Noise in AlGaN/GaN HEMTs and Oscillators - Microwave Electronics ...

Committee in charge:
UNIVERSITY of CALIFORNIA
Santa Barbara
Noise of AlGaN/GaN HEMTs and Oscillators
A dissertation submitted in partial satisfaction of the
requirements for the degree of
Professor Robert A. York, Chair
Professor Umesh K. Mishra
Professor Mark J. Rodwell
Dr. Yifeng Wu
Doctor of Philosophy
in
Electrical and Computer Engineering
by
Christopher Sanabria
June 2006

The dissertation of Christopher Sanabria is approved:
Chair
June 2006

Noise of AlGaN/GaN HEMTs and Oscillators
Copyright c○ 2006
by
Christopher Sanabria
iii

EDUCATION
Curriculum Vitæ
Christopher Sanabria
Bachelor of Science in Electrical Engineering, Magna Cum Laude, University of
Notre Dame, May 2001.
Master of Science in Electrical and Computer Engineering, University of California,
Santa Barbara, December 2002.
Doctor of Philosophy in Electrical Engineering, University of California, Santa Barbara,
June 2006.
PROFESSIONAL EMPLOYMENT
May 1998 - August 1998, Intern, Delphi-Delco Electronics, Kokomo, IN.
May 1999 - August 1999, Intern, Delphi-Delco Electronics, Kokomo, IN.
May 2000 - August 2000, Intern, Texas Instruments, Houston, TX.
September 2001 - March 2002, Teaching Assistant, Department of Electrical and
Computer Engineering, University of California, Santa Barbara.
June 2003 - September 2003, Intern, Agilent Labs, Agilent Technologies, Palo Alto,
CA.
March 2002 - May 2006, Research assistant, Department of Electrical and Computer
Engineering, University of California, Santa Barbara.
iv

PUBLICATIONS
S. Gao, C. Sanabria, H. Xu, S. Heikman, U. K. Mishra and R. A. York, MMIC Class-
F Power Amplifiers using Field-Plated GaN HEMTs, accepted IEEE Proceedings on
Microwave, Antennas and Propagation, 2006.
C. Sanabria, A. Chakraborty, H. Xu, M. J. Rodwell, U. K. Mishra, and R. A. York,
The Effect of Gate Leakage on the Noise Figure of AlGaN/GaN HEMTs, IEEE Electron
Device Letters, January 2006, pp. 19-21.
C. Sanabria, H. Xu, A. Chakraborty, M. J. Rodwell, U. K. Mishra, and R. A. York,
Noise Figure Measurements and Modeling of Field-Plated AlGaN/GaN HEMTs, International
Conference on Nitride Semiconductors, Bremen, Germany, August 2005.
C. Sanabria, H. Xu, S. Heikman, U. K. Mishra, R. A. York, A GaN Differential Oscillator
with Improved Harmonic Performance, IEEE Microwave and Wireless Components
Letters, July 2005, pp. 463-465.
H. Xu, C. Sanabria, S. Heikman, S. Keller, U. K. Mishra, and R. A. York, High
Power GaN Oscillators using Field-Plated HEMT Structure, IEEE Microwave Theory
and Technique International Microwave Symposium, June 2005.
C. Sanabria, H. Xu, T. Palacios, A. Chakraborty, S. Heikman, U. K. Mishra, R. A.
York, Influence of Epitaxial Structure in the Noise Figure of AlGaN/GaN HEMTs,
IEEE Microwave Theory and Technique Transactions, Vol. 53, February 2005, pp.
762-769.
H. Xu, C. Sanabria, Y. Wei, S. Heikman, S. Keller, U. K. Mishra, and R. A. York,
Characterization of two field-plated GaN HEMT structures, IEEE Topical Workshop
on Power Amplifiers for Wireless Communications, September 2004.
H. Xu, C. Sanabria, A. Chini, Y. Wei, S. Heikman, S. Keller, U. K. Mishra and R. A.
York, A new field-plated GaN HEMT structure with improved power and noise performance,
IEEE Lester Eastman Conference on High Performance Devices, August
2004.
H. Xu, C. Sanabria, A. Chini, S. Keller, U. K. Mishra, and R. A. York, A C-band
high-dynamic range GaN HEMT low-noise amplifier, IEEE Microwave and Wireless
Components Letters, Vol. 14, June 2004, pp. 262 264.
v

C. Sanabria, H. Xu, T. Palacios, A. Chakraborty, S. Heikman, U. K. Mishra, R. A.
York, Influence of the Heterostructure Design on Noise Figure of AlGaN/GaN HEMTs,
Device Research Conference, June 2004.
H. Xu, C. Sanabria, A. Chini, S. Keller, U. K. Mishra, and R. A. York, Robust Cband
MMIC Low Noise Amplifier using AlGaN/GaN HEMT Power Devices, 8th Wide-
Bandgap III-Nitride Workshop, September 2003.
vi

Abstract
Noise of AlGaN/GaN HEMTs and Oscillators
by
Christopher Sanabria
GaN HEMTs will likely become the solid-state device of choice for power in mi-
crowave and millimeter-wave circuits. These products, such as base stations and other
communication systems, tend to be space-constrained. Hence solutions continuously
move from a hybrid (circuit board plus components) approach to a microwave mono-
lithic integrated circuit (MMIC). To be successful in a MMIC design, GaN will have
to perform well in other areas besides power. One of the most crucial metrics of a
system is its noise. The noise of GaN devices and circuits has only been critically
examined in the last five years.
This work will investigate several aspects of the noise performance of GaN HEMTs.
Measurements of noise figure (NF) and low-frequency noise (LFN) are used to char-
acterize devices. Modeling useful for calculations and circuit simulation are applied,
with some introduced. Several studies of NF and LFN are presented. Some confirm
or challenge previous publications while others are new observations. Two differen-
tial oscillators were built to characterize the phase noise. As it is believed that GaN
vii

HEMTs will replace GaAs HEMTs in various applications, the NF, LFN, and phase
noise of the two are compared.
viii

Contents
List of Figures xii
List of Tables xvi
1 Introduction 1
1.1 Motivation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1
1.2 Literature Review of Noise in GaN HEMTs . . . . . . . . . . . . . . 5
1.3 Thesis Outline . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8
References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9
2 Noise Figure Modeling of AlGaN/GaN HEMTs 12
2.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12
2.2 Noise Sources . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13
2.2.1 Thermal Noise . . . . . . . . . . . . . . . . . . . . . . . . . 13
2.2.2 ShotNoise . . . . . . . . . . . . . . . . . . . . . . . . . . . 15
2.2.3 Other Sources of Noise . . . . . . . . . . . . . . . . . . . . . 16
2.3 Equivalent Circuit Model . . . . . . . . . . . . . . . . . . . . . . . . 17
2.4 Noise Figure and Noise Parameters . . . . . . . . . . . . . . . . . . . 21
2.5 HEMT Noise Figure Models . . . . . . . . . . . . . . . . . . . . . . 25
2.5.1 van der Ziel and Pucel Models . . . . . . . . . . . . . . . . . 25
2.5.2 Fukui Model . . . . . . . . . . . . . . . . . . . . . . . . . . 28
2.5.3 Pospieszalski Model . . . . . . . . . . . . . . . . . . . . . . 29
2.5.4 Pospieszalski and Correlated Noise Models Applied to Al-
GaN/GaN HEMTs . . . . . . . . . . . . . . . . . . . . . . . 31
2.6 A Proposed Noise Figure Model . . . . . . . . . . . . . . . . . . . . 35
2.6.1 Setup Details . . . . . . . . . . . . . . . . . . . . . . . . . . 36
2.6.2 Derivation of Noise Parameters . . . . . . . . . . . . . . . . 39
2.6.3 Derivation of Drain Noise Source . . . . . . . . . . . . . . . 44
2.6.4 Noise Parameter Scaling . . . . . . . . . . . . . . . . . . . . 49
2.6.5 Discussion of the Model . . . . . . . . . . . . . . . . . . . . 53
2.7 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 57
ix

References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 57
3 Noise Figure Measurements and Studies 60
3.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 60
3.2 Device Details . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 61
3.3 Noise Figure Measurement Setup and Method . . . . . . . . . . . . . 62
3.4 Bias Dependence . . . . . . . . . . . . . . . . . . . . . . . . . . . . 68
3.5 GaN HEMT Noise Figure Studies . . . . . . . . . . . . . . . . . . . 75
3.5.1 Substrate . . . . . . . . . . . . . . . . . . . . . . . . . . . . 75
3.5.2 Al Composition in the Barrier . . . . . . . . . . . . . . . . . 76
3.5.3 AlN Interlayer . . . . . . . . . . . . . . . . . . . . . . . . . 78
3.5.4 Gate Leakage . . . . . . . . . . . . . . . . . . . . . . . . . . 81
3.5.5 Field-Plated Devices . . . . . . . . . . . . . . . . . . . . . . 84
3.5.6 Thick-Epitaxial Cap Devices . . . . . . . . . . . . . . . . . . 91
3.6 Comparison of High-Performance GaN HEMTs to Other Material Systems
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 93
3.7 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 95
References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 96
4 Low-Frequency Noise of GaN HEMTs 101
4.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 101
4.2 Review of Low-Frequency Noise . . . . . . . . . . . . . . . . . . . . 102
4.3 Low-Frequency Noise Setup . . . . . . . . . . . . . . . . . . . . . . 107
4.4 GaN HEMT Low-Frequency Noise Modeling . . . . . . . . . . . . . 113
4.5 GaN HEMT Low-Frequency Noise Studies . . . . . . . . . . . . . . 119
4.5.1 Substrate . . . . . . . . . . . . . . . . . . . . . . . . . . . . 119
4.5.2 Passivation . . . . . . . . . . . . . . . . . . . . . . . . . . . 119
4.5.3 Thick-Epitaxial Cap Devices . . . . . . . . . . . . . . . . . . 121
4.5.4 Field-Plated Devices . . . . . . . . . . . . . . . . . . . . . . 122
4.6 Comparison to GaAs HEMTs . . . . . . . . . . . . . . . . . . . . . . 123
4.7 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 125
References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 126
5 GaN HEMT Based Oscillators 128
5.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 128
5.2 Concerning Phase Noise . . . . . . . . . . . . . . . . . . . . . . . . 129
5.3 MMIC Process Description . . . . . . . . . . . . . . . . . . . . . . . 134
5.4 Differential Oscillators . . . . . . . . . . . . . . . . . . . . . . . . . 135
5.4.1 High Linearity Oscillator . . . . . . . . . . . . . . . . . . . . 135
5.4.2 Low-Phase Noise Oscillator . . . . . . . . . . . . . . . . . . 140
5.5 Comparison to Other Oscillators . . . . . . . . . . . . . . . . . . . . 143
x

5.6 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 146
References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 147
6 Summary, Conclusions, and Future Directions 149
6.1 Summary and Conclusions . . . . . . . . . . . . . . . . . . . . . . . 149
6.2 FuturePaths . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 151
A ADS Files 154
A.1 Small-Signal Extraction . . . . . . . . . . . . . . . . . . . . . . . . . 155
A.2 Noise Figure Simulation . . . . . . . . . . . . . . . . . . . . . . . . 158
A.3 Correlated Noise Model Extraction . . . . . . . . . . . . . . . . . . . 160
B Matlab Code for Noise Parameter Modeling 163
C Matlab Code for Pospieszalski Noise Parameter Modeling 166
xi

List of Figures
1.1 Cartoon of a very simple transmitter. . . . . . . . . . . . . . . . . . . 2
1.2 Cartoon of a CDMA-like spectrum with four channels. . . . . . . . . 3
2.1 Cartoon showing the device small-signal model on a cross section of
a HEMT. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 18
2.2 Equivalent model of a transistor driven by a noisy source of impedance
Zsource. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 22
2.3 Noise and gain circles on a Smith Chart. . . . . . . . . . . . . . . . . 24
2.4 Pucel noise model in a small-signal circuit. . . . . . . . . . . . . . . 27
2.5 Pospieszalski noise model in a small-signal circuit. . . . . . . . . . . 29
2.6 Comparison of Correlated Noise and Pospieszalski models to measured
noise parameters versus frequency. . . . . . . . . . . . . . . . . 34
2.7 A simplified HEMT circuit model including noise sources. . . . . . . 36
2.8 Cartoon showing the effect of source degeneration. . . . . . . . . . . 38
2.9 Circuit model used for deriving noise figure. . . . . . . . . . . . . . . 39
2.10 Cartoon used for deriving the channel noise. . . . . . . . . . . . . . . 47
2.11 Variation in Γ for different drain and gate voltages. . . . . . . . . . . 49
2.12 Noise parameters versus total gate width. . . . . . . . . . . . . . . . 51
2.13 Noise parameters versus number of gate fingers for a constant total
gatewidth. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 52
2.14 Noise parameters predicted with the proposed model and compared to
measurements. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 53
2.15 Relative contributions of different noise sources to the overall noise
figure. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 55
3.1 Typical epitaxial structures for the devices in this work. . . . . . . . . 61
3.2 Schematic of the source-pull noise figure setup. . . . . . . . . . . . . 63
3.3 Coplanar waveguide attenuator. . . . . . . . . . . . . . . . . . . . . . 65
3.4 Noise factor, fτ and fmax for devices from different samples versus
current. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 65
xii

3.5 Variation in expected minimum noise figure with changes in three
small-signal parameters. . . . . . . . . . . . . . . . . . . . . . . . . 68
3.6 Change in noise parameters with drain-source voltage. . . . . . . . . 69
3.7 Typical plots of the noise parameters versus drain source current with
Correlated Noise and Pospieszalski models. . . . . . . . . . . . . . . 71
3.8 Noise variables for the Pospieszalski and a CN noise model versus
drain-source current. . . . . . . . . . . . . . . . . . . . . . . . . . . 73
3.9 Minimum noise figure, small signal associated and maximum gain for
devices on sapphire and SiC substrates. . . . . . . . . . . . . . . . . 75
3.10 Noise parameters versus frequency for devices of different aluminum
composition in the barrier. . . . . . . . . . . . . . . . . . . . . . . . 77
3.11 Minimum noise figure of samples with different aluminum composition
in the barrier at varying drain-source current. . . . . . . . . . . . 78
3.12 Minimum noise figure, fτ, and fmax versus drain-source current for a
sample with and without an AlN interlayer. . . . . . . . . . . . . . . 79
3.13 (a) Associated and maximum gain and (b) source resistance for devices
with and without an AlN interlayer at different applied currents. 80
3.14 (a) Minimum noise figure, (b) device associated gain, and maximum
gain versus frequency for devices with different gate leakage currents 82
3.15 Simulated (line) and measured (crosses) noise parameters for devices
with different gate leakage currents. . . . . . . . . . . . . . . . . . . 83
3.16 fτ and fmax of devices with different field-plate lengths. . . . . . . . . 84
3.17 Noise parameters versus frequency for devices with field plates of differentlength.
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 85
3.18 Typical change in gate leakage for devices of increasing field-plate
length. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 87
3.19 Electric field profile for a device with and without a field plate. . . . . 87
3.20 Small-signal parameters that change with a field plate. . . . . . . . . 89
3.21 Minimum noise figure versus gate width for devices with and without
a longfieldplate. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 90
3.22 Minimum noise figure of the field-plated devices at different measurement
frequencies. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 90
3.23 Noise parameters versus drain-source current of a thick cap device
(triangles) and a standard HEMT (squares). . . . . . . . . . . . . . . 92
3.24 Minimum noise figure of two 0.15 µm gate length transistors provided
by Tomás Palacios. . . . . . . . . . . . . . . . . . . . . . . . . . . . 95
4.1 Sketch of the key features of low-frequency noise. . . . . . . . . . . . 103
4.2 Variation of α with (a) drain-source voltage bias and (b) frequency of
extraction for two devices on the same sample. . . . . . . . . . . . . 106
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4.3 Measured noise floor of the HP 3561A DSA only and with the SRS
SR560 LNA (short-circuited input). . . . . . . . . . . . . . . . . . . 109
4.4 Schematic of the setup used for device drain-side low-frequency noise
measurements. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 110
4.5 A typical low-frequency plot. . . . . . . . . . . . . . . . . . . . . . . 112
4.6 Plots of the measured drain low-frequency noise with (a) change in
drain-source current and (b) voltage. . . . . . . . . . . . . . . . . . . 114
4.7 Measured gate low-frequency noise versus gate-source voltage (and
current). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 115
4.8 Change in low-frequency noise with gate width at various decade frequencies
for three devices. . . . . . . . . . . . . . . . . . . . . . . . 116
4.9 Change in low-frequency noise with gate length. . . . . . . . . . . . . 116
4.10 Proposed low-frequency noise modeling of the HEMT with a gate and
drain noise source. . . . . . . . . . . . . . . . . . . . . . . . . . . . 117
4.11 Measurement of devices on a sapphire and SiC substrate at a bias of
Vds 5V,Ids 30mA . . . . . . . . . . . . . . . . . . . . . . . . . . . 120
4.12 (a) Low-frequency noise of a device before and after passivation. (b)
Low-frequency noise at 10 Hz and 1 kHz of a device before and after
passivation at different Vgs . . . . . . . . . . . . . . . . . . . . . . . . 120
4.13 Comparison of standard passivated HEMTs to an unpassivated thick
cap HEMTs. Bias is Vds =5VandIds = 30 mA. . . . . . . . . . . . . 122
4.14 Low-frequency noise of field-plated devices. . . . . . . . . . . . . . . 123
4.15 Low-frequency noise comparison of GaN and GaAs HEMTs. . . . . . 124
5.1 Examples of typical phase noise plots. . . . . . . . . . . . . . . . . . 131
5.2 Circuit schematic of the oscillator (biasing not shown). . . . . . . . . 136
5.3 Photograph of the high linearity oscillator. . . . . . . . . . . . . . . . 136
5.4 Measurements of the oscillator: (a) power spectrum (b) frequency
pulling. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 138
5.5 Output power, second harmonic power, and efficiency of the highlinearity
oscillator. . . . . . . . . . . . . . . . . . . . . . . . . . . . 138
5.6 Circuit schematic of the low-phase noise oscillator (biasing not shown). 140
5.7 Photograph of the low-phase noise oscillator. . . . . . . . . . . . . . 141
5.8 Measured phase noise of the oscillator. . . . . . . . . . . . . . . . . . 142
5.9 Phase noise at 100 kHz and 1 MHz offsets versus drain-source bias
for a few oscillators. . . . . . . . . . . . . . . . . . . . . . . . . . . . 142
5.10 Relative comparison of GaN oscillator to a typical oscillator with low
phase noise. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 146
A.1 First page of template small signal parameter extraction.dds. . . . . 156
xiv

A.2 Schematic used for simulating S-parameters of the small-signal circuit
and for optimization. . . . . . . . . . . . . . . . . . . . . . . . . . . 158
A.3 Schematic used for simulating noise parameters. . . . . . . . . . . . . 159
A.4 Schematic used for extracting correlated noise model noise variables. 162
A.5 Data display used for extracting correlated noise model noise variables. 162
xv

List of Tables
2.1 Extracted small-signal parameters for various samples. Devices have
a gate geometry of 0.7 × 150 µm. . . . . . . . . . . . . . . . . . . . 21
2.2 Comparison of Pospieszalski and Correlated Noise models to measured
data. Devices have a gate geometry of 0.7 × 150 µm . . . . . . 33
2.3 Comparison of the various noise models’ input and output noise currents. 56
3.1 Minimum noise figure for devices in many technologies. . . . . . . . 94
5.1 Comparison of GaN oscillators from this and other works to oscillators
in other materials (FET, MMICs, only). . . . . . . . . . . . . . . 144
xvi

Acknowledgements
BEHIND the candy Santa Barbara exterior of sun, perfect weather, surfing, and
tourists is a university that is a powerhouse of research that I didn’t have the
foggiest idea existed until I decided to come to graduate school. I’ve been impressed
with the faculty, facilities, labs, peers, and the graduate sciences and engineering programs
at UCSB. It has made for a great research experience and I want to thank and
acknowledge all those who have helped me along the way toward getting my Ph.D.
I would first like to thank my advisor Professor Robert York. Not only did he
take me in, he has provided (along with my co-advisor) five years of constant, uninterrupted,
financial support. Watching peers struggle with funding shortfalls and
changing projects has made me realize what a blessing funding is. I would also like
to thank him for giving me a great deal of freedom. This was frightening for me at
first as I thought I would become lost, but later I realized what research I wanted to do
and was able to do it without restraint. Professor York has always steered me in the
right direction on important matters of publications, research, and things in general.
We had many good, frank, talks that I enjoyed.
I thank my co-advisor Professor Umesh Mishra for many things. The first is the
amusement of watching someone juggle the work of five men like some god with 10
arms. Yet, when I needed to discuss work, we always got a few minutes in and I never
felt pushed away. I also salute the GaN program he has put together at UCSB. Umesh
is one of the smartest, and slyest, individuals I have met and it was fun to be around
for the show. I also really appreciate the happy hours he would host.
My other committee members, Professor Mark Rodwell and Dr. Yifeng Wu, have
been a great help to me not only in preparing the thesis but in important research
discussions over the years. Professor Rodwell’s class notes on noise and exchanges
have steered me through to the basic truths about noise figure. With Dr. Wu I’ve had
many conversations: load-pull, noise, circuits, and even high-end audio equipment. I
have enjoyed it all. I also thank Professor Long for the conversations that we have
had.
My peers in the trenches have been of tremendous help toward this work. Hongtao
Xu taught me his fabrication techniques for MMICs and offered very useful suggestions
for my microwave circuits. We worked collectively on several projects and became
friends. Tomás Palacios, the wonder Spaniard, has been of tremendous help. His
enormous curiosity, knowledge, and keen eye helped me out several times by pointing
me in the right direction or giving me inspiration that lead to useful research. My
group mates (past and present), Nadia, Val, Raj, Jaehoon, Jiwei, Justin, Paolo (e-lo?),
Vicki, Conradin, Jim, and Pengcheng have helped me out many a time (or helped provide
a refreshing work break). The small army known as Professor Mishra’s group
have also helped a great deal: Rob, Siddarth, Likun (Mona), Mike, Dario, Arpan, Ale,
Naiqian, Sten, Lee M., Ilan, Yuvaraj, Felix, Pei Yi, Eric, Chang, Chris, Jeff, Karl, and
xvii

Man Hoi. I would especially like to thank those who grew my material for devices and
circuits, Arpan, Sten, Stacia, and Nick, without whom I would have had no project.
I also had useful discussions with students in the groups of both Professors Rodwell
and Long. I had many conversations, interactions, and chats with Vikas and Joe,
whose projects focused heavily on phase noise. Vikas also provided the GaAs devices
that were measured in this work and both of them helped with equipment and setups.
Navin, Zack, and Paidi all gave me some useful information at one point or another.
Also, I had discussions with Adam about low-frequency noise and Professor Elliot
Brown let me borrow some equipment from his personal collection for a measurement.
I thank Agilent and Maury for their technical support on various pieces of equipment
(I called a lot). I am greatful to the cleanroom staff (Jack, Bob, Neil, Tom,
Brian T., Bill, Don, Mike, Luis and Ning) who kept our excellent facilities going 24x7
and for being available for the occasional evening crisis. The assistants over the year
(Masika, Pam, Emeka, Lee B., and Laura) have been a big help with red tape. I thank
Val de Veyra and the other assistants in the ECE graduate student office, with whom I
had a good laugh because of a non-unique nickname in my email address book.
I very much thank Dr. Harry Dietrich and the Office of Naval Research (ONR) who
funded and oversaw the Center for Advance Nitride Electronics (CANE) program that
I was on.
I would also like to thank Dr. Joy Vann-Hamilton. Joy, who was director of the
Minority Engineering Program (MEP) while I was an undergraduate at the University
of Notre Dame, listened to all my unhappy college complaints, pointed me toward
resources that got me through undergraduate, and is solely responsible for my going
to graduate school. Grad school wasn’t even on my radar and I didn’t think I had the
talent. I can’t thank her enough.
As if I hadn’t thanked enough people and entities, I would also like to thank all my
friends who made my time here enjoyable (even if it was jokes at my expense, Perk
and Dave). Also, I don’t know what my parents did that I turned out the way I did,
but I want to give them applause for all that they have done. Don’t worry, I won’t do
anything to embarrass you like I did at high school graduation.
Finally, no stay in Santa Barbara is complete without picking up a wife. Sarah, who
would have guessed we would meet here instead of at Notre Dame? I thank you for
handling all my rants with grace, giving me hope when I had none, distracting me so I
would realize there are a whole lot of interesting things to do in the world, and being
some one worth living for.
“Thanks y’all”...
xviii

