</strong>utes <strong>in</strong> <strong>and</strong> I never<br />
felt pushed away. I also salute the <strong>GaN</strong> program he has put together at UCSB. Umesh<br />
is one of the smartest, <strong>and</strong> slyest, <strong>in</strong>dividuals I have met <strong>and</strong> it was fun to be around<br />
for the show. I also really appreciate the happy hours he would host.<br />
My other committee members, Professor Mark Rodwell <strong>and</strong> Dr. Yifeng Wu, have<br />
been a great help to me not only <strong>in</strong> prepar<strong>in</strong>g the thesis but <strong>in</strong> important research<br />
discussions over the years. Professor Rodwell’s class notes on noise <strong>and</strong> exchanges<br />
have steered me through to the basic truths about noise figure. With Dr. Wu I’ve had<br />
many conversations: load-pull, noise, circuits, <strong>and</strong> even high-end audio equipment. I<br />
have enjoyed it all. I also thank Professor Long for the conversations that we have<br />
had.<br />
My peers <strong>in</strong> the trenches have been of tremendous help toward this work. Hongtao<br />
Xu taught me his fabrication techniques for MMICs <strong>and</strong> offered very useful suggestions<br />
for my microwave circuits. We worked collectively on several projects <strong>and</strong> became<br />
friends. Tomás Palacios, the wonder Spaniard, has been of tremendous help. His<br />
enormous curiosity, knowledge, <strong>and</strong> keen eye helped me out several times by po<strong>in</strong>t<strong>in</strong>g<br />
me <strong>in</strong> the right direction or giv<strong>in</strong>g me <strong>in</strong>spiration that lead to useful research. My<br />
group mates (past <strong>and</strong> present), Nadia, Val, Raj, Jaehoon, Jiwei, Just<strong>in</strong>, Paolo (e-lo?),<br />
Vicki, Conrad<strong>in</strong>, Jim, <strong>and</strong> Pengcheng have helped me out many a time (or helped provide<br />
a refresh<strong>in</strong>g work break). The small army known as Professor Mishra’s group<br />
have also helped a great deal: Rob, Siddarth, Likun (Mona), Mike, Dario, Arpan, Ale,<br />
Naiqian, Sten, Lee M., Ilan, Yuvaraj, Felix, Pei Yi, Eric, Chang, Chris, Jeff, Karl, <strong>and</strong><br />
xvii
Man Hoi. I would especially like to thank those who grew my material for devices <strong>and</strong><br />
circuits, Arpan, Sten, Stacia, <strong>and</strong> Nick, without whom I would have had no project.<br />
I also had useful discussions with students <strong>in</strong> the groups of both Professors Rodwell<br />
<strong>and</strong> Long. I had many conversations, <strong>in</strong>teractions, <strong>and</strong> chats with Vikas <strong>and</strong> Joe,<br />
whose projects focused heavily on phase noise. Vikas also provided the GaAs devices<br />
that were measured <strong>in</strong> this work <strong>and</strong> both of them helped with equipment <strong>and</strong> setups.<br />
Nav<strong>in</strong>, Zack, <strong>and</strong> Paidi all gave me some useful <strong>in</strong>formation at one po<strong>in</strong>t or another.<br />
Also, I had discussions with Adam about low-frequency noise <strong>and</strong> Professor Elliot<br />
Brown let me borrow some equipment from his personal collection for a measurement.<br />
I thank Agilent <strong>and</strong> Maury for their technical support on various pieces of equipment<br />
(I called a lot). I am greatful to the cleanroom staff (Jack, Bob, Neil, Tom,<br />
Brian T., Bill, Don, Mike, Luis <strong>and</strong> N<strong>in</strong>g) who kept our excellent facilities go<strong>in</strong>g 24x7<br />
<strong>and</strong> for be<strong>in</strong>g available for the occasional even<strong>in</strong>g crisis. The assistants over the year<br />
(Masika, Pam, Emeka, Lee B., <strong>and</strong> Laura) have been a big help with red tape. I thank<br />
Val de Veyra <strong>and</strong> the other assistants <strong>in</strong> the ECE graduate student office, with whom I<br />
had a good laugh because of a non-unique nickname <strong>in</strong> my email address book.<br />
I very much thank Dr. Harry Dietrich <strong>and</strong> the Office of Naval Research (ONR) who<br />
funded <strong>and</strong> oversaw the Center for Advance Nitride <strong>Electronics</strong> (CANE) program that<br />
I was on.<br />
I would also like to thank Dr. Joy Vann-Hamilton. Joy, who was director of the<br />
M<strong>in</strong>ority Eng<strong>in</strong>eer<strong>in</strong>g Program (MEP) while I was an undergraduate at the University<br />
of Notre Dame, listened to all my unhappy college compla<strong>in</strong>ts, po<strong>in</strong>ted me toward<br />
resources that got me through undergraduate, <strong>and</strong> is solely responsible for my go<strong>in</strong>g<br />
to graduate school. Grad school wasn’t even on my radar <strong>and</strong> I didn’t th<strong>in</strong>k I had the<br />
talent. I can’t thank her enough.<br />
As if I hadn’t thanked enough people <strong>and</strong> entities, I would also like to thank all my<br />
friends who made my time here enjoyable (even if it was jokes at my expense, Perk<br />
<strong>and</strong> Dave). Also, I don’t know what my parents did that I turned out the way I did,<br />
but I want to give them applause for all that they have done. Don’t worry, I won’t do<br />
anyth<strong>in</strong>g to embarrass you like I did at high school graduation.<br />
F<strong>in</strong>ally, no stay <strong>in</strong> Santa Barbara is complete without pick<strong>in</strong>g up a wife. Sarah, who<br />
would have guessed we would meet here <strong>in</strong>stead of at Notre Dame? I thank you for<br />
h<strong>and</strong>l<strong>in</strong>g all my rants with grace, giv<strong>in</strong>g me hope when I had none, distract<strong>in</strong>g me so I<br />
would realize there are a whole lot of <strong>in</strong>terest<strong>in</strong>g th<strong>in</strong>gs to do <strong>in</strong> the world, <strong>and</strong> be<strong>in</strong>g<br />
some one worth liv<strong>in</strong>g for.<br />
“Thanks y’all”...<br />
xviii
For those who never quit.<br />
xix
1.1 Motivation<br />
1<br />
Introduction<br />
GALLIUM nitride (<strong>GaN</strong>) <strong>and</strong> its related compound materials, <strong>in</strong>dium nitride<br />
(InN) <strong>and</strong> alum<strong>in</strong>um nitride (AlN), have already been commercialized for<br />
several applications. This is an impressive feat for an immature technology where each<br />
year research cont<strong>in</strong>ues to br<strong>in</strong>g improvements. The reason for this rush to market is<br />
the needs the nitrides are address<strong>in</strong>g. For optical applications, <strong>GaN</strong>-based solutions<br />
<strong>in</strong>clude LEDs, lasers, <strong>and</strong> detectors <strong>in</strong> the UV <strong>and</strong> blue wavelengths. For electronic<br />
applications, <strong>GaN</strong> high electron mobility transistors (<strong>HEMTs</strong>) provide some of the<br />
highest microwave power performance to be found from solid state devices.<br />
<strong>GaN</strong>-based electronics have two major setbacks. The first is the cost. This re-<br />
sults largely from the expensive substrates needed, with the better substrates currently<br />
cost<strong>in</strong>g nearly an order of magnitude more than lower-performance options. The other<br />
hurdle is growth immaturity, which causes reliability to be mediocre. Because of these<br />
disadvantages, if another material system (Si, GaAs, InP, etc.) can meet the needs of an<br />
1
CHAPTER 1. INTRODUCTION<br />
application, <strong>in</strong>dustry will choose it over <strong>GaN</strong>. This means <strong>GaN</strong> <strong>HEMTs</strong> are be<strong>in</strong>g con-<br />
sidered ma<strong>in</strong>ly for power amplifiers <strong>in</strong> microwave products such as base stations [1,2].<br />
Industry has a great need for these products to be compact. Designers cont<strong>in</strong>uously<br />
move from hybrid (a circuit board with discrete components) to <strong>in</strong>tegrated (a s<strong>in</strong>gle,<br />
small chip) solutions. Instead of a chip with just a power amplifier, it is preferred to<br />
have the amplifier, <strong>and</strong> complete transmit <strong>and</strong> receive paths, <strong>in</strong> a s<strong>in</strong>gle chip called a<br />
front-end module (FEM). Figure 1.1 shows an example of a simple transmitter, <strong>and</strong> the<br />
preferred <strong>in</strong>tegration boundary of power amplifier plus other components. It may be<br />
possible that <strong>GaN</strong> monolithic microwave <strong>in</strong>tegrated circuits (MMICs) provide better<br />
performance <strong>in</strong> terms of power, radiation hardness, <strong>and</strong> operation temperature, lead<strong>in</strong>g<br />
to future products.<br />
From<br />
DSP<br />
Modulator<br />
Oscillator<br />
Mixer Filter Power<br />
Amp.<br />
Ideally implemented as a s<strong>in</strong>gle transmitter MMIC<br />
Figure 1.1: Cartoon of a very simple transmitter.<br />
2<br />
Antenna
CHAPTER 1. INTRODUCTION<br />
Power<br />
Channel<br />
Width<br />
Channel<br />
Space<br />
<strong>Noise</strong><br />
Side<br />
B<strong>and</strong><br />
Frequency<br />
<strong>Noise</strong><br />
Floor<br />
Figure 1.2: Cartoon of a CDMA-like spectrum with four channels.<br />
Basic <strong>GaN</strong> MMIC build<strong>in</strong>g blocks are now appear<strong>in</strong>g <strong>in</strong> the literature [3–7], <strong>and</strong><br />
it is only a matter of time before <strong>GaN</strong> transmit <strong>and</strong> receive MMICs are made. An<br />
important metric of such circuits will be their noise performance. In particular, phase<br />
noise <strong>and</strong> noise figure (NF) are common figures of merit for characteriz<strong>in</strong>g noise. A<br />
ma<strong>in</strong> focus of this work is exam<strong>in</strong><strong>in</strong>g these aspects of <strong>GaN</strong> <strong>HEMTs</strong> <strong>and</strong> oscillators.<br />
Communication channel spac<strong>in</strong>g is set based on specifications of the maximum<br />
noise a channel will produce out-of-b<strong>and</strong>. This is shown <strong>in</strong> figure 1.2. Sett<strong>in</strong>g the<br />
space between channels as small as possible is extremely important due to regulated<br />
b<strong>and</strong>width restrictions. 1 Typically the component that sets the m<strong>in</strong>imum on this noise<br />
1In fact, whenever the Federal Communications Commission (FCC) auctions b<strong>and</strong>width the sell<strong>in</strong>g<br />
price is <strong>in</strong> the hundreds of millions [8].<br />
3
CHAPTER 1. INTRODUCTION<br />
performance is an oscillator <strong>in</strong> the circuit, as <strong>in</strong> figure 1.1. An oscillator provides<br />
a signal source at a (usually variable) reference frequency. In addition, oscillators<br />
produce a large amount of noise at frequencies close to the reference frequency. This<br />
is called phase noise.<br />
It is understood that various device noise sources contribute to the phase noise.<br />
These <strong>in</strong>clude thermal, shot, <strong>and</strong> low-frequency (also called flicker, or 1/f) sources.<br />
The quantitative analysis of how these sources contribute to the phase noise is difficult<br />
even for the simplest of cases. A qualitative description that embodies many important<br />
po<strong>in</strong>ts was presented by Leeson [9], <strong>and</strong> is described as<br />
⎡<br />
L (∆ω) = 10 log ⎣ 2FkT<br />
Psig<br />
⎧<br />
⎨<br />
⎩ 1+<br />
� ω0<br />
2Q∆ω<br />
� ⎫<br />
2 �<br />
�<br />
⎬ ∆ω1/f 3<br />
1+<br />
⎭ |∆ω|<br />
⎤<br />
⎦ (1.1.1)<br />
where the script L is the phase noise <strong>in</strong> a 1 Hz b<strong>and</strong>width at an offset angular fre-<br />
quency, ∆w, from the carrier angular frequency, ω0, Q is the quality of the resonator,<br />
Psig the signal power, <strong>and</strong> F the effective noise figure. 2 Shot <strong>and</strong> thermal noise sources<br />
contribute to F, a measure of the background noise of the device <strong>and</strong> circuit. The low-<br />
frequency noise (LFN) contributes through ∆ω1/f 3, a corner frequency for the phase<br />
noise that presumably relates to the corner frequency of the LFN. From equation 1.1.1,<br />
we can discern that knowledge of the noise sources <strong>in</strong> the device <strong>and</strong> circuit will help<br />
<strong>in</strong> underst<strong>and</strong><strong>in</strong>g the phase noise, <strong>and</strong> if we can reduce them the phase noise will be<br />
2 The parameter F here is not the device noise figure or factor but an “Effective noise figure” which<br />
some see as just a fitt<strong>in</strong>g parameter. F <strong>in</strong> this chapter should not be confused with noise factor <strong>in</strong> the<br />
other chapters.<br />
4
CHAPTER 1. INTRODUCTION<br />
improved. Leeson’s equation also tells us that if Psig can be <strong>in</strong>creased, we should<br />
see an improvement <strong>in</strong> phase noise. Because <strong>GaN</strong> devices are capable of provid<strong>in</strong>g<br />
an order of magnitude more power than gallium arsenide (GaAs) devices, the next<br />
best commercial material, it is of great <strong>in</strong>terest to know if the phase noise of <strong>GaN</strong><br />
circuits can be better than GaAs circuits. One of the goals of this work is to answer<br />
this question.<br />
This dissertation will look at several aspects of the noise performance of <strong>GaN</strong><br />
<strong>HEMTs</strong>. NF <strong>and</strong> LFN measurements are used to evaluate the noise performance of<br />
the <strong>GaN</strong> <strong>HEMTs</strong>. Comparisons are made to measurements of GaAs <strong>HEMTs</strong>, the most<br />
similar commercial device, which <strong>GaN</strong> is try<strong>in</strong>g to displace. Models for NF <strong>and</strong> LFN<br />
noise, some old <strong>and</strong> some new, are presented. To study the phase noise, differen-<br />
tial oscillators were constructed <strong>and</strong> measured. Their performance is expla<strong>in</strong>ed <strong>in</strong> the<br />
context of LFN.<br />
A quick review of previous noise measurements <strong>and</strong> studies of <strong>GaN</strong> <strong>HEMTs</strong> <strong>and</strong><br />
oscillators is now presented, followed by a sketch of this work.<br />
1.2 Literature Review of <strong>Noise</strong> <strong>in</strong> <strong>GaN</strong> <strong>HEMTs</strong><br />
This section gives a short background of the <strong>GaN</strong> HEMT literature for NF, LFN,<br />
<strong>and</strong> phase noise prior to this work (late 2002). Most publications after this po<strong>in</strong>t <strong>in</strong><br />
time are already referenced throughout the work. More background <strong>in</strong>formation on<br />
5
CHAPTER 1. INTRODUCTION<br />
each noise subject can also be found at the beg<strong>in</strong>n<strong>in</strong>g of its respective chapter.<br />
Of the three types of noise measurements performed on <strong>GaN</strong> <strong>HEMTs</strong>, LFN has<br />
the longest history. Reports of measurements first started to appear <strong>in</strong> 1998 [10, 11].<br />
Because LFN measurements can be used as a way of monitor<strong>in</strong>g crystal quality, some<br />
reports came from materials scientists [12]. Physicists have measured <strong>GaN</strong> LFN <strong>and</strong><br />
are us<strong>in</strong>g some of the follow<strong>in</strong>g arguments to expla<strong>in</strong> it: tail states near the b<strong>and</strong> gap<br />
edge [11], mobility fluctuations [13], <strong>and</strong> tunnel<strong>in</strong>g of electrons from the channel to<br />
traps <strong>in</strong> surround<strong>in</strong>g layers [12]. No theory is yet accepted as the best explanation.<br />
Various other LFN papers have appeared [12,14–16]. Most measurements are at very<br />
low bias<strong>in</strong>gs such that the device is <strong>in</strong> the l<strong>in</strong>ear region. The only publication that stud-<br />
ies gate <strong>and</strong> dra<strong>in</strong> LFN for the full bias<strong>in</strong>g range of a <strong>GaN</strong> HEMT is Hsu et al. [17].<br />
This paper will be returned to <strong>in</strong> chapter 4. Due to the use of the Hooge parame-<br />
ter, the devices not be<strong>in</strong>g optimized <strong>HEMTs</strong> (some are doped channel HFETs), <strong>and</strong><br />
measurements only <strong>in</strong> the l<strong>in</strong>ear region, many of the above results are not of use to a<br />
circuit designer or device eng<strong>in</strong>eer who is try<strong>in</strong>g to characterize <strong>and</strong> optimize LFN.<br />
Accurate measurements of LFN can also be difficult. Therefore, this work presents<br />
measurements <strong>and</strong> model<strong>in</strong>g of LFN that will be of use to the eng<strong>in</strong>eer<strong>in</strong>g community.<br />
The first published NF report for a <strong>GaN</strong> HEMT was performed by P<strong>in</strong>g <strong>in</strong> 2000 [18].<br />
For a 0.25 x 100 µm gate device, a m<strong>in</strong>imum noise figure (NFm<strong>in</strong>) of 1.06 dB <strong>and</strong> a<br />
ga<strong>in</strong> of 12 dB at a frequency of 10 GHz was demonstrated. This was followed shortly<br />
6
CHAPTER 1. INTRODUCTION<br />
by Nguyen [19], present<strong>in</strong>g a NFm<strong>in</strong> of 0.6 dB at 10 GHz <strong>and</strong> 13.5 dB ga<strong>in</strong> with a<br />
0.15 x 100 µm gate. Other results [20, 21], with improved performance, followed<br />
the next year. After optimiz<strong>in</strong>g the device geometry, Moon showed <strong>in</strong> 2002 that a<br />
<strong>GaN</strong> HEMT could present similar NF at a similar bias<strong>in</strong>g to a GaAs HEMT [22]. The<br />
next notable result <strong>in</strong> the field was when Lu showed that <strong>GaN</strong> <strong>HEMTs</strong> on a sapphire<br />
substrate can have similar NFm<strong>in</strong> performance to <strong>HEMTs</strong> on a SiC substrate [23]. All<br />
previously published results had been on SiC substrates. This work seeks to extend<br />
on the noise figure literature <strong>and</strong> to confirm or deny some of the previously published<br />
results, <strong>in</strong> addition to add<strong>in</strong>g new studies. Table 3.1 lists many <strong>GaN</strong> (as well as GaAs,<br />
SiGe, <strong>and</strong> InP) HEMT NF results.<br />
Prior to this work, <strong>GaN</strong> oscillator references were scarce. The first <strong>GaN</strong> oscillator<br />
was reported by Shealy <strong>in</strong> 2001 [24]. The phase noise was respectable: -92 dBc at<br />
100 kHz for a 6 GHz carrier frequency. While Shealy’s work was a hybrid design, the<br />
first MMIC oscillator was presented by Kaper <strong>in</strong> 2002 [25]. He estimated (but did not<br />
show measurements) the phase noise to be -87 dBc at 100 kHz. These works left room<br />
for further <strong>in</strong>vestigation. A summary of all published <strong>GaN</strong> oscillators appears <strong>in</strong> table<br />
5.1.<br />
The exist<strong>in</strong>g literature was th<strong>in</strong> at the beg<strong>in</strong>n<strong>in</strong>g of this project. The noise research<br />
of <strong>GaN</strong> has s<strong>in</strong>ce approximately doubled to tripled. Because noise is difficult to mea-<br />
sure, second <strong>and</strong> third op<strong>in</strong>ions are valuable. This work will do this, <strong>in</strong> addition to its<br />
7
CHAPTER 1. INTRODUCTION<br />
own unique studies <strong>and</strong> model<strong>in</strong>g.<br />
1.3 Thesis Outl<strong>in</strong>e<br />
Chapter 2 builds up to a NF model. This model is an extension of previous mod-<br />
els <strong>and</strong> fills the need of underst<strong>and</strong><strong>in</strong>g how various noise sources <strong>and</strong> small-signal<br />
parameters <strong>in</strong>fluence NF <strong>and</strong> other noise parameters without the need for prior NF<br />
measurements. The chapter starts with reviews of noise sources, the equivalent circuit<br />
model, NF <strong>and</strong> parameters, <strong>and</strong> previous models. The proposed model is then derived<br />
<strong>and</strong> discussed <strong>in</strong> detail.<br />
With the model<strong>in</strong>g <strong>in</strong> place, several NF studies are presented <strong>in</strong> chapter 3. Effects<br />
of bias <strong>and</strong> gate leakage are studied. Different epitaxial structures are compared, as<br />
is the addition of a field plate. High-frequency <strong>GaN</strong> HEMT devices were borrowed,<br />
measured, <strong>and</strong> compared to <strong>HEMTs</strong> <strong>in</strong> other technologies (<strong>in</strong> particular, GaAs).<br />
A LFN setup was constructed <strong>and</strong> measurements performed to help underst<strong>and</strong> the<br />
phase noise performance. Chapter 4 covers these results. It first shows through mea-<br />
surements why the Hooge parameter should not be used for compar<strong>in</strong>g devices (only<br />
materials). LFN versus bias shows the need for an improved model for the dra<strong>in</strong> noise,<br />
which was then added. LFN studies are then presented <strong>and</strong> comparisons to measured<br />
GaAs <strong>HEMTs</strong> are made.<br />
Differential oscillators are constructed <strong>in</strong> chapter 5 <strong>and</strong> phase noise is measured<br />
8
CHAPTER 1. INTRODUCTION<br />
<strong>and</strong> evaluated. The first version had excellent l<strong>in</strong>earity but poor phase noise. A second<br />
version had good phase noise. The oscillators are compared to other published <strong>GaN</strong><br />
oscillators <strong>and</strong> to differential oscillators <strong>in</strong> Si <strong>and</strong> GaAs technologies.<br />
References<br />
[1] T. Kikkawa, T. Maniwa, H. Hayashi, M. Kanamura, S. Yokokama, M. Nishi,<br />
N. Adachi, M. Yokoyama, Y. Tateno, <strong>and</strong> K. Josh<strong>in</strong>, “An Over 200-W Output<br />
Power <strong>GaN</strong> HEMT Push-Pull Amplifier with High Reliability,” IEEE <strong>Microwave</strong><br />
Theory <strong>and</strong> Tech. Symp., pp. 1347–1350, 2004.<br />
[2] Y. Okamoto, Y. Ando, T. Nakayama, K. Hataya, H. Miyamoto, T. Inoue, M. Senda,<br />
K. Hirata, M. Kosaki, N. Shibata, <strong>and</strong> M. Kuzuhara, “High-Power Recessed-Gate<br />
<strong>Al<strong>GaN</strong></strong><strong>GaN</strong> HFET With a Field-Modulat<strong>in</strong>g Plate,” IEEE Trans. Electron Devices,<br />
vol. 51, no. 12, pp. 2217–2222, Dec. 2004.<br />
[3] H. Ishida, Y. Hirose, T. Murata, Y. Ikeda, T. Matsuno, K. Inoue, Y. Uemoto,<br />
T. Tanaka, T. Egawa, <strong>and</strong> D. Ueda, “A High-Power RF Switch IC Us<strong>in</strong>g Al-<br />
<strong>GaN</strong>/<strong>GaN</strong> HFETs with S<strong>in</strong>gle-Stage Configuration,” Electron Devices, IEEE<br />
Transactions on, vol. 52, no. 8, pp. 1893–1899, 2005.<br />
[4] H. Xu, C. Sanabria, A. Ch<strong>in</strong>i, S. Keller, U. Mishra, <strong>and</strong> R. A. York, “Low Phase-<br />
<strong>Noise</strong> 5 GHz <strong>Al<strong>GaN</strong></strong>/<strong>GaN</strong> HEMT Oscillator Integrated with BaxSr1−xTiO3 Th<strong>in</strong><br />
Films,” IEEE <strong>Microwave</strong> Theory <strong>and</strong> Tech. Symp., pp. 1509–1512, 2004.<br />
[5] V. Kaper, R. Thompson, T. Prunty, <strong>and</strong> J. Shealy, “Signal Generation, Control,<br />
<strong>and</strong> Frequency Conversion <strong>Al<strong>GaN</strong></strong>/<strong>GaN</strong> HEMT MMICs,” <strong>Microwave</strong> Theory <strong>and</strong><br />
Techniques, IEEE Transactions on, vol. 53, no. 1, pp. 55–65, 2005.<br />
[6] G. Ellis, J.-S. Moon, D. Wong, M. Micovic, A. Kurdoghlian, P. Hashimoto, <strong>and</strong><br />
M. Hu, “Wideb<strong>and</strong> <strong>Al<strong>GaN</strong></strong>/<strong>GaN</strong> HEMT MMIC Low <strong>Noise</strong> Amplifier,” <strong>in</strong> <strong>Microwave</strong><br />
Symposium Digest, 2004 IEEE MTT-S International, vol. 1, 2004, pp.<br />
153–156 Vol.1.<br />
[7] H. Xu, C. Sanabria, A. Ch<strong>in</strong>i, S. Keller, U. Mishra, <strong>and</strong> R. York, “A C-B<strong>and</strong> High-<br />
Dynamic Range <strong>GaN</strong> HEMT Low-<strong>Noise</strong> Amplifier,” IEEE <strong>Microwave</strong> Components<br />
Lett., vol. 14, no. 6, pp. 262–264, Jun. 2004.<br />
[8] R. Rast, “The Dawn of Digital TV,” Spectrum, IEEE, vol. 42, no. 10, pp. 26–31,<br />
2005.<br />
[9] D. Leeson, “A Simple Model of Feedback Oscillator <strong>Noise</strong> Spectrum,” Proc. IEEE,<br />
vol. 54, no. 2, pp. 329–330, 1966.<br />
9
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[10] D. V. Kuksenkov, H. Temk<strong>in</strong>, R. Gaska, <strong>and</strong> J. W. Yang, “Low-Frequency <strong>Noise</strong><br />
<strong>in</strong> <strong>Al<strong>GaN</strong></strong>/<strong>GaN</strong> Heterostructure Field Effect Transistors,” IEEE Electron Devices<br />
Lett., vol. 19, no. 7, pp. 222–224, July 1998.<br />
[11] M. E. Lev<strong>in</strong>shte<strong>in</strong>, F. Pascal, S. Contreras, W. Knap, S. L. Rumyantsev, R. Gaska,<br />
J. W. Yang, <strong>and</strong> M. S. Shur, “Low-Frequency <strong>Noise</strong> <strong>in</strong> <strong>GaN</strong>/GaAlN Heterojunctions.”<br />
Applied Physics Letters, vol. 72, no. 23, pp. 3053–5, June 1998.<br />
[12] A. Bal<strong>and</strong><strong>in</strong>, Ed., <strong>Noise</strong> <strong>and</strong> Fluctuations Control <strong>in</strong> Electronic Devices. Stevenson<br />
Ranch, CA: American Scientific Publishers, 2002.<br />
[13] J. A. Garrido, B. E. Foutz, J. A. Smart, J. R. Shealy, M. J. Murphy, W. J. Schaff,<br />
L. F. Eastman, <strong>and</strong> E. Munoz, “Low-Frequency <strong>Noise</strong> <strong>and</strong> Mobility Fluctuations<br />
<strong>in</strong> <strong>Al<strong>GaN</strong></strong>/<strong>GaN</strong> Heterostructure Field-Effect Transistors.” Applied Physics Letters,<br />
vol. 76, no. 23, pp. 3442–4, June 2000.<br />
[14] M. Lev<strong>in</strong>shte<strong>in</strong>, S. Rumyantsev, M. Shur, R. Gaska, <strong>and</strong> M. Khan, “Low Frequency<br />
<strong>and</strong> 1/f <strong>Noise</strong> <strong>in</strong> Wide-Gap Semiconductors: Silicon Carbide <strong>and</strong> Gallium Nitride,”<br />
Circuits, Devices <strong>and</strong> Systems, IEE Proceed<strong>in</strong>gs [see also IEE Proceed<strong>in</strong>gs G-<br />
Circuits, Devices <strong>and</strong> Systems], vol. 149, no. 1, pp. 32–39, 2002.<br />
[15] A. Bal<strong>and</strong><strong>in</strong>, S. Morozov, S. Cai, R. Li, K. Wang, G. Wijeratne, <strong>and</strong><br />
C. Viswanathan, “Low Flicker-<strong>Noise</strong> <strong>GaN</strong>/<strong>Al<strong>GaN</strong></strong> Heterostructure Field-Effect<br />
Transistors for <strong>Microwave</strong> Communications,” <strong>Microwave</strong> Theory <strong>and</strong> Techniques,<br />
IEEE Transactions on, vol. 47, no. 8, pp. 1413–1417, 1999.<br />
[16] S. Rumyantsev, N. Pala, M. Shur, M. Lev<strong>in</strong>shte<strong>in</strong>, R. Gaska, X. Hu, J. Yang,<br />
G. Sim<strong>in</strong>, <strong>and</strong> M. Khan, “Low Frequency <strong>Noise</strong> <strong>in</strong> <strong>GaN</strong>-Based Transistors,” <strong>in</strong><br />
High Performance Devices, 2000. Proceed<strong>in</strong>gs. 2000 IEEE/Cornell Conference<br />
on, 2000, pp. 257–264.<br />
[17] S. Hsu, P. Valizadeh, D. Pavlidis, J. Moon, M. Micovic, D. Wong, <strong>and</strong> T. Hussa<strong>in</strong>,<br />
“Characterization <strong>and</strong> Analysis of Gate <strong>and</strong> Dra<strong>in</strong> Low-Frequency <strong>Noise</strong> <strong>in</strong><br />
<strong>Al<strong>GaN</strong></strong>/<strong>GaN</strong> <strong>HEMTs</strong>,” <strong>in</strong> High Performance Devices, 2002. Proceed<strong>in</strong>gs. IEEE<br />
Lester Eastman Conference on, 2002, pp. 453–460.<br />
[18] A. P<strong>in</strong>g, E. P<strong>in</strong>er, J. Redw<strong>in</strong>g, M. Khan, <strong>and</strong> I. Adesida, “<strong>Microwave</strong> <strong>Noise</strong> Performance<br />
of <strong>Al<strong>GaN</strong></strong>/<strong>GaN</strong> <strong>HEMTs</strong>,” Electron. Lett., vol. 36, no. 2, pp. 175–176, Jan.<br />
2000.<br />
[19] N. Nguyen, M. Micovic, W.-S. Wong, P. Hashimoto, P. Janke, D. Harvey, <strong>and</strong><br />
C. Nguyen, “Robust Low <strong>Microwave</strong> <strong>Noise</strong> <strong>GaN</strong> MODFETs with 0.6 dB <strong>Noise</strong><br />
Figure at 10 GHz,” IEEE Electron. Lett., vol. 36, pp. 469–471, March 2000.<br />
[20] S. Hsu <strong>and</strong> D. Pavlidis, “Low <strong>Noise</strong> <strong>Al<strong>GaN</strong></strong>/<strong>GaN</strong> MODFETs with High Breakdown<br />
<strong>and</strong> Power Characteristics,” Gallium Arsenide Integrated Circuit (GaAs IC)<br />
Symposium, 2001. 23rd Annual Technical Digest, pp. 229–232, Oct. 2001.<br />
10
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[21] W. Lu, J. Yang, M. Khan, <strong>and</strong> I. Adesida, “<strong>Al<strong>GaN</strong></strong>/<strong>GaN</strong> <strong>HEMTs</strong> on SiC with over<br />
100 GHz fT <strong>and</strong> Low <strong>Microwave</strong> <strong>Noise</strong>,” IEEE Trans. Electron Devices, vol. 48,<br />
no. 3, pp. 581–585, Mar. 2001.<br />
[22] J. Moon, M. Micovic, A. Kurdoghlian, P. Janke, P. Hashimoto, W.-S. Wong, L. Mc-<br />
Cray, <strong>and</strong> C. Nguyen, “<strong>Microwave</strong> <strong>Noise</strong> Performance of <strong>Al<strong>GaN</strong></strong><strong>GaN</strong> <strong>HEMTs</strong><br />
With Small DC Power Dissipation,” IEEE Electron Devices Lett., vol. 23, no. 11,<br />
pp. 637–639, Nov. 2002.<br />
[23] W. Lu, V. Kumar, R. Schw<strong>in</strong>dt, E. P<strong>in</strong>er, <strong>and</strong> I. Adesida, “DC, RF, <strong>and</strong> <strong>Microwave</strong><br />
<strong>Noise</strong> Performance of <strong>Al<strong>GaN</strong></strong>/<strong>GaN</strong> <strong>HEMTs</strong> on Sapphire Substrates,” IEEE Trans.<br />
<strong>Microwave</strong> Theory Tech., vol. 50, pp. 2499–2503, Nov. 2002.<br />
[24] J. B. Shealy, J. A. Smart, <strong>and</strong> J. R. Shealy, “Low-Phase <strong>Noise</strong> <strong>Al<strong>GaN</strong></strong>/<strong>GaN</strong> FET-<br />
Based Voltage Controlled <strong>Oscillators</strong> (VCOs),” IEEE <strong>Microwave</strong> Components<br />
Lett., vol. 11, no. 6, pp. 244–245, Jun. 2001.<br />
[25] V. Kaper, V. Tilak, H. Kim, R. Thompson, T. Prunty, J. Smart, L. F. Eastman, <strong>and</strong><br />
J. Shealy, “High Power Monolithic <strong>Al<strong>GaN</strong></strong>/<strong>GaN</strong> HEMT Oscillator,” IEEE GaAs<br />
Digest, pp. 251–254, 2002.<br />
11
2<br />
<strong>Noise</strong> Figure Model<strong>in</strong>g of <strong>Al<strong>GaN</strong></strong>/<strong>GaN</strong><br />
<strong>HEMTs</strong><br />
2.1 Introduction<br />
TO characterize, compare, <strong>and</strong> improve the noise performance of devices, a<br />
theoretical framework is needed that identifies the noise sources, how these<br />
sources contribute to the overall noise, <strong>and</strong> how the noise changes with other param-<br />
eters, such as bias <strong>and</strong> match<strong>in</strong>g conditions. A common approach is to add discrete<br />
noise sources to a small-signal model [1–3]. Depend<strong>in</strong>g on the model, the sources may<br />
be correlated, add<strong>in</strong>g complexity to the derivation <strong>and</strong> <strong>in</strong>terpretation of the particular<br />
model.<br />
This chapter first fills <strong>in</strong> background for the model. <strong>Noise</strong> sources of <strong>in</strong>terest to<br />
noise figure (NF) are reviewed, as is a full small-signal model. NF is then def<strong>in</strong>ed<br />
<strong>in</strong> § 2.4, along with the noise parameters NFm<strong>in</strong> , Γopt <strong>and</strong> rn. Those familiar with<br />
noise sources, NF, <strong>and</strong> small-signal model<strong>in</strong>g could skip these sections <strong>and</strong> cont<strong>in</strong>ue<br />
on to § 2.5. The more widely-used models are presented along with their strengths<br />
12
CHAPTER 2. NOISE FIGURE MODELING OF ALGAN/GAN HEMTS<br />
<strong>and</strong> weaknesses <strong>in</strong> § 2.5. <strong>Noise</strong> model<strong>in</strong>g derived from these previous models is then<br />
<strong>in</strong>troduced. Its strengths <strong>and</strong> weaknesses are also discussed. F<strong>in</strong>ally, the NF model<br />
is used for simulation of device noise figure performance of <strong>Al<strong>GaN</strong></strong>/<strong>GaN</strong> <strong>HEMTs</strong>,<br />
compared to other models, <strong>and</strong> discussed <strong>in</strong> depth.<br />
2.2 <strong>Noise</strong> Sources<br />
The two most common types of noise are shot <strong>and</strong> thermal noise. Both are referred<br />
to as “flat” or “white,” mean<strong>in</strong>g the noise power versus frequency is constant. Each<br />
will be reviewed <strong>in</strong> this section. The relevance of other noise sources to NF is also<br />
discussed.<br />
2.2.1 Thermal <strong>Noise</strong><br />
Thermal noise was first studied <strong>in</strong> detail by Johnson <strong>in</strong> 1927 [4], <strong>and</strong> expla<strong>in</strong>ed<br />
mathematically by Nyquist [5]. Its physical orig<strong>in</strong> is the agitation of electrons <strong>in</strong> a<br />
conductor. The r<strong>and</strong>om scatter<strong>in</strong>g of electrons by atoms followed by their relaxation<br />
back to a ground state leads to fluctuations that can be measured as a voltage or current.<br />
The use of statistical analysis <strong>and</strong> thermal physics [6] leads to the follow<strong>in</strong>g expression<br />
that represents the available noise power from a resistance <strong>in</strong>to a matched load<br />
PT hermal =<br />
⎡<br />
⎣ hf<br />
2 +<br />
13<br />
exp � hf<br />
kT<br />
⎤<br />
hf<br />
� ⎦ ∆f (2.2.1)<br />
− 1
CHAPTER 2. NOISE FIGURE MODELING OF ALGAN/GAN HEMTS<br />
where h is Planck’s constant, k is Boltzmann’s constant, T is temperature, <strong>and</strong> f is the<br />
frequency.<br />
The term ∆f is the b<strong>and</strong>width <strong>in</strong> which the noise is be<strong>in</strong>g measured. To determ<strong>in</strong>e<br />
the total noise com<strong>in</strong>g from, for example, an amplifier, this expression would be <strong>in</strong>te-<br />
grated over the b<strong>and</strong>width of the amplifier. A noise measurement might be performed<br />
over a small b<strong>and</strong>width, less than one Hertz for some low-frequency noise measure-<br />
ments, show<strong>in</strong>g the need to keep this fact <strong>in</strong> m<strong>in</strong>d. When values are quoted <strong>and</strong> a<br />
b<strong>and</strong>width is not specified, it is assumed to be a 1 Hz b<strong>and</strong>width. This convention is<br />
followed <strong>in</strong> this work.<br />
Equation 2.2.1 is a general expression, <strong>and</strong> is needed if operat<strong>in</strong>g at cryogenic tem-<br />
peratures or extreme frequencies (such as the THz range). For most eng<strong>in</strong>eer<strong>in</strong>g pur-<br />
poses, the simpler expression<br />
PT hermal ≈ kT∆f (2.2.2)<br />
can be used. A h<strong>and</strong>y value from this expression is that the available noise at room<br />
temperature <strong>in</strong> a 1 Hz b<strong>and</strong>width is -174 dBm (4 × 10 −21 W).<br />
When the load is not matched, or the noise needs to be expressed as a voltage or<br />
current (described by a variance), the follow<strong>in</strong>g forms are useful:<br />
�<br />
v 2 �<br />
n =4kTR∆f (2.2.3)<br />
�<br />
i 2 �<br />
n = 4kT<br />
∆f (2.2.4)<br />
R<br />
14
CHAPTER 2. NOISE FIGURE MODELING OF ALGAN/GAN HEMTS<br />
R is the resistance of the noise generat<strong>in</strong>g material or medium. A 1kΩ resistor gener-<br />
ates 4 nV/ √ Hz of noise. Not every resistor represented <strong>in</strong> a circuit schematic generates<br />
noise. For example, rπ <strong>in</strong> a bipolar transistor is a manifestation of the transistor’s I-V<br />
characteristics, <strong>and</strong> is not a real resistance.<br />
Ideal reactive components do not generate noise. However, because real <strong>in</strong>ductors<br />
<strong>and</strong> capacitors are lossy, the circuit-modeled parasitic resistances of these components<br />
will generate thermal noise. Also, these components shape the b<strong>and</strong>width of the noise<br />
<strong>in</strong> ways similar to shap<strong>in</strong>g a signal.<br />
F<strong>in</strong>ally, the above equations only apply at thermal equilibrium. A biased transistor<br />
is not at thermal equilibrium. However, a small-signal model of a HEMT, which does<br />
not <strong>in</strong>clude bias, can have its parasitic resistances considered at thermal equilibrium.<br />
Later, <strong>in</strong> § 2.6.3, the channel noise, which is a form of non-equilibrium thermal noise,<br />
are derived. Further <strong>in</strong>formation on thermal noise can be found <strong>in</strong> [6–9].<br />
2.2.2 Shot <strong>Noise</strong><br />
Shot noise was reported <strong>and</strong> expla<strong>in</strong>ed by W. Schottky <strong>in</strong> 1918. The analogy of this<br />
noise to buck shot be<strong>in</strong>g dropped <strong>in</strong>to a bucket is the basis for its name [8]. Shot noise<br />
exists when two conditions are met: (1) a DC current is flow<strong>in</strong>g <strong>and</strong> (2) the charge<br />
carriers compos<strong>in</strong>g the DC current cross a potential barrier. This second condition<br />
is why resistors <strong>and</strong> the channel of a HEMT do not generate shot noise. The noise<br />
15
CHAPTER 2. NOISE FIGURE MODELING OF ALGAN/GAN HEMTS<br />
exists because charge is discrete <strong>and</strong> will cross the potential barrier at r<strong>and</strong>om times.<br />
If the charge crossed at the same time or equal time <strong>in</strong>tervals, the spectrum of the shot<br />
noise would not be white <strong>and</strong> could be better dealt with <strong>in</strong> circuit design (possibly by<br />
filter<strong>in</strong>g).<br />
As with thermal noise, shot noise is not constant at all frequencies. The noise de-<br />
creases at frequencies above which the transit time across the barrier is short compared<br />
to the <strong>in</strong>verse of this frequency [7]. Because devices are operated at frequencies well<br />
below this, the noise can be considered flat [7].<br />
Us<strong>in</strong>g math from r<strong>and</strong>om processes [9], shot noise is describe by the follow<strong>in</strong>g<br />
equation for current fluctuations:<br />
�<br />
i 2 �<br />
n =2qIDC∆f (2.2.5)<br />
with q be<strong>in</strong>g electronic charge (1.6 × 10 −19 C), IDC the DC current (Amps), <strong>and</strong> ∆f<br />
aga<strong>in</strong> the b<strong>and</strong>width of <strong>in</strong>terest.<br />
2.2.3 Other Sources of <strong>Noise</strong><br />
Shot <strong>and</strong> thermal are the important noise sources for NF model<strong>in</strong>g. Others exist, <strong>and</strong><br />
at frequencies lower than RF should be considered. They will be briefly mentioned<br />
here. Flicker <strong>and</strong> generation-recomb<strong>in</strong>ation noise (covered <strong>in</strong> detail <strong>in</strong> chapter 4) are<br />
important for oscillator phase noise, but are not of concern for NF measurements <strong>in</strong><br />
the RF frequency range. Burst noise is <strong>in</strong>terpreted as a type of low-frequency noise<br />
16
CHAPTER 2. NOISE FIGURE MODELING OF ALGAN/GAN HEMTS<br />
with a 1/f 2 spectrum. It also would not affect NF measurements <strong>in</strong> the GHz range, nor<br />
has it been reported <strong>in</strong> <strong>GaN</strong>-based <strong>HEMTs</strong>. Avalanche noise is a form of shot noise,<br />
<strong>and</strong> usually applies to a semiconductor junction. With a high enough field across a<br />
junction, avalanche multiplication can occur [10]. This <strong>in</strong>crease <strong>in</strong> carriers leads to<br />
an <strong>in</strong>crease <strong>in</strong> the shot noise proportional to the cube of the multiplication factor [9].<br />
While the fields can be very high, no evidence has been shown that this type of noise<br />
appears <strong>in</strong> <strong>GaN</strong>-based <strong>HEMTs</strong>. As will be seen <strong>in</strong> model<strong>in</strong>g later, shot <strong>and</strong> thermal<br />
types of noise are sufficient to predict the noise figure of <strong>GaN</strong> <strong>HEMTs</strong>.<br />
2.3 Equivalent Circuit Model<br />
A small-signal model will be used <strong>in</strong> determ<strong>in</strong><strong>in</strong>g the device noise figure. Device<br />
small-signal model<strong>in</strong>g has been covered extensively <strong>in</strong> the literature [11–17]. Here<br />
a short summary will be given. The model used <strong>in</strong> this work is superimposed on<br />
the cross section of a HEMT <strong>in</strong> figure 2.1. The parameters are bias-dependent but<br />
frequency <strong>in</strong>dependent. In this chapter <strong>and</strong> chapter 3, the parameters are extracted at<br />
the bias of best device m<strong>in</strong>imum noise figure performance.<br />
At the heart of the model is the gate-source capacitance, Cgs, <strong>and</strong> the transconduc-<br />
tance, gm. The phase associated with gm, ωτ, is a necessary delay that accounts for<br />
channel charge to redistribute after a change <strong>in</strong> gate voltage. The dra<strong>in</strong>-source resis-<br />
tance, Rds, is a measure of how effectively a signal can be extracted from the device.<br />
17
CHAPTER 2. NOISE FIGURE MODELING OF ALGAN/GAN HEMTS<br />
Ls<br />
Rs<br />
Vc +<br />
-<br />
Source Gate<br />
Cpgs<br />
Cgs<br />
Ri<br />
g me jwτ v c<br />
R ds<br />
Cds<br />
Rgd<br />
C gd<br />
Cpds<br />
Lg<br />
R g<br />
Rd<br />
Cpgd<br />
L d<br />
Dra<strong>in</strong><br />
Figure 2.1: Cartoon show<strong>in</strong>g the device small-signal model on a cross section of a<br />
HEMT.<br />
This is because it will reduce the effective load of the device. There are two primary<br />
causes for its degradation: conduction <strong>in</strong> the buffer due to poor growth (traps) <strong>and</strong><br />
spread of electrons from the 2DEG when the device is under extreme bias<strong>in</strong>g (very<br />
high electric fields).<br />
The channel <strong>and</strong> gate-dra<strong>in</strong> resistances, Ri <strong>and</strong> Rgd, have vague physical <strong>in</strong>terpre-<br />
tations. Ri is regarded as either a physical channel resistance or charg<strong>in</strong>g resistance<br />
for Cgs. Because it is hard to extract separately from the gate resistance, Rg, the two<br />
are sometimes lumped together. The gate-dra<strong>in</strong> capacitance, Cgd, is setup by the space<br />
charge region between the gate <strong>and</strong> dra<strong>in</strong>, similar to Cgs, but typically an order of mag-<br />
nitude smaller. It <strong>in</strong>troduces a bothersome feedback which reduces the high-frequency<br />
18
CHAPTER 2. NOISE FIGURE MODELING OF ALGAN/GAN HEMTS<br />
performance of the device. The gate-dra<strong>in</strong> resistance, Rgd, is also argued as a charg<strong>in</strong>g<br />
resistance for Cgd. Any capacitance between the dra<strong>in</strong> <strong>and</strong> source, which will be very<br />
small, is accounted for with Cds.<br />
The parameters Cgs, gm, τ, Ri, Rds, Rgd, Cgd, <strong>and</strong> Cds taken together are referred to<br />
as the <strong>in</strong>tr<strong>in</strong>sic device. The other elements of the model are unfortunate side-effects of<br />
hav<strong>in</strong>g to provide physical connections to the device <strong>and</strong> the parasitic <strong>and</strong> distributed<br />
effects that occur when operat<strong>in</strong>g at frequencies <strong>in</strong> the GHz range. These parasitic<br />
elements are called the extr<strong>in</strong>sic elements of the device.<br />
The dra<strong>in</strong> <strong>and</strong> source resistances, Rd <strong>and</strong> Rs, come from two physical processes.<br />
The first is the f<strong>in</strong>ite resistance of the 2DEG, <strong>and</strong> so the access regions between gate<br />
source <strong>and</strong> gate dra<strong>in</strong> contribute to these parasitics. The second source is the non-<br />
ideal ohmic contact behavior between the metal pads <strong>and</strong> the semiconductor. These<br />
resistances scale directly with the device width as used <strong>in</strong> § 2.6.5. Because the gate<br />
length is short (0.7 µm here), the resistances of the gate metals contribute to Rg.<br />
From an AC viewpo<strong>in</strong>t, the signal decays as it propagates along the length of the gate<br />
resistance. A distributed model argument shows this resistance to be approximately<br />
1/3 of its DC value [14]. All of these resistances generate thermal noise. Rs <strong>and</strong><br />
Rg will be important for model<strong>in</strong>g of noise figure as seen later. Because Rd is at<br />
the output, <strong>and</strong> its magnitude of noise is far smaller than the channel noise, it can be<br />
ignored.<br />
19
CHAPTER 2. NOISE FIGURE MODELING OF ALGAN/GAN HEMTS<br />
The dra<strong>in</strong>, gate, <strong>and</strong> source <strong>in</strong>ductances, Ld Lg, <strong>and</strong> Ls, respectively, account for<br />
signal delay along the various contact pads. Lg is usually largest, <strong>and</strong> will affect<br />
any <strong>in</strong>put match (noise or power) to the device. F<strong>in</strong>ally there are the various pad<br />
capacitances between their respective device term<strong>in</strong>als: Cpgs, Cpgd, <strong>and</strong> Cpds. Cpgs<br />
<strong>and</strong> Cpgd are small, while Cpds for devices used <strong>in</strong> this work is of the same order as<br />
Cgd.<br />
S-parameter measurements of devices along with open <strong>and</strong> shorted test structures<br />
were used to f<strong>in</strong>d the small-signal parameters. In addition, DC measurements of TLM<br />
structures <strong>and</strong> some basic h<strong>and</strong> calculations [14] were used to determ<strong>in</strong>e Rg, Rs, <strong>and</strong><br />
Rd. For a better fit, optimization was performed us<strong>in</strong>g Advanced Design System<br />
(ADS). It is important to have accurate small-signal parameters; any discrepancies<br />
directly translate <strong>in</strong>to <strong>in</strong>correct noise figure parameter prediction. Some ADS files<br />
useful for extract<strong>in</strong>g <strong>and</strong> optimiz<strong>in</strong>g the small-signal parameters can be found <strong>in</strong> ap-<br />
pendix A.<br />
Extracted small-signal parameters of devices from various samples are displayed <strong>in</strong><br />
table 2.1. The top half of the table is the <strong>in</strong>tr<strong>in</strong>sic parameters, while the bottom half is<br />
the extr<strong>in</strong>sic parameters. Many of the extr<strong>in</strong>sic parasitics come from the geometry of<br />
the device or the pad parasitics <strong>and</strong> will be the same for the different samples. These<br />
parameters will be used <strong>in</strong> this chapter <strong>and</strong> <strong>in</strong> chapter 3.<br />
20
CHAPTER 2. NOISE FIGURE MODELING OF ALGAN/GAN HEMTS<br />
Sample: 15% 25% 25% 27% 35% 35%<br />
on SiC w/AlN<br />
Intr<strong>in</strong>sic Ri (Ω) 6.2 8.24 8.86 9.23 8.23 4.07<br />
Parameters Rds (Ω) 577 588 622 562 833 627<br />
Rgd (Ω) 75.7 287 238 96 96.2 33.4<br />
Cgd (fF) 19 19.1 13.5 20.6 18.7 29.9<br />
Cds (fF) 2.97 2.33 1.34 2.34 1.66 1.13<br />
Cgs (pF) 0.23 0.265 0.22 0.191 0.191 0.215<br />
gm (mS) 34.1 37 33.2 33 30.5 34.9<br />
τ (ps) 1.2 2.25 2.6 2 2.25 2.03<br />
Extr<strong>in</strong>sic Rs (Ω) 10.2 6.18 5.19 4.04 4.31 5.30<br />
Parameters Rd (Ω) 17.9 10.24 8.99 7.41 7.20 7.54<br />
Rg (Ω) ←− 3.03 −→<br />
Ls (pH) ←− 12 −→<br />
Ld (pH) ←− 22.3 −→<br />
Lg (pH) ←− 45.6 −→<br />
Cpgs (fF) ←− 1.38 −→<br />
Cpds (fF) ←− 29.6 −→<br />
Cpgd (fF) ←− 5.4 −→<br />
Table 2.1: Extracted small-signal parameters for various samples. Devices have a gate<br />
geometry of 0.7 × 150 µm.<br />
2.4 <strong>Noise</strong> Figure <strong>and</strong> <strong>Noise</strong> Parameters<br />
An amplifier provides ga<strong>in</strong> to both the <strong>in</strong>put signal <strong>and</strong> the noise. The amplifier will<br />
also add noise from its <strong>in</strong>tr<strong>in</strong>sic noise sources. This makes the signal to noise ratio at<br />
the output worse than at the <strong>in</strong>put. Express<strong>in</strong>g a ratio of these two ratios at a reference<br />
temperature leads to the def<strong>in</strong>ition of noise figure.<br />
F ≡ (S/N)<strong>in</strong><br />
�<br />
�<br />
�<br />
�<br />
(S/N)out<br />
� T =Treference=290K<br />
(2.4.1)<br />
It can be applied to any two port [3] (by extension even to mixers [7]). Here, it will<br />
21
CHAPTER 2. NOISE FIGURE MODELING OF ALGAN/GAN HEMTS<br />
be applied to a s<strong>in</strong>gle HEMT. Sometimes NF is called noise factor, F. Traditionally,<br />
the names were <strong>in</strong>terchangeable, but now it is common that noise figure is the noise<br />
factor expressed <strong>in</strong> decibels (NF = 10 log 10(F)). This is the convention followed <strong>in</strong><br />
this work. Sometimes it is expressed as a temperature (Tnoise =(F − 1)Treference).<br />
<strong>Noise</strong> figure by itself gives no details of the noise sources of the device or amplifier.<br />
However, noise sources can be added as <strong>in</strong> Figure 2.2. Inoise is the equivalent short-<br />
circuited noise current source <strong>and</strong> Enoise the equivalent open-circuited noise voltage<br />
source. Together, they account for all noise sources of the device which can now be<br />
modeled as a noiseless two port. These two sources will likely be correlated because<br />
of the various physical noise sources of the device that contribute to them [8]. Models<br />
that describe these sources of noise are discussed <strong>in</strong> the next section. An <strong>in</strong>put is<br />
connected to the device, represented as a source impedance <strong>in</strong> figure 2.2. This <strong>in</strong>put<br />
will generate its own noise, represented as Esource. This could be thermal noise from<br />
E source<br />
+ -<br />
Z source<br />
E noise<br />
+ -<br />
I noise<br />
<strong>Noise</strong>less<br />
2-port<br />
network<br />
Figure 2.2: Equivalent model of a transistor driven by a noisy source of impedance<br />
Zsource.<br />
22
CHAPTER 2. NOISE FIGURE MODELING OF ALGAN/GAN HEMTS<br />
a passive network <strong>and</strong>/or active device noise. From this, F (<strong>and</strong> hence, NF) can be<br />
written as [8]<br />
F =1+<br />
�<br />
|Enoise + InoiseZsource| 2�<br />
〈Esource〉 2<br />
(2.4.2)<br />
As can be seen, the value of the source impedance actually affects the noise figure.<br />
Once Enoise <strong>and</strong> Inoise have been determ<strong>in</strong>ed through whichever model is applied, the<br />
noise figure can be predicted for chang<strong>in</strong>g source impedance. F can also be expressed<br />
as [18,19]:<br />
F = Fm<strong>in</strong> + 4Rn<br />
Zo<br />
|Γsource − Γopt| 2<br />
(1 −|Γsource| 2 ) |1+Γopt| 2<br />
(2.4.3)<br />
Γsource is the reflection coefficient of the source impedance. Equation 2.4.3 conta<strong>in</strong>s<br />
four parameters that taken together are called the noise parameters. They are:<br />
Fm<strong>in</strong> The best achievable noise figure. It occurs only when the source impedance is<br />
set to Zopt (conversely Γopt).<br />
|Γopt| The magnitude of the source reflection coefficient that provides the m<strong>in</strong>imum<br />
noise figure, Fm<strong>in</strong>.<br />
� Γopt The angle of the source reflection coefficient that provides Fm<strong>in</strong>.<br />
Rn An effective “slope.” The larger its value, the quicker the noise figure <strong>in</strong>creases<br />
as Γsource is changed from its optimum value. 1<br />
These parameters are usually measured as described <strong>in</strong> § 3.3. As can be reasoned<br />
from equation 2.4.3, there are circles of constant noise on an impedance or Smith<br />
1Rn has units of ohms. It can also be normalized to the reference impedance, Zo. Then the variable<br />
is usually written as rn <strong>in</strong>stead.<br />
23
CHAPTER 2. NOISE FIGURE MODELING OF ALGAN/GAN HEMTS<br />
Gmax<br />
Gmax-1dB<br />
Gmax-2dB<br />
NFm<strong>in</strong><br />
NFm<strong>in</strong>+1dB<br />
NFm<strong>in</strong>+2dB<br />
NFm<strong>in</strong>+3dB<br />
Figure 2.3: Smith Chart show<strong>in</strong>g m<strong>in</strong>imum noise figure <strong>and</strong> circles of constant noise<br />
figure (solid circles) along with maximum ga<strong>in</strong> <strong>and</strong> circles of constant ga<strong>in</strong> (dashed<br />
circles).<br />
Chart plane. This is shown <strong>in</strong> Figure 2.3. It should not be surpris<strong>in</strong>g to f<strong>in</strong>d the small-<br />
signal ga<strong>in</strong> circles <strong>and</strong> noise circles do not overlap because Γopt is an <strong>in</strong>tentional ga<strong>in</strong><br />
mismatch to m<strong>in</strong>imize noise [20].<br />
That the noise performance changes with the source match is extremely important<br />
for LNA design. In the next section, noise models for <strong>HEMTs</strong> that are more <strong>in</strong> depth<br />
than <strong>in</strong> figure 2.2 will be reviewed. Once these noise sources are determ<strong>in</strong>ed, they can<br />
be used elsewhere, such as assist<strong>in</strong>g <strong>in</strong> oscillator phase noise prediction.<br />
24
CHAPTER 2. NOISE FIGURE MODELING OF ALGAN/GAN HEMTS<br />
2.5 HEMT <strong>Noise</strong> Figure Models<br />
The major noise figure models used for <strong>HEMTs</strong> are now presented. The work by<br />
van der Ziel, Pucel, Fukui, <strong>and</strong> Pospieszalski is the basis for most other <strong>in</strong>vestigations<br />
<strong>and</strong> model<strong>in</strong>g of noise figure. The key ideas, equations, strengths <strong>and</strong> weaknesses of<br />
each will be reviewed. Shortcom<strong>in</strong>gs found <strong>in</strong> each will show the need for further<br />
work <strong>and</strong> provide motivation for the next section.<br />
2.5.1 van der Ziel <strong>and</strong> Pucel Models<br />
The theoretical work for noise sources <strong>in</strong> FETs at microwave frequencies was <strong>in</strong>-<br />
troduced by van der Ziel <strong>in</strong> the early 1960s [3, 21, 22]. He derived noise sources for<br />
the channel <strong>and</strong> “<strong>in</strong>duced gate noise.” This gate noise is expla<strong>in</strong>ed as fluctuat<strong>in</strong>g noise<br />
<strong>in</strong> the channel capacitively coupl<strong>in</strong>g to the gate through Cgs <strong>and</strong> Cgd, caus<strong>in</strong>g an ef-<br />
fective, <strong>and</strong> correlated, noise source at the gate. The gate noise, channel (dra<strong>in</strong>) noise,<br />
correlation (C), <strong>and</strong> cross-term 〈igi∗ d 〉 can be written as [3]<br />
�<br />
i 2 �<br />
g<br />
=4kTaδ ω2C 2 gs<br />
5gd0<br />
∆f (2.5.1)<br />
�<br />
i 2 �<br />
d =4kTaΓgd0∆f (2.5.2)<br />
C = 〈igi∗ d 〉<br />
�� �<br />
i 2 g<br />
〈i 2 d 〉<br />
(2.5.3)<br />
〈igi ∗ d〉 = 2<br />
3 jωCgskTa∆f (2.5.4)<br />
25
CHAPTER 2. NOISE FIGURE MODELING OF ALGAN/GAN HEMTS<br />
ω is the angular frequency, Ta is the ambient temperature, gd0 is the dra<strong>in</strong>-source con-<br />
ductance when Vds is zero, δ is a parameter van der Ziel gives as 4/3, <strong>and</strong> Γ will be<br />
derived <strong>in</strong> § 2.6.2 (for now, it can be considered a constant of 2/3). Van der Ziel orig-<br />
<strong>in</strong>ally found a correlation of 0.395j for JFETs [3]. For aggressively-scaled <strong>HEMTs</strong>,<br />
the correlation is experimentally found to be ∼0.7j [23,24]. Van der Ziel does give ex-<br />
pressions for noise figure, but they are often <strong>in</strong> terms of more complicated parameters,<br />
under specific conditions, or for different devices, mak<strong>in</strong>g them of limited use [3].<br />
While the gate <strong>and</strong> dra<strong>in</strong> noise expressions above allow for noise prediction, for accu-<br />
rate results the correlation must be measured. This is because small changes <strong>in</strong> cor-<br />
relation can have a large effect <strong>in</strong> predicted noise parameters. Also, the noise sources<br />
are bias-<strong>and</strong> frequency-dependent.<br />
In 1975, Pucel <strong>and</strong> his co-workers took what was learned from van der Ziel <strong>and</strong><br />
extended it <strong>in</strong> a very detailed publication [2]. Their work was explicitly for a GaAs<br />
MESFET (<strong>and</strong> thus more applicable to a HEMT), whereas van der Ziel’s work was<br />
ma<strong>in</strong>ly for JFETs. The Pucel model<strong>in</strong>g takes <strong>in</strong>to account velocity saturation <strong>and</strong> how<br />
the noise changes with bias based on changes <strong>in</strong> the small-signal parameters <strong>and</strong> their<br />
noise variables P, R, <strong>and</strong> C. The model also uses a gate <strong>and</strong> dra<strong>in</strong> noise source that<br />
are correlated, shown <strong>in</strong> a small-signal model <strong>in</strong> figure 2.4. In this figure, the gate<br />
<strong>and</strong> dra<strong>in</strong> noise sources account for all noise generated by the <strong>in</strong>tr<strong>in</strong>sic device (<strong>in</strong>side<br />
the dashed “<strong>Noise</strong>less” box). The parasitic resistances, Rg, Rs, <strong>and</strong> Rd, still generate<br />
26
CHAPTER 2. NOISE FIGURE MODELING OF ALGAN/GAN HEMTS<br />
Gate<br />
Lg<br />
Rg<br />
Ri gme Rds Cgs<br />
jwτ Ig v Cds<br />
+<br />
c<br />
Id Vc Cpgs<br />
-<br />
Rgd Cgd<br />
Cpgd<br />
Rs<br />
Ls<br />
Source<br />
<strong>Noise</strong>less<br />
Figure 2.4: Pucel noise model <strong>in</strong> a small-signal circuit.<br />
Rd<br />
Ld<br />
Cpds<br />
thermal noise. The gate <strong>and</strong> dra<strong>in</strong> noise sources are related to the noise variables by<br />
P =<br />
R =<br />
〈i 2 d 〉<br />
4kTa |Y21| 2 ∆f =<br />
|Y21| 2<br />
4kTa |Y11| 2 ∆f<br />
〈i 2 d 〉<br />
4kTagm∆f<br />
�<br />
i 2 �<br />
g =<br />
gm<br />
4kTaω2C 2 �<br />
i<br />
gs∆f<br />
2 �<br />
g<br />
Dra<strong>in</strong><br />
(2.5.5)<br />
(2.5.6)<br />
<strong>and</strong> the same correlation as <strong>in</strong> equation 2.5.3. Although Pucel determ<strong>in</strong>ed very de-<br />
tailed expressions for these noise variables, for accurate results the model<strong>in</strong>g had to<br />
be fitted to data. Today, if this model is used, the parameters are determ<strong>in</strong>ed empiri-<br />
cally [7], fitt<strong>in</strong>g to noise figure measurements. An excellent paper us<strong>in</strong>g this model on<br />
<strong>GaN</strong> <strong>HEMTs</strong> that shows directly how to extract these parameters from measurements<br />
is found <strong>in</strong> [25]. This method also treats both parts of the correlation, magnitude <strong>and</strong><br />
phase, as variables to be determ<strong>in</strong>ed <strong>in</strong>stead of restrict<strong>in</strong>g the phase to 90 ◦ (strictly<br />
imag<strong>in</strong>ary). This formulation is used <strong>in</strong> this work. Information about an ADS project<br />
27
CHAPTER 2. NOISE FIGURE MODELING OF ALGAN/GAN HEMTS<br />
that helps <strong>in</strong> determ<strong>in</strong><strong>in</strong>g these parameters, conta<strong>in</strong>s a small-signal circuit with this<br />
type of noise model<strong>in</strong>g, <strong>and</strong> calculates noise figure can be found <strong>in</strong> appendix A. Be-<br />
cause it uses the same correlation as van der Ziel’s model<strong>in</strong>g, the Pucel model suffers<br />
the same drawbacks. As mentioned, the parameters usually must be determ<strong>in</strong>ed from<br />
measurements, limit<strong>in</strong>g its predictive power. Because the noise sources are similar for<br />
both models, they will be referred to as correlated noise (CN) models <strong>in</strong> this work.<br />
2.5.2 Fukui Model<br />
Fukui garnered much attention <strong>in</strong> the late 1970s with the <strong>in</strong>troduction of his empir-<br />
ical model [26]. Although it <strong>in</strong>volved empirical parameters, it was far simpler than<br />
the previously reported noise models, was expressed directly <strong>in</strong> terms of the noise<br />
parameters, <strong>and</strong> made clear how key small-signal parameters contributed to the noise<br />
performance. The model is also convenient because the noise at different frequencies<br />
<strong>and</strong> device scal<strong>in</strong>g can be easily determ<strong>in</strong>ed. His expressions for the noise parameters<br />
are:<br />
�<br />
Rg + Rs<br />
Fm<strong>in</strong> = 1+k1fCgs<br />
gm<br />
� �<br />
1<br />
Ropt = k3 + Rg + Rs<br />
4gm<br />
Xopt = k4<br />
fCgs<br />
Rn = k2<br />
g2 m<br />
28<br />
(2.5.7)<br />
(2.5.8)<br />
(2.5.9)<br />
(2.5.10)
CHAPTER 2. NOISE FIGURE MODELING OF ALGAN/GAN HEMTS<br />
The variables k1−4, are the fitt<strong>in</strong>g parameters, <strong>and</strong> will change with the device tech-<br />
nology <strong>and</strong> bias. While this model can be useful for h<strong>and</strong> calculations, the Pucel <strong>and</strong><br />
Pospieszalski models are more complete <strong>and</strong> directly usable <strong>in</strong> a simulator such as<br />
ADS.<br />
2.5.3 Pospieszalski Model<br />
In the late 1980’s, Pospieszalski <strong>in</strong>troduced a new noise figure model that took a<br />
different approach than the previous methods by remov<strong>in</strong>g correlation between the<br />
noise sources [1]. There are only two noise sources for the entire transistor: thermal<br />
noise of Ri <strong>and</strong> Rds. Instead of these resistors be<strong>in</strong>g at ambient temperature, Ta, they<br />
are at higher effective temperatures Tg <strong>and</strong> Td, shown <strong>in</strong> figure 2.5. Tg is usually<br />
(but not always) close to room temperature, while Td can be several thous<strong>and</strong> degrees<br />
Kelv<strong>in</strong>. These elevated temperatures are not l<strong>in</strong>ked to a physical temperature. There<br />
Gate<br />
Lg<br />
Rg<br />
Ri<br />
T = Tg<br />
+<br />
Vc<br />
-<br />
Cpgs<br />
Cgs<br />
4kTg/Ri∆f<br />
Rgd Cgd<br />
Cpgd<br />
gme jwτ vc<br />
R s<br />
Ls<br />
Source<br />
Rds<br />
T = Td<br />
4kTd/Rds∆f<br />
Figure 2.5: Pospieszalski noise model <strong>in</strong> a small-signal circuit. Resistances (<strong>and</strong> their<br />
thermal noise sources) Ri <strong>and</strong> Rds are at elevated temperatures Tg <strong>and</strong> Td respectively.<br />
29<br />
Rd<br />
Cds<br />
Ld<br />
Cpds<br />
Dra<strong>in</strong>
CHAPTER 2. NOISE FIGURE MODELING OF ALGAN/GAN HEMTS<br />
have been attempts to l<strong>in</strong>k these noise temperatures to the device physics, but none<br />
were viewed as successful. The noise can be described by the noise temperatures Tg<br />
<strong>and</strong> Td as:<br />
�<br />
f<br />
Fm<strong>in</strong> = 1+2<br />
Ropt =<br />
+ 2f<br />
� 2 RiTd<br />
fT RdsTa<br />
�<br />
�<br />
�<br />
�RiTgTd<br />
+<br />
fTTa Rds<br />
�<br />
��<br />
�<br />
� 2<br />
� fT TgRiRds<br />
1<br />
f<br />
Xopt =<br />
ωCgs<br />
Rn = TgRi<br />
Ta<br />
+<br />
Td<br />
� f<br />
fT<br />
+ R 2 i<br />
� 2 R 2 i T 2 d<br />
R 2 ds<br />
(2.5.11)<br />
(2.5.12)<br />
(2.5.13)<br />
Td<br />
TaRdsg2 (1 + ω<br />
m<br />
2 C 2 gsR 2 i ) (2.5.14)<br />
After measur<strong>in</strong>g S-parameters <strong>and</strong> noise parameters, the noise temperatures can be<br />
extracted by solv<strong>in</strong>g the above equations. A Matlab script us<strong>in</strong>g equations 2.5.11<br />
<strong>and</strong> 2.5.12 to perform this calculation can be found <strong>in</strong> appendix C. A criteria that<br />
Pospieszalski mentions for the model to work is<br />
1 ≤ 4 Ropt<br />
Rn(F − 1)<br />
< 2 (2.5.15)<br />
The lower limit is fundamental <strong>and</strong> is because the noise of a 2-port modeled by a pair<br />
of noise sources must be Hermitian <strong>and</strong> non-negative def<strong>in</strong>ite as shown by Pospieszal-<br />
ski [27]. The upper limit comes from the model itself [1]. As with the other models, it<br />
can be used to determ<strong>in</strong>e the match for noise <strong>and</strong> expected noise at other frequencies.<br />
The model is criticized for its dependence on Ri as a thermal noise source, which is<br />
30
CHAPTER 2. NOISE FIGURE MODELING OF ALGAN/GAN HEMTS<br />
hard to determ<strong>in</strong>e precisely, <strong>and</strong> for the noise temperatures not hav<strong>in</strong>g a physical basis.<br />
As with the other models, the noise parameters must be measured prior to model<strong>in</strong>g.<br />
Thus the model does not “predict” noise. In addition, the noise temperatures change<br />
with device bias [28]. How they change with bias is reported <strong>in</strong> the literature, but not<br />
modeled or predicted. Information for an ADS project that conta<strong>in</strong>s a small-signal<br />
circuit with this type of noise model<strong>in</strong>g <strong>and</strong> that calculates noise figure can be found<br />
<strong>in</strong> appendix A.<br />
2.5.4 Pospieszalski <strong>and</strong> Correlated <strong>Noise</strong> Models Applied to Al-<br />
<strong>GaN</strong>/<strong>GaN</strong> <strong>HEMTs</strong><br />
Based on the above discussion, the Pospieszalski <strong>and</strong> CN models are useful for:<br />
1. Model<strong>in</strong>g device noise figure <strong>in</strong> a circuit simulator versus frequency <strong>and</strong> <strong>in</strong>put<br />
match<br />
2. Devices that are stable <strong>and</strong> well-characterized, such that the noise variables of<br />
the model (Tg, Td, R, P, C) do not change<br />
3. Predict<strong>in</strong>g noise at frequencies outside the range of available measurement equipment.<br />
4. When the bias <strong>in</strong> a design will not be much different from what gives the best<br />
NF performance<br />
Thus, they are useful for basic LNA designs as shown <strong>in</strong> [17, 29]. The application of<br />
these models to <strong>GaN</strong>-based <strong>HEMTs</strong> is relatively new, with very few publications [25,<br />
28,30].<br />
In table 2.2, the Pospieszalski <strong>and</strong> CN model have been applied to devices from six<br />
samples. The fτ <strong>and</strong> fmax of the different devices at the bias<strong>in</strong>g for best NFm<strong>in</strong> are<br />
31
CHAPTER 2. NOISE FIGURE MODELING OF ALGAN/GAN HEMTS<br />
listed along with the bias at the top of the table. The next section conta<strong>in</strong>s the mea-<br />
sured noise parameters, obta<strong>in</strong>ed as described <strong>in</strong> § 3.3, along with the ga<strong>in</strong> that could<br />
be expected from the device hav<strong>in</strong>g an <strong>in</strong>put match of Γopt <strong>and</strong> an output match for<br />
small-signal ga<strong>in</strong>. These noise measurements, along with the small-signal parameters<br />
from table 2.1, were used to calculate the noise variables for both the Pospieszalski<br />
<strong>and</strong> a CN model. These models’ variables are listed <strong>in</strong> table 2.2 with the predicted<br />
noise parameters us<strong>in</strong>g each model at 5 GHz. The fit is generally very good. Both<br />
models predict NFm<strong>in</strong> <strong>and</strong> |Γopt| well. The Pospieszalski model does not predict � Γopt<br />
as well as the other parameters, <strong>and</strong> the CN model has trouble with predict<strong>in</strong>g rn.<br />
From equation 2.5.13, it is seen that the Pospieszalski model’s prediction of Xopt only<br />
depends on Cgs. A better prediction agreement would be expected. An explanation for<br />
this discrepancy will be offered <strong>in</strong> § 3.5.4. Both these models fit the noise parameters<br />
versus frequency, shown <strong>in</strong> figure 2.6 for one of the sets of measurements <strong>in</strong> table 2.2.<br />
Variations <strong>in</strong> the predicted Tg of Pospieszalski’s model is large, a factor of 4. This<br />
is likely because of the differences <strong>in</strong> Ri <strong>in</strong> the measurements of table 2.1, but they<br />
change by only a factor of 2. This high sensitivity to Ri might make the model difficult<br />
to use <strong>in</strong> predict<strong>in</strong>g noise. However, it should be stressed that the model works well<br />
without the need for correlation.<br />
32
CHAPTER 2. NOISE FIGURE MODELING OF ALGAN/GAN HEMTS<br />
�<br />
�<br />
�<br />
Sample: 15% 25% 25% 27% 35% 35%<br />
on SiC w/AlN<br />
Ids @NFm<strong>in</strong> 20 13 10 19 11 10<br />
Vds @NFm<strong>in</strong> 4 4 7 4 5 4<br />
fτ @NFm<strong>in</strong> 19.7 19.4 21.4 23.3 22.3 21.3<br />
fmax @NFm<strong>in</strong> 30.2 33.6 39 42.9 43.7 40.4<br />
Measure <strong>Noise</strong> Parameters <strong>and</strong> Associated Ga<strong>in</strong><br />
NFm<strong>in</strong> (dB) 1.14 1.13 1.1 1.16 1.15 1.18<br />
rn 0.772 0.707 0.648 0.83 0.796 0.723<br />
Γopt 0.727 0.716 0.746 0.774 0.76 0.733<br />
Γopt 20.5 21.3 23.2 19.8 19.5 23.9<br />
Ga<strong>in</strong>assoc. (dB) 14 13.7 14.6 14.3 14 12.7<br />
Us<strong>in</strong>g Pospieszalski Model<br />
NFm<strong>in</strong> (dB) 1.18 1.1 1.1 1.04 1.07 1.03<br />
rn 0.749 0.597 0.729 0.81 0.839 0.721<br />
Γopt 0.702 0.666 0.715 0.744 0.744 0.72<br />
Γopt 25.7 27.3 26.3 22.7 22.3 26.9<br />
Tg (K) 607 292 250 358 462 988<br />
Td (K) 3445 3018 3893 3469 4454 3966<br />
Us<strong>in</strong>g a Correlated <strong>Noise</strong> Model<br />
NFm<strong>in</strong> (dB) 1.23 1.3 1.21 1.28 1.25 1.33<br />
rn 1.21 0.989 0.831 1.04 0.977 0.95<br />
Γopt 0.806 0.758 0.778 0.797 0.783 0.766<br />
Γopt �<br />
i<br />
19.2 21 22.5 19.6 19.2 23.6<br />
2 �� �<br />
−24 A2<br />
g 10 Hz<br />
〈i<br />
7.05 12.00 3.55 7.09 7.23 6.74<br />
2 d〉 � �<br />
−22 A2<br />
10 Hz 4.56 5.60 4.14 5.93 4.79 5.36<br />
|C| 0.802 0.799 0.821 0.803 0.759 0.739<br />
� C (degrees) 103 101 129 114 114 118<br />
Table 2.2: Comparison of Pospieszalski <strong>and</strong> Correlated <strong>Noise</strong> models to measured<br />
data. Devices have a gate geometry of 0.7 × 150 µm .<br />
33
CHAPTER 2. NOISE FIGURE MODELING OF ALGAN/GAN HEMTS<br />
NF m<strong>in</strong> (dB)<br />
r n<br />
|Γ opt |<br />
2.6<br />
2.4<br />
2.2<br />
2.0<br />
1.8<br />
1.6<br />
1.4<br />
1.2<br />
1.0<br />
0.8<br />
1.8<br />
1.5<br />
1.2<br />
0.9<br />
0.6<br />
0.3<br />
0.0<br />
1.0<br />
0.8<br />
0.6<br />
0.4<br />
0.2<br />
0.0<br />
Measured<br />
Pospieszalski Model<br />
CN Model<br />
4 6 8 10 12<br />
4 6 8 10 12<br />
Measured<br />
Pospieszalski<br />
CN Model<br />
4 6 8 10 12<br />
Frequency (GHz)<br />
Figure 2.6: Comparison of Correlated <strong>Noise</strong> <strong>and</strong> Pospieszalski models to measured<br />
noise parameters versus frequency.<br />
34<br />
180<br />
150<br />
120<br />
90<br />
60<br />
30<br />
0<br />
Angle Γopt (deg.)