For those who never quit.
xix

1.1 Motivation
1
Introduction
GALLIUM nitride (GaN) and its related compound materials, indium nitride
(InN) and aluminum nitride (AlN), have already been commercialized for
several applications. This is an impressive feat for an immature technology where each
year research continues to bring improvements. The reason for this rush to market is
the needs the nitrides are addressing. For optical applications, GaN-based solutions
include LEDs, lasers, and detectors in the UV and blue wavelengths. For electronic
applications, GaN high electron mobility transistors (HEMTs) provide some of the
highest microwave power performance to be found from solid state devices.
GaN-based electronics have two major setbacks. The first is the cost. This re-
sults largely from the expensive substrates needed, with the better substrates currently
costing nearly an order of magnitude more than lower-performance options. The other
hurdle is growth immaturity, which causes reliability to be mediocre. Because of these
disadvantages, if another material system (Si, GaAs, InP, etc.) can meet the needs of an
1

CHAPTER 1. INTRODUCTION
application, industry will choose it over GaN. This means GaN HEMTs are being con-
sidered mainly for power amplifiers in microwave products such as base stations [1,2].
Industry has a great need for these products to be compact. Designers continuously
move from hybrid (a circuit board with discrete components) to integrated (a single,
small chip) solutions. Instead of a chip with just a power amplifier, it is preferred to
have the amplifier, and complete transmit and receive paths, in a single chip called a
front-end module (FEM). Figure 1.1 shows an example of a simple transmitter, and the
preferred integration boundary of power amplifier plus other components. It may be
possible that GaN monolithic microwave integrated circuits (MMICs) provide better
performance in terms of power, radiation hardness, and operation temperature, leading
to future products.
From
DSP
Modulator
Oscillator
Mixer Filter Power
Amp.
Ideally implemented as a single transmitter MMIC
Figure 1.1: Cartoon of a very simple transmitter.
2
Antenna

CHAPTER 1. INTRODUCTION
Power
Channel
Width
Channel
Space
Noise
Side
Band
Frequency
Noise
Floor
Figure 1.2: Cartoon of a CDMA-like spectrum with four channels.
Basic GaN MMIC building blocks are now appearing in the literature [3–7], and
it is only a matter of time before GaN transmit and receive MMICs are made. An
important metric of such circuits will be their noise performance. In particular, phase
noise and noise figure (NF) are common figures of merit for characterizing noise. A
main focus of this work is examining these aspects of GaN HEMTs and oscillators.
Communication channel spacing is set based on specifications of the maximum
noise a channel will produce out-of-band. This is shown in figure 1.2. Setting the
space between channels as small as possible is extremely important due to regulated
bandwidth restrictions. 1 Typically the component that sets the minimum on this noise
1In fact, whenever the Federal Communications Commission (FCC) auctions bandwidth the selling
price is in the hundreds of millions [8].
3

CHAPTER 1. INTRODUCTION
performance is an oscillator in the circuit, as in figure 1.1. An oscillator provides
a signal source at a (usually variable) reference frequency. In addition, oscillators
produce a large amount of noise at frequencies close to the reference frequency. This
is called phase noise.
It is understood that various device noise sources contribute to the phase noise.
These include thermal, shot, and low-frequency (also called flicker, or 1/f) sources.
The quantitative analysis of how these sources contribute to the phase noise is difficult
even for the simplest of cases. A qualitative description that embodies many important
points was presented by Leeson [9], and is described as
⎡
L (∆ω) = 10 log ⎣ 2FkT
Psig
⎧
⎨
⎩ 1+
� ω0
2Q∆ω
� ⎫
2 �
�
⎬ ∆ω1/f 3
1+
⎭ |∆ω|
⎤
⎦ (1.1.1)
where the script L is the phase noise in a 1 Hz bandwidth at an offset angular fre-
quency, ∆w, from the carrier angular frequency, ω0, Q is the quality of the resonator,
Psig the signal power, and F the effective noise figure. 2 Shot and thermal noise sources
contribute to F, a measure of the background noise of the device and circuit. The low-
frequency noise (LFN) contributes through ∆ω1/f 3, a corner frequency for the phase
noise that presumably relates to the corner frequency of the LFN. From equation 1.1.1,
we can discern that knowledge of the noise sources in the device and circuit will help
in understanding the phase noise, and if we can reduce them the phase noise will be
2 The parameter F here is not the device noise figure or factor but an “Effective noise figure” which
some see as just a fitting parameter. F in this chapter should not be confused with noise factor in the
other chapters.
4

CHAPTER 1. INTRODUCTION
improved. Leeson’s equation also tells us that if Psig can be increased, we should
see an improvement in phase noise. Because GaN devices are capable of providing
an order of magnitude more power than gallium arsenide (GaAs) devices, the next
best commercial material, it is of great interest to know if the phase noise of GaN
circuits can be better than GaAs circuits. One of the goals of this work is to answer
this question.
This dissertation will look at several aspects of the noise performance of GaN
HEMTs. NF and LFN measurements are used to evaluate the noise performance of
the GaN HEMTs. Comparisons are made to measurements of GaAs HEMTs, the most
similar commercial device, which GaN is trying to displace. Models for NF and LFN
noise, some old and some new, are presented. To study the phase noise, differen-
tial oscillators were constructed and measured. Their performance is explained in the
context of LFN.
A quick review of previous noise measurements and studies of GaN HEMTs and
oscillators is now presented, followed by a sketch of this work.
1.2 Literature Review of Noise in GaN HEMTs
This section gives a short background of the GaN HEMT literature for NF, LFN,
and phase noise prior to this work (late 2002). Most publications after this point in
time are already referenced throughout the work. More background information on
5

CHAPTER 1. INTRODUCTION
each noise subject can also be found at the beginning of its respective chapter.
Of the three types of noise measurements performed on GaN HEMTs, LFN has
the longest history. Reports of measurements first started to appear in 1998 [10, 11].
Because LFN measurements can be used as a way of monitoring crystal quality, some
reports came from materials scientists [12]. Physicists have measured GaN LFN and
are using some of the following arguments to explain it: tail states near the band gap
edge [11], mobility fluctuations [13], and tunneling of electrons from the channel to
traps in surrounding layers [12]. No theory is yet accepted as the best explanation.
Various other LFN papers have appeared [12,14–16]. Most measurements are at very
low biasings such that the device is in the linear region. The only publication that stud-
ies gate and drain LFN for the full biasing range of a GaN HEMT is Hsu et al. [17].
This paper will be returned to in chapter 4. Due to the use of the Hooge parame-
ter, the devices not being optimized HEMTs (some are doped channel HFETs), and
measurements only in the linear region, many of the above results are not of use to a
circuit designer or device engineer who is trying to characterize and optimize LFN.
Accurate measurements of LFN can also be difficult. Therefore, this work presents
measurements and modeling of LFN that will be of use to the engineering community.
The first published NF report for a GaN HEMT was performed by Ping in 2000 [18].
For a 0.25 x 100 µm gate device, a minimum noise figure (NFmin) of 1.06 dB and a
gain of 12 dB at a frequency of 10 GHz was demonstrated. This was followed shortly
6

CHAPTER 1. INTRODUCTION
by Nguyen [19], presenting a NFmin of 0.6 dB at 10 GHz and 13.5 dB gain with a
0.15 x 100 µm gate. Other results [20, 21], with improved performance, followed
the next year. After optimizing the device geometry, Moon showed in 2002 that a
GaN HEMT could present similar NF at a similar biasing to a GaAs HEMT [22]. The
next notable result in the field was when Lu showed that GaN HEMTs on a sapphire
substrate can have similar NFmin performance to HEMTs on a SiC substrate [23]. All
previously published results had been on SiC substrates. This work seeks to extend
on the noise figure literature and to confirm or deny some of the previously published
results, in addition to adding new studies. Table 3.1 lists many GaN (as well as GaAs,
SiGe, and InP) HEMT NF results.
Prior to this work, GaN oscillator references were scarce. The first GaN oscillator
was reported by Shealy in 2001 [24]. The phase noise was respectable: -92 dBc at
100 kHz for a 6 GHz carrier frequency. While Shealy’s work was a hybrid design, the
first MMIC oscillator was presented by Kaper in 2002 [25]. He estimated (but did not
show measurements) the phase noise to be -87 dBc at 100 kHz. These works left room
for further investigation. A summary of all published GaN oscillators appears in table
5.1.
The existing literature was thin at the beginning of this project. The noise research
of GaN has since approximately doubled to tripled. Because noise is difficult to mea-
sure, second and third opinions are valuable. This work will do this, in addition to its
7

CHAPTER 1. INTRODUCTION
own unique studies and modeling.
1.3 Thesis Outline
Chapter 2 builds up to a NF model. This model is an extension of previous mod-
els and fills the need of understanding how various noise sources and small-signal
parameters influence NF and other noise parameters without the need for prior NF
measurements. The chapter starts with reviews of noise sources, the equivalent circuit
model, NF and parameters, and previous models. The proposed model is then derived
and discussed in detail.
With the modeling in place, several NF studies are presented in chapter 3. Effects
of bias and gate leakage are studied. Different epitaxial structures are compared, as
is the addition of a field plate. High-frequency GaN HEMT devices were borrowed,
measured, and compared to HEMTs in other technologies (in particular, GaAs).
A LFN setup was constructed and measurements performed to help understand the
phase noise performance. Chapter 4 covers these results. It first shows through mea-
surements why the Hooge parameter should not be used for comparing devices (only
materials). LFN versus bias shows the need for an improved model for the drain noise,
which was then added. LFN studies are then presented and comparisons to measured
GaAs HEMTs are made.
Differential oscillators are constructed in chapter 5 and phase noise is measured
8

CHAPTER 1. INTRODUCTION
and evaluated. The first version had excellent linearity but poor phase noise. A second
version had good phase noise. The oscillators are compared to other published GaN
oscillators and to differential oscillators in Si and GaAs technologies.
References
[1] T. Kikkawa, T. Maniwa, H. Hayashi, M. Kanamura, S. Yokokama, M. Nishi,
N. Adachi, M. Yokoyama, Y. Tateno, and K. Joshin, “An Over 200-W Output
Power GaN HEMT Push-Pull Amplifier with High Reliability,” IEEE Microwave
Theory and Tech. Symp., pp. 1347–1350, 2004.
[2] Y. Okamoto, Y. Ando, T. Nakayama, K. Hataya, H. Miyamoto, T. Inoue, M. Senda,
K. Hirata, M. Kosaki, N. Shibata, and M. Kuzuhara, “High-Power Recessed-Gate
AlGaNGaN HFET With a Field-Modulating Plate,” IEEE Trans. Electron Devices,
vol. 51, no. 12, pp. 2217–2222, Dec. 2004.
[3] H. Ishida, Y. Hirose, T. Murata, Y. Ikeda, T. Matsuno, K. Inoue, Y. Uemoto,
T. Tanaka, T. Egawa, and D. Ueda, “A High-Power RF Switch IC Using Al-
GaN/GaN HFETs with Single-Stage Configuration,” Electron Devices, IEEE
Transactions on, vol. 52, no. 8, pp. 1893–1899, 2005.
[4] H. Xu, C. Sanabria, A. Chini, S. Keller, U. Mishra, and R. A. York, “Low Phase-
Noise 5 GHz AlGaN/GaN HEMT Oscillator Integrated with BaxSr1−xTiO3 Thin
Films,” IEEE Microwave Theory and Tech. Symp., pp. 1509–1512, 2004.
[5] V. Kaper, R. Thompson, T. Prunty, and J. Shealy, “Signal Generation, Control,
and Frequency Conversion AlGaN/GaN HEMT MMICs,” Microwave Theory and
Techniques, IEEE Transactions on, vol. 53, no. 1, pp. 55–65, 2005.
[6] G. Ellis, J.-S. Moon, D. Wong, M. Micovic, A. Kurdoghlian, P. Hashimoto, and
M. Hu, “Wideband AlGaN/GaN HEMT MMIC Low Noise Amplifier,” in Microwave
Symposium Digest, 2004 IEEE MTT-S International, vol. 1, 2004, pp.
153–156 Vol.1.
[7] H. Xu, C. Sanabria, A. Chini, S. Keller, U. Mishra, and R. York, “A C-Band High-
Dynamic Range GaN HEMT Low-Noise Amplifier,” IEEE Microwave Components
Lett., vol. 14, no. 6, pp. 262–264, Jun. 2004.
[8] R. Rast, “The Dawn of Digital TV,” Spectrum, IEEE, vol. 42, no. 10, pp. 26–31,
2005.
[9] D. Leeson, “A Simple Model of Feedback Oscillator Noise Spectrum,” Proc. IEEE,
vol. 54, no. 2, pp. 329–330, 1966.
9

CHAPTER 1. INTRODUCTION
[10] D. V. Kuksenkov, H. Temkin, R. Gaska, and J. W. Yang, “Low-Frequency Noise
in AlGaN/GaN Heterostructure Field Effect Transistors,” IEEE Electron Devices
Lett., vol. 19, no. 7, pp. 222–224, July 1998.
[11] M. E. Levinshtein, F. Pascal, S. Contreras, W. Knap, S. L. Rumyantsev, R. Gaska,
J. W. Yang, and M. S. Shur, “Low-Frequency Noise in GaN/GaAlN Heterojunctions.”
Applied Physics Letters, vol. 72, no. 23, pp. 3053–5, June 1998.
[12] A. Balandin, Ed., Noise and Fluctuations Control in Electronic Devices. Stevenson
Ranch, CA: American Scientific Publishers, 2002.
[13] J. A. Garrido, B. E. Foutz, J. A. Smart, J. R. Shealy, M. J. Murphy, W. J. Schaff,
L. F. Eastman, and E. Munoz, “Low-Frequency Noise and Mobility Fluctuations
in AlGaN/GaN Heterostructure Field-Effect Transistors.” Applied Physics Letters,
vol. 76, no. 23, pp. 3442–4, June 2000.
[14] M. Levinshtein, S. Rumyantsev, M. Shur, R. Gaska, and M. Khan, “Low Frequency
and 1/f Noise in Wide-Gap Semiconductors: Silicon Carbide and Gallium Nitride,”
Circuits, Devices and Systems, IEE Proceedings [see also IEE Proceedings G-
Circuits, Devices and Systems], vol. 149, no. 1, pp. 32–39, 2002.
[15] A. Balandin, S. Morozov, S. Cai, R. Li, K. Wang, G. Wijeratne, and
C. Viswanathan, “Low Flicker-Noise GaN/AlGaN Heterostructure Field-Effect
Transistors for Microwave Communications,” Microwave Theory and Techniques,
IEEE Transactions on, vol. 47, no. 8, pp. 1413–1417, 1999.
[16] S. Rumyantsev, N. Pala, M. Shur, M. Levinshtein, R. Gaska, X. Hu, J. Yang,
G. Simin, and M. Khan, “Low Frequency Noise in GaN-Based Transistors,” in
High Performance Devices, 2000. Proceedings. 2000 IEEE/Cornell Conference
on, 2000, pp. 257–264.
[17] S. Hsu, P. Valizadeh, D. Pavlidis, J. Moon, M. Micovic, D. Wong, and T. Hussain,
“Characterization and Analysis of Gate and Drain Low-Frequency Noise in
AlGaN/GaN HEMTs,” in High Performance Devices, 2002. Proceedings. IEEE
Lester Eastman Conference on, 2002, pp. 453–460.
[18] A. Ping, E. Piner, J. Redwing, M. Khan, and I. Adesida, “Microwave Noise Performance
of AlGaN/GaN HEMTs,” Electron. Lett., vol. 36, no. 2, pp. 175–176, Jan.
2000.
[19] N. Nguyen, M. Micovic, W.-S. Wong, P. Hashimoto, P. Janke, D. Harvey, and
C. Nguyen, “Robust Low Microwave Noise GaN MODFETs with 0.6 dB Noise
Figure at 10 GHz,” IEEE Electron. Lett., vol. 36, pp. 469–471, March 2000.
[20] S. Hsu and D. Pavlidis, “Low Noise AlGaN/GaN MODFETs with High Breakdown
and Power Characteristics,” Gallium Arsenide Integrated Circuit (GaAs IC)
Symposium, 2001. 23rd Annual Technical Digest, pp. 229–232, Oct. 2001.
10

CHAPTER 1. INTRODUCTION
[21] W. Lu, J. Yang, M. Khan, and I. Adesida, “AlGaN/GaN HEMTs on SiC with over
100 GHz fT and Low Microwave Noise,” IEEE Trans. Electron Devices, vol. 48,
no. 3, pp. 581–585, Mar. 2001.
[22] J. Moon, M. Micovic, A. Kurdoghlian, P. Janke, P. Hashimoto, W.-S. Wong, L. Mc-
Cray, and C. Nguyen, “Microwave Noise Performance of AlGaNGaN HEMTs
With Small DC Power Dissipation,” IEEE Electron Devices Lett., vol. 23, no. 11,
pp. 637–639, Nov. 2002.
[23] W. Lu, V. Kumar, R. Schwindt, E. Piner, and I. Adesida, “DC, RF, and Microwave
Noise Performance of AlGaN/GaN HEMTs on Sapphire Substrates,” IEEE Trans.
Microwave Theory Tech., vol. 50, pp. 2499–2503, Nov. 2002.
[24] J. B. Shealy, J. A. Smart, and J. R. Shealy, “Low-Phase Noise AlGaN/GaN FET-
Based Voltage Controlled Oscillators (VCOs),” IEEE Microwave Components
Lett., vol. 11, no. 6, pp. 244–245, Jun. 2001.
[25] V. Kaper, V. Tilak, H. Kim, R. Thompson, T. Prunty, J. Smart, L. F. Eastman, and
J. Shealy, “High Power Monolithic AlGaN/GaN HEMT Oscillator,” IEEE GaAs
Digest, pp. 251–254, 2002.
11

2
Noise Figure Modeling of AlGaN/GaN
HEMTs
2.1 Introduction
TO characterize, compare, and improve the noise performance of devices, a
theoretical framework is needed that identifies the noise sources, how these
sources contribute to the overall noise, and how the noise changes with other param-
eters, such as bias and matching conditions. A common approach is to add discrete
noise sources to a small-signal model [1–3]. Depending on the model, the sources may
be correlated, adding complexity to the derivation and interpretation of the particular
model.
This chapter first fills in background for the model. Noise sources of interest to
noise figure (NF) are reviewed, as is a full small-signal model. NF is then defined
in § 2.4, along with the noise parameters NFmin , Γopt and rn. Those familiar with
noise sources, NF, and small-signal modeling could skip these sections and continue
on to § 2.5. The more widely-used models are presented along with their strengths
12

CHAPTER 2. NOISE FIGURE MODELING OF ALGAN/GAN HEMTS
and weaknesses in § 2.5. Noise modeling derived from these previous models is then
introduced. Its strengths and weaknesses are also discussed. Finally, the NF model
is used for simulation of device noise figure performance of AlGaN/GaN HEMTs,
compared to other models, and discussed in depth.
2.2 Noise Sources
The two most common types of noise are shot and thermal noise. Both are referred
to as “flat” or “white,” meaning the noise power versus frequency is constant. Each
will be reviewed in this section. The relevance of other noise sources to NF is also
discussed.
2.2.1 Thermal Noise
Thermal noise was first studied in detail by Johnson in 1927 [4], and explained
mathematically by Nyquist [5]. Its physical origin is the agitation of electrons in a
conductor. The random scattering of electrons by atoms followed by their relaxation
back to a ground state leads to fluctuations that can be measured as a voltage or current.
The use of statistical analysis and thermal physics [6] leads to the following expression
that represents the available noise power from a resistance into a matched load
PT hermal =
⎡
⎣ hf
2 +
13
exp � hf
kT
⎤
hf
� ⎦ ∆f (2.2.1)
− 1

CHAPTER 2. NOISE FIGURE MODELING OF ALGAN/GAN HEMTS
where h is Planck’s constant, k is Boltzmann’s constant, T is temperature, and f is the
frequency.
The term ∆f is the bandwidth in which the noise is being measured. To determine
the total noise coming from, for example, an amplifier, this expression would be inte-
grated over the bandwidth of the amplifier. A noise measurement might be performed
over a small bandwidth, less than one Hertz for some low-frequency noise measure-
ments, showing the need to keep this fact in mind. When values are quoted and a
bandwidth is not specified, it is assumed to be a 1 Hz bandwidth. This convention is
followed in this work.
Equation 2.2.1 is a general expression, and is needed if operating at cryogenic tem-
peratures or extreme frequencies (such as the THz range). For most engineering pur-
poses, the simpler expression
PT hermal ≈ kT∆f (2.2.2)
can be used. A handy value from this expression is that the available noise at room
temperature in a 1 Hz bandwidth is -174 dBm (4 × 10 −21 W).
When the load is not matched, or the noise needs to be expressed as a voltage or
current (described by a variance), the following forms are useful:
�
v 2 �
n =4kTR∆f (2.2.3)
�
i 2 �
n = 4kT
∆f (2.2.4)
R
14

CHAPTER 2. NOISE FIGURE MODELING OF ALGAN/GAN HEMTS
R is the resistance of the noise generating material or medium. A 1kΩ resistor gener-
ates 4 nV/ √ Hz of noise. Not every resistor represented in a circuit schematic generates
noise. For example, rπ in a bipolar transistor is a manifestation of the transistor’s I-V
characteristics, and is not a real resistance.
Ideal reactive components do not generate noise. However, because real inductors
and capacitors are lossy, the circuit-modeled parasitic resistances of these components
will generate thermal noise. Also, these components shape the bandwidth of the noise
in ways similar to shaping a signal.
Finally, the above equations only apply at thermal equilibrium. A biased transistor
is not at thermal equilibrium. However, a small-signal model of a HEMT, which does
not include bias, can have its parasitic resistances considered at thermal equilibrium.
Later, in § 2.6.3, the channel noise, which is a form of non-equilibrium thermal noise,
are derived. Further information on thermal noise can be found in [6–9].
2.2.2 Shot Noise
Shot noise was reported and explained by W. Schottky in 1918. The analogy of this
noise to buck shot being dropped into a bucket is the basis for its name [8]. Shot noise
exists when two conditions are met: (1) a DC current is flowing and (2) the charge
carriers composing the DC current cross a potential barrier. This second condition
is why resistors and the channel of a HEMT do not generate shot noise. The noise
15