CHAPTER 2. NOISE FIGURE MODELING OF ALGAN/GAN HEMTS<br />
Lee’s study of the CN models to <strong>Al<strong>GaN</strong></strong>/<strong>GaN</strong> <strong>HEMTs</strong> experimentally f<strong>in</strong>ds that the<br />
correlation tends to a constant of 0.7 [25]. The average value for |C| found <strong>in</strong> table<br />
2.2 is 0.718, <strong>in</strong> agreement with Lee. The average phase was found to be 110 ◦ , which<br />
is higher than the expected 90 ◦ . However, when Lee de-embeds contributions from<br />
extr<strong>in</strong>sic shot <strong>and</strong> thermal noise sources he f<strong>in</strong>ds the phase to be very close to 90 ◦ [25].<br />
The average gate noise from table 2.2 is 7.3 pA 2 /Hz <strong>and</strong> the average dra<strong>in</strong> noise is 506<br />
pA 2 /Hz.<br />
Average values for the Pospieszalski noise variables are Tg of 493 K <strong>and</strong> Td of<br />
3708 K. These numbers are only approximately close to those found <strong>in</strong> [28]; however,<br />
<strong>in</strong> that reference the devices which had a gate length of 0.35 µm (compared to 0.7 µm<br />
here) had an fτ of only 30 GHz, <strong>and</strong> thus were excessively noisy. Despite the accu-<br />
racy <strong>in</strong> the Pospieszalski model, the condition <strong>in</strong> equation 2.5.15 was not met for the<br />
model<strong>in</strong>g <strong>in</strong> table 2.2. The upper limit was broken; values of 8 were common.<br />
2.6 A Proposed <strong>Noise</strong> Figure Model<br />
A model that was developed for some of the noise studies <strong>in</strong> chapter 3 is now pre-<br />
sented. It uses some of the formulation of the CN models, but without correlation <strong>and</strong><br />
replacement of the <strong>in</strong>duced gate noise with a shot noise source. In addition, this model<br />
can give accurate noise parameter results without prior noise parameter measurements.<br />
35
CHAPTER 2. NOISE FIGURE MODELING OF ALGAN/GAN HEMTS<br />
Gate<br />
R g +R i +R s<br />
I s<br />
+<br />
Vc -<br />
E r<br />
C' gs<br />
Source<br />
g' m v c<br />
R ds<br />
Dra<strong>in</strong><br />
Figure 2.7: A simplified HEMT circuit model <strong>in</strong>clud<strong>in</strong>g noise sources.<br />
2.6.1 Setup Details<br />
A circuit schematic of the model is represented <strong>in</strong> figure 2.7 with six small-signal<br />
parameters <strong>and</strong> three noise sources. A full small-signal model is still used for small-<br />
signal parameter extraction from a HEMT, but only Rg, Rs, Ri, Cgs, gm, <strong>and</strong> Rds are<br />
used. The noise sources are Er, Is, <strong>and</strong> Ic. Er is thermal noise from the two parasitic<br />
resistances <strong>and</strong> channel resistance. Its voltage spectral density is written as<br />
�<br />
E 2 �<br />
r =4kT (Rs + Rg + Ri)∆f (2.6.1)<br />
Is is a shot noise source. The DC current used for it is from a three-term<strong>in</strong>al measure-<br />
ment at the bias of S-parameter extraction. This source can be represented between<br />
gate-<strong>and</strong>-source or gate-<strong>and</strong>-dra<strong>in</strong> with the result<strong>in</strong>g derivations be<strong>in</strong>g the same. The<br />
current spectral density of this shot noise term is<br />
�<br />
I 2 �<br />
s =2qIgs∆f (2.6.2)<br />
36<br />
I c
CHAPTER 2. NOISE FIGURE MODELING OF ALGAN/GAN HEMTS<br />
Igs is the measured gate leakage current.<br />
The f<strong>in</strong>al noise source is Ic. It represents distributed thermal noise <strong>in</strong> the channel,<br />
<strong>and</strong> is the same as found by van der Ziel [3]<br />
�<br />
I 2 �<br />
c =4kTΓgm∆f (2.6.3)<br />
Γ is a bias dependent quantity. For a saturated <strong>GaN</strong> HEMT <strong>and</strong> most other FETs, it<br />
is a constant value of 2/3. It will be derived <strong>in</strong> detail <strong>in</strong> § 2.6.3. All three mentioned<br />
noise sources will be assumed to be uncorrelated, greatly simplify<strong>in</strong>g the math.<br />
The derivation of the noise parameters is also simplified if the source resistance<br />
can be transformed up from the source node to Ri. This is often done <strong>in</strong> device<br />
small-signal circuit calculations through the use of source degeneration, 2 illustrated<br />
<strong>in</strong> figure 2.8. Source degeneration modifies the values of Cgs <strong>and</strong> gm as follows [31]<br />
C ′ gs =<br />
Cgs<br />
1+gmRs<br />
gm<br />
g ′ m =<br />
1+gmRs<br />
(2.6.4)<br />
(2.6.5)<br />
with Rs, Cgs, <strong>and</strong> gm be<strong>in</strong>g values extracted from the device <strong>and</strong> C ′ gs <strong>and</strong> g ′ m the<br />
degenerate values that appear <strong>in</strong> figure 2.7 <strong>and</strong> the math that follows. These equations<br />
hold for ωC ′ gs Rs ≪ 1. The thermal noise of Rs, ERs, can be moved to the <strong>in</strong>put with<br />
the same condition that ωC ′ gsRs ≪ 1. As is seen, the effect of this degeneration is a<br />
reduction <strong>in</strong> the effective Cgs, <strong>and</strong> gm. Because the gate-dra<strong>in</strong> capacitance, Cgd, is not<br />
2The technique is also called emitter degeneration, depend<strong>in</strong>g on if the device <strong>in</strong> question is a FET<br />
or BJT type of device.<br />
37
CHAPTER 2. NOISE FIGURE MODELING OF ALGAN/GAN HEMTS<br />
Gate<br />
+<br />
Vc -<br />
R i<br />
Cgs<br />
Source<br />
R s<br />
E Rs<br />
Dra<strong>in</strong><br />
g mv c<br />
Gate<br />
E Rs<br />
+<br />
Vc -<br />
R i+R s<br />
C'gs<br />
Source<br />
Figure 2.8: Cartoon show<strong>in</strong>g the effect of source degeneration.<br />
Dra<strong>in</strong><br />
g' mv c<br />
used <strong>in</strong> this model, Ri, Rg, <strong>and</strong> Rs can be lumped together as one resistance, further<br />
simplify<strong>in</strong>g the derivation.<br />
Several assumptions have been made. The most worrisome is neglect<strong>in</strong>g the <strong>in</strong>-<br />
tr<strong>in</strong>sic feedback capacitance, Cgd. Pospieszalski has shown [1] at typical noise mea-<br />
surement frequencies remov<strong>in</strong>g Cgd from the model<strong>in</strong>g <strong>in</strong>troduces only a small error<br />
(less than the typical precision of a noise measurement setup). So long as the mea-<br />
surements are made far enough from the device fτ, it should not cause alarm. As an<br />
example, a device with an fτ of 50 GHz will probably not be used for LNA applica-<br />
tions greater than half the device unity current ga<strong>in</strong> frequency. A derivation <strong>in</strong>clud<strong>in</strong>g<br />
Cgd was carried out but the expressions were too complicated for <strong>in</strong>sight to be ga<strong>in</strong>ed<br />
from them.<br />
Another important assumption is that the noise sources are uncorrelated. It is not<br />
38
CHAPTER 2. NOISE FIGURE MODELING OF ALGAN/GAN HEMTS<br />
be<strong>in</strong>g implied that physically all the noise processes are not <strong>in</strong>fluenc<strong>in</strong>g one another.<br />
However, to have a simple enough <strong>and</strong> <strong>in</strong>sightful model, it is a necessary assumption.<br />
As mentioned earlier, it has already been shown that not us<strong>in</strong>g correlation can give<br />
accurate results [1,32].<br />
F<strong>in</strong>ally, neglect<strong>in</strong>g many of the extr<strong>in</strong>sic parasitics is a m<strong>in</strong>or assumption. The<br />
<strong>in</strong>ductances (Lg, Ls, Ld) <strong>and</strong> capacitances (Cpgs, Cpgd, Cpds) do not affect the noise<br />
parameters as much as the <strong>in</strong>tr<strong>in</strong>sic parameters. This will be seen <strong>in</strong> § 2.6.5. Also, the<br />
thermal noise of Rd pales <strong>in</strong> comparison to the noise generated by the channel.<br />
2.6.2 Derivation of <strong>Noise</strong> Parameters<br />
A load, RL, signal generator (not a noise source), Vgen, <strong>and</strong> generator impedance,<br />
Zgen = Rgen + Xgen, are added to the model, redrawn <strong>in</strong> figure 2.9. Also, for conve-<br />
nience, the collected resistances are renamed to<br />
X gen<br />
V gen<br />
R gen<br />
E gen<br />
Z <strong>in</strong><br />
R <strong>in</strong><br />
I s<br />
+<br />
Vc -<br />
E r<br />
C' gs<br />
g' m v c<br />
Figure 2.9: Circuit model used for deriv<strong>in</strong>g noise figure.<br />
39<br />
R ds<br />
I c<br />
R L<br />
+<br />
Vout -
CHAPTER 2. NOISE FIGURE MODELING OF ALGAN/GAN HEMTS<br />
R<strong>in</strong> = Rg + Ri + Rs<br />
(2.6.6)<br />
Assume for the moment that the <strong>in</strong>put <strong>and</strong> output are matched for power: RL = Rds<br />
<strong>and</strong> Zgen = Z∗ <strong>in</strong> . equation 2.4.1 can then be rewritten<br />
F = (S/N)<strong>in</strong><br />
(S/N)out<br />
=<br />
|Vgen| 2<br />
4Zgen /〈v<strong>in</strong>,noisev∗ <strong>in</strong>,noise〉<br />
4Zgen<br />
|AvVgen| 2<br />
4Rds /〈vout,noisev∗ out,noise〉<br />
4Rds<br />
= 1<br />
|Av| 2<br />
�<br />
vout,noisev ∗ out,noise<br />
�<br />
v<strong>in</strong>,noisev ∗ <strong>in</strong>,noise<br />
�<br />
� (2.6.7)<br />
with Av def<strong>in</strong>ed as the voltage ga<strong>in</strong>, vsignal,out = Avvgen. An <strong>in</strong>terest<strong>in</strong>g po<strong>in</strong>t is<br />
that because noise figure is a ratio of powers, the output <strong>and</strong> <strong>in</strong>put match cancel <strong>in</strong><br />
equation 2.6.7. This does not mean that the source impedance has no effect on noise<br />
figure nor that a matched load has no effect on the output power. It means that the ratio<br />
of signal-to-noise at the <strong>in</strong>put only or the output only is not affected by the match<strong>in</strong>g<br />
conditions.<br />
We need to def<strong>in</strong>e the <strong>in</strong>put noise voltage. This may be from an active device, or<br />
it may be unknown, but the derivation depends only on signal-to-noise ratio <strong>and</strong> the<br />
source impedance. Here thermal noise of Zgen, represented as Egen <strong>in</strong> figure 2.9, is<br />
used. The <strong>in</strong>put noise can be written as<br />
�<br />
v 2 �<br />
<strong>in</strong> =4kTRgen<br />
(2.6.8)<br />
The b<strong>and</strong>width (∆ f, assumed to be 1 Hz) will no longer be <strong>in</strong>cluded. The noise figure<br />
is now<br />
F = 1<br />
|Av| 2<br />
�<br />
vout,noisev∗ �<br />
out,noise<br />
4kTRgen<br />
40<br />
(2.6.9)
CHAPTER 2. NOISE FIGURE MODELING OF ALGAN/GAN HEMTS<br />
The output noise, vout,noise, will depend on the contributions from the <strong>in</strong>dividual <strong>in</strong>-<br />
ternal noise sources <strong>in</strong> the device <strong>and</strong> the <strong>in</strong>put noise. Because the HEMT is modeled<br />
by a small-signal circuit with noise sources, the output noise can be calculated with<br />
st<strong>and</strong>ard small-signal methods.<br />
The easiest contribution to the output noise to calculate is the channel noise. It is<br />
merely Ohm’s law, Ic(Rds||RL). Théven<strong>in</strong> <strong>and</strong> Norton representations can be used<br />
such that the voltage ga<strong>in</strong>s from Vgen, Egen, <strong>and</strong> Er to the output will be the same.<br />
This is the ga<strong>in</strong> of a common source configuration as found <strong>in</strong> circuit textbooks [31]:<br />
vout<br />
Av =<br />
Egen,Vgen,Er<br />
= − ωτ<br />
ω<br />
jRL||Rds<br />
(Rgen + R<strong>in</strong>)+j(Xgen − 1/(ωC ′ gs))<br />
with ω be<strong>in</strong>g the angular frequency (2π×frequency) <strong>and</strong> def<strong>in</strong><strong>in</strong>g<br />
ωτ = g ′ m/C ′ gs<br />
(2.6.10)<br />
(2.6.11)<br />
The other ga<strong>in</strong> needed is the shot noise contribution. Us<strong>in</strong>g Norton <strong>and</strong> Théven<strong>in</strong><br />
equivalent circuits aga<strong>in</strong>, it is easily found.<br />
As = vout<br />
Is<br />
= − ωτ<br />
ω<br />
jRL||Rds(Rgen + jXgen)<br />
(Rgen + R<strong>in</strong>)+j(Xgen − 1/(ωC ′ gs))<br />
As expected, it is similar to Av. The total output noise is then expressed as<br />
vout,noise = Av(Egen + Er) − (Rds||RL)Ic + AsIs<br />
(2.6.12)<br />
(2.6.13)<br />
but what is needed is the spectral density, <strong>and</strong> thus, noise power. Tak<strong>in</strong>g the complex<br />
conjugate, followed by a statistical average, gives<br />
�<br />
vout,noisev∗ � ��<br />
2<br />
out,noise = |Av| E2 �<br />
gen + 〈E2 r 〉 �<br />
+ | (Rds||RL) | 2 〈I2 c 〉<br />
41
CHAPTER 2. NOISE FIGURE MODELING OF ALGAN/GAN HEMTS<br />
+|As| 2 〈I2 �<br />
2<br />
s 〉 + |Av| ErE ∗ �<br />
gen + A∗ �<br />
vRL||Rds IcE∗ �<br />
gen<br />
+ ... 10 other cross terms (2.6.14)<br />
It is not possible to calculate the various correlations. Most cross-terms will be zero<br />
(shot <strong>and</strong> thermal noise will not be correlated). For simplicity, all sources are assumed<br />
to be uncorrelated. Equation 2.6.14 is then reduced to<br />
�<br />
vout,noisev ∗ � ��<br />
2<br />
out,noise = |Av| E 2 �<br />
gen + �<br />
E 2 ��<br />
�<br />
2<br />
r + | (Rds||RL) | I 2 � �<br />
2<br />
c + |As| I 2 �<br />
s<br />
(2.6.15)<br />
F<strong>in</strong>ally, comb<strong>in</strong><strong>in</strong>g equations 2.6.8, 2.6.9, 2.6.10, 2.6.12, 2.6.13, <strong>and</strong> equation 2.6.15<br />
we obta<strong>in</strong> an expression for noise figure:<br />
F =1+ R<strong>in</strong><br />
with<br />
Rgen<br />
+ b R2 gen + X 2 gen<br />
Rgen<br />
+ a<br />
�<br />
�<br />
�<br />
�<br />
Rgen � R<strong>in</strong><br />
�<br />
+ Rgen + j Xgen − 1<br />
ωC ′ ��<br />
���� 2<br />
gs<br />
(2.6.16)<br />
a = g ′ mΓ � �<br />
ω 2<br />
ωτ<br />
b =<br />
qIgs<br />
2kTreference<br />
(2.6.17)<br />
(2.6.18)<br />
The factor of 1 is the <strong>in</strong>put noise contribution to the noise figure. If the device does<br />
not generate noise, noise figure would be 1. There would then be no degradation <strong>in</strong><br />
the signal to noise ratio go<strong>in</strong>g <strong>in</strong>to <strong>and</strong> com<strong>in</strong>g out of the device. Equation 2.6.16<br />
describes the noise figure <strong>in</strong> terms of the match provided to the device, the device<br />
small-signal parameters, <strong>and</strong> the measured gate-leakage. There are no fitt<strong>in</strong>g param-<br />
42
CHAPTER 2. NOISE FIGURE MODELING OF ALGAN/GAN HEMTS<br />
eters. This is not the m<strong>in</strong>imum noise figure. To determ<strong>in</strong>e it, we f<strong>in</strong>d the source<br />
impedance that m<strong>in</strong>imizes equation 2.6.16. This is found by tak<strong>in</strong>g partial derivatives<br />
<strong>and</strong> solv<strong>in</strong>g equal to zero.<br />
�<br />
�<br />
F = Fm<strong>in</strong><br />
� ∂F ∂F =0, ∂Rgen ∂Xgen =0<br />
(2.6.19)<br />
This leads to the follow<strong>in</strong>g expressions for the optimal source impedance that provides<br />
the m<strong>in</strong>imum noise figure:<br />
�<br />
�<br />
�<br />
Ropt =<br />
Xopt = 1<br />
ωCgs<br />
a<br />
a + b<br />
�1+aR<strong>in</strong> a + b R<strong>in</strong> + ab<br />
(a + b) 2<br />
1<br />
(ωCgs) 2<br />
(2.6.20)<br />
(2.6.21)<br />
The last parameter, the noise resistance, can be obta<strong>in</strong>ed by us<strong>in</strong>g equation 2.4.3<br />
<strong>and</strong> the equation for noise figure, 2.6.16, at two different source impedances. The<br />
most convenient to choose are the m<strong>in</strong>imum noise figure <strong>and</strong> when the source is at<br />
its reference impedance, Γgen =0. We shall call the later FZ0. Enter<strong>in</strong>g this <strong>in</strong>to<br />
equation 2.4.3 <strong>and</strong> rearrang<strong>in</strong>g,<br />
Rn = Z0<br />
4 (FZ0<br />
�<br />
�<br />
� 1<br />
− Fm<strong>in</strong>) �1+<br />
�<br />
�<br />
�2<br />
�<br />
�<br />
Γopt �<br />
(2.6.22)<br />
An explicit expression is complicated. A Matlab script that implements all four of<br />
the noise parameters can be found <strong>in</strong> appendix B. These equations will be discussed<br />
43
CHAPTER 2. NOISE FIGURE MODELING OF ALGAN/GAN HEMTS<br />
more <strong>in</strong> § 2.6.5, <strong>and</strong> used <strong>in</strong> chapter 3. For the moment, let us turn our attention to the<br />
factor Γ, <strong>and</strong> the derivation of the channel noise source.<br />
2.6.3 Derivation of Dra<strong>in</strong> <strong>Noise</strong> Source<br />
We will quickly go through the derivation of Γ (<strong>and</strong>, therefore, the channel noise<br />
source) to show that it is not a fitt<strong>in</strong>g parameter. Van der Ziel has shown the formula-<br />
tion for a MOSFET [3]. Here, it will be explicitly done for a HEMT. The formulation<br />
<strong>in</strong>volves the DC dra<strong>in</strong> current, Id, so it is needed as well. Assume for the moment that<br />
the device is biased <strong>in</strong> the l<strong>in</strong>ear region (no velocity saturation). Follow<strong>in</strong>g arguments<br />
as found <strong>in</strong> [11,33], the dra<strong>in</strong> current can be written <strong>in</strong> general as<br />
Id = g(Vx) dVx<br />
dx<br />
= qµWns(x) dVx<br />
dx<br />
(2.6.23)<br />
W is the device width (cm), ns(x) is the sheet charge of the 2DEG (cm−2 ), <strong>and</strong> µ<br />
is the mobility � cm2 �<br />
. Vx is the potential difference at a distance x from the source,<br />
Vs<br />
relative to the source. g(Vx) is the channel conductivity per unit length at some po<strong>in</strong>t<br />
along the channel, which depends on Vx.<br />
An expression is needed for ns(x) <strong>in</strong> terms of Vx. First, an effective capacitance can<br />
be def<strong>in</strong>ed [11,33]<br />
C = Q<br />
V<br />
= εB<br />
d +∆d<br />
(2.6.24)<br />
with εB <strong>and</strong> d be<strong>in</strong>g the dielectric permittivity <strong>and</strong> thickness of the <strong>Al<strong>GaN</strong></strong> layer re-<br />
spectively <strong>and</strong> ∆d the centroid of the electron wave functions <strong>in</strong> the quantum well<br />
44
CHAPTER 2. NOISE FIGURE MODELING OF ALGAN/GAN HEMTS<br />
(that is, the 2DEG). The charge of this capacitance is qns(x), with a voltage along the<br />
channel of Vg − Vt − Vx. Vt is the threshold voltage. Comb<strong>in</strong><strong>in</strong>g all this together <strong>and</strong><br />
rearrang<strong>in</strong>g<br />
ns(x) =<br />
<strong>and</strong> substitut<strong>in</strong>g <strong>in</strong>to equation 2.6.23<br />
We can now def<strong>in</strong>e<br />
εB<br />
q(d +∆d) (Vg − Vt − Vx) (2.6.25)<br />
Id = µεBW<br />
d +∆d (Vg − Vt − Vx) dVx<br />
dx<br />
(2.6.26)<br />
g(Vx) = µεBW<br />
d +∆d (Vg − Vt − Vx) (2.6.27)<br />
Its usefulness will soon be apparent. Id can now be found. Because of cont<strong>in</strong>uity, the<br />
DC current enter<strong>in</strong>g <strong>and</strong> leav<strong>in</strong>g the device must be the same. Integrat<strong>in</strong>g over the<br />
length of the device, L,<br />
which gives<br />
� L<br />
0<br />
Iddx = IdL =<br />
� Vd<br />
0<br />
g(Vx)dVx<br />
Id = µεBW<br />
�<br />
(Vg − Vt)Vd −<br />
L(d +∆d)<br />
From this, the transconductance (gm)<br />
gm = ∂Id<br />
∂Vg<br />
= µεBW<br />
L(d +∆d) Vd<br />
45<br />
�<br />
2 Vd 2<br />
(2.6.29)<br />
(2.6.28)<br />
(2.6.30)
CHAPTER 2. NOISE FIGURE MODELING OF ALGAN/GAN HEMTS<br />
<strong>and</strong> the saturation current, Id,sat, can be found. The saturation current is found by<br />
differentiat<strong>in</strong>g equation 2.6.29 with respect to Vd <strong>and</strong> sett<strong>in</strong>g it equal to zero. This<br />
returns the voltage of Vd that maximizes Id, which we will call Vd,sat. However, if the<br />
device has a short channel, the velocity may saturate before the above condition. Then<br />
the voltage that the current saturates is the lesser of the follow<strong>in</strong>g two quantities:<br />
or<br />
Vd,sat = Vg − Vt<br />
Vd,sat = EcritLg<br />
(2.6.31)<br />
(2.6.32)<br />
Ecrit is the critical field strength <strong>and</strong> Lg is the device gate length. Putt<strong>in</strong>g equa-<br />
tion 2.6.31 back <strong>in</strong>to equation 2.6.29, we f<strong>in</strong>d the saturation current result<strong>in</strong>g from<br />
channel p<strong>in</strong>ch off.<br />
Id,sat = 1 µεBW<br />
2 L(d +∆d) (Vg − Vt) 2<br />
(2.6.33)<br />
equation 2.6.29 only works for a device <strong>in</strong> the l<strong>in</strong>ear region until the device saturates,<br />
Id = Id,sat. Beyond this, the current can be approximated to be the same as Id,sat (if<br />
short-channel effects are ignored).<br />
We will follow the work of van der Ziel to derive the channel noise [3]. Assume<br />
that a thermal voltage noise source, vn, creates a dra<strong>in</strong> noise current fluctuation, ∆Id,<br />
along the distributed channel. This is shown <strong>in</strong> figure 2.10. The thermal noise source<br />
can be written as<br />
〈vnv ∗ n〉 = 4kT<br />
g(V )<br />
46<br />
(2.6.34)
CHAPTER 2. NOISE FIGURE MODELING OF ALGAN/GAN HEMTS<br />
Similar to equation 2.6.23, we can write an expression for the dra<strong>in</strong> current fluctua-<br />
tions:<br />
∆Id = g(V ) dV<br />
dx + vng(V ) (2.6.35)<br />
with V = Vx +∆V (x, t). Separat<strong>in</strong>g the derivative <strong>and</strong> <strong>in</strong>tegrat<strong>in</strong>g gives<br />
� L<br />
0<br />
∆Iddx =<br />
� L<br />
0<br />
g(V )dV +<br />
� L<br />
0<br />
vng(V )dx (2.6.36)<br />
An expression for the noise only is desired. If we consider the dra<strong>in</strong> AC shorted, the<br />
first term on the right of the equality <strong>in</strong> equation 2.6.36 will be zero. Cont<strong>in</strong>u<strong>in</strong>g we<br />
have<br />
∆IdL =<br />
Tak<strong>in</strong>g the spectral density we have<br />
� L<br />
〈∆Id∆I ∗ d〉 = 1<br />
L2 � L<br />
〈vnv<br />
0<br />
∗ n〉 g 2 (V )dx = 4kT<br />
L2 0<br />
vng(V )dx (2.6.37)<br />
� L<br />
0<br />
g(V )dx (2.6.38)<br />
with the use of equation 2.6.35. The variable be<strong>in</strong>g <strong>in</strong>tegrated over, x, can be changed<br />
to V through the use of equation 2.6.23. It is rearranged here as<br />
V x (x) + ∆V x (x,t)<br />
g(V )<br />
dx = dV (2.6.39)<br />
g(V)<br />
_<br />
Id<br />
+<br />
I d + ∆I d (t)<br />
... ...<br />
_<br />
+<br />
V n<br />
V x (x+∆x) + ∆V x (x+∆x,t)<br />
Figure 2.10: Cartoon used for deriv<strong>in</strong>g the channel noise.<br />
47<br />
_<br />
+
CHAPTER 2. NOISE FIGURE MODELING OF ALGAN/GAN HEMTS<br />
Substitut<strong>in</strong>g <strong>and</strong> chang<strong>in</strong>g the limits of <strong>in</strong>tegration we arrive at the follow<strong>in</strong>g key equa-<br />
tion:<br />
〈∆Id∆I ∗ �<br />
d 〉 = i 2 �<br />
d = 4kT<br />
L2 � Vd<br />
g<br />
Id 0<br />
2 (Vx)dVx<br />
(2.6.40)<br />
It is now clear the usefulness of know<strong>in</strong>g Id <strong>and</strong> g(Vx) explicitly. Comb<strong>in</strong><strong>in</strong>g equa-<br />
tions 2.6.27, 2.6.29, <strong>and</strong> 2.6.40 leads to an expression for the noise<br />
with<br />
Γ=<br />
�<br />
i 2 �<br />
d =4kTgmΓ (2.6.41)<br />
1 − Vd<br />
Vg−Vt +<br />
1 − 1<br />
V 2 d<br />
3(Vg−Vt) 2<br />
Vd<br />
2 Vg−Vt<br />
(2.6.42)<br />
When the device saturates, the value of Vd that saturates the current is used <strong>in</strong><br />
equation 2.6.42 <strong>in</strong>stead of the value past saturation. Equation 2.6.42 then becomes<br />
Γ=2/3. A plot of Γ for different gate <strong>and</strong> dra<strong>in</strong> bias<strong>in</strong>gs is <strong>in</strong> figure 2.11. A thresh-<br />
old voltage of -6 V has been assumed. It can be <strong>in</strong>ferred from this graph that a device<br />
operat<strong>in</strong>g <strong>in</strong> the l<strong>in</strong>ear region has a larger Γ.<br />
One f<strong>in</strong>al note: while there was no evidence of hot electron effects <strong>in</strong> devices pre-<br />
sented <strong>in</strong> this chapter, van der Ziel mentions that they will change the expected noise.<br />
Instead of equation 2.6.40, the follow<strong>in</strong>g equation would have to be used [3]<br />
�<br />
i 2 �<br />
d = 4kT<br />
L2 � Vd<br />
Te(x)g(Vx)<br />
Id 0<br />
2 dVx<br />
(2.6.43)<br />
Te is the effective electron temperature. He gives an empirical relationship for it <strong>in</strong><br />
48
CHAPTER 2. NOISE FIGURE MODELING OF ALGAN/GAN HEMTS<br />
Γ<br />
1<br />
0.95<br />
0.9<br />
0.85<br />
0.8<br />
0.75<br />
0.7<br />
V g =-6<br />
V g =0<br />
Decreas<strong>in</strong>g V g<br />
0.65<br />
0 1 2 3 4 5 6 7 8<br />
V ds (V)<br />
Figure 2.11: Variation <strong>in</strong> Γ for different dra<strong>in</strong> <strong>and</strong> gate voltages. The gate voltage is<br />
varied from -6 to 0 V by steps of 1 V. The threshold voltage is -6 V.<br />
terms of the electric field relative to the critical field value:<br />
Te(x) =<br />
�<br />
1+ E<br />
Ecrit<br />
�n<br />
(2.6.44)<br />
n is either 0, 1, or 2. If it is zero, then we have equation 2.6.40. This leads to values of<br />
Γ a few times 1 (as opposed to less than 1 when n = 0).<br />
2.6.4 <strong>Noise</strong> Parameter Scal<strong>in</strong>g<br />
To the above model, scal<strong>in</strong>g can be added for vary<strong>in</strong>g gate width <strong>and</strong> number of gate<br />
f<strong>in</strong>gers. Simple l<strong>in</strong>ear scal<strong>in</strong>g based on a start<strong>in</strong>g device width of 150 µm <strong>and</strong> 1 gate<br />
f<strong>in</strong>ger was performed. This allows prediction for a comfortable range of usable gate<br />
49
CHAPTER 2. NOISE FIGURE MODELING OF ALGAN/GAN HEMTS<br />
f<strong>in</strong>gers <strong>and</strong> widths, but will not be accurate for large devices (1 mm or greater). Based<br />
on [34], the follow<strong>in</strong>g equations can be used to scale the small-signal parameters:<br />
with<br />
Rs,new = Rs,old/s1 Ri,new = Ri,old/s1 Rg,new = Rg,olds2<br />
Cgs,new = Cgs,olds1 Igs,new = Igs,olds1 gm,new = gm,olds1<br />
s1 = Wg,new<br />
Wg,old<br />
s2 = Wg,new/n 2 new<br />
Wg,old/n 2 old<br />
(2.6.45)<br />
(2.6.46)<br />
(2.6.47)<br />
The parameters labeled as new, are the values to be determ<strong>in</strong>ed based on the un-<br />
scaled extracted values, the old parameters. n is the number of gate f<strong>in</strong>gers. The<br />
simulated noise parameters versus gate width for a s<strong>in</strong>gle f<strong>in</strong>gered device are <strong>in</strong> fig-<br />
ure 2.12. With <strong>in</strong>creas<strong>in</strong>g unity-gate width, the noise <strong>in</strong>creases. However, the mag-<br />
nitude of the optimal match decreases, which may make match<strong>in</strong>g simpler. Also, the<br />
noise resistance drops, mak<strong>in</strong>g a design more robust <strong>in</strong> terms of the expected noise.<br />
These predicted results agree with measurements <strong>in</strong> [17]. At small gate widths, Rs<br />
<strong>and</strong> Ri will be large <strong>and</strong> keep a lower bound on NFm<strong>in</strong> (not shown <strong>in</strong> figure 2.12).<br />
The noise <strong>in</strong>creases with a wider gate f<strong>in</strong>ger because of <strong>in</strong>creas<strong>in</strong>g gate resistance <strong>and</strong><br />
gate leakage current (F αIgs,R 2 g <strong>in</strong> equation 2.6.16). So as the width <strong>in</strong>creases, NFm<strong>in</strong><br />
goes from be<strong>in</strong>g limited by Rs <strong>and</strong> Ri to Rg <strong>and</strong> Igs. The noise parameters are also<br />
simulated aga<strong>in</strong>st number of gate f<strong>in</strong>gers <strong>in</strong> figure 2.13. Due to layout constra<strong>in</strong>ts <strong>and</strong><br />
considerations for symmetric designs (particularly CPW implementations), the gate<br />
50
CHAPTER 2. NOISE FIGURE MODELING OF ALGAN/GAN HEMTS<br />
NF m<strong>in</strong> (dB)<br />
r n<br />
1.6<br />
1.4<br />
1.2<br />
1<br />
0.8<br />
0 200 400 600<br />
Gate Width (µm)<br />
6<br />
4<br />
2<br />
0<br />
0 200 400 600<br />
Gate Width (µm)<br />
|Γ opt |<br />
Phase Γ opt [deg.]<br />
1<br />
0.8<br />
0.6<br />
0.4<br />
0 200 400 600<br />
Gate Width (µm)<br />
(a) (b)<br />
40<br />
30<br />
20<br />
10<br />
0<br />
0 200 400 600<br />
Gate Width (µm)<br />
(c) (d)<br />
Figure 2.12: (a) M<strong>in</strong>imum noise figure, (b) magnitude <strong>and</strong> (d) phase of optimum<br />
source reflection, <strong>and</strong> noise resistance (c) all versus total gate width. Simulation frequency<br />
is 5 GHz.<br />
f<strong>in</strong>ger number was kept to even values or a s<strong>in</strong>gle gate. The total gate width is kept<br />
constant at 150 µm. A change <strong>in</strong> this parameter for small devices does little to affect<br />
the match or the noise resistance. In go<strong>in</strong>g from one to two gate f<strong>in</strong>gers, there is a<br />
slight improvement <strong>in</strong> noise figure. This can be expla<strong>in</strong>ed solely by an improvement<br />
<strong>in</strong> gate resistance. Beyond two f<strong>in</strong>gers, there is little additional benefit. These scal<strong>in</strong>g<br />
51
CHAPTER 2. NOISE FIGURE MODELING OF ALGAN/GAN HEMTS<br />
results will be used <strong>in</strong> § 3.5.4 <strong>and</strong> § 3.5.5.<br />
Therefore, the best geometry is a smaller total gate width, to keep Rg <strong>and</strong> Igs from<br />
becom<strong>in</strong>g to large, <strong>and</strong> two or four gate f<strong>in</strong>gers. Too small a device, <strong>and</strong> Rs <strong>and</strong> Ri<br />
will be too large. Many papers published for best NFm<strong>in</strong> performance typically have<br />
device widths of ∼100 µm .<br />
NF m<strong>in</strong> (dB)<br />
r n<br />
1<br />
0.95<br />
0.9<br />
0.85<br />
0 2 4 6 8 10<br />
Gate F<strong>in</strong>gers<br />
0.8<br />
0.78<br />
0.76<br />
0.74<br />
0.72<br />
0.7<br />
0 2 4 6 8 10<br />
Gate F<strong>in</strong>gers<br />
|Γ opt |<br />
(degrees)<br />
Phase Γ opt<br />
0.8<br />
0.79<br />
0.78<br />
0.77<br />
0.76<br />
0 2 4 6 8 10<br />
Gate F<strong>in</strong>gers<br />
(a) (b)<br />
18<br />
17<br />
16<br />
15<br />
14<br />
0 2 4 6 8 10<br />
Gate F<strong>in</strong>gers<br />
(c) (d)<br />
Figure 2.13: (a) M<strong>in</strong>imum noise figure, (b) magnitude <strong>and</strong> (d) phase of optimum<br />
source reflection, <strong>and</strong> noise resistance (c) all versus number of gate f<strong>in</strong>gers for a constant<br />
total gate width.<br />
52
CHAPTER 2. NOISE FIGURE MODELING OF ALGAN/GAN HEMTS<br />
2.6.5 Discussion of the Model<br />
The model is now checked aga<strong>in</strong>st measurements, compared to the other noise mod-<br />
els, <strong>and</strong> its limitations are discussed. Figure 2.14 shows noise parameter data for the<br />
35% device of table 2.1 <strong>and</strong> prediction us<strong>in</strong>g the model <strong>in</strong> Matlab <strong>and</strong> a circuit simula-<br />
tion. The fit for all four parameters is very good for both the small-signal simulation<br />
<strong>and</strong> the equations entered <strong>in</strong>to Matlab. The small-signal simulation us<strong>in</strong>g ADS is for a<br />
NF m<strong>in</strong> (dB)<br />
r n<br />
2.5<br />
2<br />
1.5<br />
1<br />
0.5<br />
4 6 8 10 12<br />
Frequency (GHz)<br />
1<br />
0.9<br />
0.8<br />
0.7<br />
0.6<br />
0.5<br />
4 6 8 10 12<br />
Frequency (GHz)<br />
|Γ opt |<br />
Angle Γ opt (Degress)<br />
0.8<br />
0.75<br />
0.7<br />
0.65<br />
0.6<br />
0.55<br />
4 6 8 10 12<br />
Frequency (GHz)<br />
60<br />
50<br />
40<br />
30<br />
20<br />
10<br />
4 6 8 10 12<br />
Frequency (GHz)<br />
Figure 2.14: <strong>Noise</strong> parameters predicted us<strong>in</strong>g the model (solid l<strong>in</strong>e) <strong>and</strong> <strong>in</strong> a full<br />
small-signal circuit simulation (dotted l<strong>in</strong>e) compared to measurements (crosses). The<br />
small-signal parameters are from table 2.1.<br />
53
CHAPTER 2. NOISE FIGURE MODELING OF ALGAN/GAN HEMTS<br />
full small-signal model (<strong>in</strong>clud<strong>in</strong>g Cgd) <strong>and</strong> noise sources as <strong>in</strong> figure 2.7. The phase<br />
match of Γopt with the Matlab script could be further improved by <strong>in</strong>clud<strong>in</strong>g the gate<br />
<strong>in</strong>ductance. Only the small-signal parameters <strong>and</strong> gate leakage were needed for the<br />
Matlab script. The measured noise parameters were not needed beforeh<strong>and</strong> as with<br />
the Pospieszalski <strong>and</strong> CN models. This predictive power can help <strong>in</strong> better designs of<br />
noise performance for devices, accurate estimations of the noise <strong>and</strong> the match to the<br />
device, <strong>and</strong> underst<strong>and</strong><strong>in</strong>g differences <strong>in</strong> noise performance for devices as performed<br />
<strong>in</strong> chapter 3.<br />
Of <strong>in</strong>terest is how much different noise sources contribute to the overall noise figure.<br />
This is presented <strong>in</strong> figure 2.15 us<strong>in</strong>g the model at an optimal bias for noise perfor-<br />
mance. The channel thermal noise accounts for half the contribution to noise figure.<br />
The resistances contribute roughly <strong>in</strong> proportion to their values relative to one another<br />
as one might expect; they are all lumped together at the <strong>in</strong>put. However, Rs effectively<br />
degrades the gm <strong>and</strong> Cgs through source degeneration <strong>and</strong> should be m<strong>in</strong>imized. The<br />
gate leakage contributes about 10% for a device with a reasonably low amount of gate<br />
leakage. This can be a much larger contributer, <strong>and</strong> will be discussed <strong>in</strong> § 3.5.4.<br />
Some <strong>in</strong>sightful parallels can be drawn between this model<strong>in</strong>g (equations 2.6.16,<br />
2.6.20, 2.6.21 <strong>and</strong> 2.6.22), <strong>and</strong> Pospieszalski’s model (equations 2.5.11, 2.5.12, 2.5.13,<br />
<strong>and</strong> 2.5.14). The simplest to see is that Xopt is the same for both models if the gate<br />
leakage tends to zero. If the gate leakage is negligible, then the reactance of the match<br />
54
CHAPTER 2. NOISE FIGURE MODELING OF ALGAN/GAN HEMTS<br />
R i 18%<br />
Gate<br />
Shot<br />
<strong>Noise</strong><br />
R g 7%<br />
11%<br />
R s 11%<br />
53%<br />
Dra<strong>in</strong><br />
<strong>Noise</strong><br />
Figure 2.15: Relative contributions of different noise sources to the overall noise<br />
figure.<br />
reduces to that predicted by both Pospieszalski <strong>and</strong> Fukui. Not as easy to see is that<br />
Ropt is of similar form for both models if b → 0. The other two parameters cannot be<br />
compared so easily. However, the modeled Rn for both show that it <strong>in</strong>creases slightly<br />
with <strong>in</strong>creas<strong>in</strong>g frequency <strong>and</strong> both predict that Fm<strong>in</strong> depends on the square of the<br />
frequency (which will be l<strong>in</strong>ear <strong>in</strong> plots of NFm<strong>in</strong> vs. frequency).<br />
All the noise models discussed so far have a noise source at the gate <strong>and</strong> dra<strong>in</strong>.<br />
Table 2.3 shows typical <strong>in</strong>put <strong>and</strong> output noise currents for the models. All the models<br />
predict relatively the same magnitude of output noise. The models with correlation<br />
show an <strong>in</strong>put noise similar to one another, but two orders of magnitude smaller than<br />
what Pospieszalski or this work predicts. This means that the cross-correlation terms<br />
55
CHAPTER 2. NOISE FIGURE MODELING OF ALGAN/GAN HEMTS<br />
(see, for example, equation 2.6.14) generate more noise than the gate noise. That<br />
the model <strong>in</strong>troduced here generates noise similar to that of Pospieszalski helps to<br />
re<strong>in</strong>force its validity.<br />
�<br />
2<br />
〈i<strong>in</strong>put〉<br />
�<br />
2<br />
〈ioutput〉 10<br />
Model: van der Ziel Pucel Pospieszalski This Work<br />
�<br />
−24 A2<br />
10 5.0 7.2 3100 1370<br />
Hz�<br />
−24 A2<br />
490 480 300 490<br />
Hz<br />
Table 2.3: Comparison of the various noise models’ <strong>in</strong>put <strong>and</strong> output noise currents.<br />
The model can help <strong>in</strong> predict<strong>in</strong>g NF, but it has its limitations. The most important<br />
is the model<strong>in</strong>g fails when the ga<strong>in</strong> drops because it does not take <strong>in</strong>to account Cgd<br />
or self-heat<strong>in</strong>g effects. This means it fails at frequencies close to fτ (f >fτ/2) <strong>and</strong><br />
at high DC bias<strong>in</strong>gs (Ids > 40 mA). A derivation with Cgd was undertaken, but no<br />
closed form solutions could be found for the noise parameters <strong>and</strong> the equations were<br />
too complicated to yield <strong>in</strong>sight. It is possible that the ga<strong>in</strong> could be corrected us<strong>in</strong>g<br />
the Miller effect [31].<br />
Also, the small-signal parameters must be accurately known. The parasitics re-<br />
sistances need to be correctly modeled <strong>and</strong> the measured S-parameters must be as<br />
accurate as possible. For example, the model<strong>in</strong>g was found to be poor when superior<br />
network analyzer was substituted with a less accurate network analyzer.<br />
56
CHAPTER 2. NOISE FIGURE MODELING OF ALGAN/GAN HEMTS<br />
2.7 Summary<br />
This chapter lead up to the presentation of a noise figure model that does not need<br />
prior noise parameter measurements for accurate prediction. It will be used <strong>in</strong> other<br />
parts of this work. All necessary background lead<strong>in</strong>g up to it was <strong>in</strong>troduced, its<br />
derivation presented <strong>in</strong> full, the model’s strengths <strong>and</strong> weakness expla<strong>in</strong>ed, <strong>and</strong> how it<br />
compares to the other popular noise models discussed.<br />
References<br />
[1] M. W. Pospieszalski, “Model<strong>in</strong>g of <strong>Noise</strong> Parameters of MESFET’s <strong>and</strong> MOD-<br />
FET’s <strong>and</strong> Their Frequency <strong>and</strong> Temperature Dependence,” IEEE Trans. <strong>Microwave</strong><br />
Theory Tech., vol. 37, no. 9, pp. 1340–1350, Sept. 1989.<br />
[2] R. A. Pucel, H. A. Haus, <strong>and</strong> H. Statz, “Signal <strong>and</strong> <strong>Noise</strong> Properties of Gallium Arsenide<br />
<strong>Microwave</strong> Field-Effect Transistors,” <strong>in</strong> Advances <strong>in</strong> <strong>Electronics</strong> <strong>and</strong> Electron<br />
Physics. New York: Academic Press, 1975, vol. 38, pp. 195–265.<br />
[3] A. van der Ziel, <strong>Noise</strong> <strong>in</strong> Solid State Devices <strong>and</strong> Circuits. New York: Wiley-<br />
Interscience, 1986.<br />
[4] J. B. Johnson, “Thermal Agitation of Electricity <strong>in</strong> Conductors,” Nature, vol. 119,<br />
pp. 50–51, 1927.<br />
[5] H. Nyquist, “Thermal Agitation of Electric Charge <strong>in</strong> Conductors,” Phys. Rev.,<br />
vol. 32, pp. 110–113, 1928.<br />
[6] C. Kittel <strong>and</strong> H. Kroemer, Thermal Physics, 2nd ed. New York: W. H. Freeman<br />
<strong>and</strong> Company, 2000.<br />
[7] S. A. Maas, <strong>Noise</strong> <strong>in</strong> L<strong>in</strong>ear <strong>and</strong> Nonl<strong>in</strong>ear Circuits. Boston: Artech House, 2005.<br />
[8] T. H. Lee, The Design of CMOS Radio-Frequency Integrated Circuits, 2nd ed.<br />
New York: Cambridge University Pess, 2004.<br />
[9] M. J. Buck<strong>in</strong>gham, <strong>Noise</strong> <strong>in</strong> Electronic Devices <strong>and</strong> Systems. New York: John<br />
Wiley & Sons, 1983.<br />
[10] B. G. Streetman <strong>and</strong> S. Banerjee, Solid State Electronic Devices, 5th ed., ser. Solid<br />
State Physical <strong>Electronics</strong>. Upper Saddle River, NJ: Prentice Hall, 2000.<br />
57
CHAPTER 2. NOISE FIGURE MODELING OF ALGAN/GAN HEMTS<br />
[11] W. Liu, Fundamentals of III-V Devices: HBTs, MESFETs, <strong>and</strong> HFETs/<strong>HEMTs</strong>.<br />
New York: Wiley-Interscience, 1999.<br />
[12] B. Hughes <strong>and</strong> P. J. Tasker, “Bias Dependence of the MODFET Intr<strong>in</strong>sic Model Elements<br />
Values at <strong>Microwave</strong> Frequenices,” IEEE Trans. Electron Devices, vol. 36,<br />
no. 10, pp. 2267–2273, Oct. 1989.<br />
[13] G. Dambr<strong>in</strong>e, A. Cappy, F. Heliodore, <strong>and</strong> E. Playez, “A New Method for Determ<strong>in</strong><strong>in</strong>g<br />
the FET Small-Signal Equivalent Circuit,” IEEE Trans. <strong>Microwave</strong> Theory<br />
Tech., vol. 36, pp. 1151–1159, Jul. 1988.<br />
[14] P. H. Ladbrooke, MMIC Design: GaAs FETs <strong>and</strong> <strong>HEMTs</strong>. Boston: Artech House,<br />
Inc., 1989.<br />
[15] M. Berroth <strong>and</strong> R. Bosch, “Broad-B<strong>and</strong> Determ<strong>in</strong>ation of the FET Small-Signal<br />
Equivalent Circuit,” IEEE Trans. <strong>Microwave</strong> Theory Tech., vol. 38, pp. 891–895,<br />
Jul. 1990.<br />
[16] R. Anholt, Electrical <strong>and</strong> Thermal Characterization of MESFETs, <strong>HEMTs</strong>, <strong>and</strong><br />
HBTs. Norwood, MA: Artech House Publishers, 1994.<br />
[17] H. Xu, “MMICs us<strong>in</strong>g <strong>GaN</strong> <strong>HEMTs</strong> <strong>and</strong> Th<strong>in</strong>-Film BST Capacitors,” Ph.D. dissertation,<br />
University of California, Santa Barbara, 2005.<br />
[18] H. Rothe <strong>and</strong> W. Dahlke, “Theory of Noisy Fourpoles,” Proceed<strong>in</strong>gs of the IRE,<br />
vol. 44, pp. 811–818, Jun. 1956.<br />
[19] G. Gonzalez, <strong>Microwave</strong> Transistor Amplifiers: Analysis <strong>and</strong> Design, 2nd ed. Upper<br />
Saddle River, NJ: Prentice-Hall, Inc., 1997.<br />
[20] M. J. Rodwell, “ECE 594F Class Notes, <strong>Noise</strong> <strong>in</strong> <strong>Electronics</strong> <strong>and</strong> Optoelectronics,”<br />
2000.<br />
[21] A. van der Ziel, “Gate <strong>Noise</strong> <strong>in</strong> Field Effect Transistors at Moderately High Frequencies,”<br />
Proc. IEEE, vol. 51, pp. 461–467, Mar. 1963.<br />
[22] ——, “Thermal <strong>Noise</strong> <strong>in</strong> Field-Effect Transistors,” Proc. IRE, vol. 50, pp. 1808–<br />
1812, Aug. 1962.<br />
[23] S. Lee, “Intr<strong>in</strong>sic <strong>Noise</strong> Characteriestics of Gallium Nitride High Electron Mobility<br />
Transistors,” Ph.D. dissertation, Purdue University, Aug. 2004.<br />
[24] A. Bal<strong>and</strong><strong>in</strong>, Ed., <strong>Noise</strong> <strong>and</strong> Fluctuations Control <strong>in</strong> Electronic Devices. Stevenson<br />
Ranch, CA: American Scientific Publishers, 2002.<br />
[25] S. Lee, K. J. Webb, V. Tilak, <strong>and</strong> L. Eastman, “Intr<strong>in</strong>sic <strong>Noise</strong> Equivalent-<br />
Circuit Paramters for <strong>Al<strong>GaN</strong></strong>/<strong>GaN</strong> <strong>HEMTs</strong>,” IEEE Trans. <strong>Microwave</strong> Theory<br />
Tech., vol. 51, pp. 1567–1577, May 2003.<br />
58
CHAPTER 2. NOISE FIGURE MODELING OF ALGAN/GAN HEMTS<br />
[26] H. Fukui, “Design of <strong>Microwave</strong> GaAs MESFET’s for Broad-B<strong>and</strong> Low-<strong>Noise</strong><br />
Amplifiers,” IEEE Trans. <strong>Microwave</strong> Theory Tech., vol. 27, no. 7, pp. 643–650,<br />
Jul. 1979.<br />
[27] M. W. Pospieszalski <strong>and</strong> W. Wiatr, “Comments on ”Design of <strong>Microwave</strong> GaAs<br />
MESFET’s for Broad-B<strong>and</strong>, Low-<strong>Noise</strong> Amplifiers,” IEEE Trans. <strong>Microwave</strong> Theory<br />
Tech., vol. MTT-34, no. 1, p. 194, Jan. 1986.<br />
[28] S. Nutt<strong>in</strong>ck, E. Gebara, J. Laskar, <strong>and</strong> M. Harris, “High-Frequency <strong>Noise</strong> <strong>in</strong> Al-<br />
<strong>GaN</strong>/<strong>GaN</strong> HFETs,” IEEE <strong>Microwave</strong> Components Lett., vol. 13, no. 4, pp. 149–<br />
151, Apr. 2003.<br />
[29] H. Xu, C. Sanabria, A. Ch<strong>in</strong>i, S. Keller, U. Mishra, <strong>and</strong> R. York, “A C-B<strong>and</strong> High-<br />
Dynamic Range <strong>GaN</strong> HEMT Low-<strong>Noise</strong> Amplifier,” IEEE <strong>Microwave</strong> Components<br />
Lett., vol. 14, no. 6, pp. 262–264, Jun. 2004.<br />
[30] C. Sanabria, H. Xu, T. Palacios, A. Chakraborty, S. Heikman, U. Mishra, <strong>and</strong><br />
R. York, “Influence of Epitaxial Structure <strong>in</strong> the <strong>Noise</strong> Figure of <strong>Al<strong>GaN</strong></strong>/<strong>GaN</strong><br />
<strong>HEMTs</strong>,” IEEE Trans. <strong>Microwave</strong> Theory Tech., vol. 53, pp. 762–769, Feb. 2005.<br />
[31] P. R. Gray, P. J. Hurst, S. H. Lewis, <strong>and</strong> R. G. Meyer, Analysis <strong>and</strong> Design of<br />
Analog Integrated Circuits, 4th ed. New York: Wiley, 2001.<br />
[32] F. Danneville, H. Happy, G. Dambr<strong>in</strong>e, J.-M. Belqu<strong>in</strong>, <strong>and</strong> A. Cappy, “Microscopice<br />
<strong>Noise</strong> Model<strong>in</strong>g <strong>and</strong> Macroscopic <strong>Noise</strong> Models: How Good a Connection?”<br />
IEEE Trans. Electron Devices, vol. 41, no. 5, pp. 779–786, May 1994.<br />
[33] M. Shur, Physics of Semiconductor Devices. Prentice Hall, 1990.<br />
[34] J. M. Golio, Ed., <strong>Microwave</strong> MESFETs <strong>and</strong> <strong>HEMTs</strong>. Norwood, MA: Artech<br />
House, Inc., 1991.<br />
59
3<br />
<strong>Noise</strong> Figure Measurements <strong>and</strong> Studies<br />
3.1 Introduction<br />
WITH the frame work for noise figure laid <strong>in</strong> the previous section, we now<br />
concentrate on noise figure measurements of <strong>Al<strong>GaN</strong></strong>/<strong>GaN</strong> <strong>HEMTs</strong>. The<br />
technology used to fabricated the devices is presented first. The setup used for the<br />
measurements will be discussed, <strong>and</strong> the methodology used for comparisons expla<strong>in</strong>ed.<br />
The bulk of this chapter is devoted to several noise figure studies of <strong>Al<strong>GaN</strong></strong> <strong>HEMTs</strong>.<br />
These studies look at how different epitaxial material <strong>and</strong> device structures affect the<br />
noise figure performance. The effect of a field plate (FP) <strong>and</strong> gate leakage on noise<br />
figure are profound, <strong>and</strong> will be covered <strong>in</strong> § 3.5.4 <strong>and</strong> § 3.5.5. The model<strong>in</strong>g devel-<br />
oped <strong>in</strong> the previous chapter is used to underst<strong>and</strong> how a FP <strong>and</strong> gate leakage affect<br />
the noise performance. Another <strong>in</strong>terest<strong>in</strong>g type of <strong>GaN</strong> HEMT, known as a thick cap<br />
HEMT, was measured <strong>and</strong> will be briefly covered. It is of great <strong>in</strong>terest to know about<br />
the state-of-the-art of <strong>GaN</strong> HEMT noise performance <strong>and</strong> how it compares to <strong>HEMTs</strong><br />
<strong>in</strong> GaAs <strong>and</strong> Si material systems. This is done <strong>in</strong> § 3.6<br />
60
CHAPTER 3. NOISE FIGURE MEASUREMENTS AND STUDIES<br />
3.2 Device Details<br />
Devices from several samples with different epitaxial structures will be discussed,<br />
but they are similar from growth <strong>and</strong> process<strong>in</strong>g po<strong>in</strong>ts of view. The devices were<br />
all grown by metal-organic chemical vapor deposition (MOCVD) on both c-plane<br />
sapphire <strong>and</strong> c-plane 4H-SiC substrates. The epitaxial structures that will most com-<br />
monly appear <strong>in</strong> this work are <strong>in</strong> figure 3.1, which will be referenced throughout the<br />
chapter. The key differences <strong>in</strong> the samples are choice of substrate (sapphire or SiC)<br />
<strong>and</strong> <strong>in</strong>clusion of an AlN <strong>in</strong>terlayer between the <strong>Al<strong>GaN</strong></strong> barrier <strong>and</strong> the <strong>GaN</strong> channel.<br />
29 nm 27% <strong>Al<strong>GaN</strong></strong>: Si<br />
1700 nm UID <strong>GaN</strong><br />
65 nm AlN<br />
750 nm <strong>GaN</strong>: Fe<br />
Sapphire Substrate<br />
(a)<br />
29 nm 35% <strong>Al<strong>GaN</strong></strong>: Si<br />
0.6 nm AlN<br />
1700 nm UID <strong>GaN</strong><br />
65 nm AlN<br />
750 nm <strong>GaN</strong>: Fe<br />
Sapphire Substrate<br />
(b)<br />
29 nm 27% <strong>Al<strong>GaN</strong></strong>: Si<br />
1300 nm UID <strong>GaN</strong><br />
300 nm <strong>GaN</strong>: Fe<br />
160 nm AlN<br />
SiC Substrate<br />
Figure 3.1: Typical epitaxial structure for the devices <strong>in</strong> this work: (a) st<strong>and</strong>ard HEMT<br />
on a sapphire substrate (b) HEMT with AlN <strong>in</strong>terlayer (c) st<strong>and</strong>ard HEMT on siliconcarbide<br />
substrate<br />
After choice of substrate, growth consists of a nucleation layer. This layer may <strong>in</strong>-<br />
clude iron (Fe, an accepter) <strong>in</strong> it, as <strong>in</strong> figure 3.1 (a), to reduce the buffer conductive<br />
(caused by un<strong>in</strong>tentional dop<strong>in</strong>g). The decrease <strong>in</strong> conductivity improves the break-<br />
down of the device for power applications. An un<strong>in</strong>tentionally doped <strong>GaN</strong> layer grown<br />
61<br />
(c)
CHAPTER 3. NOISE FIGURE MEASUREMENTS AND STUDIES<br />
next will be the channel, <strong>and</strong> a 29 nm <strong>Al<strong>GaN</strong></strong> Si-doped layer f<strong>in</strong>ishes the structure. The<br />
Al composition varies with the sample, but is 27 % if not stated explicity.<br />
Device process<strong>in</strong>g began with Ti/Al/Ni/Au electron beam evaporated source <strong>and</strong><br />
dra<strong>in</strong> contacts. These were annealed at 870 ◦ C for 30 s <strong>in</strong> a rapid thermal annealer<br />
(RTA). Device isolation was achieved by reactive ion etch<strong>in</strong>g (RIE) <strong>in</strong> Cl2. Stepper<br />
photolithography Ni/Au/Ni gates were electron beam evaporated with a gate length of<br />
0.7 µm. SiN passivation was achieved with plasma-enhanced chemical vapor deposi-<br />
tion (PECVD). If a field plate is used, it would now be added as a repeated <strong>and</strong> slightly<br />
shifted gate metal layer. All devices <strong>in</strong> this chapter have a gate width of 1x150 µm,<br />
a gate-source spac<strong>in</strong>g of 0.7 µm, <strong>and</strong> a gate-dra<strong>in</strong> spac<strong>in</strong>g of 2 µm. The pads are a<br />
coplanar waveguide (CPW) layout.<br />
Typical measurements of fτ <strong>and</strong> fmax are 23 <strong>and</strong> 47 GHz respectively. Contact<br />
resistance is from 0.3 to 0.6 Ω–mm. Charge <strong>and</strong> mobility vary with the Al composition<br />
of the barrier. For compositions rang<strong>in</strong>g from 15 % to 35 %, the mobility was found<br />
to be 1100-1565 cm 2 /Vs <strong>and</strong> the charge 0.4-1.3x10 13 cm −2 by Hall measurements.<br />
More details about the device details <strong>and</strong> process<strong>in</strong>g can be found <strong>in</strong> [1–4].<br />
3.3 <strong>Noise</strong> Figure Measurement Setup <strong>and</strong> Method<br />
<strong>Noise</strong> figure measurements were performed with a PC–controlled source–pull noise<br />
figure setup. A schematic is <strong>in</strong> figure 3.2. At the heart of the system is the noise figure<br />
62
CHAPTER 3. NOISE FIGURE MEASUREMENTS AND STUDIES<br />
Bias-T<br />
RF<br />
Switch<br />
<strong>Noise</strong><br />
Source<br />
Source<br />
Tuner<br />
RF Probe<br />
Station<br />
Tuner<br />
Controller<br />
Bias<br />
Controller<br />
Network<br />
Analyzer<br />
Computer<br />
Load<br />
Tuner<br />
GPIB<br />
Cable<br />
Bias-T<br />
RF<br />
Switch<br />
<strong>Noise</strong><br />
Figure<br />
Meter<br />
BNC<br />
Cable<br />
Figure 3.2: Schematic of the source-pull noise figure setup.<br />
meter, noise source, <strong>and</strong> source tuner. The HP 8970S noise-figure meter system con-<br />
sists of the HP 8970B noise figure meter, HP 8970C test set, <strong>and</strong> a signal generator<br />
that acts as a local oscillator for the 8970C. Typical error is ±0.15 dB. To f<strong>in</strong>d the de-<br />
vice m<strong>in</strong>imum noise figure, a variable source impedance is generated by a Maury Mi-<br />
crowave MT982A02 mechanical motorized tuner. The load tuner was set to 50 Ω. The<br />
device ga<strong>in</strong> dur<strong>in</strong>g measurement could have been improved by mov<strong>in</strong>g the load tuner<br />
63
CHAPTER 3. NOISE FIGURE MEASUREMENTS AND STUDIES<br />
to a small-signal match, but due to a comb<strong>in</strong>ation of hardware <strong>and</strong> software problems<br />
better measurements were obta<strong>in</strong>ed with it at the reference impedance. However, the<br />
software automatically calculates the ga<strong>in</strong> for a noise <strong>in</strong>put match <strong>and</strong> power output<br />
match.<br />
The device S-parameters at each bias are needed. A Maury <strong>Microwave</strong> MT998C<br />
RF switch box <strong>and</strong> an HP 8722D vector network analyzer (VNA) made it possible to<br />
seamlessly switch between noise <strong>and</strong> S-parameter measurements of devices. All mea-<br />
surements were performed on-wafer with Cascade-Microtech ACP40 ground-signal-<br />
ground CPW probes. The bias was set automatically by an HP 6625A DC–power<br />
supply system. All components were controlled over a general-purpose <strong>in</strong>terface bus<br />
(GPIB) by a Maury <strong>Microwave</strong> proprietary software program which calculates the<br />
noise parameters.<br />
The accuracy of the system was checked <strong>in</strong> two ways. The first was by measur-<br />
<strong>in</strong>g devices that were characterized elsewhere. The second was fabrication of CPW<br />
on-wafer 10 dB attenuators alongside devices <strong>and</strong> circuits. The schematic <strong>and</strong> a pho-<br />
tograph of the attenuator are <strong>in</strong> figure 3.3. Figure 3.3 (c) shows the measured loss <strong>and</strong><br />
m<strong>in</strong>imum noise figure (NFm<strong>in</strong>). A passive device’s loss <strong>and</strong> NFm<strong>in</strong> will be the same <strong>in</strong><br />
decimals. As can be seen, the agreement is good.<br />
To make NF comparisons, several factors need to be taken <strong>in</strong>to consideration. First,<br />
devices across a <strong>GaN</strong> wafer are not uniform due to the quality of research-grade mate-<br />
64
CHAPTER 3. NOISE FIGURE MEASUREMENTS AND STUDIES<br />
R1<br />
Ground<br />
2R 2<br />
In<br />
R1<br />
R1<br />
Out<br />
2R 2<br />
R1<br />
In Out<br />
(a)<br />
R2<br />
Ground<br />
dB<br />
11<br />
10.8<br />
10.6<br />
10.4<br />
10.2<br />
10<br />
9.8<br />
9.6<br />
9.4<br />
9.2<br />
NF m<strong>in</strong><br />
Loss<br />
9<br />
4 5 6 7 8 9 10 11 12 13 14 15<br />
Frequency (GHz)<br />
(b) (c)<br />
Figure 3.3: Coplanar waveguide attenuator (a) schematic, (b) photograph, <strong>and</strong> (c)<br />
measured loss <strong>and</strong> m<strong>in</strong>imum noise figure aga<strong>in</strong>st frequency.<br />
F (unitless)<br />
1.9<br />
1.8<br />
1.7<br />
1.6<br />
1.5<br />
1.4<br />
1.3<br />
F<br />
1/f τ<br />
1/f max<br />
0.10<br />
0.09<br />
0.08<br />
0.07<br />
0.06<br />
0.05<br />
0.04<br />
0.03<br />
0 20 40 60 80 100 120<br />
0.02<br />
140<br />
Current (mA)<br />
(1/GHz)<br />
F (unitless)<br />
2.2<br />
2.0<br />
1.8<br />
1.6<br />
1.4<br />
1.2<br />
0 20 40 60 80 100 120 140<br />
Current (mA)<br />
Figure 3.4: <strong>Noise</strong> factor, fτ <strong>and</strong> fmax for devices from different samples versus<br />
current.<br />
65<br />
F<br />
1/f τ<br />
1/f max<br />
0.20<br />
0.18<br />
0.16<br />
0.14<br />
0.12<br />
0.10<br />
0.08<br />
0.06<br />
0.04<br />
0.02<br />
(1/GHz)
CHAPTER 3. NOISE FIGURE MEASUREMENTS AND STUDIES<br />
rial <strong>and</strong> growth reactors. These variations across a sample cause changes <strong>in</strong> the device<br />
small-signal parameters <strong>and</strong> therefore <strong>in</strong> the fτ <strong>and</strong> fmax . <strong>Noise</strong> has a relationship to<br />
fτ <strong>and</strong> fmax such that improvements <strong>in</strong> one of the quantities usually means an improve-<br />
ment <strong>in</strong> the others. Figure 3.4 helps this argument. Here the <strong>in</strong>verse of fτ, <strong>in</strong>verse of<br />
fmax, <strong>and</strong> noise factor, F (NF = 10 log 10(F)), are plotted for devices from two samples<br />
as the dra<strong>in</strong>-source current is changed. As the current <strong>in</strong>creases, all three parameters<br />
<strong>in</strong>crease. There appears to be a close relationship between F <strong>and</strong> 1/fmax. This relation-<br />
ship can be seen from the model<strong>in</strong>g <strong>in</strong> the previous chapter. fτ <strong>and</strong> fmax are usually<br />
def<strong>in</strong>ed as<br />
gm<br />
fτ =<br />
Cgs + Cgd<br />
�<br />
Rds<br />
fmax = fτ<br />
4(Ri + Rg)<br />
(3.3.1)<br />
(3.3.2)<br />
Exam<strong>in</strong><strong>in</strong>g the last term <strong>in</strong> equation 2.6.16, we see a factor 1/ω 2 tau that is very similar<br />
to equation 3.3.1. An exact <strong>in</strong>stance of fmax is not seen <strong>in</strong> equation 2.6.16 (there is no<br />
Rds), but there is some similarity. The use of source degeneration, as demonstrated <strong>in</strong><br />
§ 2.6.1, modifies Cgs <strong>and</strong> gm. This would affect fτ, fmax, <strong>and</strong> thus NFm<strong>in</strong>. That NFm<strong>in</strong><br />
would depend on fmax <strong>in</strong>stead of fτ also makes sense from a power argument: noise<br />
figure <strong>and</strong> fmax are based on power quantities while fτ is a current ga<strong>in</strong> quantity. The<br />
conclusion of this aside is that devices with similar fτ <strong>and</strong> fmax should have similar<br />
noise.<br />
Device geometry is also important when mak<strong>in</strong>g comparisons. As seen <strong>in</strong> § 2.6.4,<br />
66
CHAPTER 3. NOISE FIGURE MEASUREMENTS AND STUDIES<br />
a wider device has a larger NFm<strong>in</strong>. Also, a device of smaller gate length usually has<br />
better fτ <strong>and</strong> fmax. For a fair comparison then, only devices of the same geometry<br />
should be compared.<br />
F<strong>in</strong>ally, there is the matter of device bias. As the DC bias to the transistor is changed<br />
the noise parameters also change. The optimum bias for NFm<strong>in</strong> may change with<br />
devices from different samples. In all measurements <strong>in</strong> this work, the bias is swept<br />
twice, first Vds then Ids, to f<strong>in</strong>d the best NFm<strong>in</strong> performance possible for the device.<br />
It is better to sweep Ids than Vgs as the threshold voltage changes across a sample.<br />
The transistor’s noise parameters were then measured versus frequency at this bias. It<br />
should be noted that the best bias for noise may not be the same as that of fmax, but it<br />
is a good start<strong>in</strong>g value.<br />
To show the importance of hav<strong>in</strong>g similar devices to NF, Rs, Ri, <strong>and</strong> Cgs variations<br />
were simulated over the range of extracted values <strong>and</strong> entered <strong>in</strong>to the model of chap-<br />
ter 2. The results of this are <strong>in</strong> figure 3.5. Each parameter spans a change of NFm<strong>in</strong> of<br />
0.2 to 0.3 dB. All measurements <strong>in</strong> this work are at a bias <strong>and</strong> source-impedance for the<br />
best NFm<strong>in</strong> atta<strong>in</strong>able from the device. For measurements versus bias, a frequency was<br />
used that gave the most stable <strong>and</strong> repeatable measurement (usually 5 GHz, sometimes<br />
10 GHz). As the bias was changed, S-parameters were re-measured <strong>and</strong> the optimum<br />
source-impedance re-evaluated. When compar<strong>in</strong>g devices from different samples, fτ<br />
<strong>and</strong> fmax measurements were first performed to f<strong>in</strong>d devices with similar performance.<br />
67
CHAPTER 3. NOISE FIGURE MEASUREMENTS AND STUDIES<br />
NF m<strong>in</strong> (dB)<br />
2.2<br />
2.1<br />
2.0<br />
1.9<br />
1.8<br />
1.7<br />
R s<br />
Capacitance (pF)<br />
0.20 0.21 0.22 0.23 0.24 0.25<br />
3 4 5 6 7 8 9 10 11 12<br />
R i<br />
Resistance (Ω)<br />
Figure 3.5: Variation <strong>in</strong> expected m<strong>in</strong>imum noise figure with changes <strong>in</strong> three smallsignal<br />
parameters.<br />
3.4 Bias Dependence<br />
Transistors <strong>in</strong> Low <strong>Noise</strong> Amplifiers (LNA) are biased at low currents <strong>and</strong> voltages<br />
for maximum NF performance <strong>and</strong> to reduce power consumption. A <strong>GaN</strong> HEMT<br />
biased at a “low” bias is likely beyond the breakdown of other material technologies.<br />
Therefore, it is of <strong>in</strong>terest to know how the noise parameters change with device bias,<br />
which leads to some <strong>in</strong>terest<strong>in</strong>g results <strong>in</strong> this work. Also, know<strong>in</strong>g how the noise<br />
changes with bias is necessary for noise sources extracted from NF measurements<br />
that are <strong>in</strong>cluded <strong>in</strong> device circuit simulations for oscillator phase noise.<br />
Figure 3.6 displays all four noise parameters, the associated ga<strong>in</strong>, <strong>and</strong> maximum<br />
ga<strong>in</strong> at a frequency of 10 GHz for dra<strong>in</strong>-source voltages, Vds, 2 to 20 V. The dra<strong>in</strong>-<br />
68<br />
C gs
CHAPTER 3. NOISE FIGURE MEASUREMENTS AND STUDIES<br />
Figure 3.6: Change <strong>in</strong> noise parameters with dra<strong>in</strong>-source voltage at 10 GHz: (a)<br />
M<strong>in</strong>imum noise figure (b) magnitude <strong>and</strong> phase of optimum reflection coefficient (c)<br />
noise resistance (d) device associated <strong>and</strong> maximum ga<strong>in</strong>s.<br />
69
CHAPTER 3. NOISE FIGURE MEASUREMENTS AND STUDIES<br />
source current, Ids, is kept constant at the best bias for NFm<strong>in</strong>. The small-signal asso-<br />
ciated power ga<strong>in</strong> is that available when the <strong>in</strong>put is matched for noise <strong>and</strong> the output<br />
for power. The maximum ga<strong>in</strong> is of a small-signal <strong>in</strong>put <strong>and</strong> output conjugate match.<br />
NFm<strong>in</strong> flattens out above Vds ∼3 V. The other noise parameters are nearly flat, except<br />
for the phase which decreases slightly. This is probably from a slight change <strong>in</strong> Cgd<br />
with Vgd. From these measurements, it can be concluded that once the device saturates<br />
the noise parameters can be considered constant.<br />
What is more <strong>in</strong>terest<strong>in</strong>g is how the noise parameters change with the dra<strong>in</strong>-source<br />
current. The measured noise parameters of this are the solid circles <strong>in</strong> figure 3.7<br />
for a sample with a sapphire substrate <strong>and</strong> 35 % Al <strong>in</strong> the barrier at a measurement<br />
frequency of 5 GHz. Now we f<strong>in</strong>d that NFm<strong>in</strong> <strong>and</strong> rn <strong>in</strong>crease with current. NFm<strong>in</strong> does<br />
not <strong>in</strong>crease because of a large <strong>in</strong>crease <strong>in</strong> device noise. The reason is that the ga<strong>in</strong><br />
drops with the <strong>in</strong>creas<strong>in</strong>g current. The ga<strong>in</strong> is lower because the channel is opened<br />
(loss of transconductance) <strong>and</strong> self-heat<strong>in</strong>g (from the high currents <strong>in</strong>volved). That<br />
the ga<strong>in</strong> affects the noise figure directly is seen <strong>in</strong> equation 2.6.9. The magnitude<br />
of the optimum source reflection coefficient, Γopt, decreases with <strong>in</strong>creas<strong>in</strong>g current<br />
while its phase decreases. This is a result of the match chang<strong>in</strong>g with loss of ga<strong>in</strong> <strong>and</strong><br />
<strong>in</strong>creas<strong>in</strong>g Cgs.<br />
To further <strong>in</strong>vestigate the usefulness of the Pospieszalski <strong>and</strong> CN models, they<br />
were applied to these noise measurements. Measurements of fτ <strong>and</strong> fmax (needed<br />
70
CHAPTER 3. NOISE FIGURE MEASUREMENTS AND STUDIES<br />
(a) (b)<br />
(c) (d)<br />
Figure 3.7: Typical plots of the noise parameters versus dra<strong>in</strong> source current as measured<br />
(circles) <strong>and</strong> us<strong>in</strong>g the Pospieszalski (dash-dot l<strong>in</strong>e) <strong>and</strong> CN (solid l<strong>in</strong>e) models:<br />
(a) M<strong>in</strong>imum noise figure (b) magnitude of optimum reflection coefficient (c) noise<br />
resistance (d) <strong>and</strong> phase of optimum reflection coefficient. Measurement frequency is<br />
5 GHz.<br />
71
CHAPTER 3. NOISE FIGURE MEASUREMENTS AND STUDIES<br />
for Pospieszalski’s formulation) <strong>and</strong> extracted small-signal parameters were collected<br />
at each bias the noise parameters were measured at <strong>in</strong> figure 3.7. Then, us<strong>in</strong>g meth-<br />
ods <strong>in</strong> § 2.5, a small-signal model with noise sources from either Pospieszalski’s or<br />
the CN formulation were created <strong>in</strong> ADS. ADS was then used to simulate the noise<br />
parameters. The results were added to figure 3.7. The solid l<strong>in</strong>es are simulations us-<br />
<strong>in</strong>g the CN model <strong>and</strong> the dash-dot l<strong>in</strong>es us<strong>in</strong>g the Pospieszalski model. Both models<br />
predict the noise parameters for the <strong>GaN</strong> HEMT versus bias well <strong>and</strong> can be used for<br />
bias-dependent noise parameter model<strong>in</strong>g of <strong>GaN</strong> <strong>HEMTs</strong>.<br />
The model<strong>in</strong>g <strong>in</strong> § 2.6 does not work to predict the noise parameters versus bias.<br />
It only works at low bias<strong>in</strong>gs (Ids < ∼40 mA <strong>in</strong> this work) because it does not take<br />
<strong>in</strong>to account reduction <strong>in</strong> ga<strong>in</strong> from self-heat<strong>in</strong>g. Because the Pospieszalski <strong>and</strong> CN<br />
models are fitt<strong>in</strong>g to the data at these high biases, they predict the noise parameters<br />
correctly. However, the model can still be used to expla<strong>in</strong> trends seen <strong>in</strong> the noise<br />
parameters versus bias. Equation 2.6.22 shows that as NFm<strong>in</strong> <strong>in</strong>creases <strong>and</strong> |Γopt|<br />
decreases with <strong>in</strong>creas<strong>in</strong>g current, then Rn should <strong>in</strong>crease as well.<br />
Figure 3.8 shows how the noise variables used for the simulations <strong>in</strong> figure 3.7<br />
change with bias. These variables are the quantitative values of noise sources entered<br />
<strong>in</strong> a circuit simulator, such as ADS. For example: shot noise changes with DC cur-<br />
rent, thermal noise changes with resistance, <strong>and</strong> a Pospieszalski thermal noise source<br />
changes with the noise temperature. We see <strong>in</strong> figure 3.8 (a) that the correlation coef-<br />
72
CHAPTER 3. NOISE FIGURE MEASUREMENTS AND STUDIES<br />
(a)<br />
(c)<br />
Figure 3.8: <strong>Noise</strong> variables for the Pospieszalski <strong>and</strong> a CN noise model versus dra<strong>in</strong><br />
source current: (a) magnitude <strong>and</strong> phase of the correlation coefficient <strong>and</strong> (b) gate <strong>and</strong><br />
dra<strong>in</strong> noise for a CN model. The device gm, multiplied by a factor of 10 to better fit<br />
the scale, is also <strong>in</strong> (b). (c) Dra<strong>in</strong> <strong>and</strong> gate noise temperatures of the Pospieszalski<br />
model for vary<strong>in</strong>g current.<br />
ficient magnitude <strong>and</strong> phase are relatively flat versus current. This supports the work<br />
of S. Lee on <strong>GaN</strong> <strong>HEMTs</strong> [5,6]. After detailed analysis us<strong>in</strong>g the CN model, Lee con-<br />
cluded that the correlation coefficient could be considered constant with a magnitude<br />
73<br />
(b)
CHAPTER 3. NOISE FIGURE MEASUREMENTS AND STUDIES<br />
of 0.7 <strong>and</strong> phase of 90 ◦ after de-embedd<strong>in</strong>g extr<strong>in</strong>sic thermal <strong>and</strong> shot noise. Here,<br />
we see the same magnitude but a slightly higher phase. The <strong>in</strong>crease <strong>in</strong> phase is likely<br />
from the shot noise of the gate leakage. While Lee’s results were only versus fre-<br />
quency, we see here that it holds versus bias as well. To the author’s knowledge, there<br />
is no reference <strong>in</strong> the <strong>GaN</strong> literature that has the noise variables us<strong>in</strong>g the CN model<br />
versus bias. We might expect the <strong>in</strong>put <strong>and</strong> output noise currents <strong>in</strong> figure 3.8 (b) to<br />
behave as van der Ziel predicts <strong>in</strong> equations 2.5.1 <strong>and</strong> 2.5.2. Then the dra<strong>in</strong> noise,<br />
〈i 2 d 〉, should follow changes <strong>in</strong> gm versus bias. Ten times the value of gm (for the con-<br />
venience of plott<strong>in</strong>g) is also <strong>in</strong> figure 3.8 (b). 〈i 2 d〉 appears to follow the same trend.<br />
The gate noise, �<br />
i2 �<br />
g , also seems to follow what van der Ziel would predict (a C2 gs/gm<br />
dependence).<br />
Turn<strong>in</strong>g to the Pospieszalski model <strong>in</strong> figure 3.8 (c), the two noise temperatures are<br />
plotted aga<strong>in</strong>st Ids. The gate noise temperature is relatively flat. This agrees with the<br />
one <strong>GaN</strong> reference <strong>in</strong> the literature [7], <strong>and</strong> what is seen <strong>in</strong> GaAs <strong>HEMTs</strong>. Here, the<br />
dra<strong>in</strong> noise temperature drops. This is the opposite of what would be expected but is<br />
easily expla<strong>in</strong>ed. The sapphire sample the device was on did not have a good buffer,<br />
mak<strong>in</strong>g Rds low (less than 1 kΩ <strong>in</strong>stead of ∼1.5 kΩ). As the current <strong>in</strong>creased, Rds<br />
dropped off dramatically (900 Ω to 100 Ω). The term Td/Rds is prevalent through<br />
Pospieszalski’s equations. In fitt<strong>in</strong>g to the data, Td decreased along with Rds to keep<br />
the correct proportion. In other samples with a good buffer (only a slight drop <strong>in</strong> Rds),<br />
74
CHAPTER 3. NOISE FIGURE MEASUREMENTS AND STUDIES<br />
Td will <strong>in</strong>crease.<br />
3.5 <strong>GaN</strong> HEMT <strong>Noise</strong> Figure Studies<br />
3.5.1 Substrate<br />
The effect of substrate on the noise parameters was carried out on samples with<br />
SiC <strong>and</strong> sapphire substrates hav<strong>in</strong>g 25% Al <strong>in</strong> the barrier <strong>and</strong> structures similar to<br />
figure 3.1 (a) <strong>and</strong> (c). Versus frequency, devices from both samples had very similar<br />
Figure 3.9: M<strong>in</strong>imum noise figure, small signal associated <strong>and</strong> maximum ga<strong>in</strong> for<br />
devices on sapphire <strong>and</strong> SiC substrates.<br />
75
CHAPTER 3. NOISE FIGURE MEASUREMENTS AND STUDIES<br />
noise parameters. As the current was varied, a difference <strong>in</strong> performance of NFm<strong>in</strong><br />
emerged. Figure 3.9 shows that the sapphire sample had worse noise figure perfor-<br />
mance at higher bias<strong>in</strong>gs. At 100 mA, the difference is more than 0.5 dB. Also plotted<br />
are the associated <strong>and</strong> max ga<strong>in</strong>s for both devices shown. The sapphire sample ga<strong>in</strong>s<br />
fall much quicker as the bias <strong>in</strong>creases. As stated earlier, if the ga<strong>in</strong> drops then the<br />
noise figure will too. Devices on sapphire have degraded power performance at high<br />
bias<strong>in</strong>gs because of self-heat<strong>in</strong>g. Here, we see it affects noise figure performance as<br />
well. A previous study confirms the noise degradation is caused by self-heat<strong>in</strong>g with<br />
temperature dependent measurements [8].<br />