CHAPTER 2. NOISE FIGURE MODELING OF ALGAN/GAN HEMTS
exists because charge is discrete and will cross the potential barrier at random times.
If the charge crossed at the same time or equal time intervals, the spectrum of the shot
noise would not be white and could be better dealt with in circuit design (possibly by
filtering).
As with thermal noise, shot noise is not constant at all frequencies. The noise de-
creases at frequencies above which the transit time across the barrier is short compared
to the inverse of this frequency [7]. Because devices are operated at frequencies well
below this, the noise can be considered flat [7].
Using math from random processes [9], shot noise is describe by the following
equation for current fluctuations:
�
i 2 �
n =2qIDC∆f (2.2.5)
with q being electronic charge (1.6 × 10 −19 C), IDC the DC current (Amps), and ∆f
again the bandwidth of interest.
2.2.3 Other Sources of Noise
Shot and thermal are the important noise sources for NF modeling. Others exist, and
at frequencies lower than RF should be considered. They will be briefly mentioned
here. Flicker and generation-recombination noise (covered in detail in chapter 4) are
important for oscillator phase noise, but are not of concern for NF measurements in
the RF frequency range. Burst noise is interpreted as a type of low-frequency noise
16

CHAPTER 2. NOISE FIGURE MODELING OF ALGAN/GAN HEMTS
with a 1/f 2 spectrum. It also would not affect NF measurements in the GHz range, nor
has it been reported in GaN-based HEMTs. Avalanche noise is a form of shot noise,
and usually applies to a semiconductor junction. With a high enough field across a
junction, avalanche multiplication can occur [10]. This increase in carriers leads to
an increase in the shot noise proportional to the cube of the multiplication factor [9].
While the fields can be very high, no evidence has been shown that this type of noise
appears in GaN-based HEMTs. As will be seen in modeling later, shot and thermal
types of noise are sufficient to predict the noise figure of GaN HEMTs.
2.3 Equivalent Circuit Model
A small-signal model will be used in determining the device noise figure. Device
small-signal modeling has been covered extensively in the literature [11–17]. Here
a short summary will be given. The model used in this work is superimposed on
the cross section of a HEMT in figure 2.1. The parameters are bias-dependent but
frequency independent. In this chapter and chapter 3, the parameters are extracted at
the bias of best device minimum noise figure performance.
At the heart of the model is the gate-source capacitance, Cgs, and the transconduc-
tance, gm. The phase associated with gm, ωτ, is a necessary delay that accounts for
channel charge to redistribute after a change in gate voltage. The drain-source resis-
tance, Rds, is a measure of how effectively a signal can be extracted from the device.
17

CHAPTER 2. NOISE FIGURE MODELING OF ALGAN/GAN HEMTS
Ls
Rs
Vc +
-
Source Gate
Cpgs
Cgs
Ri
g me jwτ v c
R ds
Cds
Rgd
C gd
Cpds
Lg
R g
Rd
Cpgd
L d
Drain
Figure 2.1: Cartoon showing the device small-signal model on a cross section of a
HEMT.
This is because it will reduce the effective load of the device. There are two primary
causes for its degradation: conduction in the buffer due to poor growth (traps) and
spread of electrons from the 2DEG when the device is under extreme biasing (very
high electric fields).
The channel and gate-drain resistances, Ri and Rgd, have vague physical interpre-
tations. Ri is regarded as either a physical channel resistance or charging resistance
for Cgs. Because it is hard to extract separately from the gate resistance, Rg, the two
are sometimes lumped together. The gate-drain capacitance, Cgd, is setup by the space
charge region between the gate and drain, similar to Cgs, but typically an order of mag-
nitude smaller. It introduces a bothersome feedback which reduces the high-frequency
18

CHAPTER 2. NOISE FIGURE MODELING OF ALGAN/GAN HEMTS
performance of the device. The gate-drain resistance, Rgd, is also argued as a charging
resistance for Cgd. Any capacitance between the drain and source, which will be very
small, is accounted for with Cds.
The parameters Cgs, gm, τ, Ri, Rds, Rgd, Cgd, and Cds taken together are referred to
as the intrinsic device. The other elements of the model are unfortunate side-effects of
having to provide physical connections to the device and the parasitic and distributed
effects that occur when operating at frequencies in the GHz range. These parasitic
elements are called the extrinsic elements of the device.
The drain and source resistances, Rd and Rs, come from two physical processes.
The first is the finite resistance of the 2DEG, and so the access regions between gate
source and gate drain contribute to these parasitics. The second source is the non-
ideal ohmic contact behavior between the metal pads and the semiconductor. These
resistances scale directly with the device width as used in § 2.6.5. Because the gate
length is short (0.7 µm here), the resistances of the gate metals contribute to Rg.
From an AC viewpoint, the signal decays as it propagates along the length of the gate
resistance. A distributed model argument shows this resistance to be approximately
1/3 of its DC value [14]. All of these resistances generate thermal noise. Rs and
Rg will be important for modeling of noise figure as seen later. Because Rd is at
the output, and its magnitude of noise is far smaller than the channel noise, it can be
ignored.
19

CHAPTER 2. NOISE FIGURE MODELING OF ALGAN/GAN HEMTS
The drain, gate, and source inductances, Ld Lg, and Ls, respectively, account for
signal delay along the various contact pads. Lg is usually largest, and will affect
any input match (noise or power) to the device. Finally there are the various pad
capacitances between their respective device terminals: Cpgs, Cpgd, and Cpds. Cpgs
and Cpgd are small, while Cpds for devices used in this work is of the same order as
Cgd.
S-parameter measurements of devices along with open and shorted test structures
were used to find the small-signal parameters. In addition, DC measurements of TLM
structures and some basic hand calculations [14] were used to determine Rg, Rs, and
Rd. For a better fit, optimization was performed using Advanced Design System
(ADS). It is important to have accurate small-signal parameters; any discrepancies
directly translate into incorrect noise figure parameter prediction. Some ADS files
useful for extracting and optimizing the small-signal parameters can be found in ap-
pendix A.
Extracted small-signal parameters of devices from various samples are displayed in
table 2.1. The top half of the table is the intrinsic parameters, while the bottom half is
the extrinsic parameters. Many of the extrinsic parasitics come from the geometry of
the device or the pad parasitics and will be the same for the different samples. These
parameters will be used in this chapter and in chapter 3.
20

CHAPTER 2. NOISE FIGURE MODELING OF ALGAN/GAN HEMTS
Sample: 15% 25% 25% 27% 35% 35%
on SiC w/AlN
Intrinsic Ri (Ω) 6.2 8.24 8.86 9.23 8.23 4.07
Parameters Rds (Ω) 577 588 622 562 833 627
Rgd (Ω) 75.7 287 238 96 96.2 33.4
Cgd (fF) 19 19.1 13.5 20.6 18.7 29.9
Cds (fF) 2.97 2.33 1.34 2.34 1.66 1.13
Cgs (pF) 0.23 0.265 0.22 0.191 0.191 0.215
gm (mS) 34.1 37 33.2 33 30.5 34.9
τ (ps) 1.2 2.25 2.6 2 2.25 2.03
Extrinsic Rs (Ω) 10.2 6.18 5.19 4.04 4.31 5.30
Parameters Rd (Ω) 17.9 10.24 8.99 7.41 7.20 7.54
Rg (Ω) ←− 3.03 −→
Ls (pH) ←− 12 −→
Ld (pH) ←− 22.3 −→
Lg (pH) ←− 45.6 −→
Cpgs (fF) ←− 1.38 −→
Cpds (fF) ←− 29.6 −→
Cpgd (fF) ←− 5.4 −→
Table 2.1: Extracted small-signal parameters for various samples. Devices have a gate
geometry of 0.7 × 150 µm.
2.4 Noise Figure and Noise Parameters
An amplifier provides gain to both the input signal and the noise. The amplifier will
also add noise from its intrinsic noise sources. This makes the signal to noise ratio at
the output worse than at the input. Expressing a ratio of these two ratios at a reference
temperature leads to the definition of noise figure.
F ≡ (S/N)in
�
�
�
�
(S/N)out
� T =Treference=290K
(2.4.1)
It can be applied to any two port [3] (by extension even to mixers [7]). Here, it will
21

CHAPTER 2. NOISE FIGURE MODELING OF ALGAN/GAN HEMTS
be applied to a single HEMT. Sometimes NF is called noise factor, F. Traditionally,
the names were interchangeable, but now it is common that noise figure is the noise
factor expressed in decibels (NF = 10 log 10(F)). This is the convention followed in
this work. Sometimes it is expressed as a temperature (Tnoise =(F − 1)Treference).
Noise figure by itself gives no details of the noise sources of the device or amplifier.
However, noise sources can be added as in Figure 2.2. Inoise is the equivalent short-
circuited noise current source and Enoise the equivalent open-circuited noise voltage
source. Together, they account for all noise sources of the device which can now be
modeled as a noiseless two port. These two sources will likely be correlated because
of the various physical noise sources of the device that contribute to them [8]. Models
that describe these sources of noise are discussed in the next section. An input is
connected to the device, represented as a source impedance in figure 2.2. This input
will generate its own noise, represented as Esource. This could be thermal noise from
E source
+ -
Z source
E noise
+ -
I noise
Noiseless
2-port
network
Figure 2.2: Equivalent model of a transistor driven by a noisy source of impedance
Zsource.
22

CHAPTER 2. NOISE FIGURE MODELING OF ALGAN/GAN HEMTS
a passive network and/or active device noise. From this, F (and hence, NF) can be
written as [8]
F =1+
�
|Enoise + InoiseZsource| 2�
〈Esource〉 2
(2.4.2)
As can be seen, the value of the source impedance actually affects the noise figure.
Once Enoise and Inoise have been determined through whichever model is applied, the
noise figure can be predicted for changing source impedance. F can also be expressed
as [18,19]:
F = Fmin + 4Rn
Zo
|Γsource − Γopt| 2
(1 −|Γsource| 2 ) |1+Γopt| 2
(2.4.3)
Γsource is the reflection coefficient of the source impedance. Equation 2.4.3 contains
four parameters that taken together are called the noise parameters. They are:
Fmin The best achievable noise figure. It occurs only when the source impedance is
set to Zopt (conversely Γopt).
|Γopt| The magnitude of the source reflection coefficient that provides the minimum
noise figure, Fmin.
� Γopt The angle of the source reflection coefficient that provides Fmin.
Rn An effective “slope.” The larger its value, the quicker the noise figure increases
as Γsource is changed from its optimum value. 1
These parameters are usually measured as described in § 3.3. As can be reasoned
from equation 2.4.3, there are circles of constant noise on an impedance or Smith
1Rn has units of ohms. It can also be normalized to the reference impedance, Zo. Then the variable
is usually written as rn instead.
23

CHAPTER 2. NOISE FIGURE MODELING OF ALGAN/GAN HEMTS
Gmax
Gmax-1dB
Gmax-2dB
NFmin
NFmin+1dB
NFmin+2dB
NFmin+3dB
Figure 2.3: Smith Chart showing minimum noise figure and circles of constant noise
figure (solid circles) along with maximum gain and circles of constant gain (dashed
circles).
Chart plane. This is shown in Figure 2.3. It should not be surprising to find the small-
signal gain circles and noise circles do not overlap because Γopt is an intentional gain
mismatch to minimize noise [20].
That the noise performance changes with the source match is extremely important
for LNA design. In the next section, noise models for HEMTs that are more in depth
than in figure 2.2 will be reviewed. Once these noise sources are determined, they can
be used elsewhere, such as assisting in oscillator phase noise prediction.
24

CHAPTER 2. NOISE FIGURE MODELING OF ALGAN/GAN HEMTS
2.5 HEMT Noise Figure Models
The major noise figure models used for HEMTs are now presented. The work by
van der Ziel, Pucel, Fukui, and Pospieszalski is the basis for most other investigations
and modeling of noise figure. The key ideas, equations, strengths and weaknesses of
each will be reviewed. Shortcomings found in each will show the need for further
work and provide motivation for the next section.
2.5.1 van der Ziel and Pucel Models
The theoretical work for noise sources in FETs at microwave frequencies was in-
troduced by van der Ziel in the early 1960s [3, 21, 22]. He derived noise sources for
the channel and “induced gate noise.” This gate noise is explained as fluctuating noise
in the channel capacitively coupling to the gate through Cgs and Cgd, causing an ef-
fective, and correlated, noise source at the gate. The gate noise, channel (drain) noise,
correlation (C), and cross-term 〈igi∗ d 〉 can be written as [3]
�
i 2 �
g
=4kTaδ ω2C 2 gs
5gd0
∆f (2.5.1)
�
i 2 �
d =4kTaΓgd0∆f (2.5.2)
C = 〈igi∗ d 〉
�� �
i 2 g
〈i 2 d 〉
(2.5.3)
〈igi ∗ d〉 = 2
3 jωCgskTa∆f (2.5.4)
25

CHAPTER 2. NOISE FIGURE MODELING OF ALGAN/GAN HEMTS
ω is the angular frequency, Ta is the ambient temperature, gd0 is the drain-source con-
ductance when Vds is zero, δ is a parameter van der Ziel gives as 4/3, and Γ will be
derived in § 2.6.2 (for now, it can be considered a constant of 2/3). Van der Ziel orig-
inally found a correlation of 0.395j for JFETs [3]. For aggressively-scaled HEMTs,
the correlation is experimentally found to be ∼0.7j [23,24]. Van der Ziel does give ex-
pressions for noise figure, but they are often in terms of more complicated parameters,
under specific conditions, or for different devices, making them of limited use [3].
While the gate and drain noise expressions above allow for noise prediction, for accu-
rate results the correlation must be measured. This is because small changes in cor-
relation can have a large effect in predicted noise parameters. Also, the noise sources
are bias-and frequency-dependent.
In 1975, Pucel and his co-workers took what was learned from van der Ziel and
extended it in a very detailed publication [2]. Their work was explicitly for a GaAs
MESFET (and thus more applicable to a HEMT), whereas van der Ziel’s work was
mainly for JFETs. The Pucel modeling takes into account velocity saturation and how
the noise changes with bias based on changes in the small-signal parameters and their
noise variables P, R, and C. The model also uses a gate and drain noise source that
are correlated, shown in a small-signal model in figure 2.4. In this figure, the gate
and drain noise sources account for all noise generated by the intrinsic device (inside
the dashed “Noiseless” box). The parasitic resistances, Rg, Rs, and Rd, still generate
26

CHAPTER 2. NOISE FIGURE MODELING OF ALGAN/GAN HEMTS
Gate
Lg
Rg
Ri gme Rds Cgs
jwτ Ig v Cds
+
c
Id Vc Cpgs
-
Rgd Cgd
Cpgd
Rs
Ls
Source
Noiseless
Figure 2.4: Pucel noise model in a small-signal circuit.
Rd
Ld
Cpds
thermal noise. The gate and drain noise sources are related to the noise variables by
P =
R =
〈i 2 d 〉
4kTa |Y21| 2 ∆f =
|Y21| 2
4kTa |Y11| 2 ∆f
〈i 2 d 〉
4kTagm∆f
�
i 2 �
g =
gm
4kTaω2C 2 �
i
gs∆f
2 �
g
Drain
(2.5.5)
(2.5.6)
and the same correlation as in equation 2.5.3. Although Pucel determined very de-
tailed expressions for these noise variables, for accurate results the modeling had to
be fitted to data. Today, if this model is used, the parameters are determined empiri-
cally [7], fitting to noise figure measurements. An excellent paper using this model on
GaN HEMTs that shows directly how to extract these parameters from measurements
is found in [25]. This method also treats both parts of the correlation, magnitude and
phase, as variables to be determined instead of restricting the phase to 90 ◦ (strictly
imaginary). This formulation is used in this work. Information about an ADS project
27

CHAPTER 2. NOISE FIGURE MODELING OF ALGAN/GAN HEMTS
that helps in determining these parameters, contains a small-signal circuit with this
type of noise modeling, and calculates noise figure can be found in appendix A. Be-
cause it uses the same correlation as van der Ziel’s modeling, the Pucel model suffers
the same drawbacks. As mentioned, the parameters usually must be determined from
measurements, limiting its predictive power. Because the noise sources are similar for
both models, they will be referred to as correlated noise (CN) models in this work.
2.5.2 Fukui Model
Fukui garnered much attention in the late 1970s with the introduction of his empir-
ical model [26]. Although it involved empirical parameters, it was far simpler than
the previously reported noise models, was expressed directly in terms of the noise
parameters, and made clear how key small-signal parameters contributed to the noise
performance. The model is also convenient because the noise at different frequencies
and device scaling can be easily determined. His expressions for the noise parameters
are:
�
Rg + Rs
Fmin = 1+k1fCgs
gm
� �
1
Ropt = k3 + Rg + Rs
4gm
Xopt = k4
fCgs
Rn = k2
g2 m
28
(2.5.7)
(2.5.8)
(2.5.9)
(2.5.10)

CHAPTER 2. NOISE FIGURE MODELING OF ALGAN/GAN HEMTS
The variables k1−4, are the fitting parameters, and will change with the device tech-
nology and bias. While this model can be useful for hand calculations, the Pucel and
Pospieszalski models are more complete and directly usable in a simulator such as
ADS.
2.5.3 Pospieszalski Model
In the late 1980’s, Pospieszalski introduced a new noise figure model that took a
different approach than the previous methods by removing correlation between the
noise sources [1]. There are only two noise sources for the entire transistor: thermal
noise of Ri and Rds. Instead of these resistors being at ambient temperature, Ta, they
are at higher effective temperatures Tg and Td, shown in figure 2.5. Tg is usually
(but not always) close to room temperature, while Td can be several thousand degrees
Kelvin. These elevated temperatures are not linked to a physical temperature. There
Gate
Lg
Rg
Ri
T = Tg
+
Vc
-
Cpgs
Cgs
4kTg/Ri∆f
Rgd Cgd
Cpgd
gme jwτ vc
R s
Ls
Source
Rds
T = Td
4kTd/Rds∆f
Figure 2.5: Pospieszalski noise model in a small-signal circuit. Resistances (and their
thermal noise sources) Ri and Rds are at elevated temperatures Tg and Td respectively.
29
Rd
Cds
Ld
Cpds
Drain

CHAPTER 2. NOISE FIGURE MODELING OF ALGAN/GAN HEMTS
have been attempts to link these noise temperatures to the device physics, but none
were viewed as successful. The noise can be described by the noise temperatures Tg
and Td as:
�
f
Fmin = 1+2
Ropt =
+ 2f
� 2 RiTd
fT RdsTa
�
�
�
�RiTgTd
+
fTTa Rds
�
��
�
� 2
� fT TgRiRds
1
f
Xopt =
ωCgs
Rn = TgRi
Ta
+
Td
� f
fT
+ R 2 i
� 2 R 2 i T 2 d
R 2 ds
(2.5.11)
(2.5.12)
(2.5.13)
Td
TaRdsg2 (1 + ω
m
2 C 2 gsR 2 i ) (2.5.14)
After measuring S-parameters and noise parameters, the noise temperatures can be
extracted by solving the above equations. A Matlab script using equations 2.5.11
and 2.5.12 to perform this calculation can be found in appendix C. A criteria that
Pospieszalski mentions for the model to work is
1 ≤ 4 Ropt
Rn(F − 1)
< 2 (2.5.15)
The lower limit is fundamental and is because the noise of a 2-port modeled by a pair
of noise sources must be Hermitian and non-negative definite as shown by Pospieszal-
ski [27]. The upper limit comes from the model itself [1]. As with the other models, it
can be used to determine the match for noise and expected noise at other frequencies.
The model is criticized for its dependence on Ri as a thermal noise source, which is
30

CHAPTER 2. NOISE FIGURE MODELING OF ALGAN/GAN HEMTS
hard to determine precisely, and for the noise temperatures not having a physical basis.
As with the other models, the noise parameters must be measured prior to modeling.
Thus the model does not “predict” noise. In addition, the noise temperatures change
with device bias [28]. How they change with bias is reported in the literature, but not
modeled or predicted. Information for an ADS project that contains a small-signal
circuit with this type of noise modeling and that calculates noise figure can be found
in appendix A.
2.5.4 Pospieszalski and Correlated Noise Models Applied to Al-
GaN/GaN HEMTs
Based on the above discussion, the Pospieszalski and CN models are useful for:
1. Modeling device noise figure in a circuit simulator versus frequency and input
match
2. Devices that are stable and well-characterized, such that the noise variables of
the model (Tg, Td, R, P, C) do not change
3. Predicting noise at frequencies outside the range of available measurement equipment.
4. When the bias in a design will not be much different from what gives the best
NF performance
Thus, they are useful for basic LNA designs as shown in [17, 29]. The application of
these models to GaN-based HEMTs is relatively new, with very few publications [25,
28,30].
In table 2.2, the Pospieszalski and CN model have been applied to devices from six
samples. The fτ and fmax of the different devices at the biasing for best NFmin are
31

CHAPTER 2. NOISE FIGURE MODELING OF ALGAN/GAN HEMTS
listed along with the bias at the top of the table. The next section contains the mea-
sured noise parameters, obtained as described in § 3.3, along with the gain that could
be expected from the device having an input match of Γopt and an output match for
small-signal gain. These noise measurements, along with the small-signal parameters
from table 2.1, were used to calculate the noise variables for both the Pospieszalski
and a CN model. These models’ variables are listed in table 2.2 with the predicted
noise parameters using each model at 5 GHz. The fit is generally very good. Both
models predict NFmin and |Γopt| well. The Pospieszalski model does not predict � Γopt
as well as the other parameters, and the CN model has trouble with predicting rn.
From equation 2.5.13, it is seen that the Pospieszalski model’s prediction of Xopt only
depends on Cgs. A better prediction agreement would be expected. An explanation for
this discrepancy will be offered in § 3.5.4. Both these models fit the noise parameters
versus frequency, shown in figure 2.6 for one of the sets of measurements in table 2.2.
Variations in the predicted Tg of Pospieszalski’s model is large, a factor of 4. This
is likely because of the differences in Ri in the measurements of table 2.1, but they
change by only a factor of 2. This high sensitivity to Ri might make the model difficult
to use in predicting noise. However, it should be stressed that the model works well
without the need for correlation.
32

CHAPTER 2. NOISE FIGURE MODELING OF ALGAN/GAN HEMTS
�
�
�
Sample: 15% 25% 25% 27% 35% 35%
on SiC w/AlN
Ids @NFmin 20 13 10 19 11 10
Vds @NFmin 4 4 7 4 5 4
fτ @NFmin 19.7 19.4 21.4 23.3 22.3 21.3
fmax @NFmin 30.2 33.6 39 42.9 43.7 40.4
Measure Noise Parameters and Associated Gain
NFmin (dB) 1.14 1.13 1.1 1.16 1.15 1.18
rn 0.772 0.707 0.648 0.83 0.796 0.723
Γopt 0.727 0.716 0.746 0.774 0.76 0.733
Γopt 20.5 21.3 23.2 19.8 19.5 23.9
Gainassoc. (dB) 14 13.7 14.6 14.3 14 12.7
Using Pospieszalski Model
NFmin (dB) 1.18 1.1 1.1 1.04 1.07 1.03
rn 0.749 0.597 0.729 0.81 0.839 0.721
Γopt 0.702 0.666 0.715 0.744 0.744 0.72
Γopt 25.7 27.3 26.3 22.7 22.3 26.9
Tg (K) 607 292 250 358 462 988
Td (K) 3445 3018 3893 3469 4454 3966
Using a Correlated Noise Model
NFmin (dB) 1.23 1.3 1.21 1.28 1.25 1.33
rn 1.21 0.989 0.831 1.04 0.977 0.95
Γopt 0.806 0.758 0.778 0.797 0.783 0.766
Γopt �
i
19.2 21 22.5 19.6 19.2 23.6
2 �� �
−24 A2
g 10 Hz
〈i
7.05 12.00 3.55 7.09 7.23 6.74
2 d〉 � �
−22 A2
10 Hz 4.56 5.60 4.14 5.93 4.79 5.36
|C| 0.802 0.799 0.821 0.803 0.759 0.739
� C (degrees) 103 101 129 114 114 118
Table 2.2: Comparison of Pospieszalski and Correlated Noise models to measured
data. Devices have a gate geometry of 0.7 × 150 µm .
33

CHAPTER 2. NOISE FIGURE MODELING OF ALGAN/GAN HEMTS
NF min (dB)
r n
|Γ opt |
2.6
2.4
2.2
2.0
1.8
1.6
1.4
1.2
1.0
0.8
1.8
1.5
1.2
0.9
0.6
0.3
0.0
1.0
0.8
0.6
0.4
0.2
0.0
Measured
Pospieszalski Model
CN Model
4 6 8 10 12
4 6 8 10 12
Measured
Pospieszalski
CN Model
4 6 8 10 12
Frequency (GHz)
Figure 2.6: Comparison of Correlated Noise and Pospieszalski models to measured
noise parameters versus frequency.
34
180
150
120
90
60
30
0
Angle Γopt (deg.)