3.5.2 Al Composition <strong>in</strong> the Barrier<br />
To <strong>in</strong>vestigate if chang<strong>in</strong>g the Al composition <strong>in</strong> the <strong>Al<strong>GaN</strong></strong> barrier had an effect<br />
on noise, four samples were grown with 15%, 25%, 27%, <strong>and</strong> 35% Al on a sapphire<br />
substrate. The rest of the structure for all four samples was the same as <strong>in</strong> figure 3.1 (a).<br />
Lu previously published this study for <strong>GaN</strong> <strong>HEMTs</strong> [9]. He found that devices of high<br />
Al composition (35 %) had better noise performance than low Al composition (15 %).<br />
However, the reported fτ <strong>and</strong> fmax for the samples were not similar. fτ <strong>in</strong>creased with<br />
higher Al composition from 25 GHz to 50 GHz <strong>and</strong> fmax <strong>in</strong>creased from 55 GHz to<br />
101 GHz. The four samples <strong>in</strong> this study had reasonably similar fτ <strong>and</strong> fmax. <strong>Noise</strong><br />
parameters of the four samples for chang<strong>in</strong>g frequency are plotted <strong>in</strong> figure 3.10. Also,<br />
76
CHAPTER 3. NOISE FIGURE MEASUREMENTS AND STUDIES<br />
NF m<strong>in</strong><br />
r n<br />
2.4<br />
2.2<br />
2.0<br />
1.8<br />
1.6<br />
1.4<br />
1.2<br />
1.0<br />
2.0<br />
1.8<br />
1.6<br />
1.4<br />
1.2<br />
1.0<br />
0.8<br />
0.6<br />
0.4<br />
0.2<br />
35%<br />
27%<br />
25%<br />
15%<br />
3 4 5 6 7 8 9 10 11 12 13<br />
Frequency (GHz)<br />
(a)<br />
0.0<br />
3 4 5 6 7 8 9 10 11 12 13<br />
Frequency (GHz)<br />
(c)<br />
|Γ|<br />
Ga<strong>in</strong> (dB)<br />
1.0<br />
0.8<br />
0.6<br />
0.4<br />
0.2<br />
0.0<br />
16<br />
14<br />
12<br />
10<br />
8<br />
35%<br />
27%<br />
25%<br />
15%<br />
4 6 8 10 12<br />
Frequency (GHz)<br />
(b)<br />
6<br />
3 4 5 6 7 8 9 10 11 12 13<br />
Frequency (GHz)<br />
(d)<br />
Figure 3.10: <strong>Noise</strong> parameters versus frequency for devices of different alum<strong>in</strong>um<br />
composition <strong>in</strong> the barrier: (a) M<strong>in</strong>imum noise figure (b) magnitude <strong>and</strong> phase of<br />
optimum reflection coefficient (c) noise resistance (d) device associated ga<strong>in</strong>.<br />
77<br />
180<br />
160<br />
140<br />
120<br />
100<br />
80<br />
60<br />
40<br />
20<br />
0<br />
Phase Γ (Degrees)
CHAPTER 3. NOISE FIGURE MEASUREMENTS AND STUDIES<br />
NF m<strong>in</strong> (dB)<br />
3.8<br />
3.6<br />
3.4<br />
3.2<br />
3.0<br />
2.8<br />
2.6<br />
2.4<br />
2.2<br />
2.0<br />
1.8<br />
1.6<br />
1.4<br />
1.2<br />
35%<br />
27%<br />
25%<br />
15%<br />
1.0<br />
0 20 40 60 80 100 120 140<br />
Current (mA)<br />
Figure 3.11: M<strong>in</strong>imum noise figure of samples with different alum<strong>in</strong>um composition<br />
<strong>in</strong> the barrier at vary<strong>in</strong>g dra<strong>in</strong>-source current.<br />
NFm<strong>in</strong> for the samples versus Ids are <strong>in</strong> figure 3.11. The data are astonish<strong>in</strong>gly similar<br />
for noise measurements, <strong>and</strong> challenge the previous report. The application of the CN<br />
<strong>and</strong> Pospieszalski models to these devices, presented earlier <strong>in</strong> table 2.2, also agrees<br />
that the noise parameters should be very similar. It is <strong>in</strong>terest<strong>in</strong>g that the dra<strong>in</strong>-source<br />
current bias for best NFm<strong>in</strong> was similar for the different samples (15±5mA). For the<br />
15 % Al sample this was nearly half Ids,sat while only 8 % Ids,sat for the 35 % Al<br />
sample.<br />
3.5.3 AlN Interlayer<br />
The addition of an extremely th<strong>in</strong> (one or two monolayers) AlN layer between the<br />
<strong>GaN</strong> channel <strong>and</strong> the <strong>Al<strong>GaN</strong></strong> barrier has been found to <strong>in</strong>crease the conduction-b<strong>and</strong><br />
78
CHAPTER 3. NOISE FIGURE MEASUREMENTS AND STUDIES<br />
NF m<strong>in</strong> (dB)<br />
4.0<br />
3.5<br />
3.0<br />
2.5<br />
2.0<br />
1.5<br />
1.0<br />
0 20 40 60 80 100 120 140<br />
Current (mA)<br />
NF m<strong>in</strong> AlN<br />
NF m<strong>in</strong> no AlN<br />
f τ AlN<br />
f τ no AlN<br />
f max AlN<br />
f max no AlN<br />
Figure 3.12: M<strong>in</strong>imum noise figure, fτ, <strong>and</strong> fmax versus dra<strong>in</strong>-source current for a<br />
sample with (squares) <strong>and</strong> without (circles) an AlN <strong>in</strong>terlayer.<br />
offset, better conf<strong>in</strong><strong>in</strong>g the 2-DEG <strong>and</strong> improv<strong>in</strong>g mobility [10]. This should improve<br />
the device fτ <strong>and</strong> fmax. It is therefore worth determ<strong>in</strong><strong>in</strong>g if it improves the noise<br />
performance as well. Samples with structures as <strong>in</strong> figure 3.1 (a) <strong>and</strong> (b) with 35%<br />
Al <strong>in</strong> the barrier on sapphire substrates were measured for noise. Overall, devices on<br />
the sample with the AlN-<strong>in</strong>terlayer had fτ <strong>and</strong> fmax values marg<strong>in</strong>ally higher than the<br />
sample without. However, for the noise measurements devices with as similar of fτ<br />
<strong>and</strong> fmax as could be found were used.<br />
There were no differences <strong>in</strong> the noise parameters versus frequency, but as the dra<strong>in</strong><br />
current <strong>in</strong>creased a large difference <strong>in</strong> NFm<strong>in</strong> was apparent. This is <strong>in</strong> figure 3.12 as<br />
the solid symbols. At a current of 100 mA, there is a 0.4 dB difference <strong>and</strong> at the<br />
79<br />
45<br />
40<br />
35<br />
30<br />
25<br />
20<br />
15<br />
10<br />
5<br />
0<br />
Frequency (GHz)
CHAPTER 3. NOISE FIGURE MEASUREMENTS AND STUDIES<br />
(dB)<br />
16<br />
14<br />
12<br />
10<br />
8<br />
6<br />
4<br />
Ga<strong>in</strong> AlN layer<br />
Ga<strong>in</strong> no AlN<br />
Gmax AlN layer<br />
Gmax no AlN<br />
2<br />
0 20 40 60 80 100 120 140<br />
Current (mA)<br />
(a)<br />
R s (Ω)<br />
26<br />
24<br />
22<br />
20<br />
18<br />
16<br />
14<br />
12<br />
10<br />
8<br />
6<br />
with AlN <strong>in</strong>terlayer<br />
without AlN<br />
0 10 20 30 40 50 60 70 80 90<br />
Current (mA)<br />
(b)<br />
Figure 3.13: (a) Associated <strong>and</strong> maximum ga<strong>in</strong> <strong>and</strong> (b) source resistance for devices<br />
with <strong>and</strong> without an AlN <strong>in</strong>terlayer at different applied currents.<br />
max current a 0.8 dB difference. While the ga<strong>in</strong> (figure 3.13 (a)), f τ, <strong>and</strong> fmax (also<br />
<strong>in</strong> figure 3.12) do drop off slightly faster for the sample without the AlN, it is not as<br />
dramatic as the sapphire/SiC substrate comparison <strong>and</strong> not enough to expla<strong>in</strong> such a<br />
large NFm<strong>in</strong> difference.<br />
Rs appears to be the cause of the difference. Palacios has shown that Rs <strong>in</strong>creases<br />
drastically with dra<strong>in</strong>-source current [11]. Figure 3.13 (b) shows the measured source<br />
resistance (us<strong>in</strong>g the method <strong>in</strong> [11]) for devices from both samples. The devices with<br />
the AlN-<strong>in</strong>terlayer see an Rs <strong>in</strong>crease of about two times, while the devices without<br />
the <strong>in</strong>terlayer see an <strong>in</strong>crease of three times. These Rs measurements are only out to<br />
80 mA (equipment limitations), <strong>in</strong>stead of 135 mA as <strong>in</strong> figure 3.12. The difference<br />
<strong>in</strong> Rs would be even larger at higher biases. As seen with the model<strong>in</strong>g us<strong>in</strong>g source-<br />
degeneration <strong>in</strong> chapter 2, Rs can be thought of as directly add<strong>in</strong>g noise at the <strong>in</strong>put,<br />
80
CHAPTER 3. NOISE FIGURE MEASUREMENTS AND STUDIES<br />
which <strong>in</strong>creases the noise.<br />
As mentioned, devices on the sample with the AlN-<strong>in</strong>terlayer overall tend to have<br />
higher fτ <strong>and</strong> fmax. These devices will have a slightly better NFm<strong>in</strong>. However, the<br />
improvement is at best 0.1 dB <strong>in</strong> the X-b<strong>and</strong>.<br />
3.5.4 Gate Leakage<br />
While try<strong>in</strong>g to do a comparative study, devices from a sample (27% Al content<br />
barrier with SiC substrate) that had similar fτ <strong>and</strong> fmax did not have similar NFm<strong>in</strong>.<br />
In fact, NFm<strong>in</strong> differed by almost 1 dB despite the ga<strong>in</strong>s be<strong>in</strong>g identical as seen <strong>in</strong><br />
figure 3.14. It was realized that the gate leakage was very different for the three devices<br />
<strong>in</strong> figure 3.14. The three term<strong>in</strong>al gate leakage, Igs, at a bias of Ids = 10 mA, Vds =5V<br />
for the devices was found to be: 22 µA (or 140 µA/mm); 73 µA (or 486 µA/mm);<br />
141 µA (or 940 µA/mm). The devices are labeled as such <strong>in</strong> figure 3.14. We see that<br />
as the gate leakage <strong>in</strong>creases, so does the noise figure. To explore how gate leakage<br />
affects the noise parameters, the model<strong>in</strong>g <strong>in</strong> § 2.6 was used. Small-signal parameters<br />
that approximately matched all three devices <strong>in</strong> figure 3.14 were entered <strong>in</strong>to Matlab<br />
us<strong>in</strong>g the script <strong>in</strong> appendix B. The gate leakage was swept from 10 −8 to 10 −2 A <strong>and</strong><br />
the calculated noise parameters plotted (as l<strong>in</strong>es) <strong>in</strong> figure 3.15 with data (crosses) for<br />
the devices <strong>in</strong> figure 3.14. The circles are data from another sample that exhibits an<br />
expected amount of gate leakage. The agreement of simulation <strong>and</strong> data for NFm<strong>in</strong><br />
81
CHAPTER 3. NOISE FIGURE MEASUREMENTS AND STUDIES<br />
Figure 3.14: (a) M<strong>in</strong>imum noise figure, (b) device associated ga<strong>in</strong>, <strong>and</strong> maximum ga<strong>in</strong><br />
versus frequency for devices with different gate leakage currents. The gate leakage<br />
quoted is at the same bias as the noise measurements (Ids = 10 mA, Vds = 5 V).<br />
is excellent. The other parameters do not agree perfectly, but it should be reiterated<br />
that the small-signal parameters used were typical for all three devices (they were not<br />
identical). No change <strong>in</strong> rn was predicted or measured.<br />
Gate leakage has a large effect on the noise parameters. It must be monitored, along<br />
with fτ <strong>and</strong> fmax, when measur<strong>in</strong>g noise figure of <strong>GaN</strong> devices. While gate leakage<br />
<strong>and</strong> NFm<strong>in</strong> have been studied previously [6, 12–14], these studies are all lack<strong>in</strong>g <strong>in</strong><br />
at least one of the follow<strong>in</strong>g ways: use of fitt<strong>in</strong>g, <strong>in</strong>adequate data, only predict<strong>in</strong>g<br />
NFm<strong>in</strong>, or not applied to <strong>GaN</strong>. The comb<strong>in</strong>ation of analytical model<strong>in</strong>g (without fitt<strong>in</strong>g<br />
parameters), data presented, <strong>and</strong> agreement of model<strong>in</strong>g <strong>and</strong> data here is unique <strong>and</strong><br />
82
CHAPTER 3. NOISE FIGURE MEASUREMENTS AND STUDIES<br />
r n<br />
NF m<strong>in</strong> (dB)<br />
5<br />
4<br />
3<br />
2<br />
10 -8 10 -7 10 -6 10 -5 10 -4 10 -3 10 -2<br />
1<br />
I (A)<br />
gs<br />
2<br />
1.75<br />
1.5<br />
1.25<br />
1<br />
0.75<br />
0.5<br />
0.25<br />
|Γ opt |<br />
1<br />
0.8<br />
0.6<br />
0.4<br />
0.2<br />
10 -8 10 -7 10 -6 10 -5 10 -4 10 -3 10 -2<br />
0<br />
I (A)<br />
gs<br />
(a) (b)<br />
140<br />
10 -8 10 -7 10 -6 10 -5 10 -4 10 -3 10 -2<br />
0<br />
I (A)<br />
gs<br />
Phase Γ opt (degress)<br />
120<br />
100<br />
80<br />
60<br />
40<br />
10 -8 10 -7 10 -6 10 -5 10 -4 10 -3 10 -2<br />
20<br />
I (A)<br />
gs<br />
(c) (d)<br />
Figure 3.15: Simulated (l<strong>in</strong>e) <strong>and</strong> measured (crosses) noise parameters for devices<br />
with different gate leakage currents: (a) M<strong>in</strong>imum noise figure (b) magnitude of optimum<br />
reflection coefficient (c) noise resistance (d) phase of optimum reflection coefficient.<br />
Frequency is 10 GHz. The circles are data from another sample with the<br />
typically expected amount of gate leakage.<br />
clear.<br />
A f<strong>in</strong>al note: <strong>GaN</strong> <strong>HEMTs</strong> on MBE were measured by the author. Their power <strong>and</strong><br />
small-signal performance are comparable to MOCVD-based <strong>HEMTs</strong>, but the devices<br />
had higher gate leakage <strong>and</strong> thus ∼0.15 dB more noise.<br />
83
CHAPTER 3. NOISE FIGURE MEASUREMENTS AND STUDIES<br />
3.5.5 Field-Plated Devices<br />
The addition of a FP has led to <strong>GaN</strong> <strong>HEMTs</strong> hav<strong>in</strong>g impressive power h<strong>and</strong>l<strong>in</strong>g<br />
capability at microwave frequencies [15, 16]. There is a penalty, which is shown <strong>in</strong><br />
figure 3.16. 1 A FP <strong>in</strong>creases Cgd, <strong>and</strong> that reduces fτ <strong>and</strong> fmax. In fact, the longer<br />
the FP, the higher the breakdown <strong>and</strong> lower the fτ ,fmax , <strong>and</strong> ga<strong>in</strong> of the device. The<br />
author decided to <strong>in</strong>vestigate the noise performance. Based on the studies presented<br />
thus far, one would predict that a FP device would have worse NF performance.<br />
Frequency (GHz)<br />
60<br />
55<br />
50<br />
45<br />
40<br />
35<br />
30<br />
25<br />
20<br />
15<br />
f τ<br />
f max<br />
0.0 0.2 0.4 0.6 0.8 1.0 1.2<br />
Field-Plate Length (µm)<br />
Figure 3.16: fτ <strong>and</strong> fmax of devices with different field-plate lengths.<br />
This turned out not to be the case. Figure 3.17 (a) demonstrates that as the FP<br />
length <strong>in</strong>creases the NFm<strong>in</strong> improves despite decreas<strong>in</strong>g ga<strong>in</strong> (Figure 3.17 (d)). The<br />
1For all measurements <strong>in</strong> this section, the devices with different FP lengths are on the same die of a<br />
sample.<br />
84
CHAPTER 3. NOISE FIGURE MEASUREMENTS AND STUDIES<br />
NF m<strong>in</strong> (dB)<br />
r n<br />
1.8<br />
1.6<br />
1.4<br />
1.2<br />
1.0<br />
0.8<br />
4 6 8 10<br />
Frequency (GHz)<br />
(a)<br />
1.2<br />
1.0<br />
0.8<br />
0.6<br />
0.4<br />
1.1 µm<br />
0.9 µm<br />
0.7 µm<br />
0.5 µm<br />
None<br />
4 6 8 10<br />
Frequency (GHz)<br />
(c)<br />
|Γ|<br />
Ga<strong>in</strong> (dB)<br />
0.8<br />
0.6<br />
0.4<br />
0.2<br />
14<br />
12<br />
10<br />
8<br />
6<br />
4<br />
1.1 µm<br />
0.9 µm<br />
0.7 µm<br />
0.5 µm<br />
None<br />
0.0<br />
20<br />
4 6 8<br />
Frequency (GHz)<br />
(b)<br />
10<br />
4 6 8 10<br />
Frequency (GHz)<br />
(d)<br />
Figure 3.17: <strong>Noise</strong> parameters versus frequency for devices with field plates of different<br />
length: (a) M<strong>in</strong>imum noise figure (b) magnitude <strong>and</strong> phase of optimum reflection<br />
coefficient (c) noise resistance (d) device ga<strong>in</strong> when matched at the <strong>in</strong>put for best noise<br />
performance <strong>and</strong> the output for power performance.<br />
85<br />
180<br />
160<br />
140<br />
120<br />
100<br />
80<br />
60<br />
40<br />
Phase Γ (degree)
CHAPTER 3. NOISE FIGURE MEASUREMENTS AND STUDIES<br />
improvement is almost 0.2 dB. There is little additional improvement for a FP longer<br />
than 0.9 µm. The match changes monotonically with the FP <strong>in</strong> Figure 3.17 (b). The<br />
improvement <strong>in</strong> NF with a FP was first reported by the author <strong>in</strong> [17] <strong>and</strong> was later<br />
confirmed <strong>in</strong> [18].<br />
Several explanations to underst<strong>and</strong> this result were explored. The first was to look<br />
at the gate leakage. It was thought that maybe the FP was reduc<strong>in</strong>g the electric field<br />
<strong>and</strong> possibly the gate-dra<strong>in</strong> contribution to gate leakage. The three <strong>and</strong> two-term<strong>in</strong>al<br />
gate leakage of 100 µm wide devices with different FP lengths was measured. Some<br />
of the three-term<strong>in</strong>al measurements are <strong>in</strong> figure 3.18. The bias was set to Vds 5V<br />
(similar to noise measurements) <strong>and</strong> Vds 20 V (a low bias for power) <strong>and</strong> Vgs a volt<br />
past the threshold voltage. It does not appear that the FP lowers gate leakage. In fact,<br />
it appears to <strong>in</strong>crease slightly with the FP.<br />
Another thought was that perhaps there was a difference <strong>in</strong> electric field caus<strong>in</strong>g a<br />
change elsewhere than gate leakage. The analysis of Γ <strong>in</strong> § 2.6.3 was exam<strong>in</strong>ed to see<br />
if it might change because of a FP. This proved to not be true. A change <strong>in</strong> Γ would<br />
mean a change <strong>in</strong> the DC I–V characteristics of a FP from a non-FP device. The only<br />
real change is that the knee voltage is better def<strong>in</strong>ed for a FP device [19]. That would<br />
only cause Γ to go to its f<strong>in</strong>al value of 2/3 quicker. More proof that it was not the<br />
electric field-profile was found by two other means. One was to look at NFm<strong>in</strong> versus<br />
dra<strong>in</strong> source voltage. No difference was apparent. Another was to run an ATLAS<br />
86
CHAPTER 3. NOISE FIGURE MEASUREMENTS AND STUDIES<br />
Gate Leakage (µA)<br />
700<br />
600<br />
500<br />
400<br />
300<br />
200<br />
100<br />
0<br />
, V ds 20 V<br />
, V ds 5 V<br />
0.0 0.2 0.4 0.6 0.8 1.0 1.2<br />
Field-Plate Length (µm)<br />
Figure 3.18: Typical change <strong>in</strong> gate leakage for devices of <strong>in</strong>creas<strong>in</strong>g field-plate<br />
length. Bias<strong>in</strong>gs are Vds 5V,Ids 10 mA <strong>and</strong> Vds 20 V, Vgs one volt past threshold.<br />
Electric Field (V/cm)<br />
6.0M<br />
4.0M<br />
2.0M<br />
no FP, V ds 5 V<br />
no FP, V ds 20 V<br />
FP, V ds 5 V<br />
FP, V ds 20 V<br />
0.0<br />
0.0 0.5 1.0 1.5 2.0 2.5<br />
Distance (µm)<br />
Figure 3.19: Electric field profile for a device with <strong>and</strong> without a FP at a bias of Vds 5<br />
<strong>and</strong> 20 V with the gate biased close to Vt. The gray bars are the “physical lengths” of<br />
the gate <strong>and</strong> field plate. Atlas simulation provided by Yuvaraj Dora.<br />
87
CHAPTER 3. NOISE FIGURE MEASUREMENTS AND STUDIES<br />
simulation <strong>and</strong> look at the difference <strong>in</strong> the electric field profile. This was done, <strong>and</strong><br />
the results are <strong>in</strong> figure 3.19. 2 The simulations at Vds 5 <strong>and</strong> 20 V show the total electric<br />
field versus distance. The gate is biased close to the threshold voltage, as is the case<br />
for best NFm<strong>in</strong> results. The bars sitt<strong>in</strong>g atop the x-axis represent the gate length (short)<br />
<strong>and</strong> FP (long) lengths. While the peak electric field at the dra<strong>in</strong> edge of the gate will<br />
be significantly reduced when a HEMT is biased to 80 V or more, here for 5 <strong>and</strong> 20 V,<br />
there is no difference. In fact, at Vds 5 V, there is practically no change <strong>in</strong> the field.<br />
The small-signal parameters were also exam<strong>in</strong>ed. Those that were found to change<br />
with a FP are <strong>in</strong> figure 3.20. Cgd <strong>in</strong>creases because of the extra capacitance the FP<br />
provides. That Rgd decreases h<strong>in</strong>ts that it is either easier to charge Cgd or that the<br />
leakage has <strong>in</strong>creased the conductance between gate <strong>and</strong> dra<strong>in</strong>. Rd decreases because<br />
the effective distance between gate <strong>and</strong> dra<strong>in</strong> is reduced by the length of the FP. Ri<br />
does not appear to change. Any change <strong>in</strong> it is probably due to error <strong>in</strong> the small-signal<br />
extraction hav<strong>in</strong>g difficulty differentiat<strong>in</strong>g Rg <strong>and</strong> Ri. As the gate now has another set<br />
of f<strong>in</strong>gers <strong>in</strong> parallel, its resistance, <strong>and</strong> thus Rg, decreases. The FP <strong>and</strong> gate f<strong>in</strong>gers<br />
can be connected at their ends, further reduc<strong>in</strong>g gate resistance <strong>and</strong> the noise [20].<br />
When try<strong>in</strong>g to expla<strong>in</strong> FP device NF performance, it was first thought that Rg was<br />
the cause. However, the model<strong>in</strong>g at the time argued that the improvement <strong>in</strong> Rg was<br />
not enough to cause the difference, particularly for the results <strong>in</strong> [18]. It was later<br />
realized the devices <strong>and</strong> the model<strong>in</strong>g were not the same. Devices of different widths,<br />
2 ATLAS simulation graciously provided by Yuvaraj Dora to the author’s specifications<br />
88
CHAPTER 3. NOISE FIGURE MEASUREMENTS AND STUDIES<br />
C gd (fF)<br />
70<br />
60<br />
50<br />
40<br />
30<br />
20<br />
10<br />
0<br />
0.0 0.2 0.4 0.6 0.8 1.0<br />
Field-Plate Length (µm)<br />
70<br />
60<br />
50<br />
40<br />
30<br />
20<br />
10<br />
0<br />
R gd (Ω)<br />
Resistance (Ω)<br />
19<br />
18<br />
17<br />
16<br />
15<br />
8<br />
7<br />
6<br />
5<br />
4<br />
3<br />
2<br />
1<br />
R d<br />
R i<br />
R g<br />
0.0 0.2 0.4 0.6 0.8 1.0<br />
Field-Plate Length (µm)<br />
Figure 3.20: Small-signal parameters that change with a field plate.<br />
<strong>and</strong> with/without the FP plus gate ends shorted, were be<strong>in</strong>g compared. The scal<strong>in</strong>g<br />
<strong>and</strong> model<strong>in</strong>g of chapter 2 were used yet aga<strong>in</strong>. How NFm<strong>in</strong> changes with gate width<br />
for devices with <strong>and</strong> without a FP were simulated <strong>in</strong> Matlab <strong>and</strong> compared to the<br />
author’s <strong>and</strong> Wu’s [18] measurements. Figure 3.21 makes this clear. The agreement<br />
is very good, <strong>and</strong> it can now be concluded that the FP lower<strong>in</strong>g the gate resistance<br />
is what improves NFm<strong>in</strong>. That NFm<strong>in</strong> decreases despite the lower ga<strong>in</strong> is because the<br />
FP is act<strong>in</strong>g as an external feedback capacitance between gate <strong>and</strong> dra<strong>in</strong> (<strong>in</strong> parallel<br />
with Cgd). Lossless feedback does not harm the noise figure, but it does lower the<br />
ga<strong>in</strong> [21]).<br />
The reduction <strong>in</strong> NF does not justify the use of a FP as it reduces the ga<strong>in</strong> consider-<br />
ably (several decibels). Ga<strong>in</strong> is <strong>in</strong> short supply at microwave frequencies <strong>and</strong> reduc<strong>in</strong>g<br />
it so much may not justify NFm<strong>in</strong> improvement of just a few tenths of a decimal. In<br />
89
CHAPTER 3. NOISE FIGURE MEASUREMENTS AND STUDIES<br />
NF m<strong>in</strong> (dB)<br />
3<br />
2.5<br />
2<br />
1.5<br />
1<br />
0.5<br />
No FP<br />
Long FP<br />
Difference<br />
0<br />
0 50 100 150 200 250 300<br />
Gate Width (µm)<br />
Figure 3.21: M<strong>in</strong>imum noise figure versus gate width for devices with <strong>and</strong> without a<br />
long field plate at a simulation frequency of 10 GHz. The difference between them, <strong>in</strong><br />
decimals, is plotted as the dotted l<strong>in</strong>e. The “x’s” are from this work (150 µm ) <strong>and</strong> Y.<br />
Wu (243 µm ) [18].<br />
NF m<strong>in</strong><br />
1.8<br />
1.7<br />
1.6<br />
1.5<br />
1.4<br />
1.3<br />
1.2<br />
1.1<br />
1.0<br />
0.9<br />
0.8<br />
0.7<br />
4 GHz<br />
7 GHz<br />
10 GHz<br />
0.0 0.2 0.4 0.6 0.8 1.0 1.2<br />
Field-Plate Length (µm)<br />
Figure 3.22: M<strong>in</strong>imum noise figure of the field-plated devices at different measurement<br />
frequencies of 4, 7, <strong>and</strong> 10 GHz. As the frequency <strong>in</strong>creases, the improvement<br />
from a field plate decreases.<br />
90
CHAPTER 3. NOISE FIGURE MEASUREMENTS AND STUDIES<br />
addition, the benefit is reduced the higher the operat<strong>in</strong>g frequency because of the sk<strong>in</strong><br />
effect on the gate resistance. This is demonstrated <strong>in</strong> figure 3.22. At 4 GHz, the im-<br />
provement can be as much as 0.3 dB, but at 10 GHz the improvement is 0.1 dB. This<br />
agrees with the results <strong>in</strong> [18].<br />
3.5.6 Thick-Epitaxial Cap Devices<br />
Shen has proposed a HEMT with a thick <strong>GaN</strong> cap on top of the <strong>Al<strong>GaN</strong></strong> [22]. The<br />
advantage of this structure is that a SiN passivation is not needed. As passivation<br />
leads to problems of reliability for st<strong>and</strong>ard <strong>HEMTs</strong>, this new HEMT holds great<br />
promise. It has the record for power performance without passivation. Its small-signal<br />
characteristics are similar to st<strong>and</strong>ard <strong>HEMTs</strong>. Dr. Shen allowed the devices to be<br />
measured for noise. The performance was similar versus frequency (<strong>in</strong> particular,<br />
the ga<strong>in</strong>s), although the dra<strong>in</strong>-source current needed to be higher for optimum noise<br />
performance. The reason for this is clear after view<strong>in</strong>g the noise parameters versus<br />
bias <strong>in</strong> figure 3.23. The cap devices have a NFm<strong>in</strong> optimum bias at 45 mA <strong>in</strong>stead of<br />
10 mA as seen with normal <strong>HEMTs</strong>. Rn <strong>and</strong> NFm<strong>in</strong> follow remarkably similar trends,<br />
further re<strong>in</strong>forc<strong>in</strong>g arguments made earlier <strong>in</strong> the chapter. NF m<strong>in</strong> for the thick cap is<br />
much lower at higher bias<strong>in</strong>gs than a st<strong>and</strong>ard HEMT, but is higher at low bias<strong>in</strong>gs.<br />
The reason for this is likely the large gate leakage the device has at a low bias (68 µA<br />
at Ids 10 mA for a 150 µm wide device). If the leakage can be controlled, these devices<br />
91
CHAPTER 3. NOISE FIGURE MEASUREMENTS AND STUDIES<br />
NF m<strong>in</strong> (dB)<br />
r n<br />
3.6<br />
3.4<br />
3.2<br />
3.0<br />
2.8<br />
2.6<br />
2.4<br />
2.2<br />
2.0<br />
0 20 40 60 80 100<br />
2.0<br />
1.8<br />
1.6<br />
1.4<br />
1.2<br />
1.0<br />
0.8<br />
0.6<br />
0.4<br />
0.2<br />
St<strong>and</strong>ard HEMT<br />
Thick Cap<br />
Current (mA)<br />
(a)<br />
0.0<br />
0 20 40 60 80<br />
Current (mA)<br />
(c)<br />
100<br />
|Γ|<br />
Ga<strong>in</strong> (dB)<br />
1.0<br />
0.8<br />
0.6<br />
0.4<br />
0.2<br />
0.0<br />
0 20 40 60 80 100<br />
18<br />
16<br />
14<br />
12<br />
10<br />
8<br />
6<br />
Current (mA)<br />
(b)<br />
4<br />
0 20 40 60 80<br />
Current (mA)<br />
(d)<br />
100<br />
Figure 3.23: <strong>Noise</strong> parameters versus dra<strong>in</strong>-source current of a thick cap device <strong>and</strong><br />
a st<strong>and</strong>ard HEMT: (a) M<strong>in</strong>imum noise figure (b) magnitude <strong>and</strong> phase of optimum<br />
reflection coefficient (c) noise resistance (d) <strong>and</strong> associated ga<strong>in</strong>. Measurement frequency<br />
is 10 GHz.<br />
92<br />
180<br />
160<br />
140<br />
120<br />
100<br />
80<br />
60<br />
40<br />
20<br />
0<br />
Phase Γ (degrees)
CHAPTER 3. NOISE FIGURE MEASUREMENTS AND STUDIES<br />
show great promise for noise performance.<br />
3.6 Comparison of High-Performance <strong>GaN</strong> <strong>HEMTs</strong> to<br />
Other Material Systems<br />
By now, the reader might have asked the question, “How does <strong>GaN</strong> HEMT noise<br />
figure performance compare to other material systems?” This will now be addressed.<br />
Most all the devices <strong>in</strong> this work have a gate length of 0.7 µm due to equipment lim-<br />
itations. It is hard to f<strong>in</strong>d published noise results <strong>in</strong> the literature at such a relatively<br />
“long” gate length. In addition, many published noise figure results have large varia-<br />
tions <strong>in</strong> the accuracy of their measurements.<br />
Bear<strong>in</strong>g this disclaimer <strong>in</strong> m<strong>in</strong>d, 0.15 µm gate-length devices optimized for high-<br />
frequency performance were obta<strong>in</strong>ed from Tomás Palacios. These devices are sim-<br />
ilar to those <strong>in</strong> a recent publication that had an fτ of 150 GHz <strong>and</strong> fmax of over<br />
200 GHz [23]. The measured NFm<strong>in</strong> aga<strong>in</strong>st frequency is <strong>in</strong> figure 3.24 for two de-<br />
vices. Repeated measurements at 10 GHz gave a consistent NFm<strong>in</strong> of 0.4 dB.<br />
Keep<strong>in</strong>g <strong>in</strong> m<strong>in</strong>d this very good value, let us turn our attention to table 3.1. Here<br />
we have an abundance of data on <strong>HEMTs</strong> from different material systems: <strong>GaN</strong>,<br />
SiGe, InAlGaAs systems on GaAs <strong>and</strong> on InP. The gate lengths, gate widths, NFm<strong>in</strong>,<br />
measurement frequency for NFm<strong>in</strong>, relevant <strong>in</strong>formation, <strong>and</strong> the reference number<br />
found at the end of the chapter are all listed. Most obvious is that SiGe has some work<br />
to do before its noise performance can be competitive with the other materials. InP<br />
93
CHAPTER 3. NOISE FIGURE MEASUREMENTS AND STUDIES<br />
Lg (µm) Wg ( µm ) NFm<strong>in</strong> (dB) Freq. (GHz) Note Ref.<br />
<strong>GaN</strong> <strong>HEMTs</strong><br />
0.12 100 0.72 12 SiC substrate [24]<br />
0.15 150 0.4 10 T. Palacios, UCSB —<br />
0.15 200 0.6 10 SiC substrate [25]<br />
0.15 100 0.75 10 SiC substrate [26]<br />
0.17 100 1.1 10 Si substrate [27]<br />
0.18 100 0.7 12 Sapphire substrate [8]<br />
0.25 100 0.8 10 SiC sub., from graph [28]<br />
0.25 100 1.05 18 Sap., from graph [9]<br />
0.25 100 1.04 10 Sapphire substrate [29]<br />
0.25 200 1.9 10 SiC substrate [30]<br />
Si/SiGe <strong>HEMTs</strong><br />
0.1 100 1.6 10 from graph, pads de-emb. [31]<br />
0.1 90 1.7 10 [32]<br />
0.1 — 2.1 10 pads de-embedded [33]<br />
0.1 100 3.2 10 [34]<br />
(In,Al)GaAs/(In,Ga,Al)As on GaAs <strong>HEMTs</strong><br />
0.1 200 0.3 10 from graph [35]<br />
0.1 — 0.51 18 [36]<br />
0.1 100 0.64 26 mHEMT [37]<br />
0.1 100 1.1 40 mHEMT [37]<br />
0.13 140 0.31 12 pHEMT [38]<br />
0.13 140 0.45 18 pHEMT [38]<br />
0.25 — 0.7 18 [36]<br />
(In,Al)GaAs/(In,Ga,Al)As on InP <strong>HEMTs</strong><br />
0.1 50 0.8 60 [39]<br />
0.1 80 0.45 10 from graph [40]<br />
0.1 80 0.61 20 from graph [40]<br />
0.15 – 0.4 10 [41]<br />
0.2 – 0.48 10 [42]<br />
0.2 – 0.8 26 [42]<br />
Table 3.1: M<strong>in</strong>imum noise figure for HEMT devices <strong>in</strong> many technologies. Also listed<br />
are the gate length <strong>and</strong> width, measurement frequency, some necessary <strong>in</strong>formation,<br />
<strong>and</strong> the reference.<br />
94
CHAPTER 3. NOISE FIGURE MEASUREMENTS AND STUDIES<br />
NF m<strong>in</strong> (dB)<br />
0.9<br />
0.8<br />
0.7<br />
0.6<br />
0.5<br />
0.4<br />
0.3<br />
0.2<br />
0.1<br />
0.0<br />
6 8 10 12 14 16<br />
Frequency (GHz)<br />
Figure 3.24: M<strong>in</strong>imum noise figure of two 0.15 µm gate length transistors provided<br />
by Tomás Palacios.<br />
provides the best performance, but GaAs <strong>and</strong> <strong>GaN</strong> are close competition <strong>in</strong> the X-<br />
b<strong>and</strong>. GaAs might have slightly better performance than <strong>GaN</strong>, but a 0.1 dB advantage<br />
can be lost once the device is put <strong>in</strong> a circuit.<br />
3.7 Summary<br />
This chapter looked at a plethora of noise figure measurements of <strong>GaN</strong> <strong>HEMTs</strong>.<br />
The methodology for procedures was expla<strong>in</strong>ed <strong>and</strong> its importance made clear. Fac-<br />
tors that changed NFm<strong>in</strong> (such as an AlN-<strong>in</strong>terlayer <strong>and</strong> choice of substrate) were <strong>in</strong>-<br />
vestigated. The importance of monitor<strong>in</strong>g gate leakage was found <strong>and</strong> analyzed with<br />
the model<strong>in</strong>g <strong>in</strong> § 2.6. The unexpected result of a FP improv<strong>in</strong>g NFm<strong>in</strong> was discovered<br />
95
CHAPTER 3. NOISE FIGURE MEASUREMENTS AND STUDIES<br />
<strong>and</strong> fully <strong>in</strong>vestigated, also with the use of the model<strong>in</strong>g from § 2.6.<br />
Together with model<strong>in</strong>g from the previous chapter, this chapter helps po<strong>in</strong>t out ways<br />
of obta<strong>in</strong><strong>in</strong>g the best NFm<strong>in</strong> possible. Most important is reduc<strong>in</strong>g the gate leakage <strong>and</strong><br />
parasitic resistances at the <strong>in</strong>put. Rg <strong>and</strong> Rs also need to be m<strong>in</strong>imized. The small-<br />
signal power ga<strong>in</strong> needs to be kept as high as possible. Self-heat<strong>in</strong>g causes an <strong>in</strong>crease<br />
<strong>in</strong> NFm<strong>in</strong> because of loss of device ga<strong>in</strong>.<br />
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Theory <strong>and</strong> Tech. Symp., pp. 373–376, 1993.<br />
[14] D.-S. Sh<strong>in</strong>, J. B. Lee, S. M<strong>in</strong>, J.-E. Oh, Y. J. Park, W. Jung, <strong>and</strong> D. S. Ma, “Analytical<br />
<strong>Noise</strong> Model with the Influence of Shot <strong>Noise</strong> Induced by the Gate Leakage<br />
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IEEE Trans. Electron Devices, vol. 44, no. 11, pp. 1883 – 1887, Nov. 1997.<br />
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IEEE Electron Devices Lett., vol. 25, no. 3, pp. 117–119, Mar. 2004.<br />
[16] T. Palacios, “Optimization of the High Frequency Performance of Nitride-Based<br />
Transistors,” Ph.D. dissertation, University of California, Santa Barbara, Mar.<br />
2006.<br />
[17] C. Sanabria, H. Xu, T. Palacios, A. Chakraborty, S. Heikman, U. Mishra, <strong>and</strong><br />
R. York, “ Influence of the Heterostructure Design on <strong>Noise</strong> Figure of <strong>Al<strong>GaN</strong></strong>/<strong>GaN</strong><br />
<strong>HEMTs</strong>,” <strong>in</strong> Device Research Conference, vol. 1, Jun. 2004, pp. 43–44.<br />
[18] Y.-F. Wu, M. Moore, T. Wisleder, P. Chavarkar, <strong>and</strong> P. Parikh, “<strong>Noise</strong> Characteristics<br />
of Field-Plated <strong>GaN</strong> <strong>HEMTs</strong>,” International Journal of High Speed <strong>Electronics</strong><br />
<strong>and</strong> Systems, vol. 14, pp. 192–194, 2004.<br />
[19] A. Ch<strong>in</strong>i, D. Buttari, R. Coffie, S. Heikman, S. Keller, <strong>and</strong> U. Mishra, “12 W/mm<br />
Power Density <strong>Al<strong>GaN</strong></strong>/<strong>GaN</strong> <strong>HEMTs</strong> on Sapphire Substrate,” IEEE Electron. Lett.,<br />
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[20] H. Xu, C. Sanabria, A. Ch<strong>in</strong>i, Y. Wei, S. Heikman, S. Keller, U. Mishra, <strong>and</strong><br />
R. York, “A New Field-Plated <strong>GaN</strong> HEMT Structure with Improved Power <strong>and</strong><br />
<strong>Noise</strong> Performance,” <strong>in</strong> Lester Eastman Conference on High Performance Devices,<br />
Aug. 2004.<br />
[21] T. H. Lee, The Design of CMOS Radio-Frequency Integrated Circuits, 2nd ed.<br />
New York: Cambridge University Pess, 2004.<br />
[22] L. Shen, R. Coffie, D. Buttari, S. Heikman, A. Chakraborty, A. Ch<strong>in</strong>i,<br />
S. Keller, S. DenBaars, <strong>and</strong> U. Mishra, “High-Power Polarization-Eng<strong>in</strong>eered<br />
<strong>GaN</strong>/<strong>Al<strong>GaN</strong></strong>/<strong>GaN</strong> <strong>HEMTs</strong> Without Surface Passivation,” IEEE Electron Devices<br />
Lett., vol. 25, no. 1, pp. 7–9, Jan. 2004.<br />
[23] T. Palacios, A. Chakraborty, S. Heikman, S. Keller, S. DenBaars, <strong>and</strong> U. Mishra,<br />
“Algan/gan high electron mobility transistors with <strong>in</strong>gan back-barriers,” IEEE<br />
Electron Devices Lett., vol. 27, no. 1, pp. 13–15, Jan. 2006.<br />
[24] W. Lu, J. Yang, M. Khan, <strong>and</strong> I. Adesida, “<strong>Al<strong>GaN</strong></strong>/<strong>GaN</strong> <strong>HEMTs</strong> on SiC with over<br />
100 GHz fT <strong>and</strong> Low <strong>Microwave</strong> <strong>Noise</strong>,” IEEE Trans. Electron Devices, vol. 48,<br />
no. 3, pp. 581–585, Mar. 2001.<br />
[25] N. Nguyen, M. Micovic, W.-S. Wong, P. Hashimoto, P. Janke, D. Harvey, <strong>and</strong><br />
C. Nguyen, “Robust Low <strong>Microwave</strong> <strong>Noise</strong> <strong>GaN</strong> MODFETs with 0.6 dB <strong>Noise</strong><br />
Figure at 10 GHz,” IEEE Electron. Lett., vol. 36, pp. 469–471, March 2000.<br />
[26] J. Moon, M. Micovic, A. Kurdoghlian, P. Janke, P. Hashimoto, W.-S. Wong, L. Mc-<br />
Cray, <strong>and</strong> C. Nguyen, “<strong>Microwave</strong> <strong>Noise</strong> Performance of <strong>Al<strong>GaN</strong></strong><strong>GaN</strong> <strong>HEMTs</strong><br />
With Small DC Power Dissipation,” IEEE Electron Devices Lett., vol. 23, no. 11,<br />
pp. 637–639, Nov. 2002.<br />
[27] A. M<strong>in</strong>ko, V. Hol, S. Lepilliet, G. Dambr<strong>in</strong>e, J. C. De Jaeger, Y. Cordier, F. Semond,<br />
F. Natali, <strong>and</strong> J. Massies, “High <strong>Microwave</strong> <strong>and</strong> <strong>Noise</strong> Performance of 0.17-<br />
µm <strong>Al<strong>GaN</strong></strong><strong>GaN</strong> <strong>HEMTs</strong> on High-Resistivity Silicon Substrates,” IEEE Electron<br />
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100
4<br />
Low-Frequency <strong>Noise</strong> of <strong>GaN</strong> <strong>HEMTs</strong><br />
4.1 Introduction<br />
IT is surpris<strong>in</strong>g that a subject that has been studied for almost 80 years would not be<br />
well-understood. But such is the case of low-frequency noise (LFN), the largest<br />
contributor to phase noise of oscillators [1]. The ma<strong>in</strong> motivation of this chapter is to<br />
create a model for circuit simulation. Most of the LFN literature for <strong>GaN</strong> consists of<br />
theoretical explorations of devices (<strong>in</strong> some studies, just films), or measurements at<br />
very low device bias<strong>in</strong>g not suitable for practical device model<strong>in</strong>g. <strong>GaN</strong> HEMT LFN<br />
studies at bias<strong>in</strong>gs typical for circuits are presented <strong>in</strong> this chapter. A new empirical<br />
model is also presented. It is difficult to make LFN comparisons, particularly to most<br />
published works due to the many ways the data are presented, but measurements by<br />
the author for both GaAs <strong>and</strong> <strong>GaN</strong> <strong>HEMTs</strong> will be exam<strong>in</strong>ed. In addition to the above<br />
topics, the LFN setup will be described <strong>in</strong> detail, as most LFN setups are either poorly<br />
described <strong>in</strong> papers or cannot bias as high as is necessary for <strong>GaN</strong> <strong>HEMTs</strong>.<br />
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CHAPTER 4. LOW-FREQUENCY NOISE OF GAN HEMTS<br />
4.2 Review of Low-Frequency <strong>Noise</strong><br />
The terms LFN, flicker, 1/f, <strong>and</strong> generation-recomb<strong>in</strong>ation (G-R) noise need clari-<br />
fication. Flicker (also called 1/f) noise refers to phenomena that generate noise with a<br />
slope <strong>in</strong>versely proportional to the frequency, hence “one on f.” A sample spectrum,<br />
show<strong>in</strong>g flicker noise <strong>and</strong> other contributions, is shown <strong>in</strong> figure 4.1. Resistors <strong>and</strong><br />
bulk material tend to be strictly 1/f, but devices, <strong>in</strong>clud<strong>in</strong>g <strong>HEMTs</strong>, deviate as 1/f γ<br />
where γ is usually <strong>in</strong> the range of 0.7 to 1.3. For <strong>GaN</strong> <strong>HEMTs</strong>, experiments show γ<br />
to be between 1 <strong>and</strong> 1.3 [2–4]. Generation-recomb<strong>in</strong>ation noise refers to trap-related<br />
capture <strong>and</strong> emission of carriers creat<strong>in</strong>g a spectrum of the form<br />
SX(f) = �<br />
4∆X 2� τ<br />
1+ω2τ 2<br />
(4.2.1)<br />
that is measured as noise at low frequencies. Here, τ is the trap life time, ω the angular<br />
frequency, <strong>and</strong> X a quantity that fluctuates (usually charge or mobility). Sometimes<br />
the G-R spectrum, which will have a Lorentzian power spectral density, manifests<br />
itself as a “bulge” on a 1/f spectrum, shown <strong>in</strong> figure 4.1. There is also a theory, most<br />
often credited to McWhorter [5], 1 that a cont<strong>in</strong>uum of traps, with spectra of the form<br />
<strong>in</strong> equation 4.2.1, of different life times is the source of the 1/f noise spectrum. This<br />
model appears to work for CMOS [2], but it is not accepted for all device technologies.<br />
Therefore, when referr<strong>in</strong>g to the noise at these low frequencies (less than ∼10 MHz),<br />
be it from g-r, 1/f, or other unknown sources, the expression LFN will be used.<br />
1 In truth, he did not create the concept but extended the theory.<br />
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CHAPTER 4. LOW-FREQUENCY NOISE OF GAN HEMTS<br />
<strong>Noise</strong><br />
Spectral<br />
Density<br />
(I 2 or V 2 )<br />
1/f γ noise<br />
G-R "Bulge"<br />
1/f Reference L<strong>in</strong>e<br />
<strong>Noise</strong> spurs<br />
(outside source/<strong>in</strong>terference)<br />
Corner Frequency<br />
<strong>Noise</strong> Floor<br />
Frequency<br />
Figure 4.1: Sketch of the key features of low-frequency noise.<br />
It has already been h<strong>in</strong>ted that traps with energies <strong>in</strong> the material b<strong>and</strong>-gap are<br />
one source of LFN. There are other possible sources: surface effects (such as surface<br />
states), the bulk material itself, dislocations, tunnel<strong>in</strong>g, non-uniform channel resis-<br />
tance, quantum effects, <strong>and</strong> others. Evidence for try<strong>in</strong>g to expla<strong>in</strong> LFN from any one<br />
of these possible sources can be found <strong>in</strong> the literature. It is likely due to a comb<strong>in</strong>ation<br />
of several sources <strong>and</strong> that there will never be a unify<strong>in</strong>g 1/f model for all devices.<br />
<strong>HEMTs</strong> show orders of magnitudes more LFN noise than bipolar junction-transistor<br />
(BJT) types of devices. This suggests a surface area or high-field dependence. Early<br />
<strong>GaN</strong> <strong>HEMTs</strong> <strong>and</strong> material showed much worse LFN noise than results reported later.<br />
The excess <strong>in</strong> the LFN was attributed to traps <strong>and</strong> dislocations [3]. Le<strong>in</strong>shte<strong>in</strong> re-<br />
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CHAPTER 4. LOW-FREQUENCY NOISE OF GAN HEMTS<br />
ported [3] that <strong>GaN</strong> <strong>HEMTs</strong> had less LFN than observed <strong>in</strong> measurements of <strong>GaN</strong><br />
th<strong>in</strong> films, <strong>and</strong> suggested there was some suppression of LFN caused by the device.<br />
Some types of LFN vary with the square of bias current, such as that of diodes. A<br />
relationship that describes this, <strong>and</strong> that is used <strong>in</strong> circuit simulators is:<br />
�<br />
i 2 �<br />
g,1/f = Kf<br />
I Af<br />
DC<br />
f Ffe<br />
(4.2.2)<br />
Kf, Af, <strong>and</strong> Ffe are all fitt<strong>in</strong>g parameters, IDC is the DC current, <strong>and</strong> f is fre-<br />
quency. For mak<strong>in</strong>g theoretical comparisons of voltage, current, <strong>and</strong> resistance LFN<br />
spectrums (SV (f), SI(f), <strong>and</strong> SR(f) respectively), the spectrum is often normalized<br />
(SV (f)/V 2 DC , SI(f)/I 2 DC , <strong>and</strong> SR(f)/R 2 respectively). These spectrums are related<br />
through Ohm’s law, <strong>and</strong> lead to the question, “What’s really fluctuat<strong>in</strong>g <strong>and</strong> caus<strong>in</strong>g<br />
1/f noise?” If it is the resistance (which for <strong>HEMTs</strong>, means the channel resistance),<br />
it has been reasoned that it is because of changes <strong>in</strong> mobility or charge. Because the<br />
resistance varies with the <strong>in</strong>verse of mobility <strong>and</strong> charge, fluctuations <strong>in</strong> one of these<br />
two quantities generates 1/f noise (<strong>in</strong> theory at least). This has lead to the two ma-<br />
jor pr<strong>in</strong>ciples on which most 1/f theories are based: carrier density fluctuation <strong>and</strong><br />
mobility fluctuation model<strong>in</strong>g. The former is used <strong>in</strong> the G-R model (equation 4.2.1)<br />
discussed earlier. In fact, equation 4.2.1 can be used to describe both models. It is<br />
debated whether charge or mobility fluctuations are the source of noise; data supports<br />
both. These models have been applied to describe <strong>GaN</strong> HEMT LFN [2–4].<br />
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CHAPTER 4. LOW-FREQUENCY NOISE OF GAN HEMTS<br />
An <strong>in</strong>terest<strong>in</strong>g empirical relationship was proposed <strong>in</strong> 1969 by Hooge:<br />
SI(f)<br />
I 2 DC<br />
= αH<br />
Nf<br />
(4.2.3)<br />
where N is the number of carriers <strong>in</strong> the device <strong>and</strong> αH is a dimensionless quantity<br />
known as the Hooge parameter. It has s<strong>in</strong>ce been used to characterize many materials<br />
<strong>and</strong> devices. It has also been used as a figure of merit <strong>and</strong> at times as a constant, such<br />
as for characteriz<strong>in</strong>g 1/f noise of materials. However, accord<strong>in</strong>g to Hooge himself, it<br />
was not meant to be considered a constant [6]. αH was extracted for measurements<br />
that appear <strong>in</strong> this chapter. As seen <strong>in</strong> figure 4.2 (a) <strong>and</strong> (b), αH changes considerably,<br />
even with frequency of extraction (not surpris<strong>in</strong>g as the noise is not strictly 1/f). That<br />
αH is not constant can be seen from other published results as well [3]. Therefore,<br />
the author believes it should not be used for device comparisons <strong>and</strong> only for material<br />
comparisons.<br />
It is the aim of this chapter to create a LFN model that can be used <strong>in</strong> the computer-<br />
aided design (CAD) software program Advanced Design System (ADS) <strong>and</strong> to make<br />
comparisons of LFN <strong>in</strong> <strong>HEMTs</strong>. The theory discussed so far is not applicable to<br />
circuit model<strong>in</strong>g. There is not yet agreement <strong>in</strong> the theory, <strong>and</strong> data are generally<br />
at low bias<strong>in</strong>gs or not even for <strong>HEMTs</strong>. At high bias<strong>in</strong>gs where the electric fields<br />
are high, traps may no longer be the dom<strong>in</strong>ant source of LFN. There is little published<br />
literature of LFN models of <strong>HEMTs</strong> for use <strong>in</strong> circuit simulators. Therefore, work was<br />
started from scratch. A setup that could h<strong>and</strong>le the bias<strong>in</strong>gs typical of <strong>GaN</strong> <strong>HEMTs</strong><br />
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CHAPTER 4. LOW-FREQUENCY NOISE OF GAN HEMTS<br />
(a) (b)<br />
Figure 4.2: Variation of α with (a) dra<strong>in</strong>-source voltage bias <strong>and</strong> (b) frequency of<br />
extraction for two devices on the same sample.<br />
was built. Measurements of bias-dependence <strong>and</strong> geometry were performed. Other<br />
studies of LFN performance were performed as time permitted.<br />
A f<strong>in</strong>al consideration is how to present the data. There is little consistency <strong>in</strong> units<br />
<strong>and</strong> an astonish<strong>in</strong>g number of different choices: A 2 /Hz, V 2 /Hz, A/ √ Hz, V/ √ Hz,<br />
A 2 , V 2 , nV/ √ Hz, <strong>in</strong>put-referred versions of these <strong>and</strong> representations <strong>in</strong> dB or l<strong>in</strong>ear<br />
formats. Sufficient <strong>in</strong>formation is not always presented <strong>in</strong> published articles to be<br />
able to convert from one type of units to another. How the data is presented can also<br />
give different results. For example, normaliz<strong>in</strong>g SI(f) by I 2 gives a different trend<br />
of noise versus gate width than not normaliz<strong>in</strong>g. The author decided that present<strong>in</strong>g<br />
noise as A 2 /Hz would be most familiar <strong>and</strong> convenient for a circuit designer <strong>and</strong> for<br />
comparison purposes.<br />
More <strong>in</strong>formation about LFN can be found <strong>in</strong> [3, 7–9]. A very good <strong>and</strong> easy-to-<br />
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CHAPTER 4. LOW-FREQUENCY NOISE OF GAN HEMTS<br />
follow review can be found <strong>in</strong> [10]. The book edited by Bal<strong>and</strong><strong>in</strong>, [3], is a collection of<br />
articles about noise <strong>in</strong> <strong>GaN</strong> <strong>in</strong>clud<strong>in</strong>g two that treat LFN of <strong>GaN</strong> <strong>HEMTs</strong> extensively.<br />
4.3 Low-Frequency <strong>Noise</strong> Setup<br />
It is hard to f<strong>in</strong>d a complete description for a LFN setup. Much time was spent<br />
creat<strong>in</strong>g a satisfactory setup for <strong>GaN</strong>. Therefore, this section will expla<strong>in</strong> what an ex-<br />
perimentalist needs to know to create a setup. There are four ma<strong>in</strong> equipment concerns<br />
for a LFN setup. The first is <strong>in</strong>strumentation to measure the power spectrum versus<br />
frequency. The measurement range of <strong>in</strong>terest is usually 10 Hz to 1 MHz (possibly<br />
wider). Provided that a given spectrum analyzer can even measure such frequencies,<br />
the LFN of the analyzer itself is usually larger than the device’s noise. Increased aver-<br />
ag<strong>in</strong>g <strong>and</strong> reduction of the resolution b<strong>and</strong>width can help these problems; however, the<br />
time for a s<strong>in</strong>gle measurement becomes prohibitively long. Other <strong>in</strong>struments that can<br />
be used <strong>in</strong>clude computer-controlled oscilloscopes (a long time sample is measured<br />
<strong>and</strong> a FFT is then performed on a computer) <strong>and</strong>, the preferred tool, a dedicated FFT<br />
<strong>in</strong>strument. An HP 3561A dynamic signal analyzer (DSA) is a dedicated <strong>in</strong>strument<br />
for these types of measurements <strong>and</strong> was used <strong>in</strong> this work. It is part of the HP 3048<br />
phase-noise system. The DSA noise floor was superior to other options available <strong>and</strong><br />
the HP 3048 software could automatically control it. However, the DSA could only<br />
measure a maximum frequency of 100 kHz. Most measurements <strong>in</strong> this chapter were<br />
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CHAPTER 4. LOW-FREQUENCY NOISE OF GAN HEMTS<br />
preformed from 10 Hz to 100 kHz with ∼300 po<strong>in</strong>ts per decade.<br />
Even with the DSA, the noise floor was not adequate for some measurements.<br />
Therefore, the second equipment concern is the noise floor for which a low-noise<br />
amplifier (LNA) is needed. A Stanford Research Systems SR560 LNA was used to<br />
improve the noise floor. Its voltage ga<strong>in</strong> was typically set to 40 dB (100 V/V, the<br />
m<strong>in</strong>imum to meet the <strong>in</strong>strument’s specified noise floor) <strong>and</strong> sometimes as high as<br />
60 dB (for gate noise measurements). The HP3048 software could be adjusted for<br />
the ga<strong>in</strong>. The LNA was run off of <strong>in</strong>ternal lead-acid batteries while measur<strong>in</strong>g. The<br />
measured noise floor for the 3561A when its <strong>in</strong>put was shorted is shown together with<br />
the measured noise floor of the LNA (also shorted <strong>in</strong>put) plus 3561A <strong>in</strong> figure 4.3. An<br />
improvement of more than four orders of magnitude is seen. The measured noise floor<br />
of the LNA <strong>in</strong> figure 4.3 is identical to its specifications.<br />
The third equipment concern is bias<strong>in</strong>g the device without <strong>in</strong>terfer<strong>in</strong>g with the mea-<br />
surement. Almost all DC power supplies, <strong>in</strong>clud<strong>in</strong>g older analog models, have active<br />
circuitry to ma<strong>in</strong>ta<strong>in</strong> the bias set po<strong>in</strong>t. This, comb<strong>in</strong>ed with noise from the AC l<strong>in</strong>es,<br />
makes them impractical to use for LFN measurements. Hence, batteries are used.<br />
9 V batteries are usually preferred as they are recognized to be low-noise. For <strong>GaN</strong><br />
<strong>HEMTs</strong>, even small devices can require high current (easily 100 mA or more). An<br />
attempt to use several 9 V batteries for the dra<strong>in</strong> lead to unexpected measurement<br />
results once the device bias <strong>in</strong>creased above the knee voltage. A rechargeable 12 V<br />
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CHAPTER 4. LOW-FREQUENCY NOISE OF GAN HEMTS<br />
HP3561A alone<br />
with SR560<br />
Figure 4.3: Measured noise floor of the HP 3561A DSA only <strong>and</strong> with the SRS SR560<br />
LNA (short-circuited <strong>in</strong>put).<br />
lead-acid battery, that could output 90 mA without disturb<strong>in</strong>g the measurement, was<br />
used for the dra<strong>in</strong> bias. A 9 V battery was used for the gate bias<strong>in</strong>g (two <strong>in</strong> series for<br />
large threshold devices). These were used with a bias box (discussed more below).<br />
Biases of Vds from 0.1 to 12 V, Ids from 5 to 90 mA, <strong>and</strong> Vgs from -0.05 to -9 V could<br />
be obta<strong>in</strong>ed. This is far superior to most other setups, which are limited to bias<strong>in</strong>g<br />
conditions <strong>in</strong> the l<strong>in</strong>ear region of a <strong>GaN</strong> HEMT.<br />
The f<strong>in</strong>al equipment concern is to protect the setup from outside electrical <strong>and</strong> me-<br />
chanical <strong>in</strong>terference. The setup was located on a vibration-isolation table, which<br />
helped with mechanical <strong>in</strong>terference (although it could still be determ<strong>in</strong>ed when con-<br />
struction work took place <strong>in</strong> the build<strong>in</strong>g or when a peer would walk by the setup).<br />
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CHAPTER 4. LOW-FREQUENCY NOISE OF GAN HEMTS<br />
A metal box, that could be grounded to the rest of the setup, was made to fit over<br />
the sample <strong>and</strong> probes of the RF probe station to shield aga<strong>in</strong>st electrical <strong>in</strong>terference.<br />
This was required to get a good measurement <strong>and</strong> helped to reduce spurs by ∼30 dB.<br />
Figure 4.4 shows the full schematic of the setup. The multimeters were Fluke<br />
8012As <strong>and</strong> various h<strong>and</strong>-held battery-operated units. Multimeters for voltage <strong>and</strong><br />
current could be connected while measur<strong>in</strong>g LFN, but ohm-meters had to be discon-<br />
nected. A covered bias box was built. 10 turn, 3 W, 2 kΩ potentiometers were used<br />
to vary the bias. The value of 2 kΩ was carefully selected to allow the maximum<br />
range of measurable bias<strong>in</strong>gs. Ground loops destroy a measurement, so care must be<br />
12V<br />
Bias Box<br />
9V<br />
3W<br />
2kΩ<br />
Pot.<br />
220Ω<br />
3W<br />
2kΩ<br />
Pot.<br />
10Ω<br />
+ -<br />
RL 25pF<br />
100MΩ<br />
Voltmeter<br />
Ammeter<br />
+ -<br />
Capacitors<br />
50pF to1000µF<br />
Voltmeter<br />
SR560 LNA<br />
Ga<strong>in</strong> = 1000 V/V<br />
(60 dB)<br />
BW: 0.01 to 1MHz<br />
R ds<br />
50Ω<br />
Shielded<br />
Device<br />
1MΩ<br />
HP3561A<br />
FFT Box<br />
Figure 4.4: Schematic of the setup used for device dra<strong>in</strong>-side low-frequency noise<br />
measurements.<br />
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CHAPTER 4. LOW-FREQUENCY NOISE OF GAN HEMTS<br />
taken with the ground<strong>in</strong>g. The bias-box chassis <strong>and</strong> device shield were grounded to<br />
the negative term<strong>in</strong>al of the battery. While other setups may use a load resistance, RL,<br />
to keep the source resistance seen by the LNA a constant (mak<strong>in</strong>g it easy to convert<br />
the measured voltage spectrum to a current spectrum), the author found this additional<br />
parallel resistance to limit the measurable range of biases <strong>and</strong> the dynamic range of<br />
the DSA. Instead, the effective RL is determ<strong>in</strong>ed for each LFN measurement. This<br />
resistance is the parallel comb<strong>in</strong>ation of that seen on the dra<strong>in</strong> side of the bias box <strong>and</strong><br />
Rds of the transistor. A bank of capacitors were connected at the gate to provide an<br />
AC short while measur<strong>in</strong>g the dra<strong>in</strong> LFN.<br />
Most aspects of the measurement must be done manually, as automation would only<br />
add noise <strong>and</strong> ru<strong>in</strong> the data. The steps for a measurement are:<br />
1. Determ<strong>in</strong>e the DC Rds of the device near the bias of <strong>in</strong>terest (∆Vds/∆Ids).<br />
2. Unplug power to dra<strong>in</strong> <strong>and</strong> gate, <strong>and</strong> ground both ends of the dra<strong>in</strong> pot (us<strong>in</strong>g<br />
switches on bias-box).<br />
3. Disconnect the device <strong>and</strong> LNA.<br />
4. Measure the resistance of the bias box, Rbox. This is the parallel comb<strong>in</strong>ation of<br />
both halves of the potentiometer <strong>and</strong> associated circuitry.<br />
5. Disconnect the multimeter used to measure Rbox (this would add a voltage that<br />
disturbs the measurement).<br />
6. Reconnect the device, LNA, <strong>and</strong> bias. Wait 1 m<strong>in</strong>ute for the LNA to settle (a volt<br />
change at its <strong>in</strong>put, such as turn<strong>in</strong>g on the device or chang<strong>in</strong>g the bias, causes it<br />
to saturate).<br />
7. Measure. Adjust the measured voltage spectrum by the parallel comb<strong>in</strong>ation of<br />
resistances (SI = SV /(Rbox||Rds) 2 ).<br />
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CHAPTER 4. LOW-FREQUENCY NOISE OF GAN HEMTS<br />
Figure 4.5: A typical low-frequency plot.<br />
The setup was checked by measur<strong>in</strong>g the noise spectrum of resistors. This is flat<br />
with a voltage spectrum equal to its thermal noise. 2 A typical HEMT’s LFN is shown<br />
<strong>in</strong> figure 4.5. The dotted l<strong>in</strong>e is a 1/f reference l<strong>in</strong>e, show<strong>in</strong>g the data is very nearly 1/f<br />
<strong>in</strong> slope. There are several spurs, <strong>in</strong>clud<strong>in</strong>g one at 60 Hz (from lights <strong>and</strong> various AC<br />
sources) <strong>and</strong> another large one at ∼70 kHz (believed to be a radio signal). The spurs<br />
were found to always be present, <strong>and</strong> are removed from all other measurements <strong>in</strong> this<br />
chapter.<br />
2 Only when DC current flows through a resistor does it generate low-frequency noise.<br />
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CHAPTER 4. LOW-FREQUENCY NOISE OF GAN HEMTS<br />
4.4 <strong>GaN</strong> HEMT Low-Frequency <strong>Noise</strong> Model<strong>in</strong>g<br />
For model<strong>in</strong>g, the dra<strong>in</strong> <strong>and</strong> gate LFN bias-dependence need to be determ<strong>in</strong>ed. The<br />
setup <strong>in</strong> § 4.3 was used to measure dra<strong>in</strong> noise while an AC short was applied to the<br />
gate. LFN was measured with the dra<strong>in</strong> voltage held constant at Vds 5 V <strong>and</strong> the gate<br />
voltage swept (chang<strong>in</strong>g Ids). Then noise for a constant Ids of 30 mA <strong>and</strong> vary<strong>in</strong>g Vds<br />
was measured. Both of these results are plotted <strong>in</strong> figure 4.6. In this figure only three<br />
of the decade values are plotted from each full LFN measurement for convenience<br />
of display<strong>in</strong>g the data. Once the device saturates, the LFN does not change further<br />
with Ids (<strong>and</strong> hence Vgs). However, LFN <strong>in</strong>creases with Vds. This change, shown <strong>in</strong><br />
figure 4.6 (b), is more than an order of magnitude for the twelve volt bias range.<br />
The magnitude of these LFN measurements at low bias<strong>in</strong>gs is consistent with the<br />
literature. The only other published work of LFN noise of <strong>GaN</strong> <strong>HEMTs</strong> at high bias-<br />
<strong>in</strong>gs is by Hsu [4]. The measurements presented here for a saturated device agree with<br />
that work, <strong>in</strong>clud<strong>in</strong>g the key result that the noise changes with Vds. In fact, Hsu claims<br />
more bulg<strong>in</strong>g at higher biases (Vds > 12 V), <strong>and</strong> that the bulg<strong>in</strong>g broadens. This <strong>in</strong>-<br />
crease of LFN with Vds was also observed <strong>in</strong> the GaAs devices to be discussed <strong>in</strong> § 4.6.<br />
The slope, γ, was extracted <strong>and</strong> found to typically be about 1.15, vary<strong>in</strong>g from less<br />
than 1.1 to nearly 1.3. Bias dependence was not clear, but usually γ would decrease<br />
with <strong>in</strong>creas<strong>in</strong>g Vds <strong>and</strong> very slightly decrease with <strong>in</strong>creas<strong>in</strong>g Ids. The chang<strong>in</strong>g of<br />
γ with bias is not well understood. It has been shown to vary with temperature as<br />
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CHAPTER 4. LOW-FREQUENCY NOISE OF GAN HEMTS<br />
(a) (b)<br />
Figure 4.6: Plots of the measured dra<strong>in</strong> low-frequency noise with (a) change <strong>in</strong> dra<strong>in</strong>source<br />
current <strong>and</strong> (b) voltage.<br />
well. Previous research po<strong>in</strong>ts to trap effects, tunnel<strong>in</strong>g, <strong>and</strong> hot-carriers as directions<br />
to explore [2,4].<br />
Despite the measurements be<strong>in</strong>g of noise, devices biased the same had very similar<br />
measurements. This means that devices at the same bias can be compared. This is<br />
used as a basis for device comparison studies later <strong>in</strong> the chapter.<br />
The gate LFN was measured with the dra<strong>in</strong> AC shorted. Vds was set to 5 V <strong>and</strong> the<br />
gate voltage was varied. As seen <strong>in</strong> figure 4.7, even at its noisiest the gate LFN is more<br />
than three orders of magnitude smaller than the dra<strong>in</strong> noise. Measurements above a<br />
few kHz hit the noise floor of the setup. Hsu f<strong>in</strong>ds similar results [4], as does Riddle<br />
for GaAs MESFETs [11]. It was discovered that devices that had a large change <strong>in</strong><br />
gate leakage with applied gate bias also had a large change <strong>in</strong> LFN. Conversely, if the<br />
device gate leakage was relatively constant with gate bias, the LFN did not change<br />
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CHAPTER 4. LOW-FREQUENCY NOISE OF GAN HEMTS<br />
V,<br />
30 µA<br />
V,<br />
15 µA<br />
V,<br />
8.5 µA<br />
V gs , I gs<br />
V,<br />
4.5 µA<br />
V,<br />
2.9 µA<br />
Figure 4.7: Measured gate low-frequency noise versus gate-source voltage (<strong>and</strong><br />
current).<br />
much. The device <strong>in</strong> figure 4.7 did have a large change <strong>in</strong> leakage as evident from the<br />
x-axis label<strong>in</strong>g. γ was also very close to unity. These observations mean the gate LFN<br />
can be modeled by the st<strong>and</strong>ard diode equation, 4.2.2. This helps re<strong>in</strong>force the noise<br />
figure model<strong>in</strong>g <strong>in</strong> chapter 2 us<strong>in</strong>g a shot noise source at the gate of the transistor.<br />
It is desirable to add scal<strong>in</strong>g to circuit model<strong>in</strong>g of noise, so the effect of device<br />
geometry on LFN was also measured. Figure 4.8 shows that as the gate is made wider<br />
the dra<strong>in</strong> LFN noise <strong>in</strong>creases. This trend agrees with the low-bias <strong>GaN</strong> HEMT LFN<br />
measurements of Kuksenkov [12] <strong>and</strong> the HEMT model<strong>in</strong>g of Angelov [13]. This<br />
trend is opposite to what is exhibited by MOSFETs [14]. Given this result, it makes<br />
the gate length dependence all the more <strong>in</strong>terest<strong>in</strong>g. Figure 4.9 (a) <strong>and</strong> (b) show that a<br />
shorter gate length <strong>in</strong>creases the dra<strong>in</strong> LFN. This means that the LFN does not display<br />
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CHAPTER 4. LOW-FREQUENCY NOISE OF GAN HEMTS<br />
Figure 4.8: Change <strong>in</strong> low-frequency noise with gate width at various decade frequencies<br />
for three devices.<br />
(a) (b)<br />
Figure 4.9: (a) Change <strong>in</strong> low-frequency noise as the gate length, Lg is changed. (b)<br />
The 1 kHz data from (a) with a best fit l<strong>in</strong>e.<br />
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CHAPTER 4. LOW-FREQUENCY NOISE OF GAN HEMTS<br />
a direct area dependence. It can be speculated that the gate length dependence LFN is<br />
related to the Vds dependence.<br />
The Vds LFN dependence will harm the phase noise performance of <strong>GaN</strong> HEMT-<br />
based oscillators. Also, it is not typical of previous LFN model<strong>in</strong>g, which has a current<br />
dependence <strong>in</strong>stead. Based on the measurements presented thus far, the gate <strong>and</strong> dra<strong>in</strong><br />
have different LFN processes <strong>and</strong> should not be modeled <strong>in</strong> the same manner. It<br />
needs to be determ<strong>in</strong>ed whether the gate <strong>and</strong> dra<strong>in</strong> LFN are mathematically correlated.<br />
Measurements were performed with the gate AC shorted <strong>and</strong> not AC shorted, show<strong>in</strong>g<br />
no change <strong>in</strong> the dra<strong>in</strong> LFN. The same was done for gate LFN measurements <strong>and</strong> the<br />
dra<strong>in</strong> did not appear to have an effect. Hsu found similar results [4]. Lee shows<br />
that the gate <strong>and</strong> dra<strong>in</strong> LFN are uncorrelated [15]. Therefore, a two-current noise<br />
source model with no correlation as illustrated <strong>in</strong> figure 4.10 can be used. Based on<br />
the measurements <strong>in</strong> this work, the follow<strong>in</strong>g model of the dra<strong>in</strong> LFN for a circuit<br />
simulator is proposed:<br />
CHAPTER 4. LOW-FREQUENCY NOISE OF GAN HEMTS<br />
�<br />
i 2 �<br />
d,1/f = Ki<br />
� ��<br />
Wg,new Lg,old<br />
Wg,old<br />
Lg,new<br />
f γ<br />
� c<br />
(msVds +1)<br />
(4.4.1)<br />
where Ki, ms, <strong>and</strong> c are fitt<strong>in</strong>g parameters represent<strong>in</strong>g the magnitude of the noise,<br />
the slope change with Vds , <strong>and</strong> an exponent of the change with gate length respec-<br />
tively. Wg <strong>and</strong> Lg are def<strong>in</strong>ed the same as <strong>in</strong> § 2.6.4. Values found to work for devices<br />
presented are Ki = 4e-14, γ = 1.1, c = 1.5, <strong>and</strong> m = 2.6. As already mentioned, the<br />
gate noise can be modeled with equation 4.2.2. Due to the limitations of hitt<strong>in</strong>g the<br />
noise floor, the gate LFN geometry dependence could not be measured. However, as<br />
it depends on the Schottky contact reverse-bias gate leakage, it might be assumed that<br />
the gate LFN scales with the gate leakage as <strong>in</strong> equation 2.6.45. Parameters found to<br />
work for the gate LFN are Af = 1.15, Ffe = 1, <strong>and</strong> Kf = 2e-11.<br />
The model was used to estimate the dra<strong>in</strong> LFN corner frequency of the devices,<br />
as equipment limitations prevented the measurement of this important quantity. The<br />
noise figure model<strong>in</strong>g work <strong>in</strong> chapter 2 was used to estimate the noise floor, <strong>and</strong><br />
its <strong>in</strong>tersection with the LFN was calculated. This value varies with bias because of<br />
changes <strong>in</strong> LFN <strong>and</strong> ga<strong>in</strong>, but was estimated to be close be 1-10 MHz. This is a<br />
typical value for GaAs <strong>HEMTs</strong>. It was also attempted to use this model <strong>in</strong> phase noise<br />
circuit simulations <strong>in</strong> ADS. However, limitations <strong>in</strong> the device model <strong>and</strong> the lack<br />
of a native voltage bias-dependent low-frequency noise source component <strong>in</strong> ADS<br />
prevented accurate prediction of phase noise.<br />
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CHAPTER 4. LOW-FREQUENCY NOISE OF GAN HEMTS<br />
4.5 <strong>GaN</strong> HEMT Low-Frequency <strong>Noise</strong> Studies<br />
4.5.1 Substrate<br />
There has already been some work compar<strong>in</strong>g the noise of <strong>GaN</strong> <strong>HEMTs</strong> on different<br />
substrates [3]. The f<strong>in</strong>d<strong>in</strong>gs were that SiC was less noisy than sapphire, hav<strong>in</strong>g Hooge<br />
parameters one to two orders of magnitude smaller. But the measurements were at<br />
a low bias <strong>and</strong> it has already been expla<strong>in</strong>ed why the Hooge parameter should not<br />
be used for device comparisons. There is no data published compar<strong>in</strong>g devices that<br />
are <strong>in</strong> the saturation region. This was undertaken, <strong>and</strong> is presented <strong>in</strong> figure 4.11.<br />
The devices are both biased at Vds 5 V <strong>and</strong> Ids 10 mA. Across the spectrum, there<br />
is no apparent difference. While there appears to be a slight amount of bulg<strong>in</strong>g, it is<br />
not stronger for either device. This suggests that at typical device bias<strong>in</strong>gs the LFN<br />
is suppressed or another noise mechanism is stronger. Also, identical <strong>GaN</strong> HEMT-<br />
based oscillators on both substrates constructed by the author (§ 5.4.1) did not show a<br />
difference <strong>in</strong> LFN.<br />
4.5.2 Passivation<br />
There are two previous publications on the effect passivation has on LFN <strong>in</strong> <strong>GaN</strong>.<br />
The first [16] measured <strong>HEMTs</strong> at a very low bias <strong>and</strong> normalized the noise to the<br />
dra<strong>in</strong> current. They showed that the passivation does improve the LFN performance,<br />
119
CHAPTER 4. LOW-FREQUENCY NOISE OF GAN HEMTS<br />
Figure 4.11: Measurement of devices on a sapphire <strong>and</strong> SiC substrate at a bias of Vds<br />
5V,Ids 30 mA<br />
(a) (b)<br />
Figure 4.12: (a) Low-frequency noise of a device before <strong>and</strong> after passivation. (b)<br />
Low-frequency noise at 10 Hz <strong>and</strong> 1 kHz of a device before <strong>and</strong> after passivation at<br />
different Vgs .<br />
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CHAPTER 4. LOW-FREQUENCY NOISE OF GAN HEMTS<br />
but based on their measurements the improvement varied with gate bias from as large<br />
as an order of magnitude to almost no improvement. The other study also found<br />
an improvement with passivation but only measured TLM structures [17]. LFN was<br />