CHAPTER 2. NOISE FIGURE MODELING OF ALGAN/GAN HEMTS
Lee’s study of the CN models to AlGaN/GaN HEMTs experimentally finds that the
correlation tends to a constant of 0.7 [25]. The average value for |C| found in table
2.2 is 0.718, in agreement with Lee. The average phase was found to be 110 ◦ , which
is higher than the expected 90 ◦ . However, when Lee de-embeds contributions from
extrinsic shot and thermal noise sources he finds the phase to be very close to 90 ◦ [25].
The average gate noise from table 2.2 is 7.3 pA 2 /Hz and the average drain noise is 506
pA 2 /Hz.
Average values for the Pospieszalski noise variables are Tg of 493 K and Td of
3708 K. These numbers are only approximately close to those found in [28]; however,
in that reference the devices which had a gate length of 0.35 µm (compared to 0.7 µm
here) had an fτ of only 30 GHz, and thus were excessively noisy. Despite the accu-
racy in the Pospieszalski model, the condition in equation 2.5.15 was not met for the
modeling in table 2.2. The upper limit was broken; values of 8 were common.
2.6 A Proposed Noise Figure Model
A model that was developed for some of the noise studies in chapter 3 is now pre-
sented. It uses some of the formulation of the CN models, but without correlation and
replacement of the induced gate noise with a shot noise source. In addition, this model
can give accurate noise parameter results without prior noise parameter measurements.
35

CHAPTER 2. NOISE FIGURE MODELING OF ALGAN/GAN HEMTS
Gate
R g +R i +R s
I s
+
Vc -
E r
C' gs
Source
g' m v c
R ds
Drain
Figure 2.7: A simplified HEMT circuit model including noise sources.
2.6.1 Setup Details
A circuit schematic of the model is represented in figure 2.7 with six small-signal
parameters and three noise sources. A full small-signal model is still used for small-
signal parameter extraction from a HEMT, but only Rg, Rs, Ri, Cgs, gm, and Rds are
used. The noise sources are Er, Is, and Ic. Er is thermal noise from the two parasitic
resistances and channel resistance. Its voltage spectral density is written as
�
E 2 �
r =4kT (Rs + Rg + Ri)∆f (2.6.1)
Is is a shot noise source. The DC current used for it is from a three-terminal measure-
ment at the bias of S-parameter extraction. This source can be represented between
gate-and-source or gate-and-drain with the resulting derivations being the same. The
current spectral density of this shot noise term is
�
I 2 �
s =2qIgs∆f (2.6.2)
36
I c

CHAPTER 2. NOISE FIGURE MODELING OF ALGAN/GAN HEMTS
Igs is the measured gate leakage current.
The final noise source is Ic. It represents distributed thermal noise in the channel,
and is the same as found by van der Ziel [3]
�
I 2 �
c =4kTΓgm∆f (2.6.3)
Γ is a bias dependent quantity. For a saturated GaN HEMT and most other FETs, it
is a constant value of 2/3. It will be derived in detail in § 2.6.3. All three mentioned
noise sources will be assumed to be uncorrelated, greatly simplifying the math.
The derivation of the noise parameters is also simplified if the source resistance
can be transformed up from the source node to Ri. This is often done in device
small-signal circuit calculations through the use of source degeneration, 2 illustrated
in figure 2.8. Source degeneration modifies the values of Cgs and gm as follows [31]
C ′ gs =
Cgs
1+gmRs
gm
g ′ m =
1+gmRs
(2.6.4)
(2.6.5)
with Rs, Cgs, and gm being values extracted from the device and C ′ gs and g ′ m the
degenerate values that appear in figure 2.7 and the math that follows. These equations
hold for ωC ′ gs Rs ≪ 1. The thermal noise of Rs, ERs, can be moved to the input with
the same condition that ωC ′ gsRs ≪ 1. As is seen, the effect of this degeneration is a
reduction in the effective Cgs, and gm. Because the gate-drain capacitance, Cgd, is not
2The technique is also called emitter degeneration, depending on if the device in question is a FET
or BJT type of device.
37

CHAPTER 2. NOISE FIGURE MODELING OF ALGAN/GAN HEMTS
Gate
+
Vc -
R i
Cgs
Source
R s
E Rs
Drain
g mv c
Gate
E Rs
+
Vc -
R i+R s
C'gs
Source
Figure 2.8: Cartoon showing the effect of source degeneration.
Drain
g' mv c
used in this model, Ri, Rg, and Rs can be lumped together as one resistance, further
simplifying the derivation.
Several assumptions have been made. The most worrisome is neglecting the in-
trinsic feedback capacitance, Cgd. Pospieszalski has shown [1] at typical noise mea-
surement frequencies removing Cgd from the modeling introduces only a small error
(less than the typical precision of a noise measurement setup). So long as the mea-
surements are made far enough from the device fτ, it should not cause alarm. As an
example, a device with an fτ of 50 GHz will probably not be used for LNA applica-
tions greater than half the device unity current gain frequency. A derivation including
Cgd was carried out but the expressions were too complicated for insight to be gained
from them.
Another important assumption is that the noise sources are uncorrelated. It is not
38

CHAPTER 2. NOISE FIGURE MODELING OF ALGAN/GAN HEMTS
being implied that physically all the noise processes are not influencing one another.
However, to have a simple enough and insightful model, it is a necessary assumption.
As mentioned earlier, it has already been shown that not using correlation can give
accurate results [1,32].
Finally, neglecting many of the extrinsic parasitics is a minor assumption. The
inductances (Lg, Ls, Ld) and capacitances (Cpgs, Cpgd, Cpds) do not affect the noise
parameters as much as the intrinsic parameters. This will be seen in § 2.6.5. Also, the
thermal noise of Rd pales in comparison to the noise generated by the channel.
2.6.2 Derivation of Noise Parameters
A load, RL, signal generator (not a noise source), Vgen, and generator impedance,
Zgen = Rgen + Xgen, are added to the model, redrawn in figure 2.9. Also, for conve-
nience, the collected resistances are renamed to
X gen
V gen
R gen
E gen
Z in
R in
I s
+
Vc -
E r
C' gs
g' m v c
Figure 2.9: Circuit model used for deriving noise figure.
39
R ds
I c
R L
+
Vout -

CHAPTER 2. NOISE FIGURE MODELING OF ALGAN/GAN HEMTS
Rin = Rg + Ri + Rs
(2.6.6)
Assume for the moment that the input and output are matched for power: RL = Rds
and Zgen = Z∗ in . equation 2.4.1 can then be rewritten
F = (S/N)in
(S/N)out
=
|Vgen| 2
4Zgen /〈vin,noisev∗ in,noise〉
4Zgen
|AvVgen| 2
4Rds /〈vout,noisev∗ out,noise〉
4Rds
= 1
|Av| 2
�
vout,noisev ∗ out,noise
�
vin,noisev ∗ in,noise
�
� (2.6.7)
with Av defined as the voltage gain, vsignal,out = Avvgen. An interesting point is
that because noise figure is a ratio of powers, the output and input match cancel in
equation 2.6.7. This does not mean that the source impedance has no effect on noise
figure nor that a matched load has no effect on the output power. It means that the ratio
of signal-to-noise at the input only or the output only is not affected by the matching
conditions.
We need to define the input noise voltage. This may be from an active device, or
it may be unknown, but the derivation depends only on signal-to-noise ratio and the
source impedance. Here thermal noise of Zgen, represented as Egen in figure 2.9, is
used. The input noise can be written as
�
v 2 �
in =4kTRgen
(2.6.8)
The bandwidth (∆ f, assumed to be 1 Hz) will no longer be included. The noise figure
is now
F = 1
|Av| 2
�
vout,noisev∗ �
out,noise
4kTRgen
40
(2.6.9)

CHAPTER 2. NOISE FIGURE MODELING OF ALGAN/GAN HEMTS
The output noise, vout,noise, will depend on the contributions from the individual in-
ternal noise sources in the device and the input noise. Because the HEMT is modeled
by a small-signal circuit with noise sources, the output noise can be calculated with
standard small-signal methods.
The easiest contribution to the output noise to calculate is the channel noise. It is
merely Ohm’s law, Ic(Rds||RL). Thévenin and Norton representations can be used
such that the voltage gains from Vgen, Egen, and Er to the output will be the same.
This is the gain of a common source configuration as found in circuit textbooks [31]:
vout
Av =
Egen,Vgen,Er
= − ωτ
ω
jRL||Rds
(Rgen + Rin)+j(Xgen − 1/(ωC ′ gs))
with ω being the angular frequency (2π×frequency) and defining
ωτ = g ′ m/C ′ gs
(2.6.10)
(2.6.11)
The other gain needed is the shot noise contribution. Using Norton and Thévenin
equivalent circuits again, it is easily found.
As = vout
Is
= − ωτ
ω
jRL||Rds(Rgen + jXgen)
(Rgen + Rin)+j(Xgen − 1/(ωC ′ gs))
As expected, it is similar to Av. The total output noise is then expressed as
vout,noise = Av(Egen + Er) − (Rds||RL)Ic + AsIs
(2.6.12)
(2.6.13)
but what is needed is the spectral density, and thus, noise power. Taking the complex
conjugate, followed by a statistical average, gives
�
vout,noisev∗ � ��
2
out,noise = |Av| E2 �
gen + 〈E2 r 〉 �
+ | (Rds||RL) | 2 〈I2 c 〉
41

CHAPTER 2. NOISE FIGURE MODELING OF ALGAN/GAN HEMTS
+|As| 2 〈I2 �
2
s 〉 + |Av| ErE ∗ �
gen + A∗ �
vRL||Rds IcE∗ �
gen
+ ... 10 other cross terms (2.6.14)
It is not possible to calculate the various correlations. Most cross-terms will be zero
(shot and thermal noise will not be correlated). For simplicity, all sources are assumed
to be uncorrelated. Equation 2.6.14 is then reduced to
�
vout,noisev ∗ � ��
2
out,noise = |Av| E 2 �
gen + �
E 2 ��
�
2
r + | (Rds||RL) | I 2 � �
2
c + |As| I 2 �
s
(2.6.15)
Finally, combining equations 2.6.8, 2.6.9, 2.6.10, 2.6.12, 2.6.13, and equation 2.6.15
we obtain an expression for noise figure:
F =1+ Rin
with
Rgen
+ b R2 gen + X 2 gen
Rgen
+ a
�
�
�
�
Rgen � Rin
�
+ Rgen + j Xgen − 1
ωC ′ ��
���� 2
gs
(2.6.16)
a = g ′ mΓ � �
ω 2
ωτ
b =
qIgs
2kTreference
(2.6.17)
(2.6.18)
The factor of 1 is the input noise contribution to the noise figure. If the device does
not generate noise, noise figure would be 1. There would then be no degradation in
the signal to noise ratio going into and coming out of the device. Equation 2.6.16
describes the noise figure in terms of the match provided to the device, the device
small-signal parameters, and the measured gate-leakage. There are no fitting param-
42

CHAPTER 2. NOISE FIGURE MODELING OF ALGAN/GAN HEMTS
eters. This is not the minimum noise figure. To determine it, we find the source
impedance that minimizes equation 2.6.16. This is found by taking partial derivatives
and solving equal to zero.
�
�
F = Fmin
� ∂F ∂F =0, ∂Rgen ∂Xgen =0
(2.6.19)
This leads to the following expressions for the optimal source impedance that provides
the minimum noise figure:
�
�
�
Ropt =
Xopt = 1
ωCgs
a
a + b
�1+aRin a + b Rin + ab
(a + b) 2
1
(ωCgs) 2
(2.6.20)
(2.6.21)
The last parameter, the noise resistance, can be obtained by using equation 2.4.3
and the equation for noise figure, 2.6.16, at two different source impedances. The
most convenient to choose are the minimum noise figure and when the source is at
its reference impedance, Γgen =0. We shall call the later FZ0. Entering this into
equation 2.4.3 and rearranging,
Rn = Z0
4 (FZ0
�
�
� 1
− Fmin) �1+
�
�
�2
�
�
Γopt �
(2.6.22)
An explicit expression is complicated. A Matlab script that implements all four of
the noise parameters can be found in appendix B. These equations will be discussed
43

CHAPTER 2. NOISE FIGURE MODELING OF ALGAN/GAN HEMTS
more in § 2.6.5, and used in chapter 3. For the moment, let us turn our attention to the
factor Γ, and the derivation of the channel noise source.
2.6.3 Derivation of Drain Noise Source
We will quickly go through the derivation of Γ (and, therefore, the channel noise
source) to show that it is not a fitting parameter. Van der Ziel has shown the formula-
tion for a MOSFET [3]. Here, it will be explicitly done for a HEMT. The formulation
involves the DC drain current, Id, so it is needed as well. Assume for the moment that
the device is biased in the linear region (no velocity saturation). Following arguments
as found in [11,33], the drain current can be written in general as
Id = g(Vx) dVx
dx
= qµWns(x) dVx
dx
(2.6.23)
W is the device width (cm), ns(x) is the sheet charge of the 2DEG (cm−2 ), and µ
is the mobility � cm2 �
. Vx is the potential difference at a distance x from the source,
Vs
relative to the source. g(Vx) is the channel conductivity per unit length at some point
along the channel, which depends on Vx.
An expression is needed for ns(x) in terms of Vx. First, an effective capacitance can
be defined [11,33]
C = Q
V
= εB
d +∆d
(2.6.24)
with εB and d being the dielectric permittivity and thickness of the AlGaN layer re-
spectively and ∆d the centroid of the electron wave functions in the quantum well
44

CHAPTER 2. NOISE FIGURE MODELING OF ALGAN/GAN HEMTS
(that is, the 2DEG). The charge of this capacitance is qns(x), with a voltage along the
channel of Vg − Vt − Vx. Vt is the threshold voltage. Combining all this together and
rearranging
ns(x) =
and substituting into equation 2.6.23
We can now define
εB
q(d +∆d) (Vg − Vt − Vx) (2.6.25)
Id = µεBW
d +∆d (Vg − Vt − Vx) dVx
dx
(2.6.26)
g(Vx) = µεBW
d +∆d (Vg − Vt − Vx) (2.6.27)
Its usefulness will soon be apparent. Id can now be found. Because of continuity, the
DC current entering and leaving the device must be the same. Integrating over the
length of the device, L,
which gives
� L
0
Iddx = IdL =
� Vd
0
g(Vx)dVx
Id = µεBW
�
(Vg − Vt)Vd −
L(d +∆d)
From this, the transconductance (gm)
gm = ∂Id
∂Vg
= µεBW
L(d +∆d) Vd
45
�
2 Vd 2
(2.6.29)
(2.6.28)
(2.6.30)

CHAPTER 2. NOISE FIGURE MODELING OF ALGAN/GAN HEMTS
and the saturation current, Id,sat, can be found. The saturation current is found by
differentiating equation 2.6.29 with respect to Vd and setting it equal to zero. This
returns the voltage of Vd that maximizes Id, which we will call Vd,sat. However, if the
device has a short channel, the velocity may saturate before the above condition. Then
the voltage that the current saturates is the lesser of the following two quantities:
or
Vd,sat = Vg − Vt
Vd,sat = EcritLg
(2.6.31)
(2.6.32)
Ecrit is the critical field strength and Lg is the device gate length. Putting equa-
tion 2.6.31 back into equation 2.6.29, we find the saturation current resulting from
channel pinch off.
Id,sat = 1 µεBW
2 L(d +∆d) (Vg − Vt) 2
(2.6.33)
equation 2.6.29 only works for a device in the linear region until the device saturates,
Id = Id,sat. Beyond this, the current can be approximated to be the same as Id,sat (if
short-channel effects are ignored).
We will follow the work of van der Ziel to derive the channel noise [3]. Assume
that a thermal voltage noise source, vn, creates a drain noise current fluctuation, ∆Id,
along the distributed channel. This is shown in figure 2.10. The thermal noise source
can be written as
〈vnv ∗ n〉 = 4kT
g(V )
46
(2.6.34)

CHAPTER 2. NOISE FIGURE MODELING OF ALGAN/GAN HEMTS
Similar to equation 2.6.23, we can write an expression for the drain current fluctua-
tions:
∆Id = g(V ) dV
dx + vng(V ) (2.6.35)
with V = Vx +∆V (x, t). Separating the derivative and integrating gives
� L
0
∆Iddx =
� L
0
g(V )dV +
� L
0
vng(V )dx (2.6.36)
An expression for the noise only is desired. If we consider the drain AC shorted, the
first term on the right of the equality in equation 2.6.36 will be zero. Continuing we
have
∆IdL =
Taking the spectral density we have
� L
〈∆Id∆I ∗ d〉 = 1
L2 � L
〈vnv
0
∗ n〉 g 2 (V )dx = 4kT
L2 0
vng(V )dx (2.6.37)
� L
0
g(V )dx (2.6.38)
with the use of equation 2.6.35. The variable being integrated over, x, can be changed
to V through the use of equation 2.6.23. It is rearranged here as
V x (x) + ∆V x (x,t)
g(V )
dx = dV (2.6.39)
g(V)
_
Id
+
I d + ∆I d (t)
... ...
_
+
V n
V x (x+∆x) + ∆V x (x+∆x,t)
Figure 2.10: Cartoon used for deriving the channel noise.
47
_
+

CHAPTER 2. NOISE FIGURE MODELING OF ALGAN/GAN HEMTS
Substituting and changing the limits of integration we arrive at the following key equa-
tion:
〈∆Id∆I ∗ �
d 〉 = i 2 �
d = 4kT
L2 � Vd
g
Id 0
2 (Vx)dVx
(2.6.40)
It is now clear the usefulness of knowing Id and g(Vx) explicitly. Combining equa-
tions 2.6.27, 2.6.29, and 2.6.40 leads to an expression for the noise
with
Γ=
�
i 2 �
d =4kTgmΓ (2.6.41)
1 − Vd
Vg−Vt +
1 − 1
V 2 d
3(Vg−Vt) 2
Vd
2 Vg−Vt
(2.6.42)
When the device saturates, the value of Vd that saturates the current is used in
equation 2.6.42 instead of the value past saturation. Equation 2.6.42 then becomes
Γ=2/3. A plot of Γ for different gate and drain biasings is in figure 2.11. A thresh-
old voltage of -6 V has been assumed. It can be inferred from this graph that a device
operating in the linear region has a larger Γ.
One final note: while there was no evidence of hot electron effects in devices pre-
sented in this chapter, van der Ziel mentions that they will change the expected noise.
Instead of equation 2.6.40, the following equation would have to be used [3]
�
i 2 �
d = 4kT
L2 � Vd
Te(x)g(Vx)
Id 0
2 dVx
(2.6.43)
Te is the effective electron temperature. He gives an empirical relationship for it in
48

CHAPTER 2. NOISE FIGURE MODELING OF ALGAN/GAN HEMTS
Γ
1
0.95
0.9
0.85
0.8
0.75
0.7
V g =-6
V g =0
Decreasing V g
0.65
0 1 2 3 4 5 6 7 8
V ds (V)
Figure 2.11: Variation in Γ for different drain and gate voltages. The gate voltage is
varied from -6 to 0 V by steps of 1 V. The threshold voltage is -6 V.
terms of the electric field relative to the critical field value:
Te(x) =
�
1+ E
Ecrit
�n
(2.6.44)
n is either 0, 1, or 2. If it is zero, then we have equation 2.6.40. This leads to values of
Γ a few times 1 (as opposed to less than 1 when n = 0).
2.6.4 Noise Parameter Scaling
To the above model, scaling can be added for varying gate width and number of gate
fingers. Simple linear scaling based on a starting device width of 150 µm and 1 gate
finger was performed. This allows prediction for a comfortable range of usable gate
49

CHAPTER 2. NOISE FIGURE MODELING OF ALGAN/GAN HEMTS
fingers and widths, but will not be accurate for large devices (1 mm or greater). Based
on [34], the following equations can be used to scale the small-signal parameters:
with
Rs,new = Rs,old/s1 Ri,new = Ri,old/s1 Rg,new = Rg,olds2
Cgs,new = Cgs,olds1 Igs,new = Igs,olds1 gm,new = gm,olds1
s1 = Wg,new
Wg,old
s2 = Wg,new/n 2 new
Wg,old/n 2 old
(2.6.45)
(2.6.46)
(2.6.47)
The parameters labeled as new, are the values to be determined based on the un-
scaled extracted values, the old parameters. n is the number of gate fingers. The
simulated noise parameters versus gate width for a single fingered device are in fig-
ure 2.12. With increasing unity-gate width, the noise increases. However, the mag-
nitude of the optimal match decreases, which may make matching simpler. Also, the
noise resistance drops, making a design more robust in terms of the expected noise.
These predicted results agree with measurements in [17]. At small gate widths, Rs
and Ri will be large and keep a lower bound on NFmin (not shown in figure 2.12).
The noise increases with a wider gate finger because of increasing gate resistance and
gate leakage current (F αIgs,R 2 g in equation 2.6.16). So as the width increases, NFmin
goes from being limited by Rs and Ri to Rg and Igs. The noise parameters are also
simulated against number of gate fingers in figure 2.13. Due to layout constraints and
considerations for symmetric designs (particularly CPW implementations), the gate
50

CHAPTER 2. NOISE FIGURE MODELING OF ALGAN/GAN HEMTS
NF min (dB)
r n
1.6
1.4
1.2
1
0.8
0 200 400 600
Gate Width (µm)
6
4
2
0
0 200 400 600
Gate Width (µm)
|Γ opt |
Phase Γ opt [deg.]
1
0.8
0.6
0.4
0 200 400 600
Gate Width (µm)
(a) (b)
40
30
20
10
0
0 200 400 600
Gate Width (µm)
(c) (d)
Figure 2.12: (a) Minimum noise figure, (b) magnitude and (d) phase of optimum
source reflection, and noise resistance (c) all versus total gate width. Simulation frequency
is 5 GHz.
finger number was kept to even values or a single gate. The total gate width is kept
constant at 150 µm. A change in this parameter for small devices does little to affect
the match or the noise resistance. In going from one to two gate fingers, there is a
slight improvement in noise figure. This can be explained solely by an improvement
in gate resistance. Beyond two fingers, there is little additional benefit. These scaling
51