measured for a sample before <strong>and</strong> after passivation. In figure 4.12 (a), the LFN is<br />
plotted for a device with <strong>and</strong> without passivation at Vds 5 V <strong>and</strong> Ids 10 mA. Passivation<br />
improves the LFN by an order of magnitude across the spectrum. Passivation causes<br />
a slight change <strong>in</strong> threshold voltage, so measurements were taken at different gate<br />
bias<strong>in</strong>gs with Vds still at 5 V. The measured data at 10 Hz <strong>and</strong> 1 kHz is plotted <strong>in</strong><br />
figure 4.12 (b). The improvement stays relatively constant with gate voltage. It is<br />
believed that suppression of surface state traps, along with the <strong>in</strong>crease of channel<br />
charge, cause the improvement.<br />
4.5.3 Thick-Epitaxial Cap Devices<br />
After consider<strong>in</strong>g the result of passivation on LFN, it is <strong>in</strong>terest<strong>in</strong>g to look now at a<br />
device that does not require passivation. Devices of similar design to those <strong>in</strong> § 3.5.6<br />
(<strong>Al<strong>GaN</strong></strong> was used to cap the device <strong>in</strong>stead of <strong>GaN</strong>) were measured. Figure 4.13 shows<br />
LFN measurements of a few thick-cap devices (that have no passivation) <strong>and</strong> st<strong>and</strong>ard<br />
passivated <strong>HEMTs</strong>. The performance of the thick-cap devices is as good as, if not<br />
slightly better than, a passivated st<strong>and</strong>ard HEMT device. It can be concluded that a<br />
LFN mechanism on the channel surface can be suppressed with either passivation or<br />
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CHAPTER 4. LOW-FREQUENCY NOISE OF GAN HEMTS<br />
Figure 4.13: Comparison of st<strong>and</strong>ard passivated <strong>HEMTs</strong> to an unpassivated thick cap<br />
<strong>HEMTs</strong>. Bias is Vds =5V<strong>and</strong>Ids = 30 mA.<br />
with another epitaxial layer.<br />
4.5.4 Field-Plated Devices<br />
A field plate (FP) was shown to lower NF <strong>in</strong> this work (§ 3.5.5). It has also been<br />
shown that a FP improves oscillator phase noise <strong>in</strong> [18]. In fact, the longer the FP, the<br />
less the phase noise. As the 30 dB/decade slope of this data suggests that a 1/f type of<br />
noise is dom<strong>in</strong>at<strong>in</strong>g the phase noise, it might be reasoned that the LFN of FP <strong>and</strong> non-<br />
FP devices is different. If there is a difference, it is not apparent <strong>in</strong> the measurements<br />
shown <strong>in</strong> figure 4.14. In part (a) of the figure, all FP <strong>and</strong> non-FP transistors display<br />
the same LFN at different frequencies when biased under the same conditions. The<br />
second plot, (b), shows that as Vds <strong>in</strong>creases, all devices’ LFN <strong>in</strong>crease at nearly equal<br />
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CHAPTER 4. LOW-FREQUENCY NOISE OF GAN HEMTS<br />
(a) (b)<br />
Figure 4.14: (a) Decade low-frequency noise data for devices with different FP lengths<br />
at a bias of Vds 5 V <strong>and</strong> Ids 30 mA. (b) 100 Hz low-frequency noise for different FP<br />
lengths at Vds 3, 5, <strong>and</strong> 8 V.<br />
rates. The answer to the orig<strong>in</strong> of the phase noise improvement with a FP will need to<br />
be answered elsewhere.<br />
4.6 Comparison to GaAs <strong>HEMTs</strong><br />
In the previous chapter the NF of <strong>GaN</strong> was shown to be similar to GaAs. Let us now<br />
exam<strong>in</strong>e the LFN of these two materials. A few <strong>GaN</strong> LFN reports have claimed that<br />
the noise is comparable (such as [2]). These previous results are usually done with a<br />
measured <strong>GaN</strong> device <strong>and</strong> <strong>in</strong>formation for a GaAs device from a data sheet or another<br />
paper. In addition, the Hooge parameter is used as the figure of merit.<br />
The author obta<strong>in</strong>ed GaAs <strong>HEMTs</strong> <strong>and</strong> measured the LFN of these devices. They<br />
are from the TriQu<strong>in</strong>t TQP13 pHEMT process, with an fτ of ∼95 GHz. The device<br />
123
CHAPTER 4. LOW-FREQUENCY NOISE OF GAN HEMTS<br />
gate geometry is 0.13 x 93 µm. This is not the same as the 0.7 x 100 µm <strong>GaN</strong> HEMT<br />
devices to which they are compared to. However, based on the model presented <strong>in</strong> this<br />
chapter, approximat<strong>in</strong>g the magnitude of the GaAs devices to be 3 times smaller than<br />
what is actually measured should make for a fair comparison. The question arises<br />
of how to bias the different devices. The follow<strong>in</strong>g bias was chosen: 1.5 times the<br />
knee voltage of the fully open channel <strong>and</strong> 3/4 the total gate bias (positive turn-on to<br />
negative cut-off).<br />
Figure 4.15 shows the measurements of (a) the full spectrum of one <strong>GaN</strong> <strong>and</strong> one<br />
GaAs device <strong>and</strong> (b) selected frequency po<strong>in</strong>ts for a few <strong>GaN</strong> <strong>and</strong> GaAs devices.<br />
The GaAs has not been corrected for its difference <strong>in</strong> geometry. Consider<strong>in</strong>g this<br />
difference, the LFN from a few kHz to 1 MHz is similar for both types of devices.<br />
The slope (γ) of the GaAs devices was found to typically be 0.8 (it is common <strong>in</strong> the<br />
(a) (b)<br />
Figure 4.15: Low-frequency noise comparison of (a) a <strong>GaN</strong> <strong>and</strong> GaAs HEMT (full<br />
spectrum) <strong>and</strong> (b) multiple <strong>GaN</strong> <strong>and</strong> GaAs <strong>HEMTs</strong> (decade measurements). Bias for<br />
all devices is Vgs = 3/4 Vtotal, Vds = 1.5 Vknee.<br />
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CHAPTER 4. LOW-FREQUENCY NOISE OF GAN HEMTS<br />
GaAs FET literature for γ to be between 0.7 <strong>and</strong> 1), which is much less than the 1.2 for<br />
<strong>GaN</strong>. Therefore, at lower frequencies GaAs has less noise. In § 5.5, it will be shown<br />
that the close-to-carrier phase noise of <strong>GaN</strong> oscillators is worse than for GaAs-based<br />
oscillators because of these different slopes.<br />
4.7 Summary<br />
This chapter has provided a useful collection of quality high-bias low-frequency<br />
noise data. It was shown that the noise depends heavily on Vds while rema<strong>in</strong><strong>in</strong>g nearly<br />
constant to a chang<strong>in</strong>g gate voltage. The geometry dependence has also been shown to<br />
be different than what is seen <strong>in</strong> other devices. A scalable, bias-dependent, empirical<br />
model was proposed that can be used <strong>in</strong> circuit simulators. It was demonstrated that<br />
neither the choice of substrate nor the addition of a FP change the LFN. Suppression<br />
of LFN from surface effects was demonstrated through measurements of unpassivated<br />
<strong>and</strong> thick-cap devices. References to the literature were added to support all measure-<br />
ments where previous work exists. The full details of a LFN setup were expla<strong>in</strong>ed. A<br />
f<strong>in</strong>al note is that bulg<strong>in</strong>g (g-r noise presumably from traps) would occasionally show<br />
up. The bulge would be very broad with a spectrum from around 100 Hz to 1 kHz. It<br />
was not always present, even across the same sample. With improvement of material<br />
it can be expected that the LFN will improve.<br />
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CHAPTER 4. LOW-FREQUENCY NOISE OF GAN HEMTS<br />
References<br />
[1] A. Hajimiri <strong>and</strong> T. Lee, The Design of Low <strong>Noise</strong> <strong>Oscillators</strong>. Boston: Kluwer<br />
Academic Publishers, 1999.<br />
[2] A. Bal<strong>and</strong><strong>in</strong>, S. Morozov, S. Cai, R. Li, K. Wang, G. Wijeratne, <strong>and</strong><br />
C. Viswanathan, “Low Flicker-<strong>Noise</strong> <strong>GaN</strong>/<strong>Al<strong>GaN</strong></strong> Heterostructure Field-Effect<br />
Transistors for <strong>Microwave</strong> Communications,” <strong>Microwave</strong> Theory <strong>and</strong> Techniques,<br />
IEEE Transactions on, vol. 47, no. 8, pp. 1413–1417, 1999.<br />
[3] A. Bal<strong>and</strong><strong>in</strong>, Ed., <strong>Noise</strong> <strong>and</strong> Fluctuations Control <strong>in</strong> Electronic Devices. Stevenson<br />
Ranch, CA: American Scientific Publishers, 2002.<br />
[4] S. Hsu, P. Valizadeh, D. Pavlidis, J. Moon, M. Micovic, D. Wong, <strong>and</strong> T. Hussa<strong>in</strong>,<br />
“Characterization <strong>and</strong> Analysis of Gate <strong>and</strong> Dra<strong>in</strong> Low-Frequency <strong>Noise</strong> <strong>in</strong><br />
<strong>Al<strong>GaN</strong></strong>/<strong>GaN</strong> <strong>HEMTs</strong>,” <strong>in</strong> High Performance Devices, 2002. Proceed<strong>in</strong>gs. IEEE<br />
Lester Eastman Conference on, 2002, pp. 453–460.<br />
[5] A. L. McWhorter, “Semiconductor Surface Physics,” R. H. K<strong>in</strong>ston, Ed. Philadelphia:<br />
Univ. of Pennsylvania Press, 1956, pp. 207–228.<br />
[6] F. N. Hooge, “1/f <strong>Noise</strong> Sources,” IEEE Trans. Electron Devices, vol. 41, no. 11,<br />
pp. 1926–35, Nov. 1994.<br />
[7] A. van der Ziel, “Unified Presentation of 1/f <strong>Noise</strong> <strong>in</strong> Electron Devices: Fundamental<br />
1/f <strong>Noise</strong> Sources,” Proc. IEEE, vol. 76, no. 3, pp. 233–258, 1988.<br />
[8] ——, <strong>Noise</strong> <strong>in</strong> Solid State Devices <strong>and</strong> Circuits. New York: Wiley-Interscience,<br />
1986.<br />
[9] M. J. Buck<strong>in</strong>gham, <strong>Noise</strong> <strong>in</strong> Electronic Devices <strong>and</strong> Systems. New York: John<br />
Wiley & Sons, 1983.<br />
[10] D. A. Bell, “A survey of 1/f noise <strong>in</strong> electrical conductors.” Journal of Physics C:<br />
Solid State Physics, vol. 13, no. 24, pp. 4425–37, Aug. 1980.<br />
[11] A. N. Riddle, “Oscillator <strong>Noise</strong>: Theory <strong>and</strong> Characterization,” Ph.D. dissertation,<br />
North Carol<strong>in</strong>a State University, 1986.<br />
[12] D. V. Kuksenkov, H. Temk<strong>in</strong>, R. Gaska, <strong>and</strong> J. W. Yang, “Low-Frequency <strong>Noise</strong><br />
<strong>in</strong> <strong>Al<strong>GaN</strong></strong>/<strong>GaN</strong> Heterostructure Field Effect Transistors,” IEEE Electron Devices<br />
Lett., vol. 19, no. 7, pp. 222–224, July 1998.<br />
[13] I. Angelov, R. Kozhuharov, <strong>and</strong> H. Zirath, “A Simple Bias Dependant LF FET<br />
<strong>Noise</strong> Model for CAD,” <strong>in</strong> <strong>Microwave</strong> Symposium Digest, 2001 IEEE MTT-S International,<br />
vol. 1, 2001, pp. 407–410 vol.1.<br />
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[14] T. H. Lee, The Design of CMOS Radio-Frequency Integrated Circuits, 2nd ed.<br />
New York: Cambridge University Pess, 2004.<br />
[15] S. Lee, “Intr<strong>in</strong>sic <strong>Noise</strong> Characteriestics of Gallium Nitride High Electron Mobility<br />
Transistors,” Ph.D. dissertation, Purdue University, Aug. 2004.<br />
[16] A. V. Vertiatchikh <strong>and</strong> L. Eastman, “Effect of the Surface <strong>and</strong> Barrier Defects<br />
on the <strong>Al<strong>GaN</strong></strong>/<strong>GaN</strong> HEMT Low-Frequency <strong>Noise</strong> Performance,” IEEE Electron<br />
Devices Lett., vol. 24, no. 9, pp. 535–537, Sept. 2003.<br />
[17] S. A. Vitusevich, M. V. Petrychuk, S. V. Danylyuk, A. M. Kurak<strong>in</strong>, N. Kle<strong>in</strong>, <strong>and</strong><br />
A. E. Belyaev, “Influence of Surface Passivation on Low-Frequency <strong>Noise</strong> Properties<br />
of <strong>Al<strong>GaN</strong></strong>/<strong>GaN</strong> High Electron Mobility Transistor Structures,” phys. stat. sol.<br />
(a), no. 5, pp. 816–819, Mar. 2005.<br />
[18] H. Xu, C. Sanabria, S. Heikman, S. Keller, U. Mishra, <strong>and</strong> R. York, “High Power<br />
<strong>GaN</strong> <strong>Oscillators</strong> Us<strong>in</strong>g Field-Plated HEMT Structure,” <strong>in</strong> <strong>Microwave</strong> Symposium<br />
Digest, 2005 IEEE MTT-S International, 2005, pp. 1345–1348.<br />
127
5.1 Introduction<br />
5<br />
<strong>GaN</strong> HEMT Based <strong>Oscillators</strong><br />
OSCILLATORS are a key component of many communication systems. They<br />
set fundamental limits of channel spac<strong>in</strong>g because of their phase noise. This<br />
work has demonstrated that NF <strong>and</strong> LFN of <strong>GaN</strong> <strong>HEMTs</strong> are only slightly worse<br />
than the far more technologically mature GaAs <strong>HEMTs</strong>. Here the phase noise will<br />
be compared to similar <strong>in</strong>tegrated circuit designs <strong>in</strong> Si <strong>and</strong> GaAs. Some guidel<strong>in</strong>es<br />
for low-phase noise design are discussed. A recently-developed MMIC process at<br />
UCSB [1] was ideal for mak<strong>in</strong>g the designs, <strong>and</strong> it will be reviewed briefly. The focus<br />
of the chapter is the design <strong>and</strong> measurement of two LC differential oscillators. The<br />
first did not have impressive phase noise performance but its l<strong>in</strong>earity was excellent.<br />
It is also the first <strong>GaN</strong> differential oscillator to appear <strong>in</strong> the literature [2]. A second<br />
similar oscillator was fabricated that had fairly good phase noise performance. These<br />
oscillators are compared to other published results of differential oscillators <strong>in</strong> Si <strong>and</strong><br />
GaAs, as well as <strong>GaN</strong> HEMT oscillators of all designs.<br />
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CHAPTER 5. GAN HEMT BASED OSCILLATORS<br />
5.2 Concern<strong>in</strong>g Phase <strong>Noise</strong><br />
The study of phase noise is a difficult undertak<strong>in</strong>g. Entire books <strong>and</strong> dissertations<br />
are devoted to its study [3–5]. Even today there is still not a consensus of how best to<br />
approach the problem [6]. The reason for the difficulty of underst<strong>and</strong><strong>in</strong>g phase noise<br />
stems from three challenges. The first is that an oscillator is a non-l<strong>in</strong>ear problem, <strong>and</strong><br />
simple analytical analysis cannot capture all key aspects. The rigorous work is usually<br />
too complicated for clear <strong>in</strong>sight or practical design. LFN is the largest contributor to<br />
phase noise, <strong>and</strong> the lack of its full underst<strong>and</strong><strong>in</strong>g underm<strong>in</strong>es any complete study of<br />
phase noise. It is not unheard of for a designer to simulate phase noise without LFN<br />
model<strong>in</strong>g <strong>in</strong> the circuit because of this shortcom<strong>in</strong>g. F<strong>in</strong>ally, the circuit design impacts<br />
the phase noise, possibly <strong>in</strong> profound ways [5].<br />
Def<strong>in</strong><strong>in</strong>g phase noise is much simpler than design<strong>in</strong>g for it. Any signal source is<br />
bound to have fluctuations <strong>in</strong> phase <strong>and</strong> amplitude. We can write these fluctuations as<br />
v(t) =v0(1 − a(t)) cos(ω0t + ψ(t)) (5.2.1)<br />
v0 <strong>and</strong> ω0 are the amplitude <strong>and</strong> angular frequency of resonance of the oscillator.<br />
The amplitude fluctuations, a(t), <strong>and</strong> phase fluctuations, ψ(t), are both stochastic pro-<br />
cesses. The power spectral density close to the carrier frequency is found to be [7]<br />
Sv(ω) = v2 0<br />
2 {4π(1 −〈φψ(0)〉)δ(ω − ω0)+Sa(ω − ω0)<br />
+Sψ(ω − ω0)+2Im[Sψa(ω − ω0)]} (5.2.2)<br />
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CHAPTER 5. GAN HEMT BASED OSCILLATORS<br />
Here we see the signal amplitude (v 2 0/2) at the resonant frequency, along with an<br />
autocorrelation term, φψ, from the phase fluctuations that reduces it. Sa is noise added<br />
to the spectrum from the amplitude fluctuations, <strong>and</strong> is commonly known as amplitude<br />
modulation (AM) noise. The phase fluctuations contribute to the spectrum through Sψ,<br />
<strong>and</strong> is known as phase modulation (PM) or phase noise. A correlation term between<br />
the amplitude <strong>and</strong> phase fluctuations can also contribute to the spectrum through the<br />
cross spectral density, Sψa, called AM-PM noise. AM-PM noise is an odd function<br />
(the others are even), <strong>and</strong> can lead to asymmetry of the noise spectrum around the<br />
carrier. Proper circuit design reduces AM-PM noise. The nonl<strong>in</strong>earities of the ga<strong>in</strong>-<br />
produc<strong>in</strong>g element <strong>in</strong> an oscillator (usually, but not always, a transistor) provides a<br />
restor<strong>in</strong>g force that not only keeps the amplitude stable but also greatly reduces AM<br />
noise. This means the noise near an oscillator’s resonance frequency is dom<strong>in</strong>ated by<br />
phase noise.<br />
Bear<strong>in</strong>g <strong>in</strong> m<strong>in</strong>d that there is AM, PM, <strong>and</strong> AM-PM noise, but PM (phase noise)<br />
dom<strong>in</strong>ates, the phase noise can be observed with a spectrum analyzer. In fact, an Ag-<br />
ilent E4440 spectrum analyzer with a phase noise personality was used for measure-<br />
ments that appear <strong>in</strong> this chapter. Phase noise appears as a broaden<strong>in</strong>g of the frequency<br />
of oscillation, shown <strong>in</strong> figure 5.1 (a). Its f<strong>in</strong>e detail of shape varies, <strong>and</strong> is typically<br />
one of three cases as seen <strong>in</strong> figure 5.1 (b-d). The resonator acts as a filter. Above or<br />
below the resonant frequency a voltage signal would drop proportionally to 1/f, but<br />
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CHAPTER 5. GAN HEMT BASED OSCILLATORS<br />
Power<br />
Power<br />
1/f 3<br />
1/f 2<br />
(a)<br />
(c)<br />
ω 0<br />
<strong>Noise</strong> Floor<br />
Frequency<br />
<strong>Noise</strong> Floor<br />
Frequency<br />
Power<br />
Power<br />
1/f 3<br />
1/f 3<br />
1/f<br />
(b)<br />
(d)<br />
<strong>Noise</strong> Floor<br />
Frequency<br />
<strong>Noise</strong> Floor<br />
Frequency<br />
Figure 5.1: (a) A typical spectrum of an oscillator. (b-d) are zoomed <strong>in</strong> plots of the<br />
circled portion <strong>in</strong> (a). The power <strong>in</strong> the various plots are not scaled to one another.<br />
the power would drop 1/f 2 (20 dB/decade). This is exactly what happens to both flat<br />
(such as thermal) noise sources <strong>and</strong> up-converted LFN lead<strong>in</strong>g to 20 dB/decade <strong>and</strong><br />
30 dB/decade slopes respectively. An oscillator with a very high Q, <strong>and</strong> the best noise<br />
performance (the plots <strong>in</strong> figure 5.1 are not to scale to each other), would have a shape<br />
such as that <strong>in</strong> figure 5.1 (b). The 1/f 3 region is the resonator filter<strong>in</strong>g up-converted<br />
LFN, while the 1/f regions are up-converted LFN that is outside the resonator b<strong>and</strong>-<br />
width. If there were no LFN (a blissful ideality), the slope of the entire range would be<br />
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CHAPTER 5. GAN HEMT BASED OSCILLATORS<br />
just 20 dB/decade. Figure 5.1 (c) is the most typical spectrum observed. Here aga<strong>in</strong><br />
is filter<strong>in</strong>g of LFN, but now we see thermal noise be<strong>in</strong>g filtered as well. The last case,<br />
figure 5.1 (d), is for an oscillator with an enormous amount of LFN. We will return<br />
to this qualitative analysis later. Phase noise is specified <strong>in</strong> decibels below the carrier<br />
(dBc) <strong>in</strong> a 1 Hz b<strong>and</strong>width at a offset-frequency from the carrier. For example, a phase<br />
noise of -132 dBc/Hz at 100 kHz means the noise at a frequency 100 kHz <strong>in</strong> addition<br />
to the oscillation frequency is 132 dB below the power the oscillator has at its resonant<br />
frequency (ω0).<br />
A concise background of phase noise would require more than a chapter. Despite<br />
the complexity of phase noise, there are some guidel<strong>in</strong>es that tend to show up repeat-<br />
edly [3,5–9]:<br />
• Increase the tank Q: This is the most important factor for improv<strong>in</strong>g phase<br />
noise. Higher Q means more suppression of off-carrier frequency components.<br />
• M<strong>in</strong>imize the LFN: Probably the next most important parameter after Q. Choice<br />
of device (bipolars <strong>in</strong> general have much less LFN than FETs) <strong>and</strong> device geometry<br />
can help, as well as improvement <strong>in</strong> material quality. But usually little<br />
can be done to quell LFN.<br />
• Increase the Signal Amplitude: If all other <strong>in</strong>fluences could be considered<br />
constant, a larger signal amplitude <strong>in</strong>creases signal to noise ratio <strong>and</strong> reduces<br />
the phase noise.<br />
• M<strong>in</strong>imize Other <strong>Noise</strong> Sources: Flat noise sources determ<strong>in</strong>e the phase noise<br />
<strong>in</strong> the 20 dB/decade range.<br />
• Properly Design the Loop Ga<strong>in</strong>: Design<strong>in</strong>g the phase shift of the loop to have<br />
a maximum derivative at the center of the resonance of the loop ga<strong>in</strong> maximizes<br />
the resonator’s ability to attenuate phase noise.<br />
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CHAPTER 5. GAN HEMT BASED OSCILLATORS<br />
• L<strong>in</strong>earize Cgs: The non-l<strong>in</strong>earity of Cgs with Vgs makes the oscillator less symmetric<br />
<strong>and</strong> <strong>in</strong>creases noise. Additional capacitance can smooth Cgs <strong>and</strong> improve<br />
phase noise. [3,10]<br />
• Optimize the Circuit: Some oscillator topologies, particularly the Colpitts,<br />
provide better phase noise than others. Design of the circuit <strong>in</strong>fluences the<br />
phase noise performance. Use of techniques, such as automatic ga<strong>in</strong> control<br />
<strong>and</strong> tapped resonators, can help as well.<br />
The last po<strong>in</strong>t is the largest topic to expound upon. However, the other po<strong>in</strong>ts go<br />
far toward the goal of improv<strong>in</strong>g phase noise. Because of the very large powers <strong>GaN</strong><br />
<strong>HEMTs</strong> can produce, the improvement of phase noise with signal amplitude is of great<br />
<strong>in</strong>terest to <strong>GaN</strong> circuits <strong>and</strong> provides the motivation for build<strong>in</strong>g the oscillators <strong>in</strong> this<br />
chapter.<br />
To simulate phase noise, very accurate device small-signal, large-signal, <strong>and</strong> noise<br />
model<strong>in</strong>g must be available. In addition, simulators vary <strong>in</strong> their accuracy <strong>in</strong> predict<strong>in</strong>g<br />
phase noise. Model<strong>in</strong>g from the previous chapters was used to attempt simulations<br />
of phase noise. However, the device model had some shortcom<strong>in</strong>gs (discussed <strong>in</strong><br />
§ 6.2) that prevented even accurate model<strong>in</strong>g of the 20 dB/decade phase noise from<br />
filtered thermal noise. Some <strong>in</strong>terest<strong>in</strong>g results could be determ<strong>in</strong>ed: the gate-leakage<br />
shot noise was found to be negligible compared to contributions of the gate resistance<br />
thermal noise, the channel noise, <strong>and</strong> the LFN. It was also noted that a field plate (FP)<br />
did help the simulated phase noise results. A surpris<strong>in</strong>g simulated improvement of<br />
10 dB of a very long FP HEMT oscillator over a non-FP oscillator agrees with the<br />
work of Dr. Xu [11]. The practices outl<strong>in</strong>ed above were followed as well as possible.<br />
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CHAPTER 5. GAN HEMT BASED OSCILLATORS<br />
5.3 MMIC Process Description<br />
The MMIC process developed by Hongtao Xu was used for circuit fabrication [1].<br />
It <strong>in</strong>tegrates capacitors, <strong>in</strong>ductors, resistors, <strong>and</strong> transmission l<strong>in</strong>es. This follows the<br />
HEMT process described <strong>in</strong> § 3.2, but with additional steps. There are now two addi-<br />
tional metal layers (metal 1, 1 µm of gold, <strong>and</strong> metal 2, 3 µm of gold), a resistor layer<br />
(NiCr), <strong>and</strong> a dielectric spacer layer (3 µm of PMGI). Inductors are made with metal<br />
1 as an under-pass metal, then the dielectric spacer, <strong>and</strong> metal 2 to f<strong>in</strong>ish the over-pass<br />
<strong>and</strong> most of the metalization of the square <strong>in</strong>ductors. Capacitors are made with the<br />
gate metal as a bottom electrode <strong>and</strong> the same film used for passivation as the capac-<br />
itor dielectric. Metal 1 becomes the top electrode, <strong>and</strong> metal 2 connects the capacitor<br />
bottom <strong>and</strong> top to the rest of the circuit (metal 2 is used over the PMGI to contact the<br />
top electrode without short<strong>in</strong>g the capacitor). Resistor composition is Ti/SiO2/NiCr<br />
<strong>and</strong> is protected by the same SiN film used for the capacitors <strong>and</strong> passivation. Trans-<br />
mission l<strong>in</strong>es are made exclusively with the thick metal 2. The same material structure<br />
<strong>in</strong> § 3.2 is used here. Full details of the process, along with a process flow chart, can<br />
be found <strong>in</strong> Hongtao Xu’s dissertation [1].<br />
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CHAPTER 5. GAN HEMT BASED OSCILLATORS<br />
5.4 Differential <strong>Oscillators</strong><br />
5.4.1 High L<strong>in</strong>earity Oscillator<br />
Some familiarity with oscillators will be assumed <strong>in</strong> this <strong>and</strong> the next subsection.<br />
A background can be found <strong>in</strong> textbooks such as [8]. The oscillators were designed<br />
primarily as test vehicles, mak<strong>in</strong>g the circuit design more flexible <strong>and</strong> less conven-<br />
tional than typical commercial configurations. Design goals were to m<strong>in</strong>imize phase<br />
noise <strong>and</strong> maximize power <strong>and</strong> l<strong>in</strong>earity without regard to other constra<strong>in</strong>ts such as<br />
device size or ease of implementation. Design started with a basic cross-coupled pair<br />
of 2 × 100 µm-wide <strong>HEMTs</strong>, seen <strong>in</strong> figure 5.2. Typically the dra<strong>in</strong> bias would be set<br />
with a current mirror at the HEMT sources (marked with an S) but it was desired to<br />
have the freedom to change the bias. This also elim<strong>in</strong>ates the LFN from devices <strong>in</strong> the<br />
current mirror.<br />
The tank, represented by the capacitor Ct <strong>and</strong> <strong>in</strong>ductors Lt, primarily set the reso-<br />
nance frequency. A fixed capacitor was used <strong>in</strong>stead of a varactor to improve the Q of<br />
the resonator <strong>and</strong> allow better <strong>in</strong>sight of the phase noise performance of the <strong>HEMTs</strong>.<br />
The passive components used for the tank were based on measurements of fabricated<br />
capacitors <strong>and</strong> <strong>in</strong>ductors at 5 GHz, with the best Q components picked for the desired<br />
oscillation frequency. Typical unloaded Q values at 5 GHz are 25 <strong>and</strong> 65 for the square<br />
spiral <strong>in</strong>ductors <strong>and</strong> the SiN capacitors respectively.<br />
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CHAPTER 5. GAN HEMT BASED OSCILLATORS<br />
Load<br />
C 2<br />
L 1<br />
S<br />
L t<br />
C 1<br />
C 3<br />
L 2<br />
L 3<br />
C t<br />
L 3<br />
C 3<br />
L 2<br />
L t<br />
C 1<br />
S<br />
L 1<br />
C 2<br />
Load<br />
Figure 5.2: Circuit schematic of the oscillator (bias<strong>in</strong>g not shown).<br />
Lt<br />
L2<br />
L1<br />
C1<br />
C3<br />
C2<br />
Ct<br />
Figure 5.3: Photograph of the high l<strong>in</strong>earity oscillator. Darker areas are the two<br />
<strong>HEMTs</strong>. Passive components are labeled as <strong>in</strong> figure 5.2.<br />
136<br />
C2<br />
C3<br />
C1<br />
L1<br />
L2<br />
Lt
CHAPTER 5. GAN HEMT BASED OSCILLATORS<br />
The output is taken on either side of the tank. To keep from load<strong>in</strong>g the tank, <strong>and</strong><br />
to match to a 50 Ω output, an L-match (L1 <strong>and</strong> C2) is used. Bias is provided at the<br />
gate <strong>and</strong> through the L-matches with the output. This required the use of off-chip<br />
bias-Ts for the RF/DC ports, but not for the gate bias port. The gate uses large square<br />
<strong>in</strong>ductors (L2) as RF chokes. C1 is a DC block that prevents the dra<strong>in</strong> of the <strong>HEMTs</strong><br />
from short<strong>in</strong>g, <strong>and</strong> C3 isolates the DC of the gate <strong>and</strong> dra<strong>in</strong>. The lengths of l<strong>in</strong>e used<br />
to cross-connect the <strong>HEMTs</strong> are modeled by the <strong>in</strong>ductors L3. The photograph of the<br />
oscillator <strong>in</strong> figure 5.3 labels most of the circuit elements found <strong>in</strong> figure 5.2. Circuit<br />
size is 2 x 1.65 mm 2 .<br />
The circuit was simulated us<strong>in</strong>g ADS. Transient <strong>and</strong> harmonic simulations were<br />
performed. Monitor<strong>in</strong>g these, along with the dynamic load-l<strong>in</strong>e at the dra<strong>in</strong> port of the<br />
<strong>HEMTs</strong>, the circuit was optimized to give as l<strong>in</strong>ear an output as possible.<br />
Measurements were performed on-wafer with air-coplanar (Cascade Microtech ACP-<br />
40 GSG) probes. Off-chip bias-Ts were used for both the dra<strong>in</strong>s <strong>and</strong> gates. One side<br />
of the oscillator was term<strong>in</strong>ated <strong>in</strong> a dummy 50 Ω load. All measurements that follow<br />
(power, l<strong>in</strong>earity, phase noise) were performed us<strong>in</strong>g an Agilent E4440 spectrum ana-<br />
lyzer with phase noise personality. Figure 5.4 (a) shows the measured spectrum from<br />
one side provid<strong>in</strong>g 22.9 dBm of power at a 4.166 GHz oscillation frequency. The cir-<br />
cuit is biased at Vds 20 V, Ids 233 mA, <strong>and</strong> Vgs -1 V. The analyzer had a 10 MHz span<br />
<strong>and</strong> 33 kHz resolution b<strong>and</strong>width for the measurement. How the power <strong>and</strong> efficiency<br />
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CHAPTER 5. GAN HEMT BASED OSCILLATORS<br />
(a) (b)<br />
Figure 5.4: Measurements of the oscillator: (a) power spectrum (b) frequency pull<strong>in</strong>g.<br />
(a) (b)<br />
Figure 5.5: Output power (s<strong>in</strong>gle-sided), second harmonic power, <strong>and</strong> efficiency (full<br />
circuit) of the high-l<strong>in</strong>earity oscillator for changes <strong>in</strong> device (a) dra<strong>in</strong>-source voltage<br />
<strong>and</strong> (b) gate-source voltage.<br />
138
CHAPTER 5. GAN HEMT BASED OSCILLATORS<br />
compare to other oscillators will be discussed <strong>in</strong> § 5.5.<br />
Of <strong>in</strong>terest is the oscillator pull<strong>in</strong>g, which is the change <strong>in</strong> oscillation frequency<br />
with DC bias. This was measured for both the gate <strong>and</strong> dra<strong>in</strong> voltages <strong>and</strong> plotted <strong>in</strong><br />
figure 5.4 (b). It is typical to express the pull<strong>in</strong>g as a ratio of change <strong>in</strong> frequency to<br />
change <strong>in</strong> bias. Approximat<strong>in</strong>g the data as l<strong>in</strong>ear <strong>in</strong> figure 5.4 (b) gives a pull<strong>in</strong>g of<br />
4.3 MHz/V for the gate <strong>and</strong> 0.6 MHz/V for the dra<strong>in</strong>. These changes are less than<br />
0.4% of the frequency of oscillation.<br />
The power, 2nd harmonic, <strong>and</strong> efficiency for changes <strong>in</strong> bias appear <strong>in</strong> figure 5.5 (a)<br />
<strong>and</strong> (b). The third harmonic was so small as to be buried <strong>in</strong> the noise floor of the spec-<br />
trum analyzer, mak<strong>in</strong>g it ∼70 dB below the carrier. The 2nd harmonic was typically<br />
better than 30 dBc for all bias<strong>in</strong>gs measured. If the output were taken differentially,<br />
even harmonics would cancel <strong>and</strong> the oscillator would make for an extremely l<strong>in</strong>ear<br />
source.<br />
This oscillator was the first <strong>GaN</strong> differential oscillator to be reported <strong>in</strong> the litera-<br />
ture, <strong>and</strong> also the best reported l<strong>in</strong>earity for a <strong>GaN</strong> oscillator [2]. However, the phase<br />
noise was not impressive, be<strong>in</strong>g only -86.3 dBc <strong>and</strong> -115.7 dBc at best. A second,<br />
similar, oscillator was constructed <strong>and</strong> is now presented.<br />
139
CHAPTER 5. GAN HEMT BASED OSCILLATORS<br />
5.4.2 Low-Phase <strong>Noise</strong> Oscillator<br />
The previous design was modified to improve phase noise performance. The Q<br />
of the various <strong>in</strong>ductors was reasoned to be a limit<strong>in</strong>g factor, <strong>and</strong> were replaced. Mi-<br />
crostrip l<strong>in</strong>es, Lt <strong>in</strong> figure 5.6, were used <strong>in</strong> place of the tank <strong>in</strong>ductors. The L-matches<br />
were changed to tapped capacitors to help preserve the loaded tank Q. This meant the<br />
dra<strong>in</strong> bias<strong>in</strong>g needed to be applied through the tank microstrip <strong>in</strong>ductors. To provide<br />
an AC ground across Lt, the large block<strong>in</strong>g capacitor 2C3 was added. The circuit,<br />
shown <strong>in</strong> figure 5.7, was slightly smaller than the previous at 2 x 1.4 mm 2 .<br />
Load<br />
C 1<br />
C 2<br />
S<br />
2C 3<br />
L t Lt<br />
C 4<br />
L 2<br />
L 1<br />
C t<br />
L 1<br />
C 4<br />
L 2<br />
S<br />
C 2<br />
C 1<br />
Load<br />
Figure 5.6: Circuit schematic of the low-phase noise oscillator (bias<strong>in</strong>g not shown).<br />
140
CHAPTER 5. GAN HEMT BASED OSCILLATORS<br />
L 2<br />
L t<br />
C 1<br />
C 2<br />
C 3<br />
C 4<br />
C t<br />
Figure 5.7: Photograph of the low-phase noise oscillator. Passive components are<br />
labeled as <strong>in</strong> figure 5.6.<br />
Figure 5.8 is a typical measured phase noise spectrum. Above 10 kHz the oscillator<br />
drift obstructs the measurement. From 10 kHz to 1 MHz the spectrum decreases with<br />
a 30 dB per decade slope, similar to figure 5.1 (d). This means the low-frequency<br />
noise (LFN) of the oscillator dom<strong>in</strong>ates <strong>and</strong> hides the 20 dB per decade thermal noise<br />
region. So far, no published <strong>GaN</strong>-oscillator phase-noise measurements have shown<br />
a strict 20 dB per decade slope below a 1 MHz offset [2, 11–15]. A phase noise<br />
measurement above a 1 MHz offset usually approaches a spectrum analyzer’s noise<br />
floor, hence the lack of phase noise measurements <strong>in</strong> the literature at larger offsets.<br />
Now to answer the key question: does an <strong>in</strong>crease of oscillator power improve the<br />
phase noise? After the optimal bias for Vgs was determ<strong>in</strong>ed <strong>and</strong> set, Vds was varied.<br />
141<br />
C 4<br />
C 3<br />
L t<br />
C 1<br />
C 2<br />
L 2
CHAPTER 5. GAN HEMT BASED OSCILLATORS<br />
Figure 5.8: Measured phase noise of the oscillator.<br />
Figure 5.9: Phase noise at 100 kHz <strong>and</strong> 1 MHz offsets versus dra<strong>in</strong>-source bias for a<br />
few oscillators.<br />
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CHAPTER 5. GAN HEMT BASED OSCILLATORS<br />
The power of the oscillators <strong>in</strong>creases from 15 dBm to 18 dBm as Vds <strong>in</strong>creased from<br />