CHAPTER 2. NOISE FIGURE MODELING OF ALGAN/GAN HEMTS
results will be used in § 3.5.4 and § 3.5.5.
Therefore, the best geometry is a smaller total gate width, to keep Rg and Igs from
becoming to large, and two or four gate fingers. Too small a device, and Rs and Ri
will be too large. Many papers published for best NFmin performance typically have
device widths of ∼100 µm .
NF min (dB)
r n
1
0.95
0.9
0.85
0 2 4 6 8 10
Gate Fingers
0.8
0.78
0.76
0.74
0.72
0.7
0 2 4 6 8 10
Gate Fingers
|Γ opt |
(degrees)
Phase Γ opt
0.8
0.79
0.78
0.77
0.76
0 2 4 6 8 10
Gate Fingers
(a) (b)
18
17
16
15
14
0 2 4 6 8 10
Gate Fingers
(c) (d)
Figure 2.13: (a) Minimum noise figure, (b) magnitude and (d) phase of optimum
source reflection, and noise resistance (c) all versus number of gate fingers for a constant
total gate width.
52

CHAPTER 2. NOISE FIGURE MODELING OF ALGAN/GAN HEMTS
2.6.5 Discussion of the Model
The model is now checked against measurements, compared to the other noise mod-
els, and its limitations are discussed. Figure 2.14 shows noise parameter data for the
35% device of table 2.1 and prediction using the model in Matlab and a circuit simula-
tion. The fit for all four parameters is very good for both the small-signal simulation
and the equations entered into Matlab. The small-signal simulation using ADS is for a
NF min (dB)
r n
2.5
2
1.5
1
0.5
4 6 8 10 12
Frequency (GHz)
1
0.9
0.8
0.7
0.6
0.5
4 6 8 10 12
Frequency (GHz)
|Γ opt |
Angle Γ opt (Degress)
0.8
0.75
0.7
0.65
0.6
0.55
4 6 8 10 12
Frequency (GHz)
60
50
40
30
20
10
4 6 8 10 12
Frequency (GHz)
Figure 2.14: Noise parameters predicted using the model (solid line) and in a full
small-signal circuit simulation (dotted line) compared to measurements (crosses). The
small-signal parameters are from table 2.1.
53

CHAPTER 2. NOISE FIGURE MODELING OF ALGAN/GAN HEMTS
full small-signal model (including Cgd) and noise sources as in figure 2.7. The phase
match of Γopt with the Matlab script could be further improved by including the gate
inductance. Only the small-signal parameters and gate leakage were needed for the
Matlab script. The measured noise parameters were not needed beforehand as with
the Pospieszalski and CN models. This predictive power can help in better designs of
noise performance for devices, accurate estimations of the noise and the match to the
device, and understanding differences in noise performance for devices as performed
in chapter 3.
Of interest is how much different noise sources contribute to the overall noise figure.
This is presented in figure 2.15 using the model at an optimal bias for noise perfor-
mance. The channel thermal noise accounts for half the contribution to noise figure.
The resistances contribute roughly in proportion to their values relative to one another
as one might expect; they are all lumped together at the input. However, Rs effectively
degrades the gm and Cgs through source degeneration and should be minimized. The
gate leakage contributes about 10% for a device with a reasonably low amount of gate
leakage. This can be a much larger contributer, and will be discussed in § 3.5.4.
Some insightful parallels can be drawn between this modeling (equations 2.6.16,
2.6.20, 2.6.21 and 2.6.22), and Pospieszalski’s model (equations 2.5.11, 2.5.12, 2.5.13,
and 2.5.14). The simplest to see is that Xopt is the same for both models if the gate
leakage tends to zero. If the gate leakage is negligible, then the reactance of the match
54

CHAPTER 2. NOISE FIGURE MODELING OF ALGAN/GAN HEMTS
R i 18%
Gate
Shot
Noise
R g 7%
11%
R s 11%
53%
Drain
Noise
Figure 2.15: Relative contributions of different noise sources to the overall noise
figure.
reduces to that predicted by both Pospieszalski and Fukui. Not as easy to see is that
Ropt is of similar form for both models if b → 0. The other two parameters cannot be
compared so easily. However, the modeled Rn for both show that it increases slightly
with increasing frequency and both predict that Fmin depends on the square of the
frequency (which will be linear in plots of NFmin vs. frequency).
All the noise models discussed so far have a noise source at the gate and drain.
Table 2.3 shows typical input and output noise currents for the models. All the models
predict relatively the same magnitude of output noise. The models with correlation
show an input noise similar to one another, but two orders of magnitude smaller than
what Pospieszalski or this work predicts. This means that the cross-correlation terms
55

CHAPTER 2. NOISE FIGURE MODELING OF ALGAN/GAN HEMTS
(see, for example, equation 2.6.14) generate more noise than the gate noise. That
the model introduced here generates noise similar to that of Pospieszalski helps to
reinforce its validity.
�
2
〈iinput〉
�
2
〈ioutput〉 10
Model: van der Ziel Pucel Pospieszalski This Work
�
−24 A2
10 5.0 7.2 3100 1370
Hz�
−24 A2
490 480 300 490
Hz
Table 2.3: Comparison of the various noise models’ input and output noise currents.
The model can help in predicting NF, but it has its limitations. The most important
is the modeling fails when the gain drops because it does not take into account Cgd
or self-heating effects. This means it fails at frequencies close to fτ (f >fτ/2) and
at high DC biasings (Ids > 40 mA). A derivation with Cgd was undertaken, but no
closed form solutions could be found for the noise parameters and the equations were
too complicated to yield insight. It is possible that the gain could be corrected using
the Miller effect [31].
Also, the small-signal parameters must be accurately known. The parasitics re-
sistances need to be correctly modeled and the measured S-parameters must be as
accurate as possible. For example, the modeling was found to be poor when superior
network analyzer was substituted with a less accurate network analyzer.
56

CHAPTER 2. NOISE FIGURE MODELING OF ALGAN/GAN HEMTS
2.7 Summary
This chapter lead up to the presentation of a noise figure model that does not need
prior noise parameter measurements for accurate prediction. It will be used in other
parts of this work. All necessary background leading up to it was introduced, its
derivation presented in full, the model’s strengths and weakness explained, and how it
compares to the other popular noise models discussed.
References
[1] M. W. Pospieszalski, “Modeling of Noise Parameters of MESFET’s and MOD-
FET’s and Their Frequency and Temperature Dependence,” IEEE Trans. Microwave
Theory Tech., vol. 37, no. 9, pp. 1340–1350, Sept. 1989.
[2] R. A. Pucel, H. A. Haus, and H. Statz, “Signal and Noise Properties of Gallium Arsenide
Microwave Field-Effect Transistors,” in Advances in Electronics and Electron
Physics. New York: Academic Press, 1975, vol. 38, pp. 195–265.
[3] A. van der Ziel, Noise in Solid State Devices and Circuits. New York: Wiley-
Interscience, 1986.
[4] J. B. Johnson, “Thermal Agitation of Electricity in Conductors,” Nature, vol. 119,
pp. 50–51, 1927.
[5] H. Nyquist, “Thermal Agitation of Electric Charge in Conductors,” Phys. Rev.,
vol. 32, pp. 110–113, 1928.
[6] C. Kittel and H. Kroemer, Thermal Physics, 2nd ed. New York: W. H. Freeman
and Company, 2000.
[7] S. A. Maas, Noise in Linear and Nonlinear Circuits. Boston: Artech House, 2005.
[8] T. H. Lee, The Design of CMOS Radio-Frequency Integrated Circuits, 2nd ed.
New York: Cambridge University Pess, 2004.
[9] M. J. Buckingham, Noise in Electronic Devices and Systems. New York: John
Wiley & Sons, 1983.
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State Physical Electronics. Upper Saddle River, NJ: Prentice Hall, 2000.
57

CHAPTER 2. NOISE FIGURE MODELING OF ALGAN/GAN HEMTS
[11] W. Liu, Fundamentals of III-V Devices: HBTs, MESFETs, and HFETs/HEMTs.
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the FET Small-Signal Equivalent Circuit,” IEEE Trans. Microwave Theory
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[14] P. H. Ladbrooke, MMIC Design: GaAs FETs and HEMTs. Boston: Artech House,
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58

CHAPTER 2. NOISE FIGURE MODELING OF ALGAN/GAN HEMTS
[26] H. Fukui, “Design of Microwave GaAs MESFET’s for Broad-Band Low-Noise
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59

3
Noise Figure Measurements and Studies
3.1 Introduction
WITH the frame work for noise figure laid in the previous section, we now
concentrate on noise figure measurements of AlGaN/GaN HEMTs. The
technology used to fabricated the devices is presented first. The setup used for the
measurements will be discussed, and the methodology used for comparisons explained.
The bulk of this chapter is devoted to several noise figure studies of AlGaN HEMTs.
These studies look at how different epitaxial material and device structures affect the
noise figure performance. The effect of a field plate (FP) and gate leakage on noise
figure are profound, and will be covered in § 3.5.4 and § 3.5.5. The modeling devel-
oped in the previous chapter is used to understand how a FP and gate leakage affect
the noise performance. Another interesting type of GaN HEMT, known as a thick cap
HEMT, was measured and will be briefly covered. It is of great interest to know about
the state-of-the-art of GaN HEMT noise performance and how it compares to HEMTs
in GaAs and Si material systems. This is done in § 3.6
60

CHAPTER 3. NOISE FIGURE MEASUREMENTS AND STUDIES
3.2 Device Details
Devices from several samples with different epitaxial structures will be discussed,
but they are similar from growth and processing points of view. The devices were
all grown by metal-organic chemical vapor deposition (MOCVD) on both c-plane
sapphire and c-plane 4H-SiC substrates. The epitaxial structures that will most com-
monly appear in this work are in figure 3.1, which will be referenced throughout the
chapter. The key differences in the samples are choice of substrate (sapphire or SiC)
and inclusion of an AlN interlayer between the AlGaN barrier and the GaN channel.
29 nm 27% AlGaN: Si
1700 nm UID GaN
65 nm AlN
750 nm GaN: Fe
Sapphire Substrate
(a)
29 nm 35% AlGaN: Si
0.6 nm AlN
1700 nm UID GaN
65 nm AlN
750 nm GaN: Fe
Sapphire Substrate
(b)
29 nm 27% AlGaN: Si
1300 nm UID GaN
300 nm GaN: Fe
160 nm AlN
SiC Substrate
Figure 3.1: Typical epitaxial structure for the devices in this work: (a) standard HEMT
on a sapphire substrate (b) HEMT with AlN interlayer (c) standard HEMT on siliconcarbide
substrate
After choice of substrate, growth consists of a nucleation layer. This layer may in-
clude iron (Fe, an accepter) in it, as in figure 3.1 (a), to reduce the buffer conductive
(caused by unintentional doping). The decrease in conductivity improves the break-
down of the device for power applications. An unintentionally doped GaN layer grown
61
(c)

CHAPTER 3. NOISE FIGURE MEASUREMENTS AND STUDIES
next will be the channel, and a 29 nm AlGaN Si-doped layer finishes the structure. The
Al composition varies with the sample, but is 27 % if not stated explicity.
Device processing began with Ti/Al/Ni/Au electron beam evaporated source and
drain contacts. These were annealed at 870 ◦ C for 30 s in a rapid thermal annealer
(RTA). Device isolation was achieved by reactive ion etching (RIE) in Cl2. Stepper
photolithography Ni/Au/Ni gates were electron beam evaporated with a gate length of
0.7 µm. SiN passivation was achieved with plasma-enhanced chemical vapor deposi-
tion (PECVD). If a field plate is used, it would now be added as a repeated and slightly
shifted gate metal layer. All devices in this chapter have a gate width of 1x150 µm,
a gate-source spacing of 0.7 µm, and a gate-drain spacing of 2 µm. The pads are a
coplanar waveguide (CPW) layout.
Typical measurements of fτ and fmax are 23 and 47 GHz respectively. Contact
resistance is from 0.3 to 0.6 Ω–mm. Charge and mobility vary with the Al composition
of the barrier. For compositions ranging from 15 % to 35 %, the mobility was found
to be 1100-1565 cm 2 /Vs and the charge 0.4-1.3x10 13 cm −2 by Hall measurements.
More details about the device details and processing can be found in [1–4].
3.3 Noise Figure Measurement Setup and Method
Noise figure measurements were performed with a PC–controlled source–pull noise
figure setup. A schematic is in figure 3.2. At the heart of the system is the noise figure
62

CHAPTER 3. NOISE FIGURE MEASUREMENTS AND STUDIES
Bias-T
RF
Switch
Noise
Source
Source
Tuner
RF Probe
Station
Tuner
Controller
Bias
Controller
Network
Analyzer
Computer
Load
Tuner
GPIB
Cable
Bias-T
RF
Switch
Noise
Figure
Meter
BNC
Cable
Figure 3.2: Schematic of the source-pull noise figure setup.
meter, noise source, and source tuner. The HP 8970S noise-figure meter system con-
sists of the HP 8970B noise figure meter, HP 8970C test set, and a signal generator
that acts as a local oscillator for the 8970C. Typical error is ±0.15 dB. To find the de-
vice minimum noise figure, a variable source impedance is generated by a Maury Mi-
crowave MT982A02 mechanical motorized tuner. The load tuner was set to 50 Ω. The
device gain during measurement could have been improved by moving the load tuner
63

CHAPTER 3. NOISE FIGURE MEASUREMENTS AND STUDIES
to a small-signal match, but due to a combination of hardware and software problems
better measurements were obtained with it at the reference impedance. However, the
software automatically calculates the gain for a noise input match and power output
match.
The device S-parameters at each bias are needed. A Maury Microwave MT998C
RF switch box and an HP 8722D vector network analyzer (VNA) made it possible to
seamlessly switch between noise and S-parameter measurements of devices. All mea-
surements were performed on-wafer with Cascade-Microtech ACP40 ground-signal-
ground CPW probes. The bias was set automatically by an HP 6625A DC–power
supply system. All components were controlled over a general-purpose interface bus
(GPIB) by a Maury Microwave proprietary software program which calculates the
noise parameters.
The accuracy of the system was checked in two ways. The first was by measur-
ing devices that were characterized elsewhere. The second was fabrication of CPW
on-wafer 10 dB attenuators alongside devices and circuits. The schematic and a pho-
tograph of the attenuator are in figure 3.3. Figure 3.3 (c) shows the measured loss and
minimum noise figure (NFmin). A passive device’s loss and NFmin will be the same in
decimals. As can be seen, the agreement is good.
To make NF comparisons, several factors need to be taken into consideration. First,
devices across a GaN wafer are not uniform due to the quality of research-grade mate-
64

CHAPTER 3. NOISE FIGURE MEASUREMENTS AND STUDIES
R1
Ground
2R 2
In
R1
R1
Out
2R 2
R1
In Out
(a)
R2
Ground
dB
11
10.8
10.6
10.4
10.2
10
9.8
9.6
9.4
9.2
NF min
Loss
9
4 5 6 7 8 9 10 11 12 13 14 15
Frequency (GHz)
(b) (c)
Figure 3.3: Coplanar waveguide attenuator (a) schematic, (b) photograph, and (c)
measured loss and minimum noise figure against frequency.
F (unitless)
1.9
1.8
1.7
1.6
1.5
1.4
1.3
F
1/f τ
1/f max
0.10
0.09
0.08
0.07
0.06
0.05
0.04
0.03
0 20 40 60 80 100 120
0.02
140
Current (mA)
(1/GHz)
F (unitless)
2.2
2.0
1.8
1.6
1.4
1.2
0 20 40 60 80 100 120 140
Current (mA)
Figure 3.4: Noise factor, fτ and fmax for devices from different samples versus
current.
65
F
1/f τ
1/f max
0.20
0.18
0.16
0.14
0.12
0.10
0.08
0.06
0.04
0.02
(1/GHz)

CHAPTER 3. NOISE FIGURE MEASUREMENTS AND STUDIES
rial and growth reactors. These variations across a sample cause changes in the device
small-signal parameters and therefore in the fτ and fmax . Noise has a relationship to
fτ and fmax such that improvements in one of the quantities usually means an improve-
ment in the others. Figure 3.4 helps this argument. Here the inverse of fτ, inverse of
fmax, and noise factor, F (NF = 10 log 10(F)), are plotted for devices from two samples
as the drain-source current is changed. As the current increases, all three parameters
increase. There appears to be a close relationship between F and 1/fmax. This relation-
ship can be seen from the modeling in the previous chapter. fτ and fmax are usually
defined as
gm
fτ =
Cgs + Cgd
�
Rds
fmax = fτ
4(Ri + Rg)
(3.3.1)
(3.3.2)
Examining the last term in equation 2.6.16, we see a factor 1/ω 2 tau that is very similar
to equation 3.3.1. An exact instance of fmax is not seen in equation 2.6.16 (there is no
Rds), but there is some similarity. The use of source degeneration, as demonstrated in
§ 2.6.1, modifies Cgs and gm. This would affect fτ, fmax, and thus NFmin. That NFmin
would depend on fmax instead of fτ also makes sense from a power argument: noise
figure and fmax are based on power quantities while fτ is a current gain quantity. The
conclusion of this aside is that devices with similar fτ and fmax should have similar
noise.
Device geometry is also important when making comparisons. As seen in § 2.6.4,
66

CHAPTER 3. NOISE FIGURE MEASUREMENTS AND STUDIES
a wider device has a larger NFmin. Also, a device of smaller gate length usually has
better fτ and fmax. For a fair comparison then, only devices of the same geometry
should be compared.
Finally, there is the matter of device bias. As the DC bias to the transistor is changed
the noise parameters also change. The optimum bias for NFmin may change with
devices from different samples. In all measurements in this work, the bias is swept
twice, first Vds then Ids, to find the best NFmin performance possible for the device.
It is better to sweep Ids than Vgs as the threshold voltage changes across a sample.
The transistor’s noise parameters were then measured versus frequency at this bias. It
should be noted that the best bias for noise may not be the same as that of fmax, but it
is a good starting value.
To show the importance of having similar devices to NF, Rs, Ri, and Cgs variations
were simulated over the range of extracted values and entered into the model of chap-
ter 2. The results of this are in figure 3.5. Each parameter spans a change of NFmin of
0.2 to 0.3 dB. All measurements in this work are at a bias and source-impedance for the
best NFmin attainable from the device. For measurements versus bias, a frequency was
used that gave the most stable and repeatable measurement (usually 5 GHz, sometimes
10 GHz). As the bias was changed, S-parameters were re-measured and the optimum
source-impedance re-evaluated. When comparing devices from different samples, fτ
and fmax measurements were first performed to find devices with similar performance.
67

CHAPTER 3. NOISE FIGURE MEASUREMENTS AND STUDIES
NF min (dB)
2.2
2.1
2.0
1.9
1.8
1.7
R s
Capacitance (pF)
0.20 0.21 0.22 0.23 0.24 0.25
3 4 5 6 7 8 9 10 11 12
R i
Resistance (Ω)
Figure 3.5: Variation in expected minimum noise figure with changes in three smallsignal
parameters.
3.4 Bias Dependence
Transistors in Low Noise Amplifiers (LNA) are biased at low currents and voltages
for maximum NF performance and to reduce power consumption. A GaN HEMT
biased at a “low” bias is likely beyond the breakdown of other material technologies.
Therefore, it is of interest to know how the noise parameters change with device bias,
which leads to some interesting results in this work. Also, knowing how the noise
changes with bias is necessary for noise sources extracted from NF measurements
that are included in device circuit simulations for oscillator phase noise.
Figure 3.6 displays all four noise parameters, the associated gain, and maximum
gain at a frequency of 10 GHz for drain-source voltages, Vds, 2 to 20 V. The drain-
68
C gs

CHAPTER 3. NOISE FIGURE MEASUREMENTS AND STUDIES
Figure 3.6: Change in noise parameters with drain-source voltage at 10 GHz: (a)
Minimum noise figure (b) magnitude and phase of optimum reflection coefficient (c)
noise resistance (d) device associated and maximum gains.
69

CHAPTER 3. NOISE FIGURE MEASUREMENTS AND STUDIES
source current, Ids, is kept constant at the best bias for NFmin. The small-signal asso-
ciated power gain is that available when the input is matched for noise and the output
for power. The maximum gain is of a small-signal input and output conjugate match.
NFmin flattens out above Vds ∼3 V. The other noise parameters are nearly flat, except
for the phase which decreases slightly. This is probably from a slight change in Cgd
with Vgd. From these measurements, it can be concluded that once the device saturates
the noise parameters can be considered constant.
What is more interesting is how the noise parameters change with the drain-source
current. The measured noise parameters of this are the solid circles in figure 3.7
for a sample with a sapphire substrate and 35 % Al in the barrier at a measurement
frequency of 5 GHz. Now we find that NFmin and rn increase with current. NFmin does
not increase because of a large increase in device noise. The reason is that the gain
drops with the increasing current. The gain is lower because the channel is opened
(loss of transconductance) and self-heating (from the high currents involved). That
the gain affects the noise figure directly is seen in equation 2.6.9. The magnitude
of the optimum source reflection coefficient, Γopt, decreases with increasing current
while its phase decreases. This is a result of the match changing with loss of gain and
increasing Cgs.
To further investigate the usefulness of the Pospieszalski and CN models, they
were applied to these noise measurements. Measurements of fτ and fmax (needed
70

CHAPTER 3. NOISE FIGURE MEASUREMENTS AND STUDIES
(a) (b)
(c) (d)
Figure 3.7: Typical plots of the noise parameters versus drain source current as measured
(circles) and using the Pospieszalski (dash-dot line) and CN (solid line) models:
(a) Minimum noise figure (b) magnitude of optimum reflection coefficient (c) noise
resistance (d) and phase of optimum reflection coefficient. Measurement frequency is
5 GHz.
71

CHAPTER 3. NOISE FIGURE MEASUREMENTS AND STUDIES
for Pospieszalski’s formulation) and extracted small-signal parameters were collected
at each bias the noise parameters were measured at in figure 3.7. Then, using meth-
ods in § 2.5, a small-signal model with noise sources from either Pospieszalski’s or
the CN formulation were created in ADS. ADS was then used to simulate the noise
parameters. The results were added to figure 3.7. The solid lines are simulations us-
ing the CN model and the dash-dot lines using the Pospieszalski model. Both models
predict the noise parameters for the GaN HEMT versus bias well and can be used for
bias-dependent noise parameter modeling of GaN HEMTs.
The modeling in § 2.6 does not work to predict the noise parameters versus bias.
It only works at low biasings (Ids < ∼40 mA in this work) because it does not take
into account reduction in gain from self-heating. Because the Pospieszalski and CN
models are fitting to the data at these high biases, they predict the noise parameters
correctly. However, the model can still be used to explain trends seen in the noise
parameters versus bias. Equation 2.6.22 shows that as NFmin increases and |Γopt|
decreases with increasing current, then Rn should increase as well.
Figure 3.8 shows how the noise variables used for the simulations in figure 3.7
change with bias. These variables are the quantitative values of noise sources entered
in a circuit simulator, such as ADS. For example: shot noise changes with DC cur-
rent, thermal noise changes with resistance, and a Pospieszalski thermal noise source
changes with the noise temperature. We see in figure 3.8 (a) that the correlation coef-
72

CHAPTER 3. NOISE FIGURE MEASUREMENTS AND STUDIES
(a)
(c)
Figure 3.8: Noise variables for the Pospieszalski and a CN noise model versus drain
source current: (a) magnitude and phase of the correlation coefficient and (b) gate and
drain noise for a CN model. The device gm, multiplied by a factor of 10 to better fit
the scale, is also in (b). (c) Drain and gate noise temperatures of the Pospieszalski
model for varying current.
ficient magnitude and phase are relatively flat versus current. This supports the work
of S. Lee on GaN HEMTs [5,6]. After detailed analysis using the CN model, Lee con-
cluded that the correlation coefficient could be considered constant with a magnitude
73
(b)