6 V to 35 V. Below Vds 5 V the power drops quickly (it was typically 7 dBm at Vds<br />
4 V). Phase noise for devices with different Vds is plotted <strong>in</strong> figure 5.9. The phase<br />
noise does not improve with an <strong>in</strong>crease <strong>in</strong> signal power, but actually <strong>in</strong>creases. This<br />
agrees with measurements <strong>in</strong> [12]. Of <strong>in</strong>terest is that the general shape of figure 5.9 is<br />
similar to the measured LFN bias dependence <strong>in</strong> figure 4.6. While proper design can<br />
help to lower the offset frequency where the 30 dB/decade <strong>and</strong> 20 dB/decade slopes<br />
meet, only Hajimiri’s model [5] addresses how this can be accomplished <strong>and</strong> its ability<br />
to do this is still debated. With these results <strong>in</strong> m<strong>in</strong>d, we now compare <strong>GaN</strong> oscillators<br />
to other material systems for phase noise <strong>and</strong> for other oscillator measurements.<br />
5.5 Comparison to Other <strong>Oscillators</strong><br />
A summary of measurements of several oscillators is found <strong>in</strong> table 5.1. Listed are<br />
the measured frequency of oscillation (or range if the oscillator is tunable), the total<br />
device (or devices) width, the oscillator power at its resonance frequency <strong>in</strong> addition<br />
to second <strong>and</strong> third harmonics, the best efficiency of which the oscillator was capable,<br />
phase noise measurements at 100 kHz <strong>and</strong> 1 MHz offsets, <strong>and</strong> the reference for each<br />
work.<br />
The table is separated <strong>in</strong>to four parts depend<strong>in</strong>g on oscillator type. All oscillators <strong>in</strong><br />
the table are either HEMT or MESFET-based (no BJTs or HBTs) <strong>and</strong> <strong>in</strong>tegrated (no<br />
143
CHAPTER 5. GAN HEMT BASED OSCILLATORS<br />
Desc. Carrier Device Fund. 2nd 3rd Best Phase <strong>Noise</strong> Ref.<br />
Freq. Width Power Harm. Harm. Eff. 100 kHz,1 MHz<br />
GHz mm dBm dBm dBm % dBc/Hz<br />
<strong>GaN</strong> HEMT <strong>Oscillators</strong><br />
Colpitts 5.3 0.2 20.5 -11.5 – 14.1 -105 -123 [12]<br />
Hartley 9.56 1.5 32.3 – – 16 -87 -115 [16]<br />
VCO 9 ± 0.5 1.5 31.8 10.8 4.8 21 -77 – [14]<br />
Colpitts,<br />
1.1 µm FP<br />
5.02 0.5 30 ∼8 – 24 -104 -132 [11]<br />
GaAs MESFET Oscillator<br />
GaAs<br />
VCO<br />
11.5±0.3 – 9 >20 – – -91 -119 [17]<br />
Differential <strong>Oscillators</strong> (Fixed Frequency), This Work<br />
§ 5.4.1 4.16 0.4 22.9 -19.2
CHAPTER 5. GAN HEMT BASED OSCILLATORS<br />
<strong>in</strong> its circuit <strong>and</strong> [11] used a FP on the devices <strong>in</strong> the oscillator, provid<strong>in</strong>g astonish-<br />
<strong>in</strong>g improvements <strong>in</strong> phase noise (∼10 dB over the same circuit us<strong>in</strong>g devices with<br />
no FP). The oscillators <strong>in</strong> Si <strong>and</strong> GaAs technologies all used varactors for frequency<br />
tun<strong>in</strong>g. This will degrade the tank Q <strong>and</strong> lead to poorer phase noise performance. As<br />
a safe assumption, assume that the phase noise would be -10 dBc/Hz lower (better)<br />
than what is stated <strong>in</strong> the table. With this adjustment, we see that <strong>GaN</strong> has better or<br />
comparable phase noise at a 1 MHz offset, but by offsets ≤ 100 kHz the phase noise<br />
is worse. Work by Rice [15] agrees with these measurements. The reason for this<br />
difference is because <strong>GaN</strong> oscillators are dom<strong>in</strong>ated by their LFN <strong>and</strong> never show the<br />
20 dB/decade slope from thermal noise. This is better-expla<strong>in</strong>ed by figure 5.10. Here<br />
the phase noise is displayed comparatively for a <strong>GaN</strong> oscillator <strong>and</strong> a typical low-noise<br />
oscillator <strong>in</strong> GaAs or Si. Note that the magnitudes of the phase noise are not the same,<br />
as phase noise is expressed relative to the carrier. The measured absolute power of the<br />
phase noise sideb<strong>and</strong>s for the <strong>GaN</strong> oscillator will be much larger than <strong>in</strong> GaAs or Si.<br />
<strong>GaN</strong> oscillators provide at least an order of magnitude more power than the other<br />
technologies. For the total device width of the <strong>HEMTs</strong>, the oscillators <strong>in</strong> this work<br />
provide an average amount of power compared to the other <strong>GaN</strong> oscillators. The<br />
st<strong>and</strong>out is the FP HEMT oscillator, with 2 W/mm. The l<strong>in</strong>earity of the first oscillator<br />
<strong>in</strong> this work is second to none. The efficiencies of the <strong>GaN</strong> oscillators appears to be<br />
much higher than GaAs <strong>and</strong> Si.<br />
145
CHAPTER 5. GAN HEMT BASED OSCILLATORS<br />
Figure 5.10: Relative comparison of <strong>GaN</strong> oscillator to a typical oscillator with low<br />
phase noise (figure courtesy of Dr. Robert York).<br />
5.6 Summary<br />
Two <strong>GaN</strong> HEMT-based differential oscillators were presented. The first displayed<br />
very good harmonic suppression but poor phase noise. This oscillator was also the first<br />
<strong>GaN</strong> differential oscillator to appear <strong>in</strong> the literature [2]. The second oscillator showed<br />
excellent phase noise performance at a 1 MHz offset of -132 dBc/Hz. However, be-<br />
cause <strong>GaN</strong> oscillator phase noise appears to be dom<strong>in</strong>ated by very large amounts of<br />
LFN, the noise performance is worse at offsets closer to the carrier. The hoped-for<br />
benefit of better phase noise with more oscillator power is shattered by measurements<br />
that show that more power actually <strong>in</strong>creases the phase noise. This could be expected<br />
because of the HEMT dra<strong>in</strong> LFN bias dependence with Vds. Because of these two<br />
146
CHAPTER 5. GAN HEMT BASED OSCILLATORS<br />
problems, <strong>GaN</strong> does not appear to have an advantage over GaAs or Si oscillators for<br />
phase noise.<br />
References<br />
[1] H. Xu, “MMICs us<strong>in</strong>g <strong>GaN</strong> <strong>HEMTs</strong> <strong>and</strong> Th<strong>in</strong>-Film BST Capacitors,” Ph.D. dissertation,<br />
University of California, Santa Barbara, 2005.<br />
[2] C. Sanabria, H. Xu, S. Heikman, U. Mishra, <strong>and</strong> R. York, “A <strong>GaN</strong> Differential<br />
Oscillator With Improved Harmonic Performance,” IEEE <strong>Microwave</strong> Components<br />
Lett., vol. 15, pp. 463–465, Jul. 2005.<br />
[3] A. N. Riddle, “Oscillator <strong>Noise</strong>: Theory <strong>and</strong> Characterization,” Ph.D. dissertation,<br />
North Carol<strong>in</strong>a State University, 1986.<br />
[4] W. P. Rob<strong>in</strong>s, Phase <strong>Noise</strong> <strong>in</strong> Signal Sources. London, UK.: Peter Peregr<strong>in</strong>us<br />
Ltd., 1982.<br />
[5] A. Hajimiri <strong>and</strong> T. Lee, The Design of Low <strong>Noise</strong> <strong>Oscillators</strong>. Boston: Kluwer<br />
Academic Publishers, 1999.<br />
[6] S. A. Maas, <strong>Noise</strong> <strong>in</strong> L<strong>in</strong>ear <strong>and</strong> Nonl<strong>in</strong>ear Circuits. Boston: Artech House, 2005.<br />
[7] M. J. Buck<strong>in</strong>gham, <strong>Noise</strong> <strong>in</strong> Electronic Devices <strong>and</strong> Systems. New York: John<br />
Wiley & Sons, 1983.<br />
[8] T. H. Lee, The Design of CMOS Radio-Frequency Integrated Circuits, 2nd ed.<br />
New York: Cambridge University Pess, 2004.<br />
[9] D. Leeson, “A Simple Model of Feedback Oscillator <strong>Noise</strong> Spectrum,” Proc. IEEE,<br />
vol. 54, no. 2, pp. 329–330, 1966.<br />
[10] V. Manan <strong>and</strong> S. Long, “A Low Power <strong>and</strong> Low <strong>Noise</strong> p-HEMT Ku B<strong>and</strong> VCO,”<br />
<strong>Microwave</strong> <strong>and</strong> Wireless Components Letters, IEEE [see also IEEE <strong>Microwave</strong><br />
<strong>and</strong> Guided Wave Letters], vol. 16, no. 3, pp. 131–133, 2006.<br />
[11] H. Xu, C. Sanabria, S. Heikman, S. Keller, U. Mishra, <strong>and</strong> R. York, “High Power<br />
<strong>GaN</strong> <strong>Oscillators</strong> Us<strong>in</strong>g Field-Plated HEMT Structure,” <strong>in</strong> <strong>Microwave</strong> Symposium<br />
Digest, 2005 IEEE MTT-S International, 2005, pp. 1345–1348.<br />
[12] H. Xu, C. Sanabria, A. Ch<strong>in</strong>i, S. Keller, U. Mishra, <strong>and</strong> R. A. York, “Low Phase-<br />
<strong>Noise</strong> 5 GHz <strong>Al<strong>GaN</strong></strong>/<strong>GaN</strong> HEMT Oscillator Integrated with BaxSr1−xTiO3 Th<strong>in</strong><br />
Films,” IEEE <strong>Microwave</strong> Theory <strong>and</strong> Tech. Symp., pp. 1509–1512, 2004.<br />
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[13] J. B. Shealy, J. A. Smart, <strong>and</strong> J. R. Shealy, “Low-Phase <strong>Noise</strong> <strong>Al<strong>GaN</strong></strong>/<strong>GaN</strong> FET-<br />
Based Voltage Controlled <strong>Oscillators</strong> (VCOs),” IEEE <strong>Microwave</strong> Components<br />
Lett., vol. 11, no. 6, pp. 244–245, Jun. 2001.<br />
[14] V. Kaper, R. Thompson, T. Prunty, <strong>and</strong> J. R. Shealy, “Signal Generation, Control<br />
<strong>and</strong> Frequency Conversion <strong>Al<strong>GaN</strong></strong>/<strong>GaN</strong> HEMT MMICs,” IEEE <strong>Microwave</strong> Theory<br />
<strong>and</strong> Tech. Symp., pp. 1145–1148, 2004.<br />
[15] P. Rice, R. Sloan, M. Moore, A. R. Barnes, M. J. Uren, N. Malbert, <strong>and</strong> N. Labat,<br />
“A 10 GHz Dielectric Resonator Oscillator Us<strong>in</strong>g <strong>GaN</strong> Technology,” IEEE<br />
<strong>Microwave</strong> Theory <strong>and</strong> Tech. Symp., pp. 1497–1500, 2004.<br />
[16] V. S. Kaper, V. Tilak, H. Kim, A. V. Vertiatchikh, R. M. Thompson, T. R. Prunty,<br />
L. Eastman, <strong>and</strong> J. R. Shealy, “High-Power Monolithic <strong>Al<strong>GaN</strong></strong>/<strong>GaN</strong> HEMT Oscillator,”<br />
IEEE J. Solid-State Circuits, vol. 38, no. 9, pp. 1457–1461, Sept. 2003.<br />
[17] C.-H. Lee, S. Han, B. Mat<strong>in</strong>pour, <strong>and</strong> J. Laskar, “A Low Phase <strong>Noise</strong> X-b<strong>and</strong><br />
MMIC GaAs MESFET VCO,” <strong>Microwave</strong> <strong>and</strong> Guided Wave Letters, IEEE [see<br />
also IEEE <strong>Microwave</strong> <strong>and</strong> Wireless Components Letters], vol. 10, no. 8, pp. 325–<br />
327, 2000.<br />
[18] P. K<strong>in</strong>get, “A Fully Integrated 2.7 V 0.35 m CMOS VCO for 5 GHz Wireless<br />
Applications,” ISSCC Dig. Tech. Papers, p. 226227, 1998.<br />
[19] M. Soyuer, K. Jenk<strong>in</strong>s, J. Burghartz, <strong>and</strong> M. Hulvey, “A 3-V 4-GHz nMOS<br />
Voltage-Controlled Oscillator with Integrated Resonator,” Solid-State Circuits,<br />
IEEE Journal of, vol. 31, no. 12, pp. 2042–2045, 1996.<br />
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S. Hong, “5 6 GHz-B<strong>and</strong> GaAs MESFET-Based Cross-Coupled Differential Oscillator<br />
MMICs With Low Phase-<strong>Noise</strong> Performance,” IEEE <strong>Microwave</strong> Components<br />
Lett., vol. 11, no. 12, pp. 495–497, Dec. 2001.<br />
148
6<br />
Summary, Conclusions, <strong>and</strong> Future<br />
Directions For <strong>Noise</strong> Studies<br />
6.1 Summary <strong>and</strong> Conclusions<br />
THIS dissertation has looked at several aspects of the noise performance of<br />
<strong>GaN</strong> <strong>HEMTs</strong>: noise figure, low-frequency noise, <strong>and</strong> phase noise. The noise<br />
figure of <strong>GaN</strong> <strong>HEMTs</strong> is comparable to GaAs <strong>HEMTs</strong>. However, the gate leakage<br />
needs to be well-controlled. Source resistance might also be too large a contributor for<br />
small devices. At high bias<strong>in</strong>gs, self-heat<strong>in</strong>g causes the ga<strong>in</strong> to drop, <strong>and</strong> an <strong>in</strong>crease<br />
<strong>in</strong> source resistance quickly degrades the noise figure performance.<br />
A simple model, that <strong>in</strong>cluded device scal<strong>in</strong>g, was put together that not only pre-<br />
dicts the m<strong>in</strong>imum noise figure well, but also the other noise parameters: |Γopt|,� Γopt,<br />
<strong>and</strong> rn. It is useful for h<strong>and</strong> <strong>and</strong> Matlab calculations to predict <strong>and</strong> underst<strong>and</strong> noise<br />
without the need for noise parameter measurements beforeh<strong>and</strong>. It was successfully<br />
used to underst<strong>and</strong> how gate leakage <strong>and</strong> a field plate <strong>in</strong>fluence noise figure. The<br />
model does not work when the ga<strong>in</strong> of the transistor drops, such as at high bias<strong>in</strong>gs<br />
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CHAPTER 6. SUMMARY, CONCLUSIONS, AND FUTURE DIRECTIONS<br />
or frequencies close to fτ. It was shown that the Pospieszalski <strong>and</strong> correlated noise<br />
models can be successfully applied to <strong>GaN</strong> <strong>HEMTs</strong>, even for noise versus bias.<br />
Summariz<strong>in</strong>g the other noise figure studies, devices on either SiC or sapphire sub-<br />
strates can have the same m<strong>in</strong>imum noise figure as long as the bias is low. Thick-cap<br />
devices show low noise at high bias<strong>in</strong>gs. However, their noise at lower bias<strong>in</strong>gs is<br />
sub-par because of a very large amount of gate leakage.<br />
A low-frequency noise setup that works at bias<strong>in</strong>gs typically needed for <strong>GaN</strong> <strong>HEMTs</strong><br />
was constructed <strong>and</strong> thoroughly expla<strong>in</strong>ed. Unlike many other setups, this allowed<br />
bias dependent studies well <strong>in</strong>to the device saturation region. From this, a strong Vds<br />
dependence for the dra<strong>in</strong> was discovered <strong>and</strong> a scalable, bias dependent, model that<br />
could be entered <strong>in</strong> a circuit simulator was <strong>in</strong>troduced. The gate was found to follow<br />
the low-frequency noise model<strong>in</strong>g for a diode, as could be expected for a Schottky<br />
contact.<br />
Low-frequency noise studies were performed. Passivation was found to improve the<br />
low-frequency noise by an order of magnitude. An unpassivated thick-cap device has<br />
the same low-frequency noise performance as a passivated st<strong>and</strong>ard HEMT. A field-<br />
plate does not appear to help LFN, unlike noise figure. <strong>GaN</strong> HEMT low-frequency<br />
noise is worse than that of GaAs <strong>HEMTs</strong> because the slope of the noise is much larger.<br />
The phase noise of two <strong>GaN</strong> HEMT-based differential oscillators were explored.<br />
The first had poor phase noise, but very good harmonic suppression, <strong>and</strong> was the<br />
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CHAPTER 6. SUMMARY, CONCLUSIONS, AND FUTURE DIRECTIONS<br />
first <strong>GaN</strong> HEMT differential oscillator <strong>in</strong> the literature. The second oscillator showed<br />
excellent phase noise performance at large offsets, but poor performance at closer<br />
offsets because of the phase noise be<strong>in</strong>g dom<strong>in</strong>ated by the low-frequency noise. The<br />
<strong>GaN</strong> power advantage that was hoped would improve the oscillator signal-to-noise,<br />
<strong>and</strong> thus phase noise, was more than offset by the <strong>in</strong>crease of low-frequency noise<br />
with power. Because of these problems with low-frequency noise, <strong>GaN</strong> oscillators do<br />
not perform better - they do not even meet the performance typically seen by GaAs<br />
<strong>and</strong> Si oscillators.<br />
6.2 Future Paths<br />
Try<strong>in</strong>g to make progress <strong>in</strong> an entire field of study which is not completely under-<br />
stood <strong>and</strong> mak<strong>in</strong>g three difficult-to-use measurement systems work allows room for<br />
improvement. To improve noise figure, gate leakage needs to be controlled, but first<br />
it needs to be understood. This is no doubt the pursuit of many champions of <strong>GaN</strong><br />
research because of its implications for reliability <strong>and</strong> power performance. It would<br />
also be of <strong>in</strong>terest to look at bias dependence of ion-implanted <strong>GaN</strong> <strong>HEMTs</strong> to see<br />
if it improves the curve typically seen for m<strong>in</strong>imum noise figure versus dra<strong>in</strong>-source<br />
current. As thick-cap <strong>HEMTs</strong> do not need passivation, they are an <strong>in</strong>terest<strong>in</strong>g device<br />
with possible <strong>in</strong>dustry applications. Their noise figure performance at large current<br />
bias<strong>in</strong>gs was better than any other measured by the author. A better underst<strong>and</strong><strong>in</strong>g<br />
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CHAPTER 6. SUMMARY, CONCLUSIONS, AND FUTURE DIRECTIONS<br />
could be pursued.<br />
The work on low-frequency noise studies was only started <strong>and</strong> could be greatly<br />
exp<strong>and</strong>ed upon. In particular, while few researchers have even reported the dra<strong>in</strong> low-<br />
frequency noise Vds dependence, none have attempted to expla<strong>in</strong> it. As this seems to<br />
be directly l<strong>in</strong>ked to the measured phase noise of oscillators, it is strongly suggested<br />
it be studied <strong>in</strong> depth.<br />
There are many ways to try to improve phase noise. The oscillators presented here<br />
were relatively simple. More-sophisticated circuits should be undertaken <strong>and</strong> with<br />
smaller devices than those presented here or <strong>in</strong> other works. The researchers whose<br />
work has been discussed were design<strong>in</strong>g with high power <strong>in</strong> m<strong>in</strong>d. Before these cir-<br />
cuits can be attempted, the circuit model needs to be improved. There are several<br />
shortcom<strong>in</strong>gs. First, the ADS circuit model predicts that m<strong>in</strong>imum noise figure ver-<br />
sus dra<strong>in</strong> source current is flat, which is a glar<strong>in</strong>g problem (see figure 3.7). Dynamic<br />
source <strong>and</strong> dra<strong>in</strong> resistances must be <strong>in</strong>cluded along with self-heat<strong>in</strong>g effects. Gate<br />
leakage is not <strong>in</strong>cluded <strong>in</strong> the model <strong>and</strong> should be added. The attempt at us<strong>in</strong>g<br />
an ADS symbolically-def<strong>in</strong>ed device to generate a voltage-controlled low-frequency<br />
noise current source was not successful, as the simulator appeared to use the DC bias<br />
<strong>in</strong>stead of the vary<strong>in</strong>g large-signal voltage of the oscillation. A custom ADS compo-<br />
nent might be required, which could <strong>in</strong>volve a few hundred l<strong>in</strong>es of code. With these<br />
deficiencies corrected, it might be possible to more closely simulate phase noise <strong>and</strong><br />
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CHAPTER 6. SUMMARY, CONCLUSIONS, AND FUTURE DIRECTIONS<br />
possibly better underst<strong>and</strong> why a field plate helps the phase noise performance.<br />
153
An ADS project that conta<strong>in</strong>s files used <strong>in</strong> this work can be downloaded at<br />
http://my.ece.ucsb.edu/sanabria/research/ADS<strong>Noise</strong>Template.zap<br />
A<br />
ADS Files<br />
or by contact<strong>in</strong>g the author at sanabria@ece.ucsb.edu. The downloaded file will need<br />
to be unarchived <strong>in</strong> ADS. The project conta<strong>in</strong>s files necessary to:<br />
1. Extract <strong>and</strong> optimize the small-signal parameters, as well as to simulate a smallsignal<br />
model of the transistor for S-parameters<br />
2. Simulate noise figure with either the correlated noise or Pospieszalski model<br />
3. Extract the noise variables for the correlated noise model<br />
Steps expla<strong>in</strong><strong>in</strong>g how to do each of these functions with the project are presented <strong>in</strong><br />
the next three sections. Example files for each are provided <strong>in</strong> the project.<br />
154
APPENDIX A. ADS FILES<br />
A.1 Small-Signal Extraction<br />
To extract the small-signal model, three S-parameter measurements are needed:<br />
those of the device, a shorted-pads version of the device, <strong>and</strong> an open channel version<br />
of the device. For more details, refer to § 2.3. It may also be useful to measure<br />
extr<strong>in</strong>sic parasitic resistances through another means (such as Hall measurements).<br />
The S-parameter measurements will then need to be imported <strong>in</strong>to <strong>in</strong>dividual ADS<br />
data sets.<br />
Once the data is correctly <strong>in</strong> the ADS project, open the data display file<br />
template small signal parameter extraction.dds<br />
The middle of the first page of the dds file should look like figure A.1. This is where<br />
the S-parameters for the device, open, <strong>and</strong> short are entered. Example data sets are<br />
currently entered (Hongtao open, Hongtao short, d021218FC1...). Once these are en-<br />
tered, turn to the next page <strong>in</strong> the data display (its shortcut key comb<strong>in</strong>ation is Alt,<br />
p, e). Plots for the small-signal extr<strong>in</strong>sic capacitances are displayed, along with two<br />
markers per graph. The plots should be relatively flat, except maybe at very low fre-<br />
quencies (less than 1 GHz). Move the markers to a suitable range of values for each<br />
parameter. An average will be calculated for these (<strong>and</strong> the rest of the small-signal<br />
parameters). Cont<strong>in</strong>ue through the next two pages for the parasitic resistance <strong>and</strong> <strong>in</strong>-<br />
ductances. Then advance two pages to the <strong>in</strong>tr<strong>in</strong>sic parameters graphs page. Here<br />
there may be larger variations <strong>in</strong> the parameters. Choose values that make sense, <strong>and</strong><br />
155
APPENDIX A. ADS FILES<br />
Figure A.1: First page of template small signal parameter extraction.dds.<br />
narrow the range close to the target frequency. Advanc<strong>in</strong>g to the next page shows the<br />
calculated small-signal parameters. These can be entered <strong>in</strong>to a small-signal model of<br />
the transistor. Two have already been provided <strong>in</strong> the project:<br />
template HEMT smallsignal <strong>and</strong> Pospieszalski<strong>Noise</strong> model.dsn<br />
156
APPENDIX A. ADS FILES<br />
template HEMT smallsignal <strong>and</strong> Pucel<strong>Noise</strong> model.dsn<br />
Simply substitute your values <strong>in</strong>to one of these <strong>and</strong> save it as a new file. Once the<br />
small-signal parameters have been entered, the sub-circuit conta<strong>in</strong><strong>in</strong>g the network can<br />
be simulated for S-parameters. Open the schematic file<br />
template Sparameters extraction optimization.dsn<br />
Here there is one of the small-signal files <strong>in</strong> a subnetwork, an S-parameter simulation<br />
block, optimization blocks, <strong>and</strong> a Data Access Component for identify<strong>in</strong>g an ADS<br />
data set. This is shown <strong>in</strong> figure A.2. Leave the deactivated components out of the<br />
simulation. Exchange the subnetwork with the circuit to be simulated, <strong>and</strong> simulate.<br />
This will call the previous data display w<strong>in</strong>dow. If ADS asks to change the data set,<br />
answer “yes.” Go to the verification page. Here, S-parameters for the simulation are<br />
compared to the data set used for extraction. The fit should be good, but not excellent.<br />
The parameters can be optimized to the data. In the schematic w<strong>in</strong>dow, enter the<br />
ADS data set <strong>in</strong>to the Data Access Component that was used for the extraction. Ac-<br />
tivate all components <strong>in</strong> the schematic, then simulate. The simulation w<strong>in</strong>dow will<br />
display the f<strong>in</strong>al optimized small-signal parameters. The verification page of the data<br />
display w<strong>in</strong>dow will show S-parameters for both the <strong>in</strong>itial <strong>and</strong> optimized values. En-<br />
ter the optimized values <strong>in</strong> the circuit sub-network. Deactivate the optimization blocks<br />
aga<strong>in</strong>, <strong>and</strong> simulate. The agreement on the verification page of the data display w<strong>in</strong>-<br />
dow of the simulated <strong>and</strong> measured S-parameters should be excellent.<br />
157
APPENDIX A. ADS FILES<br />
Figure A.2: Schematic used for simulat<strong>in</strong>g S-parameters of the small-signal circuit<br />
<strong>and</strong> for optimization.<br />
A.2 <strong>Noise</strong> Figure Simulation<br />
Open the project, <strong>and</strong> then open the circuit schematic file<br />
template noise figure measure.dns<br />
You should now be at the w<strong>in</strong>dow shown <strong>in</strong> figure A.3. The subnetwork<br />
template HEMT smallsignal <strong>and</strong> Pucel<strong>Noise</strong> model<br />
conta<strong>in</strong>s a small-signal model for a HEMT that <strong>in</strong>cludes noise sources <strong>and</strong> noise vari-<br />
158
APPENDIX A. ADS FILES<br />
ables for a Correlated <strong>Noise</strong> (CN) model. How to obta<strong>in</strong> the noise variables from<br />
noise parameter measurements <strong>and</strong> small-signal parameter values is discussed <strong>in</strong> the<br />
next section. This subnetwork can also be substituted with<br />
template HEMT smallsignal <strong>and</strong> Pospieszalski<strong>Noise</strong> model.dsn<br />
which conta<strong>in</strong>s a small-signal model of a HEMT <strong>and</strong> noise sources <strong>and</strong> noise vari-<br />
ables for the Pospieszalski model. The Pospieszalski noise variables are obta<strong>in</strong>ed from<br />
noise parameter measurements <strong>and</strong> small-signal parameters with the Matlab code <strong>in</strong><br />
Figure A.3: Schematic used for simulat<strong>in</strong>g noise parameters.<br />
159
APPENDIX A. ADS FILES<br />
appendix C.<br />
Return<strong>in</strong>g to the circuit schematic, simulat<strong>in</strong>g br<strong>in</strong>gs up the data display<br />
template noise figure viewer.dds<br />
Page 3 of this data display (use the shortcut Alt, p, e to navigate through the pages)<br />
conta<strong>in</strong>s noise <strong>and</strong> ga<strong>in</strong> circles on Smith Charts, the noise parameters, stability factor,<br />
<strong>and</strong> noise figure for a 50 Ω term<strong>in</strong>ation compared to NFm<strong>in</strong> versus frequency. The<br />
other pages of the display also conta<strong>in</strong> useful <strong>in</strong>formation for design.<br />
A.3 Correlated <strong>Noise</strong> Model Extraction<br />
To extract the noise variables for this type of noise model, the small-signal param-<br />
eters need to be determ<strong>in</strong>ed <strong>and</strong> entered <strong>in</strong>to a circuit as expla<strong>in</strong>ed <strong>in</strong> the first section<br />
of this appendix. In particular, have all the small-signal parameters entered <strong>in</strong>to the<br />
variable (VAR) block of the circuit network<br />
template HEMT smallsignal <strong>and</strong> Pucel<strong>Noise</strong> model.dsn<br />
Measured noise parameters are also needed to determ<strong>in</strong>e the noise variables. Once<br />
setup, open the circuit schematic<br />
template parasitic matrix for correlation extraction.dsn<br />
which is shown <strong>in</strong> figure A.4. Here, there are two networks simulated for S-parameters.<br />
They correspond to the <strong>in</strong>tr<strong>in</strong>sic <strong>and</strong> extr<strong>in</strong>sic parameters, respectively. If the small-<br />
signal network listed above was used, its VAR block can just be pasted <strong>in</strong>to this design<br />
160
APPENDIX A. ADS FILES<br />
<strong>and</strong> the previous one deleted.<br />
Simulat<strong>in</strong>g should br<strong>in</strong>g up the data display<br />
template noise correlation extraction.dds<br />
A screen shot of it is shown <strong>in</strong> figure A.5. The noise parameters will need to be entered<br />
<strong>in</strong>to the equations <strong>in</strong>side the Change These box. Once this is done, the Cpd unnorm<br />
box <strong>and</strong> Cext will be the desired results: Cpd unnorm(1,1) is the gate noise <strong>in</strong> units<br />
of A 2 /Hz, Cpd unnorm(2,2) is the dra<strong>in</strong> noise <strong>in</strong> units of A 2 /Hz, Cpd unnorm(1,2)<br />
<strong>and</strong> Cpd unnorm(2,1) are the cross-correlation terms (not used here), <strong>and</strong> Cext is the<br />
correlation between the gate <strong>and</strong> dra<strong>in</strong> noise. Enter<strong>in</strong>g these back <strong>in</strong>to the second VAR<br />
block <strong>in</strong><br />
template HEMT smallsignal <strong>and</strong> Pucel<strong>Noise</strong> model.dsn<br />
will allow for simulation of the noise parameters.<br />
161
APPENDIX A. ADS FILES<br />
Figure A.4: Schematic used for extract<strong>in</strong>g correlated noise model noise variables.<br />
Figure A.5: Data display used for extract<strong>in</strong>g correlated noise model noise variables.<br />
162
B<br />
Matlab Code for <strong>Noise</strong><br />
Parameter Model<strong>in</strong>g<br />
THIS Matlab script computes all four of the noise parameters as developed <strong>in</strong> § 2.6,<br />
displays them <strong>in</strong> different formats, <strong>and</strong> plots m<strong>in</strong>imum noise figure versus frequency.<br />
This should facilitate the model’s use for other researchers. A copy of the file<br />
can be obta<strong>in</strong>ed by contact<strong>in</strong>g the author at sanabria@ece.ucsb.edu.<br />
% NF.m<br />
% NF <strong>and</strong> other noise parameters <strong>in</strong>clud<strong>in</strong>g gate leakage, but not Cgd.<br />
% Chris Sanabria, 12/03/04<br />
clear all;<br />
close all;<br />
% Variables (change)<br />
163
APPENDIX B. MATLAB CODE FOR NOISE PARAMETER MODELING<br />
Igs = 6e-6; % Gate leakage<br />
rge = 3.03; % Gate resistance<br />
rs = 6;<br />
gmi = 0.033;<br />
ri = 8;<br />
cgsi = 0.21e-12;<br />
rds = 1000; % Dra<strong>in</strong>-source resistance. Only used for a ga<strong>in</strong> calculation<br />
% <strong>and</strong> not for noise prediciton.<br />
G = 2/3; % Gamma, use 2/3<br />
f = [5e9 10e9]; % Operat<strong>in</strong>g frequency or frequencies<br />
Zo = 50; % Reference impedance for calculat<strong>in</strong>g reflection coefficient<br />
Ta = 290; % Kelv<strong>in</strong>. This is the <strong>in</strong>put temp., NOT the channel temp.!<br />
% Constants<br />
q = 1.6022e-019;<br />
k = 1.3807e-023;<br />
w = 2*pi*f;<br />
% Intermediates that may change<br />
r<strong>in</strong> = rge + ri + rs;<br />
gm = gmi./(1+gmi.*rs);<br />
cgs = cgsi./(1+gmi.*rs);<br />
% Intermediate variables (no chang<strong>in</strong>g)<br />
wt = gm./cgs; % That’s right, no 2pi.<br />
a = gm.*G.*(w./wt).ˆ2;<br />
b = q.*Igs./(2.*k.*Ta);<br />
xgs = -1./(2.*pi.*f.*cgs);<br />
% Optimum <strong>in</strong>put impedance (reflection coefficient) for noise<br />
Xopt = 1./(w.*cgs).*a./(a+b);<br />
Ropt = sqrt(r<strong>in</strong>./(a+b) + a./(a+b).*r<strong>in</strong>.ˆ2 + a.*b./((a+b).ˆ2.*(w.ˆ2.*cgs.ˆ2)));<br />
Zopt = Ropt + j.*Xopt;<br />
Gamopt = (Zopt-Zo)./(Zopt+Zo);<br />
% M<strong>in</strong>imum <strong>Noise</strong> Figure<br />
164
APPENDIX B. MATLAB CODE FOR NOISE PARAMETER MODELING<br />
rg = Ropt;<br />
xg = Xopt;<br />
Fm<strong>in</strong> = 1 + r<strong>in</strong>./rg + b./rg.*(rg.ˆ2+xg.ˆ2) + a./rg.*(abs(r<strong>in</strong>+rg+j.*(xg - 1./(w.*cgs)))).ˆ2;<br />
% <strong>Noise</strong> resistance<br />
% First calculate NF at Zo, then use NFm<strong>in</strong> <strong>and</strong> NF @ Zo to get rn<br />
rgzo = real(Zo);<br />
xgzo = imag(Zo);<br />
Fzo = 1 + r<strong>in</strong>./rgzo + b./rgzo.*(rgzo.ˆ2 + xgzo.ˆ2) + a./rgzo.*(abs(r<strong>in</strong>+rgzo+j.*(xgzo -<br />
1./(w.*cgs)))).ˆ2;<br />
Rn = Zo.*(Fzo - Fm<strong>in</strong>).*(abs(1 + Gamopt)).ˆ2./(4.*abs(Gamopt)); % noise resistance<br />
(not normalized)<br />
% Ga<strong>in</strong> av @ NFm<strong>in</strong>. Will not be accurate because Cgd is not <strong>in</strong>cluded<br />
Gav = abs(-(rds./2).*(wt./w).*j./((rg+r<strong>in</strong>) + j.*(xgs + xg))).ˆ2;<br />
% Display outputs<br />
disp([’Fm<strong>in</strong> = ’ num2str(Fm<strong>in</strong>)])<br />
disp(’ ’)<br />
NFm<strong>in</strong> = 10*log10(Fm<strong>in</strong>);<br />
disp([’NFm<strong>in</strong> (dB) = ’ num2str(NFm<strong>in</strong>)])<br />
% disp([’|Zopt| = ’ num2str(abs(Zopt))])<br />
% disp([’|Zopt| = ’ num2str(abs(Zopt))])<br />
% disp(’ ’)<br />
% disp([’phase Zopt = ’ num2str(angle(Zopt)/pi*180)])<br />
% disp(’ ’)<br />
disp([’r n = ’ num2str(Rn./Zo)])<br />
disp([’|Gamma opt| = ’ num2str(abs(Gamopt))])<br />
disp([’phase Gamma opt = ’ num2str(angle(Gamopt)/pi*180)])<br />
disp([’Ga<strong>in</strong> av [dB] = ’ num2str(10.*log10(Gav))])<br />
% Some plott<strong>in</strong>g<br />
figure;<br />
plot(f./1e9,NFm<strong>in</strong>,’r’)<br />
xlabel(’Frequency [GHz]’)<br />
ylabel(’NF {m<strong>in</strong>} [dB]’)<br />
165
C<br />
Matlab Code for Pospieszalski <strong>Noise</strong><br />
Parameter Model<strong>in</strong>g<br />
THIS Matlab script calculates the two noise temperatures for the Pospieszalski<br />
noise model as discussed <strong>in</strong> § 2.5.3. Because this <strong>in</strong>volves solv<strong>in</strong>g a pair of<br />
quadratic equations, it returns two sets of noise temperatures. The temperatures that<br />
are negative <strong>in</strong> value are non-physical <strong>and</strong> should not be used.<br />
% noise temps.m<br />
% Uses Pospieszalski’s model to get the two noise temperatures. You need to<br />
% have taken noise figure measurements <strong>and</strong> have extracted a small signal<br />
% model. Because the solv<strong>in</strong>g is for a pair of quadratic equations, there<br />
% are two sets of solutions. Ignore the negative temperature pair.<br />
% Chris Sanabria, March 2003<br />
clc;<br />
format compact<br />
%Input these:<br />
freq = 10e9; % Hz<br />
NFm<strong>in</strong> = 2.03; % dB<br />
rn = .755; % NOT ohms, the normalized value<br />
gam opt= 0.609*exp(j*54.4/180*pi); % Complex Reflection Coefficient<br />
ft = 22.1e9; % In Hz. Pospieszalski def<strong>in</strong>es this as gm/(Cgs*2*pi), but the<br />
% author f<strong>in</strong>ds that the measured ft can work better.<br />
Cgs = .258e-12; % Farads<br />
rgs = 7.46; % Same as Ri<br />
166
APPENDIX C. MATLAB CODE FOR POSPIESZALSKI NOISE PARAMETER MODELING<br />
rds = 1155; % Ohms<br />
gm = .032; %S<br />
To = 290; % Kelv<strong>in</strong><br />
% Intermediate Equations<br />
gds = 1/rds;<br />
Rn = rn*50;<br />
gn = 1/Rn;<br />
Zopt = (1+gam opt)/(1-gam opt)*50;<br />
Xopt = imag(Zopt);<br />
Ropt = real(Zopt);<br />
Tm<strong>in</strong> = (10ˆ(NFm<strong>in</strong>/10)-1)*To;<br />
N = Ropt/Rn;<br />
% Solve the equations<br />
[Td Tg] = solve(’Roptˆ2 = (ft/freq)ˆ2*rgs/gds*Tg/Td+rgsˆ2’,...<br />
’Tm<strong>in</strong> = 2*freq/ft*sqrt(gds*rgs*Tg*Td+(freq/ft)ˆ2*rgsˆ2*gds...<br />
ˆ2*Tdˆ2) + 2*(freq/ft)ˆ2*rgs*gds*Td’,’Td’,’Tg’);<br />
% Values are currently <strong>in</strong> Kelv<strong>in</strong><br />
disp(’Values <strong>in</strong> Kelv<strong>in</strong>’);<br />
Td = eval(Td)<br />
Tg = eval(Tg)<br />
disp(’ ’);<br />
disp(’ ’);<br />
% Values are now <strong>in</strong> degrees C<br />
disp(’Values <strong>in</strong> Celcius’);<br />
Td C = Td - 273.15<br />
Tg C = Tg - 273.15<br />
% Check the validty<br />
disp(’ ’)<br />
disp(’ ’)<br />
disp(’Validity Check’)<br />
167
APPENDIX C. MATLAB CODE FOR POSPIESZALSKI NOISE PARAMETER MODELING<br />
check = 4*N*To/Tm<strong>in</strong>;<br />
(1