CHAPTER 3. NOISE FIGURE MEASUREMENTS AND STUDIES
of 0.7 and phase of 90 ◦ after de-embedding extrinsic thermal and shot noise. Here,
we see the same magnitude but a slightly higher phase. The increase in phase is likely
from the shot noise of the gate leakage. While Lee’s results were only versus fre-
quency, we see here that it holds versus bias as well. To the author’s knowledge, there
is no reference in the GaN literature that has the noise variables using the CN model
versus bias. We might expect the input and output noise currents in figure 3.8 (b) to
behave as van der Ziel predicts in equations 2.5.1 and 2.5.2. Then the drain noise,
〈i 2 d 〉, should follow changes in gm versus bias. Ten times the value of gm (for the con-
venience of plotting) is also in figure 3.8 (b). 〈i 2 d〉 appears to follow the same trend.
The gate noise, �
i2 �
g , also seems to follow what van der Ziel would predict (a C2 gs/gm
dependence).
Turning to the Pospieszalski model in figure 3.8 (c), the two noise temperatures are
plotted against Ids. The gate noise temperature is relatively flat. This agrees with the
one GaN reference in the literature [7], and what is seen in GaAs HEMTs. Here, the
drain noise temperature drops. This is the opposite of what would be expected but is
easily explained. The sapphire sample the device was on did not have a good buffer,
making Rds low (less than 1 kΩ instead of ∼1.5 kΩ). As the current increased, Rds
dropped off dramatically (900 Ω to 100 Ω). The term Td/Rds is prevalent through
Pospieszalski’s equations. In fitting to the data, Td decreased along with Rds to keep
the correct proportion. In other samples with a good buffer (only a slight drop in Rds),
74

CHAPTER 3. NOISE FIGURE MEASUREMENTS AND STUDIES
Td will increase.
3.5 GaN HEMT Noise Figure Studies
3.5.1 Substrate
The effect of substrate on the noise parameters was carried out on samples with
SiC and sapphire substrates having 25% Al in the barrier and structures similar to
figure 3.1 (a) and (c). Versus frequency, devices from both samples had very similar
Figure 3.9: Minimum noise figure, small signal associated and maximum gain for
devices on sapphire and SiC substrates.
75

CHAPTER 3. NOISE FIGURE MEASUREMENTS AND STUDIES
noise parameters. As the current was varied, a difference in performance of NFmin
emerged. Figure 3.9 shows that the sapphire sample had worse noise figure perfor-
mance at higher biasings. At 100 mA, the difference is more than 0.5 dB. Also plotted
are the associated and max gains for both devices shown. The sapphire sample gains
fall much quicker as the bias increases. As stated earlier, if the gain drops then the
noise figure will too. Devices on sapphire have degraded power performance at high
biasings because of self-heating. Here, we see it affects noise figure performance as
well. A previous study confirms the noise degradation is caused by self-heating with
temperature dependent measurements [8].
3.5.2 Al Composition in the Barrier
To investigate if changing the Al composition in the AlGaN barrier had an effect
on noise, four samples were grown with 15%, 25%, 27%, and 35% Al on a sapphire
substrate. The rest of the structure for all four samples was the same as in figure 3.1 (a).
Lu previously published this study for GaN HEMTs [9]. He found that devices of high
Al composition (35 %) had better noise performance than low Al composition (15 %).
However, the reported fτ and fmax for the samples were not similar. fτ increased with
higher Al composition from 25 GHz to 50 GHz and fmax increased from 55 GHz to
101 GHz. The four samples in this study had reasonably similar fτ and fmax. Noise
parameters of the four samples for changing frequency are plotted in figure 3.10. Also,
76

CHAPTER 3. NOISE FIGURE MEASUREMENTS AND STUDIES
NF min
r n
2.4
2.2
2.0
1.8
1.6
1.4
1.2
1.0
2.0
1.8
1.6
1.4
1.2
1.0
0.8
0.6
0.4
0.2
35%
27%
25%
15%
3 4 5 6 7 8 9 10 11 12 13
Frequency (GHz)
(a)
0.0
3 4 5 6 7 8 9 10 11 12 13
Frequency (GHz)
(c)
|Γ|
Gain (dB)
1.0
0.8
0.6
0.4
0.2
0.0
16
14
12
10
8
35%
27%
25%
15%
4 6 8 10 12
Frequency (GHz)
(b)
6
3 4 5 6 7 8 9 10 11 12 13
Frequency (GHz)
(d)
Figure 3.10: Noise parameters versus frequency for devices of different aluminum
composition in the barrier: (a) Minimum noise figure (b) magnitude and phase of
optimum reflection coefficient (c) noise resistance (d) device associated gain.
77
180
160
140
120
100
80
60
40
20
0
Phase Γ (Degrees)

CHAPTER 3. NOISE FIGURE MEASUREMENTS AND STUDIES
NF min (dB)
3.8
3.6
3.4
3.2
3.0
2.8
2.6
2.4
2.2
2.0
1.8
1.6
1.4
1.2
35%
27%
25%
15%
1.0
0 20 40 60 80 100 120 140
Current (mA)
Figure 3.11: Minimum noise figure of samples with different aluminum composition
in the barrier at varying drain-source current.
NFmin for the samples versus Ids are in figure 3.11. The data are astonishingly similar
for noise measurements, and challenge the previous report. The application of the CN
and Pospieszalski models to these devices, presented earlier in table 2.2, also agrees
that the noise parameters should be very similar. It is interesting that the drain-source
current bias for best NFmin was similar for the different samples (15±5mA). For the
15 % Al sample this was nearly half Ids,sat while only 8 % Ids,sat for the 35 % Al
sample.
3.5.3 AlN Interlayer
The addition of an extremely thin (one or two monolayers) AlN layer between the
GaN channel and the AlGaN barrier has been found to increase the conduction-band
78

CHAPTER 3. NOISE FIGURE MEASUREMENTS AND STUDIES
NF min (dB)
4.0
3.5
3.0
2.5
2.0
1.5
1.0
0 20 40 60 80 100 120 140
Current (mA)
NF min AlN
NF min no AlN
f τ AlN
f τ no AlN
f max AlN
f max no AlN
Figure 3.12: Minimum noise figure, fτ, and fmax versus drain-source current for a
sample with (squares) and without (circles) an AlN interlayer.
offset, better confining the 2-DEG and improving mobility [10]. This should improve
the device fτ and fmax. It is therefore worth determining if it improves the noise
performance as well. Samples with structures as in figure 3.1 (a) and (b) with 35%
Al in the barrier on sapphire substrates were measured for noise. Overall, devices on
the sample with the AlN-interlayer had fτ and fmax values marginally higher than the
sample without. However, for the noise measurements devices with as similar of fτ
and fmax as could be found were used.
There were no differences in the noise parameters versus frequency, but as the drain
current increased a large difference in NFmin was apparent. This is in figure 3.12 as
the solid symbols. At a current of 100 mA, there is a 0.4 dB difference and at the
79
45
40
35
30
25
20
15
10
5
0
Frequency (GHz)

CHAPTER 3. NOISE FIGURE MEASUREMENTS AND STUDIES
(dB)
16
14
12
10
8
6
4
Gain AlN layer
Gain no AlN
Gmax AlN layer
Gmax no AlN
2
0 20 40 60 80 100 120 140
Current (mA)
(a)
R s (Ω)
26
24
22
20
18
16
14
12
10
8
6
with AlN interlayer
without AlN
0 10 20 30 40 50 60 70 80 90
Current (mA)
(b)
Figure 3.13: (a) Associated and maximum gain and (b) source resistance for devices
with and without an AlN interlayer at different applied currents.
max current a 0.8 dB difference. While the gain (figure 3.13 (a)), f τ, and fmax (also
in figure 3.12) do drop off slightly faster for the sample without the AlN, it is not as
dramatic as the sapphire/SiC substrate comparison and not enough to explain such a
large NFmin difference.
Rs appears to be the cause of the difference. Palacios has shown that Rs increases
drastically with drain-source current [11]. Figure 3.13 (b) shows the measured source
resistance (using the method in [11]) for devices from both samples. The devices with
the AlN-interlayer see an Rs increase of about two times, while the devices without
the interlayer see an increase of three times. These Rs measurements are only out to
80 mA (equipment limitations), instead of 135 mA as in figure 3.12. The difference
in Rs would be even larger at higher biases. As seen with the modeling using source-
degeneration in chapter 2, Rs can be thought of as directly adding noise at the input,
80

CHAPTER 3. NOISE FIGURE MEASUREMENTS AND STUDIES
which increases the noise.
As mentioned, devices on the sample with the AlN-interlayer overall tend to have
higher fτ and fmax. These devices will have a slightly better NFmin. However, the
improvement is at best 0.1 dB in the X-band.
3.5.4 Gate Leakage
While trying to do a comparative study, devices from a sample (27% Al content
barrier with SiC substrate) that had similar fτ and fmax did not have similar NFmin.
In fact, NFmin differed by almost 1 dB despite the gains being identical as seen in
figure 3.14. It was realized that the gate leakage was very different for the three devices
in figure 3.14. The three terminal gate leakage, Igs, at a bias of Ids = 10 mA, Vds =5V
for the devices was found to be: 22 µA (or 140 µA/mm); 73 µA (or 486 µA/mm);
141 µA (or 940 µA/mm). The devices are labeled as such in figure 3.14. We see that
as the gate leakage increases, so does the noise figure. To explore how gate leakage
affects the noise parameters, the modeling in § 2.6 was used. Small-signal parameters
that approximately matched all three devices in figure 3.14 were entered into Matlab
using the script in appendix B. The gate leakage was swept from 10 −8 to 10 −2 A and
the calculated noise parameters plotted (as lines) in figure 3.15 with data (crosses) for
the devices in figure 3.14. The circles are data from another sample that exhibits an
expected amount of gate leakage. The agreement of simulation and data for NFmin
81

CHAPTER 3. NOISE FIGURE MEASUREMENTS AND STUDIES
Figure 3.14: (a) Minimum noise figure, (b) device associated gain, and maximum gain
versus frequency for devices with different gate leakage currents. The gate leakage
quoted is at the same bias as the noise measurements (Ids = 10 mA, Vds = 5 V).
is excellent. The other parameters do not agree perfectly, but it should be reiterated
that the small-signal parameters used were typical for all three devices (they were not
identical). No change in rn was predicted or measured.
Gate leakage has a large effect on the noise parameters. It must be monitored, along
with fτ and fmax, when measuring noise figure of GaN devices. While gate leakage
and NFmin have been studied previously [6, 12–14], these studies are all lacking in
at least one of the following ways: use of fitting, inadequate data, only predicting
NFmin, or not applied to GaN. The combination of analytical modeling (without fitting
parameters), data presented, and agreement of modeling and data here is unique and
82

CHAPTER 3. NOISE FIGURE MEASUREMENTS AND STUDIES
r n
NF min (dB)
5
4
3
2
10 -8 10 -7 10 -6 10 -5 10 -4 10 -3 10 -2
1
I (A)
gs
2
1.75
1.5
1.25
1
0.75
0.5
0.25
|Γ opt |
1
0.8
0.6
0.4
0.2
10 -8 10 -7 10 -6 10 -5 10 -4 10 -3 10 -2
0
I (A)
gs
(a) (b)
140
10 -8 10 -7 10 -6 10 -5 10 -4 10 -3 10 -2
0
I (A)
gs
Phase Γ opt (degress)
120
100
80
60
40
10 -8 10 -7 10 -6 10 -5 10 -4 10 -3 10 -2
20
I (A)
gs
(c) (d)
Figure 3.15: Simulated (line) and measured (crosses) noise parameters for devices
with different gate leakage currents: (a) Minimum noise figure (b) magnitude of optimum
reflection coefficient (c) noise resistance (d) phase of optimum reflection coefficient.
Frequency is 10 GHz. The circles are data from another sample with the
typically expected amount of gate leakage.
clear.
A final note: GaN HEMTs on MBE were measured by the author. Their power and
small-signal performance are comparable to MOCVD-based HEMTs, but the devices
had higher gate leakage and thus ∼0.15 dB more noise.
83

CHAPTER 3. NOISE FIGURE MEASUREMENTS AND STUDIES
3.5.5 Field-Plated Devices
The addition of a FP has led to GaN HEMTs having impressive power handling
capability at microwave frequencies [15, 16]. There is a penalty, which is shown in
figure 3.16. 1 A FP increases Cgd, and that reduces fτ and fmax. In fact, the longer
the FP, the higher the breakdown and lower the fτ ,fmax , and gain of the device. The
author decided to investigate the noise performance. Based on the studies presented
thus far, one would predict that a FP device would have worse NF performance.
Frequency (GHz)
60
55
50
45
40
35
30
25
20
15
f τ
f max
0.0 0.2 0.4 0.6 0.8 1.0 1.2
Field-Plate Length (µm)
Figure 3.16: fτ and fmax of devices with different field-plate lengths.
This turned out not to be the case. Figure 3.17 (a) demonstrates that as the FP
length increases the NFmin improves despite decreasing gain (Figure 3.17 (d)). The
1For all measurements in this section, the devices with different FP lengths are on the same die of a
sample.
84

CHAPTER 3. NOISE FIGURE MEASUREMENTS AND STUDIES
NF min (dB)
r n
1.8
1.6
1.4
1.2
1.0
0.8
4 6 8 10
Frequency (GHz)
(a)
1.2
1.0
0.8
0.6
0.4
1.1 µm
0.9 µm
0.7 µm
0.5 µm
None
4 6 8 10
Frequency (GHz)
(c)
|Γ|
Gain (dB)
0.8
0.6
0.4
0.2
14
12
10
8
6
4
1.1 µm
0.9 µm
0.7 µm
0.5 µm
None
0.0
20
4 6 8
Frequency (GHz)
(b)
10
4 6 8 10
Frequency (GHz)
(d)
Figure 3.17: Noise parameters versus frequency for devices with field plates of different
length: (a) Minimum noise figure (b) magnitude and phase of optimum reflection
coefficient (c) noise resistance (d) device gain when matched at the input for best noise
performance and the output for power performance.
85
180
160
140
120
100
80
60
40
Phase Γ (degree)

CHAPTER 3. NOISE FIGURE MEASUREMENTS AND STUDIES
improvement is almost 0.2 dB. There is little additional improvement for a FP longer
than 0.9 µm. The match changes monotonically with the FP in Figure 3.17 (b). The
improvement in NF with a FP was first reported by the author in [17] and was later
confirmed in [18].
Several explanations to understand this result were explored. The first was to look
at the gate leakage. It was thought that maybe the FP was reducing the electric field
and possibly the gate-drain contribution to gate leakage. The three and two-terminal
gate leakage of 100 µm wide devices with different FP lengths was measured. Some
of the three-terminal measurements are in figure 3.18. The bias was set to Vds 5V
(similar to noise measurements) and Vds 20 V (a low bias for power) and Vgs a volt
past the threshold voltage. It does not appear that the FP lowers gate leakage. In fact,
it appears to increase slightly with the FP.
Another thought was that perhaps there was a difference in electric field causing a
change elsewhere than gate leakage. The analysis of Γ in § 2.6.3 was examined to see
if it might change because of a FP. This proved to not be true. A change in Γ would
mean a change in the DC I–V characteristics of a FP from a non-FP device. The only
real change is that the knee voltage is better defined for a FP device [19]. That would
only cause Γ to go to its final value of 2/3 quicker. More proof that it was not the
electric field-profile was found by two other means. One was to look at NFmin versus
drain source voltage. No difference was apparent. Another was to run an ATLAS
86

CHAPTER 3. NOISE FIGURE MEASUREMENTS AND STUDIES
Gate Leakage (µA)
700
600
500
400
300
200
100
0
, V ds 20 V
, V ds 5 V
0.0 0.2 0.4 0.6 0.8 1.0 1.2
Field-Plate Length (µm)
Figure 3.18: Typical change in gate leakage for devices of increasing field-plate
length. Biasings are Vds 5V,Ids 10 mA and Vds 20 V, Vgs one volt past threshold.
Electric Field (V/cm)
6.0M
4.0M
2.0M
no FP, V ds 5 V
no FP, V ds 20 V
FP, V ds 5 V
FP, V ds 20 V
0.0
0.0 0.5 1.0 1.5 2.0 2.5
Distance (µm)
Figure 3.19: Electric field profile for a device with and without a FP at a bias of Vds 5
and 20 V with the gate biased close to Vt. The gray bars are the “physical lengths” of
the gate and field plate. Atlas simulation provided by Yuvaraj Dora.
87

CHAPTER 3. NOISE FIGURE MEASUREMENTS AND STUDIES
simulation and look at the difference in the electric field profile. This was done, and
the results are in figure 3.19. 2 The simulations at Vds 5 and 20 V show the total electric
field versus distance. The gate is biased close to the threshold voltage, as is the case
for best NFmin results. The bars sitting atop the x-axis represent the gate length (short)
and FP (long) lengths. While the peak electric field at the drain edge of the gate will
be significantly reduced when a HEMT is biased to 80 V or more, here for 5 and 20 V,
there is no difference. In fact, at Vds 5 V, there is practically no change in the field.
The small-signal parameters were also examined. Those that were found to change
with a FP are in figure 3.20. Cgd increases because of the extra capacitance the FP
provides. That Rgd decreases hints that it is either easier to charge Cgd or that the
leakage has increased the conductance between gate and drain. Rd decreases because
the effective distance between gate and drain is reduced by the length of the FP. Ri
does not appear to change. Any change in it is probably due to error in the small-signal
extraction having difficulty differentiating Rg and Ri. As the gate now has another set
of fingers in parallel, its resistance, and thus Rg, decreases. The FP and gate fingers
can be connected at their ends, further reducing gate resistance and the noise [20].
When trying to explain FP device NF performance, it was first thought that Rg was
the cause. However, the modeling at the time argued that the improvement in Rg was
not enough to cause the difference, particularly for the results in [18]. It was later
realized the devices and the modeling were not the same. Devices of different widths,
2 ATLAS simulation graciously provided by Yuvaraj Dora to the author’s specifications
88

CHAPTER 3. NOISE FIGURE MEASUREMENTS AND STUDIES
C gd (fF)
70
60
50
40
30
20
10
0
0.0 0.2 0.4 0.6 0.8 1.0
Field-Plate Length (µm)
70
60
50
40
30
20
10
0
R gd (Ω)
Resistance (Ω)
19
18
17
16
15
8
7
6
5
4
3
2
1
R d
R i
R g
0.0 0.2 0.4 0.6 0.8 1.0
Field-Plate Length (µm)
Figure 3.20: Small-signal parameters that change with a field plate.
and with/without the FP plus gate ends shorted, were being compared. The scaling
and modeling of chapter 2 were used yet again. How NFmin changes with gate width
for devices with and without a FP were simulated in Matlab and compared to the
author’s and Wu’s [18] measurements. Figure 3.21 makes this clear. The agreement
is very good, and it can now be concluded that the FP lowering the gate resistance
is what improves NFmin. That NFmin decreases despite the lower gain is because the
FP is acting as an external feedback capacitance between gate and drain (in parallel
with Cgd). Lossless feedback does not harm the noise figure, but it does lower the
gain [21]).
The reduction in NF does not justify the use of a FP as it reduces the gain consider-
ably (several decibels). Gain is in short supply at microwave frequencies and reducing
it so much may not justify NFmin improvement of just a few tenths of a decimal. In
89

CHAPTER 3. NOISE FIGURE MEASUREMENTS AND STUDIES
NF min (dB)
3
2.5
2
1.5
1
0.5
No FP
Long FP
Difference
0
0 50 100 150 200 250 300
Gate Width (µm)
Figure 3.21: Minimum noise figure versus gate width for devices with and without a
long field plate at a simulation frequency of 10 GHz. The difference between them, in
decimals, is plotted as the dotted line. The “x’s” are from this work (150 µm ) and Y.
Wu (243 µm ) [18].
NF min
1.8
1.7
1.6
1.5
1.4
1.3
1.2
1.1
1.0
0.9
0.8
0.7
4 GHz
7 GHz
10 GHz
0.0 0.2 0.4 0.6 0.8 1.0 1.2
Field-Plate Length (µm)
Figure 3.22: Minimum noise figure of the field-plated devices at different measurement
frequencies of 4, 7, and 10 GHz. As the frequency increases, the improvement
from a field plate decreases.
90

CHAPTER 3. NOISE FIGURE MEASUREMENTS AND STUDIES
addition, the benefit is reduced the higher the operating frequency because of the skin
effect on the gate resistance. This is demonstrated in figure 3.22. At 4 GHz, the im-
provement can be as much as 0.3 dB, but at 10 GHz the improvement is 0.1 dB. This
agrees with the results in [18].
3.5.6 Thick-Epitaxial Cap Devices
Shen has proposed a HEMT with a thick GaN cap on top of the AlGaN [22]. The
advantage of this structure is that a SiN passivation is not needed. As passivation
leads to problems of reliability for standard HEMTs, this new HEMT holds great
promise. It has the record for power performance without passivation. Its small-signal
characteristics are similar to standard HEMTs. Dr. Shen allowed the devices to be
measured for noise. The performance was similar versus frequency (in particular,
the gains), although the drain-source current needed to be higher for optimum noise
performance. The reason for this is clear after viewing the noise parameters versus
bias in figure 3.23. The cap devices have a NFmin optimum bias at 45 mA instead of
10 mA as seen with normal HEMTs. Rn and NFmin follow remarkably similar trends,
further reinforcing arguments made earlier in the chapter. NF min for the thick cap is
much lower at higher biasings than a standard HEMT, but is higher at low biasings.
The reason for this is likely the large gate leakage the device has at a low bias (68 µA
at Ids 10 mA for a 150 µm wide device). If the leakage can be controlled, these devices
91

CHAPTER 3. NOISE FIGURE MEASUREMENTS AND STUDIES
NF min (dB)
r n
3.6
3.4
3.2
3.0
2.8
2.6
2.4
2.2
2.0
0 20 40 60 80 100
2.0
1.8
1.6
1.4
1.2
1.0
0.8
0.6
0.4
0.2
Standard HEMT
Thick Cap
Current (mA)
(a)
0.0
0 20 40 60 80
Current (mA)
(c)
100
|Γ|
Gain (dB)
1.0
0.8
0.6
0.4
0.2
0.0
0 20 40 60 80 100
18
16
14
12
10
8
6
Current (mA)
(b)
4
0 20 40 60 80
Current (mA)
(d)
100
Figure 3.23: Noise parameters versus drain-source current of a thick cap device and
a standard HEMT: (a) Minimum noise figure (b) magnitude and phase of optimum
reflection coefficient (c) noise resistance (d) and associated gain. Measurement frequency
is 10 GHz.
92
180
160
140
120
100
80
60
40
20
0
Phase Γ (degrees)

CHAPTER 3. NOISE FIGURE MEASUREMENTS AND STUDIES
show great promise for noise performance.
3.6 Comparison of High-Performance GaN HEMTs to
Other Material Systems
By now, the reader might have asked the question, “How does GaN HEMT noise
figure performance compare to other material systems?” This will now be addressed.
Most all the devices in this work have a gate length of 0.7 µm due to equipment lim-
itations. It is hard to find published noise results in the literature at such a relatively
“long” gate length. In addition, many published noise figure results have large varia-
tions in the accuracy of their measurements.
Bearing this disclaimer in mind, 0.15 µm gate-length devices optimized for high-
frequency performance were obtained from Tomás Palacios. These devices are sim-
ilar to those in a recent publication that had an fτ of 150 GHz and fmax of over
200 GHz [23]. The measured NFmin against frequency is in figure 3.24 for two de-
vices. Repeated measurements at 10 GHz gave a consistent NFmin of 0.4 dB.
Keeping in mind this very good value, let us turn our attention to table 3.1. Here
we have an abundance of data on HEMTs from different material systems: GaN,
SiGe, InAlGaAs systems on GaAs and on InP. The gate lengths, gate widths, NFmin,
measurement frequency for NFmin, relevant information, and the reference number
found at the end of the chapter are all listed. Most obvious is that SiGe has some work
to do before its noise performance can be competitive with the other materials. InP
93

CHAPTER 3. NOISE FIGURE MEASUREMENTS AND STUDIES
Lg (µm) Wg ( µm ) NFmin (dB) Freq. (GHz) Note Ref.
GaN HEMTs
0.12 100 0.72 12 SiC substrate [24]
0.15 150 0.4 10 T. Palacios, UCSB —
0.15 200 0.6 10 SiC substrate [25]
0.15 100 0.75 10 SiC substrate [26]
0.17 100 1.1 10 Si substrate [27]
0.18 100 0.7 12 Sapphire substrate [8]
0.25 100 0.8 10 SiC sub., from graph [28]
0.25 100 1.05 18 Sap., from graph [9]
0.25 100 1.04 10 Sapphire substrate [29]
0.25 200 1.9 10 SiC substrate [30]
Si/SiGe HEMTs
0.1 100 1.6 10 from graph, pads de-emb. [31]
0.1 90 1.7 10 [32]
0.1 — 2.1 10 pads de-embedded [33]
0.1 100 3.2 10 [34]
(In,Al)GaAs/(In,Ga,Al)As on GaAs HEMTs
0.1 200 0.3 10 from graph [35]
0.1 — 0.51 18 [36]
0.1 100 0.64 26 mHEMT [37]
0.1 100 1.1 40 mHEMT [37]
0.13 140 0.31 12 pHEMT [38]
0.13 140 0.45 18 pHEMT [38]
0.25 — 0.7 18 [36]
(In,Al)GaAs/(In,Ga,Al)As on InP HEMTs
0.1 50 0.8 60 [39]
0.1 80 0.45 10 from graph [40]
0.1 80 0.61 20 from graph [40]
0.15 – 0.4 10 [41]
0.2 – 0.48 10 [42]
0.2 – 0.8 26 [42]
Table 3.1: Minimum noise figure for HEMT devices in many technologies. Also listed
are the gate length and width, measurement frequency, some necessary information,
and the reference.
94

CHAPTER 3. NOISE FIGURE MEASUREMENTS AND STUDIES
NF min (dB)
0.9
0.8
0.7
0.6
0.5
0.4
0.3
0.2
0.1
0.0
6 8 10 12 14 16
Frequency (GHz)
Figure 3.24: Minimum noise figure of two 0.15 µm gate length transistors provided
by Tomás Palacios.
provides the best performance, but GaAs and GaN are close competition in the X-
band. GaAs might have slightly better performance than GaN, but a 0.1 dB advantage
can be lost once the device is put in a circuit.
3.7 Summary
This chapter looked at a plethora of noise figure measurements of GaN HEMTs.
The methodology for procedures was explained and its importance made clear. Fac-
tors that changed NFmin (such as an AlN-interlayer and choice of substrate) were in-
vestigated. The importance of monitoring gate leakage was found and analyzed with
the modeling in § 2.6. The unexpected result of a FP improving NFmin was discovered
95

CHAPTER 3. NOISE FIGURE MEASUREMENTS AND STUDIES
and fully investigated, also with the use of the modeling from § 2.6.
Together with modeling from the previous chapter, this chapter helps point out ways
of obtaining the best NFmin possible. Most important is reducing the gate leakage and
parasitic resistances at the input. Rg and Rs also need to be minimized. The small-
signal power gain needs to be kept as high as possible. Self-heating causes an increase
in NFmin because of loss of device gain.
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97

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98

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100

4
Low-Frequency Noise of GaN HEMTs
4.1 Introduction
IT is surprising that a subject that has been studied for almost 80 years would not be
well-understood. But such is the case of low-frequency noise (LFN), the largest
contributor to phase noise of oscillators [1]. The main motivation of this chapter is to
create a model for circuit simulation. Most of the LFN literature for GaN consists of
theoretical explorations of devices (in some studies, just films), or measurements at
very low device biasing not suitable for practical device modeling. GaN HEMT LFN
studies at biasings typical for circuits are presented in this chapter. A new empirical
model is also presented. It is difficult to make LFN comparisons, particularly to most
published works due to the many ways the data are presented, but measurements by
the author for both GaAs and GaN HEMTs will be examined. In addition to the above
topics, the LFN setup will be described in detail, as most LFN setups are either poorly
described in papers or cannot bias as high as is necessary for GaN HEMTs.
101

CHAPTER 4. LOW-FREQUENCY NOISE OF GAN HEMTS
4.2 Review of Low-Frequency Noise
The terms LFN, flicker, 1/f, and generation-recombination (G-R) noise need clari-
fication. Flicker (also called 1/f) noise refers to phenomena that generate noise with a
slope inversely proportional to the frequency, hence “one on f.” A sample spectrum,
showing flicker noise and other contributions, is shown in figure 4.1. Resistors and
bulk material tend to be strictly 1/f, but devices, including HEMTs, deviate as 1/f γ
where γ is usually in the range of 0.7 to 1.3. For GaN HEMTs, experiments show γ
to be between 1 and 1.3 [2–4]. Generation-recombination noise refers to trap-related
capture and emission of carriers creating a spectrum of the form
SX(f) = �
4∆X 2� τ
1+ω2τ 2
(4.2.1)
that is measured as noise at low frequencies. Here, τ is the trap life time, ω the angular
frequency, and X a quantity that fluctuates (usually charge or mobility). Sometimes
the G-R spectrum, which will have a Lorentzian power spectral density, manifests
itself as a “bulge” on a 1/f spectrum, shown in figure 4.1. There is also a theory, most
often credited to McWhorter [5], 1 that a continuum of traps, with spectra of the form
in equation 4.2.1, of different life times is the source of the 1/f noise spectrum. This
model appears to work for CMOS [2], but it is not accepted for all device technologies.
Therefore, when referring to the noise at these low frequencies (less than ∼10 MHz),
be it from g-r, 1/f, or other unknown sources, the expression LFN will be used.
1 In truth, he did not create the concept but extended the theory.
102

CHAPTER 4. LOW-FREQUENCY NOISE OF GAN HEMTS
Noise
Spectral
Density
(I 2 or V 2 )
1/f γ noise
G-R "Bulge"
1/f Reference Line
Noise spurs
(outside source/interference)
Corner Frequency
Noise Floor
Frequency
Figure 4.1: Sketch of the key features of low-frequency noise.
It has already been hinted that traps with energies in the material band-gap are
one source of LFN. There are other possible sources: surface effects (such as surface
states), the bulk material itself, dislocations, tunneling, non-uniform channel resis-
tance, quantum effects, and others. Evidence for trying to explain LFN from any one
of these possible sources can be found in the literature. It is likely due to a combination
of several sources and that there will never be a unifying 1/f model for all devices.
HEMTs show orders of magnitudes more LFN noise than bipolar junction-transistor
(BJT) types of devices. This suggests a surface area or high-field dependence. Early
GaN HEMTs and material showed much worse LFN noise than results reported later.
The excess in the LFN was attributed to traps and dislocations [3]. Leinshtein re-
103

CHAPTER 4. LOW-FREQUENCY NOISE OF GAN HEMTS
ported [3] that GaN HEMTs had less LFN than observed in measurements of GaN
thin films, and suggested there was some suppression of LFN caused by the device.
Some types of LFN vary with the square of bias current, such as that of diodes. A
relationship that describes this, and that is used in circuit simulators is:
�
i 2 �
g,1/f = Kf
I Af
DC
f Ffe
(4.2.2)
Kf, Af, and Ffe are all fitting parameters, IDC is the DC current, and f is fre-
quency. For making theoretical comparisons of voltage, current, and resistance LFN
spectrums (SV (f), SI(f), and SR(f) respectively), the spectrum is often normalized
(SV (f)/V 2 DC , SI(f)/I 2 DC , and SR(f)/R 2 respectively). These spectrums are related
through Ohm’s law, and lead to the question, “What’s really fluctuating and causing
1/f noise?” If it is the resistance (which for HEMTs, means the channel resistance),
it has been reasoned that it is because of changes in mobility or charge. Because the
resistance varies with the inverse of mobility and charge, fluctuations in one of these
two quantities generates 1/f noise (in theory at least). This has lead to the two ma-
jor principles on which most 1/f theories are based: carrier density fluctuation and
mobility fluctuation modeling. The former is used in the G-R model (equation 4.2.1)
discussed earlier. In fact, equation 4.2.1 can be used to describe both models. It is
debated whether charge or mobility fluctuations are the source of noise; data supports
both. These models have been applied to describe GaN HEMT LFN [2–4].
104

CHAPTER 4. LOW-FREQUENCY NOISE OF GAN HEMTS
An interesting empirical relationship was proposed in 1969 by Hooge:
SI(f)
I 2 DC
= αH
Nf
(4.2.3)
where N is the number of carriers in the device and αH is a dimensionless quantity
known as the Hooge parameter. It has since been used to characterize many materials
and devices. It has also been used as a figure of merit and at times as a constant, such
as for characterizing 1/f noise of materials. However, according to Hooge himself, it
was not meant to be considered a constant [6]. αH was extracted for measurements
that appear in this chapter. As seen in figure 4.2 (a) and (b), αH changes considerably,
even with frequency of extraction (not surprising as the noise is not strictly 1/f). That
αH is not constant can be seen from other published results as well [3]. Therefore,
the author believes it should not be used for device comparisons and only for material
comparisons.
It is the aim of this chapter to create a LFN model that can be used in the computer-
aided design (CAD) software program Advanced Design System (ADS) and to make
comparisons of LFN in HEMTs. The theory discussed so far is not applicable to
circuit modeling. There is not yet agreement in the theory, and data are generally
at low biasings or not even for HEMTs. At high biasings where the electric fields
are high, traps may no longer be the dominant source of LFN. There is little published
literature of LFN models of HEMTs for use in circuit simulators. Therefore, work was
started from scratch. A setup that could handle the biasings typical of GaN HEMTs
105

CHAPTER 4. LOW-FREQUENCY NOISE OF GAN HEMTS
(a) (b)
Figure 4.2: Variation of α with (a) drain-source voltage bias and (b) frequency of
extraction for two devices on the same sample.
was built. Measurements of bias-dependence and geometry were performed. Other
studies of LFN performance were performed as time permitted.
A final consideration is how to present the data. There is little consistency in units
and an astonishing number of different choices: A 2 /Hz, V 2 /Hz, A/ √ Hz, V/ √ Hz,
A 2 , V 2 , nV/ √ Hz, input-referred versions of these and representations in dB or linear
formats. Sufficient information is not always presented in published articles to be
able to convert from one type of units to another. How the data is presented can also
give different results. For example, normalizing SI(f) by I 2 gives a different trend
of noise versus gate width than not normalizing. The author decided that presenting
noise as A 2 /Hz would be most familiar and convenient for a circuit designer and for
comparison purposes.
More information about LFN can be found in [3, 7–9]. A very good and easy-to-
106

CHAPTER 4. LOW-FREQUENCY NOISE OF GAN HEMTS
follow review can be found in [10]. The book edited by Balandin, [3], is a collection of
articles about noise in GaN including two that treat LFN of GaN HEMTs extensively.
4.3 Low-Frequency Noise Setup
It is hard to find a complete description for a LFN setup. Much time was spent
creating a satisfactory setup for GaN. Therefore, this section will explain what an ex-
perimentalist needs to know to create a setup. There are four main equipment concerns
for a LFN setup. The first is instrumentation to measure the power spectrum versus
frequency. The measurement range of interest is usually 10 Hz to 1 MHz (possibly
wider). Provided that a given spectrum analyzer can even measure such frequencies,
the LFN of the analyzer itself is usually larger than the device’s noise. Increased aver-
aging and reduction of the resolution bandwidth can help these problems; however, the
time for a single measurement becomes prohibitively long. Other instruments that can
be used include computer-controlled oscilloscopes (a long time sample is measured
and a FFT is then performed on a computer) and, the preferred tool, a dedicated FFT
instrument. An HP 3561A dynamic signal analyzer (DSA) is a dedicated instrument
for these types of measurements and was used in this work. It is part of the HP 3048
phase-noise system. The DSA noise floor was superior to other options available and
the HP 3048 software could automatically control it. However, the DSA could only
measure a maximum frequency of 100 kHz. Most measurements in this chapter were
107

CHAPTER 4. LOW-FREQUENCY NOISE OF GAN HEMTS
preformed from 10 Hz to 100 kHz with ∼300 points per decade.
Even with the DSA, the noise floor was not adequate for some measurements.
Therefore, the second equipment concern is the noise floor for which a low-noise
amplifier (LNA) is needed. A Stanford Research Systems SR560 LNA was used to
improve the noise floor. Its voltage gain was typically set to 40 dB (100 V/V, the
minimum to meet the instrument’s specified noise floor) and sometimes as high as
60 dB (for gate noise measurements). The HP3048 software could be adjusted for
the gain. The LNA was run off of internal lead-acid batteries while measuring. The
measured noise floor for the 3561A when its input was shorted is shown together with
the measured noise floor of the LNA (also shorted input) plus 3561A in figure 4.3. An
improvement of more than four orders of magnitude is seen. The measured noise floor
of the LNA in figure 4.3 is identical to its specifications.
The third equipment concern is biasing the device without interfering with the mea-
surement. Almost all DC power supplies, including older analog models, have active
circuitry to maintain the bias set point. This, combined with noise from the AC lines,
makes them impractical to use for LFN measurements. Hence, batteries are used.
9 V batteries are usually preferred as they are recognized to be low-noise. For GaN
HEMTs, even small devices can require high current (easily 100 mA or more). An
attempt to use several 9 V batteries for the drain lead to unexpected measurement
results once the device bias increased above the knee voltage. A rechargeable 12 V
108

CHAPTER 4. LOW-FREQUENCY NOISE OF GAN HEMTS
HP3561A alone
with SR560
Figure 4.3: Measured noise floor of the HP 3561A DSA only and with the SRS SR560
LNA (short-circuited input).
lead-acid battery, that could output 90 mA without disturbing the measurement, was
used for the drain bias. A 9 V battery was used for the gate biasing (two in series for
large threshold devices). These were used with a bias box (discussed more below).
Biases of Vds from 0.1 to 12 V, Ids from 5 to 90 mA, and Vgs from -0.05 to -9 V could
be obtained. This is far superior to most other setups, which are limited to biasing
conditions in the linear region of a GaN HEMT.
The final equipment concern is to protect the setup from outside electrical and me-
chanical interference. The setup was located on a vibration-isolation table, which
helped with mechanical interference (although it could still be determined when con-
struction work took place in the building or when a peer would walk by the setup).
109

CHAPTER 4. LOW-FREQUENCY NOISE OF GAN HEMTS
A metal box, that could be grounded to the rest of the setup, was made to fit over
the sample and probes of the RF probe station to shield against electrical interference.
This was required to get a good measurement and helped to reduce spurs by ∼30 dB.
Figure 4.4 shows the full schematic of the setup. The multimeters were Fluke
8012As and various hand-held battery-operated units. Multimeters for voltage and
current could be connected while measuring LFN, but ohm-meters had to be discon-
nected. A covered bias box was built. 10 turn, 3 W, 2 kΩ potentiometers were used
to vary the bias. The value of 2 kΩ was carefully selected to allow the maximum
range of measurable biasings. Ground loops destroy a measurement, so care must be
12V
Bias Box
9V
3W
2kΩ
Pot.
220Ω
3W
2kΩ
Pot.
10Ω
+ -
RL 25pF
100MΩ
Voltmeter
Ammeter
+ -
Capacitors
50pF to1000µF
Voltmeter
SR560 LNA
Gain = 1000 V/V
(60 dB)
BW: 0.01 to 1MHz
R ds
50Ω
Shielded
Device
1MΩ
HP3561A
FFT Box
Figure 4.4: Schematic of the setup used for device drain-side low-frequency noise
measurements.
110

CHAPTER 4. LOW-FREQUENCY NOISE OF GAN HEMTS
taken with the grounding. The bias-box chassis and device shield were grounded to
the negative terminal of the battery. While other setups may use a load resistance, RL,
to keep the source resistance seen by the LNA a constant (making it easy to convert
the measured voltage spectrum to a current spectrum), the author found this additional
parallel resistance to limit the measurable range of biases and the dynamic range of
the DSA. Instead, the effective RL is determined for each LFN measurement. This
resistance is the parallel combination of that seen on the drain side of the bias box and
Rds of the transistor. A bank of capacitors were connected at the gate to provide an
AC short while measuring the drain LFN.
Most aspects of the measurement must be done manually, as automation would only
add noise and ruin the data. The steps for a measurement are:
1. Determine the DC Rds of the device near the bias of interest (∆Vds/∆Ids).
2. Unplug power to drain and gate, and ground both ends of the drain pot (using
switches on bias-box).
3. Disconnect the device and LNA.
4. Measure the resistance of the bias box, Rbox. This is the parallel combination of
both halves of the potentiometer and associated circuitry.
5. Disconnect the multimeter used to measure Rbox (this would add a voltage that
disturbs the measurement).
6. Reconnect the device, LNA, and bias. Wait 1 minute for the LNA to settle (a volt
change at its input, such as turning on the device or changing the bias, causes it
to saturate).
7. Measure. Adjust the measured voltage spectrum by the parallel combination of
resistances (SI = SV /(Rbox||Rds) 2 ).
111

CHAPTER 4. LOW-FREQUENCY NOISE OF GAN HEMTS
Figure 4.5: A typical low-frequency plot.
The setup was checked by measuring the noise spectrum of resistors. This is flat
with a voltage spectrum equal to its thermal noise. 2 A typical HEMT’s LFN is shown
in figure 4.5. The dotted line is a 1/f reference line, showing the data is very nearly 1/f
in slope. There are several spurs, including one at 60 Hz (from lights and various AC
sources) and another large one at ∼70 kHz (believed to be a radio signal). The spurs
were found to always be present, and are removed from all other measurements in this
chapter.
2 Only when DC current flows through a resistor does it generate low-frequency noise.
112

CHAPTER 4. LOW-FREQUENCY NOISE OF GAN HEMTS
4.4 GaN HEMT Low-Frequency Noise Modeling
For modeling, the drain and gate LFN bias-dependence need to be determined. The
setup in § 4.3 was used to measure drain noise while an AC short was applied to the
gate. LFN was measured with the drain voltage held constant at Vds 5 V and the gate
voltage swept (changing Ids). Then noise for a constant Ids of 30 mA and varying Vds
was measured. Both of these results are plotted in figure 4.6. In this figure only three
of the decade values are plotted from each full LFN measurement for convenience
of displaying the data. Once the device saturates, the LFN does not change further
with Ids (and hence Vgs). However, LFN increases with Vds. This change, shown in
figure 4.6 (b), is more than an order of magnitude for the twelve volt bias range.
The magnitude of these LFN measurements at low biasings is consistent with the
literature. The only other published work of LFN noise of GaN HEMTs at high bias-
ings is by Hsu [4]. The measurements presented here for a saturated device agree with
that work, including the key result that the noise changes with Vds. In fact, Hsu claims
more bulging at higher biases (Vds > 12 V), and that the bulging broadens. This in-
crease of LFN with Vds was also observed in the GaAs devices to be discussed in § 4.6.
The slope, γ, was extracted and found to typically be about 1.15, varying from less
than 1.1 to nearly 1.3. Bias dependence was not clear, but usually γ would decrease
with increasing Vds and very slightly decrease with increasing Ids. The changing of
γ with bias is not well understood. It has been shown to vary with temperature as
113

CHAPTER 4. LOW-FREQUENCY NOISE OF GAN HEMTS
(a) (b)
Figure 4.6: Plots of the measured drain low-frequency noise with (a) change in drainsource
current and (b) voltage.
well. Previous research points to trap effects, tunneling, and hot-carriers as directions
to explore [2,4].
Despite the measurements being of noise, devices biased the same had very similar
measurements. This means that devices at the same bias can be compared. This is
used as a basis for device comparison studies later in the chapter.
The gate LFN was measured with the drain AC shorted. Vds was set to 5 V and the
gate voltage was varied. As seen in figure 4.7, even at its noisiest the gate LFN is more
than three orders of magnitude smaller than the drain noise. Measurements above a
few kHz hit the noise floor of the setup. Hsu finds similar results [4], as does Riddle
for GaAs MESFETs [11]. It was discovered that devices that had a large change in
gate leakage with applied gate bias also had a large change in LFN. Conversely, if the
device gate leakage was relatively constant with gate bias, the LFN did not change
114

CHAPTER 4. LOW-FREQUENCY NOISE OF GAN HEMTS
V,
30 µA
V,
15 µA
V,
8.5 µA
V gs , I gs
V,
4.5 µA
V,
2.9 µA
Figure 4.7: Measured gate low-frequency noise versus gate-source voltage (and
current).
much. The device in figure 4.7 did have a large change in leakage as evident from the
x-axis labeling. γ was also very close to unity. These observations mean the gate LFN
can be modeled by the standard diode equation, 4.2.2. This helps reinforce the noise
figure modeling in chapter 2 using a shot noise source at the gate of the transistor.
It is desirable to add scaling to circuit modeling of noise, so the effect of device
geometry on LFN was also measured. Figure 4.8 shows that as the gate is made wider
the drain LFN noise increases. This trend agrees with the low-bias GaN HEMT LFN
measurements of Kuksenkov [12] and the HEMT modeling of Angelov [13]. This
trend is opposite to what is exhibited by MOSFETs [14]. Given this result, it makes
the gate length dependence all the more interesting. Figure 4.9 (a) and (b) show that a
shorter gate length increases the drain LFN. This means that the LFN does not display
115

CHAPTER 4. LOW-FREQUENCY NOISE OF GAN HEMTS
Figure 4.8: Change in low-frequency noise with gate width at various decade frequencies
for three devices.
(a) (b)
Figure 4.9: (a) Change in low-frequency noise as the gate length, Lg is changed. (b)
The 1 kHz data from (a) with a best fit line.
116

CHAPTER 4. LOW-FREQUENCY NOISE OF GAN HEMTS
a direct area dependence. It can be speculated that the gate length dependence LFN is
related to the Vds dependence.
The Vds LFN dependence will harm the phase noise performance of GaN HEMT-
based oscillators. Also, it is not typical of previous LFN modeling, which has a current
dependence instead. Based on the measurements presented thus far, the gate and drain
have different LFN processes and should not be modeled in the same manner. It
needs to be determined whether the gate and drain LFN are mathematically correlated.
Measurements were performed with the gate AC shorted and not AC shorted, showing
no change in the drain LFN. The same was done for gate LFN measurements and the
drain did not appear to have an effect. Hsu found similar results [4]. Lee shows
that the gate and drain LFN are uncorrelated [15]. Therefore, a two-current noise
source model with no correlation as illustrated in figure 4.10 can be used. Based on
the measurements in this work, the following model of the drain LFN for a circuit
simulator is proposed:

CHAPTER 4. LOW-FREQUENCY NOISE OF GAN HEMTS
�
i 2 �
d,1/f = Ki
� ��
Wg,new Lg,old
Wg,old
Lg,new
f γ
� c
(msVds +1)
(4.4.1)
where Ki, ms, and c are fitting parameters representing the magnitude of the noise,
the slope change with Vds , and an exponent of the change with gate length respec-
tively. Wg and Lg are defined the same as in § 2.6.4. Values found to work for devices
presented are Ki = 4e-14, γ = 1.1, c = 1.5, and m = 2.6. As already mentioned, the
gate noise can be modeled with equation 4.2.2. Due to the limitations of hitting the
noise floor, the gate LFN geometry dependence could not be measured. However, as
it depends on the Schottky contact reverse-bias gate leakage, it might be assumed that
the gate LFN scales with the gate leakage as in equation 2.6.45. Parameters found to
work for the gate LFN are Af = 1.15, Ffe = 1, and Kf = 2e-11.
The model was used to estimate the drain LFN corner frequency of the devices,
as equipment limitations prevented the measurement of this important quantity. The
noise figure modeling work in chapter 2 was used to estimate the noise floor, and
its intersection with the LFN was calculated. This value varies with bias because of
changes in LFN and gain, but was estimated to be close be 1-10 MHz. This is a
typical value for GaAs HEMTs. It was also attempted to use this model in phase noise
circuit simulations in ADS. However, limitations in the device model and the lack
of a native voltage bias-dependent low-frequency noise source component in ADS
prevented accurate prediction of phase noise.
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CHAPTER 4. LOW-FREQUENCY NOISE OF GAN HEMTS
4.5 GaN HEMT Low-Frequency Noise Studies
4.5.1 Substrate
There has already been some work comparing the noise of GaN HEMTs on different
substrates [3]. The findings were that SiC was less noisy than sapphire, having Hooge
parameters one to two orders of magnitude smaller. But the measurements were at
a low bias and it has already been explained why the Hooge parameter should not
be used for device comparisons. There is no data published comparing devices that
are in the saturation region. This was undertaken, and is presented in figure 4.11.
The devices are both biased at Vds 5 V and Ids 10 mA. Across the spectrum, there
is no apparent difference. While there appears to be a slight amount of bulging, it is
not stronger for either device. This suggests that at typical device biasings the LFN
is suppressed or another noise mechanism is stronger. Also, identical GaN HEMT-
based oscillators on both substrates constructed by the author (§ 5.4.1) did not show a
difference in LFN.
4.5.2 Passivation
There are two previous publications on the effect passivation has on LFN in GaN.
The first [16] measured HEMTs at a very low bias and normalized the noise to the
drain current. They showed that the passivation does improve the LFN performance,
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CHAPTER 4. LOW-FREQUENCY NOISE OF GAN HEMTS
Figure 4.11: Measurement of devices on a sapphire and SiC substrate at a bias of Vds
5V,Ids 30 mA
(a) (b)
Figure 4.12: (a) Low-frequency noise of a device before and after passivation. (b)
Low-frequency noise at 10 Hz and 1 kHz of a device before and after passivation at
different Vgs .
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CHAPTER 4. LOW-FREQUENCY NOISE OF GAN HEMTS
but based on their measurements the improvement varied with gate bias from as large
as an order of magnitude to almost no improvement. The other study also found
an improvement with passivation but only measured TLM structures [17]. LFN was
measured for a sample before and after passivation. In figure 4.12 (a), the LFN is
plotted for a device with and without passivation at Vds 5 V and Ids 10 mA. Passivation
improves the LFN by an order of magnitude across the spectrum. Passivation causes
a slight change in threshold voltage, so measurements were taken at different gate
biasings with Vds still at 5 V. The measured data at 10 Hz and 1 kHz is plotted in
figure 4.12 (b). The improvement stays relatively constant with gate voltage. It is
believed that suppression of surface state traps, along with the increase of channel
charge, cause the improvement.
4.5.3 Thick-Epitaxial Cap Devices
After considering the result of passivation on LFN, it is interesting to look now at a
device that does not require passivation. Devices of similar design to those in § 3.5.6
(AlGaN was used to cap the device instead of GaN) were measured. Figure 4.13 shows
LFN measurements of a few thick-cap devices (that have no passivation) and standard
passivated HEMTs. The performance of the thick-cap devices is as good as, if not
slightly better than, a passivated standard HEMT device. It can be concluded that a
LFN mechanism on the channel surface can be suppressed with either passivation or
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CHAPTER 4. LOW-FREQUENCY NOISE OF GAN HEMTS
Figure 4.13: Comparison of standard passivated HEMTs to an unpassivated thick cap
HEMTs. Bias is Vds =5VandIds = 30 mA.
with another epitaxial layer.
4.5.4 Field-Plated Devices
A field plate (FP) was shown to lower NF in this work (§ 3.5.5). It has also been
shown that a FP improves oscillator phase noise in [18]. In fact, the longer the FP, the
less the phase noise. As the 30 dB/decade slope of this data suggests that a 1/f type of
noise is dominating the phase noise, it might be reasoned that the LFN of FP and non-
FP devices is different. If there is a difference, it is not apparent in the measurements
shown in figure 4.14. In part (a) of the figure, all FP and non-FP transistors display
the same LFN at different frequencies when biased under the same conditions. The
second plot, (b), shows that as Vds increases, all devices’ LFN increase at nearly equal
122

CHAPTER 4. LOW-FREQUENCY NOISE OF GAN HEMTS
(a) (b)
Figure 4.14: (a) Decade low-frequency noise data for devices with different FP lengths
at a bias of Vds 5 V and Ids 30 mA. (b) 100 Hz low-frequency noise for different FP
lengths at Vds 3, 5, and 8 V.
rates. The answer to the origin of the phase noise improvement with a FP will need to
be answered elsewhere.
4.6 Comparison to GaAs HEMTs
In the previous chapter the NF of GaN was shown to be similar to GaAs. Let us now
examine the LFN of these two materials. A few GaN LFN reports have claimed that
the noise is comparable (such as [2]). These previous results are usually done with a
measured GaN device and information for a GaAs device from a data sheet or another
paper. In addition, the Hooge parameter is used as the figure of merit.
The author obtained GaAs HEMTs and measured the LFN of these devices. They
are from the TriQuint TQP13 pHEMT process, with an fτ of ∼95 GHz. The device
123

CHAPTER 4. LOW-FREQUENCY NOISE OF GAN HEMTS
gate geometry is 0.13 x 93 µm. This is not the same as the 0.7 x 100 µm GaN HEMT
devices to which they are compared to. However, based on the model presented in this
chapter, approximating the magnitude of the GaAs devices to be 3 times smaller than
what is actually measured should make for a fair comparison. The question arises
of how to bias the different devices. The following bias was chosen: 1.5 times the
knee voltage of the fully open channel and 3/4 the total gate bias (positive turn-on to
negative cut-off).
Figure 4.15 shows the measurements of (a) the full spectrum of one GaN and one
GaAs device and (b) selected frequency points for a few GaN and GaAs devices.
The GaAs has not been corrected for its difference in geometry. Considering this
difference, the LFN from a few kHz to 1 MHz is similar for both types of devices.
The slope (γ) of the GaAs devices was found to typically be 0.8 (it is common in the
(a) (b)
Figure 4.15: Low-frequency noise comparison of (a) a GaN and GaAs HEMT (full
spectrum) and (b) multiple GaN and GaAs HEMTs (decade measurements). Bias for
all devices is Vgs = 3/4 Vtotal, Vds = 1.5 Vknee.
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CHAPTER 4. LOW-FREQUENCY NOISE OF GAN HEMTS
GaAs FET literature for γ to be between 0.7 and 1), which is much less than the 1.2 for
GaN. Therefore, at lower frequencies GaAs has less noise. In § 5.5, it will be shown
that the close-to-carrier phase noise of GaN oscillators is worse than for GaAs-based
oscillators because of these different slopes.
4.7 Summary
This chapter has provided a useful collection of quality high-bias low-frequency
noise data. It was shown that the noise depends heavily on Vds while remaining nearly
constant to a changing gate voltage. The geometry dependence has also been shown to
be different than what is seen in other devices. A scalable, bias-dependent, empirical
model was proposed that can be used in circuit simulators. It was demonstrated that
neither the choice of substrate nor the addition of a FP change the LFN. Suppression
of LFN from surface effects was demonstrated through measurements of unpassivated
and thick-cap devices. References to the literature were added to support all measure-
ments where previous work exists. The full details of a LFN setup were explained. A
final note is that bulging (g-r noise presumably from traps) would occasionally show
up. The bulge would be very broad with a spectrum from around 100 Hz to 1 kHz. It
was not always present, even across the same sample. With improvement of material
it can be expected that the LFN will improve.
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CHAPTER 4. LOW-FREQUENCY NOISE OF GAN HEMTS
References
[1] A. Hajimiri and T. Lee, The Design of Low Noise Oscillators. Boston: Kluwer
Academic Publishers, 1999.
[2] A. Balandin, S. Morozov, S. Cai, R. Li, K. Wang, G. Wijeratne, and
C. Viswanathan, “Low Flicker-Noise GaN/AlGaN Heterostructure Field-Effect
Transistors for Microwave Communications,” Microwave Theory and Techniques,
IEEE Transactions on, vol. 47, no. 8, pp. 1413–1417, 1999.
[3] A. Balandin, Ed., Noise and Fluctuations Control in Electronic Devices. Stevenson
Ranch, CA: American Scientific Publishers, 2002.
[4] S. Hsu, P. Valizadeh, D. Pavlidis, J. Moon, M. Micovic, D. Wong, and T. Hussain,
“Characterization and Analysis of Gate and Drain Low-Frequency Noise in
AlGaN/GaN HEMTs,” in High Performance Devices, 2002. Proceedings. IEEE
Lester Eastman Conference on, 2002, pp. 453–460.
[5] A. L. McWhorter, “Semiconductor Surface Physics,” R. H. Kinston, Ed. Philadelphia:
Univ. of Pennsylvania Press, 1956, pp. 207–228.
[6] F. N. Hooge, “1/f Noise Sources,” IEEE Trans. Electron Devices, vol. 41, no. 11,
pp. 1926–35, Nov. 1994.
[7] A. van der Ziel, “Unified Presentation of 1/f Noise in Electron Devices: Fundamental
1/f Noise Sources,” Proc. IEEE, vol. 76, no. 3, pp. 233–258, 1988.
[8] ——, Noise in Solid State Devices and Circuits. New York: Wiley-Interscience,
1986.
[9] M. J. Buckingham, Noise in Electronic Devices and Systems. New York: John
Wiley & Sons, 1983.
[10] D. A. Bell, “A survey of 1/f noise in electrical conductors.” Journal of Physics C:
Solid State Physics, vol. 13, no. 24, pp. 4425–37, Aug. 1980.
[11] A. N. Riddle, “Oscillator Noise: Theory and Characterization,” Ph.D. dissertation,
North Carolina State University, 1986.
[12] D. V. Kuksenkov, H. Temkin, R. Gaska, and J. W. Yang, “Low-Frequency Noise
in AlGaN/GaN Heterostructure Field Effect Transistors,” IEEE Electron Devices
Lett., vol. 19, no. 7, pp. 222–224, July 1998.
[13] I. Angelov, R. Kozhuharov, and H. Zirath, “A Simple Bias Dependant LF FET
Noise Model for CAD,” in Microwave Symposium Digest, 2001 IEEE MTT-S International,
vol. 1, 2001, pp. 407–410 vol.1.
126

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[14] T. H. Lee, The Design of CMOS Radio-Frequency Integrated Circuits, 2nd ed.
New York: Cambridge University Pess, 2004.
[15] S. Lee, “Intrinsic Noise Characteriestics of Gallium Nitride High Electron Mobility
Transistors,” Ph.D. dissertation, Purdue University, Aug. 2004.
[16] A. V. Vertiatchikh and L. Eastman, “Effect of the Surface and Barrier Defects
on the AlGaN/GaN HEMT Low-Frequency Noise Performance,” IEEE Electron
Devices Lett., vol. 24, no. 9, pp. 535–537, Sept. 2003.
[17] S. A. Vitusevich, M. V. Petrychuk, S. V. Danylyuk, A. M. Kurakin, N. Klein, and
A. E. Belyaev, “Influence of Surface Passivation on Low-Frequency Noise Properties
of AlGaN/GaN High Electron Mobility Transistor Structures,” phys. stat. sol.
(a), no. 5, pp. 816–819, Mar. 2005.
[18] H. Xu, C. Sanabria, S. Heikman, S. Keller, U. Mishra, and R. York, “High Power
GaN Oscillators Using Field-Plated HEMT Structure,” in Microwave Symposium
Digest, 2005 IEEE MTT-S International, 2005, pp. 1345–1348.
127

5.1 Introduction
5
GaN HEMT Based Oscillators
OSCILLATORS are a key component of many communication systems. They
set fundamental limits of channel spacing because of their phase noise. This
work has demonstrated that NF and LFN of GaN HEMTs are only slightly worse
than the far more technologically mature GaAs HEMTs. Here the phase noise will
be compared to similar integrated circuit designs in Si and GaAs. Some guidelines
for low-phase noise design are discussed. A recently-developed MMIC process at
UCSB [1] was ideal for making the designs, and it will be reviewed briefly. The focus
of the chapter is the design and measurement of two LC differential oscillators. The
first did not have impressive phase noise performance but its linearity was excellent.
It is also the first GaN differential oscillator to appear in the literature [2]. A second
similar oscillator was fabricated that had fairly good phase noise performance. These
oscillators are compared to other published results of differential oscillators in Si and
GaAs, as well as GaN HEMT oscillators of all designs.
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CHAPTER 5. GAN HEMT BASED OSCILLATORS
5.2 Concerning Phase Noise
The study of phase noise is a difficult undertaking. Entire books and dissertations
are devoted to its study [3–5]. Even today there is still not a consensus of how best to
approach the problem [6]. The reason for the difficulty of understanding phase noise
stems from three challenges. The first is that an oscillator is a non-linear problem, and
simple analytical analysis cannot capture all key aspects. The rigorous work is usually
too complicated for clear insight or practical design. LFN is the largest contributor to
phase noise, and the lack of its full understanding undermines any complete study of
phase noise. It is not unheard of for a designer to simulate phase noise without LFN
modeling in the circuit because of this shortcoming. Finally, the circuit design impacts
the phase noise, possibly in profound ways [5].
Defining phase noise is much simpler than designing for it. Any signal source is
bound to have fluctuations in phase and amplitude. We can write these fluctuations as
v(t) =v0(1 − a(t)) cos(ω0t + ψ(t)) (5.2.1)
v0 and ω0 are the amplitude and angular frequency of resonance of the oscillator.
The amplitude fluctuations, a(t), and phase fluctuations, ψ(t), are both stochastic pro-
cesses. The power spectral density close to the carrier frequency is found to be [7]
Sv(ω) = v2 0
2 {4π(1 −〈φψ(0)〉)δ(ω − ω0)+Sa(ω − ω0)
+Sψ(ω − ω0)+2Im[Sψa(ω − ω0)]} (5.2.2)
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CHAPTER 5. GAN HEMT BASED OSCILLATORS
Here we see the signal amplitude (v 2 0/2) at the resonant frequency, along with an
autocorrelation term, φψ, from the phase fluctuations that reduces it. Sa is noise added
to the spectrum from the amplitude fluctuations, and is commonly known as amplitude
modulation (AM) noise. The phase fluctuations contribute to the spectrum through Sψ,
and is known as phase modulation (PM) or phase noise. A correlation term between
the amplitude and phase fluctuations can also contribute to the spectrum through the
cross spectral density, Sψa, called AM-PM noise. AM-PM noise is an odd function
(the others are even), and can lead to asymmetry of the noise spectrum around the
carrier. Proper circuit design reduces AM-PM noise. The nonlinearities of the gain-
producing element in an oscillator (usually, but not always, a transistor) provides a
restoring force that not only keeps the amplitude stable but also greatly reduces AM
noise. This means the noise near an oscillator’s resonance frequency is dominated by
phase noise.
Bearing in mind that there is AM, PM, and AM-PM noise, but PM (phase noise)
dominates, the phase noise can be observed with a spectrum analyzer. In fact, an Ag-
ilent E4440 spectrum analyzer with a phase noise personality was used for measure-
ments that appear in this chapter. Phase noise appears as a broadening of the frequency
of oscillation, shown in figure 5.1 (a). Its fine detail of shape varies, and is typically
one of three cases as seen in figure 5.1 (b-d). The resonator acts as a filter. Above or
below the resonant frequency a voltage signal would drop proportionally to 1/f, but
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CHAPTER 5. GAN HEMT BASED OSCILLATORS
Power
Power
1/f 3
1/f 2
(a)
(c)
ω 0
Noise Floor
Frequency
Noise Floor
Frequency
Power
Power
1/f 3
1/f 3
1/f
(b)
(d)
Noise Floor
Frequency
Noise Floor
Frequency
Figure 5.1: (a) A typical spectrum of an oscillator. (b-d) are zoomed in plots of the
circled portion in (a). The power in the various plots are not scaled to one another.
the power would drop 1/f 2 (20 dB/decade). This is exactly what happens to both flat
(such as thermal) noise sources and up-converted LFN leading to 20 dB/decade and
30 dB/decade slopes respectively. An oscillator with a very high Q, and the best noise
performance (the plots in figure 5.1 are not to scale to each other), would have a shape
such as that in figure 5.1 (b). The 1/f 3 region is the resonator filtering up-converted
LFN, while the 1/f regions are up-converted LFN that is outside the resonator band-
width. If there were no LFN (a blissful ideality), the slope of the entire range would be
131

CHAPTER 5. GAN HEMT BASED OSCILLATORS
just 20 dB/decade. Figure 5.1 (c) is the most typical spectrum observed. Here again
is filtering of LFN, but now we see thermal noise being filtered as well. The last case,
figure 5.1 (d), is for an oscillator with an enormous amount of LFN. We will return
to this qualitative analysis later. Phase noise is specified in decibels below the carrier
(dBc) in a 1 Hz bandwidth at a offset-frequency from the carrier. For example, a phase
noise of -132 dBc/Hz at 100 kHz means the noise at a frequency 100 kHz in addition
to the oscillation frequency is 132 dB below the power the oscillator has at its resonant
frequency (ω0).
A concise background of phase noise would require more than a chapter. Despite
the complexity of phase noise, there are some guidelines that tend to show up repeat-
edly [3,5–9]:
• Increase the tank Q: This is the most important factor for improving phase
noise. Higher Q means more suppression of off-carrier frequency components.
• Minimize the LFN: Probably the next most important parameter after Q. Choice
of device (bipolars in general have much less LFN than FETs) and device geometry
can help, as well as improvement in material quality. But usually little
can be done to quell LFN.
• Increase the Signal Amplitude: If all other influences could be considered
constant, a larger signal amplitude increases signal to noise ratio and reduces
the phase noise.
• Minimize Other Noise Sources: Flat noise sources determine the phase noise
in the 20 dB/decade range.
• Properly Design the Loop Gain: Designing the phase shift of the loop to have
a maximum derivative at the center of the resonance of the loop gain maximizes
the resonator’s ability to attenuate phase noise.
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CHAPTER 5. GAN HEMT BASED OSCILLATORS
• Linearize Cgs: The non-linearity of Cgs with Vgs makes the oscillator less symmetric
and increases noise. Additional capacitance can smooth Cgs and improve
phase noise. [3,10]
• Optimize the Circuit: Some oscillator topologies, particularly the Colpitts,
provide better phase noise than others. Design of the circuit influences the
phase noise performance. Use of techniques, such as automatic gain control
and tapped resonators, can help as well.
The last point is the largest topic to expound upon. However, the other points go
far toward the goal of improving phase noise. Because of the very large powers GaN
HEMTs can produce, the improvement of phase noise with signal amplitude is of great
interest to GaN circuits and provides the motivation for building the oscillators in this
chapter.
To simulate phase noise, very accurate device small-signal, large-signal, and noise
modeling must be available. In addition, simulators vary in their accuracy in predicting
phase noise. Modeling from the previous chapters was used to attempt simulations
of phase noise. However, the device model had some shortcomings (discussed in
§ 6.2) that prevented even accurate modeling of the 20 dB/decade phase noise from
filtered thermal noise. Some interesting results could be determined: the gate-leakage
shot noise was found to be negligible compared to contributions of the gate resistance
thermal noise, the channel noise, and the LFN. It was also noted that a field plate (FP)
did help the simulated phase noise results. A surprising simulated improvement of
10 dB of a very long FP HEMT oscillator over a non-FP oscillator agrees with the
work of Dr. Xu [11]. The practices outlined above were followed as well as possible.
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CHAPTER 5. GAN HEMT BASED OSCILLATORS
5.3 MMIC Process Description
The MMIC process developed by Hongtao Xu was used for circuit fabrication [1].
It integrates capacitors, inductors, resistors, and transmission lines. This follows the
HEMT process described in § 3.2, but with additional steps. There are now two addi-
tional metal layers (metal 1, 1 µm of gold, and metal 2, 3 µm of gold), a resistor layer
(NiCr), and a dielectric spacer layer (3 µm of PMGI). Inductors are made with metal
1 as an under-pass metal, then the dielectric spacer, and metal 2 to finish the over-pass
and most of the metalization of the square inductors. Capacitors are made with the
gate metal as a bottom electrode and the same film used for passivation as the capac-
itor dielectric. Metal 1 becomes the top electrode, and metal 2 connects the capacitor
bottom and top to the rest of the circuit (metal 2 is used over the PMGI to contact the
top electrode without shorting the capacitor). Resistor composition is Ti/SiO2/NiCr
and is protected by the same SiN film used for the capacitors and passivation. Trans-
mission lines are made exclusively with the thick metal 2. The same material structure
in § 3.2 is used here. Full details of the process, along with a process flow chart, can
be found in Hongtao Xu’s dissertation [1].
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CHAPTER 5. GAN HEMT BASED OSCILLATORS
5.4 Differential Oscillators
5.4.1 High Linearity Oscillator
Some familiarity with oscillators will be assumed in this and the next subsection.
A background can be found in textbooks such as [8]. The oscillators were designed
primarily as test vehicles, making the circuit design more flexible and less conven-
tional than typical commercial configurations. Design goals were to minimize phase
noise and maximize power and linearity without regard to other constraints such as
device size or ease of implementation. Design started with a basic cross-coupled pair
of 2 × 100 µm-wide HEMTs, seen in figure 5.2. Typically the drain bias would be set
with a current mirror at the HEMT sources (marked with an S) but it was desired to
have the freedom to change the bias. This also eliminates the LFN from devices in the
current mirror.
The tank, represented by the capacitor Ct and inductors Lt, primarily set the reso-
nance frequency. A fixed capacitor was used instead of a varactor to improve the Q of
the resonator and allow better insight of the phase noise performance of the HEMTs.
The passive components used for the tank were based on measurements of fabricated
capacitors and inductors at 5 GHz, with the best Q components picked for the desired
oscillation frequency. Typical unloaded Q values at 5 GHz are 25 and 65 for the square
spiral inductors and the SiN capacitors respectively.
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CHAPTER 5. GAN HEMT BASED OSCILLATORS
Load
C 2
L 1
S
L t
C 1
C 3
L 2
L 3
C t
L 3
C 3
L 2
L t
C 1
S
L 1
C 2
Load
Figure 5.2: Circuit schematic of the oscillator (biasing not shown).
Lt
L2
L1
C1
C3
C2
Ct
Figure 5.3: Photograph of the high linearity oscillator. Darker areas are the two
HEMTs. Passive components are labeled as in figure 5.2.
136
C2
C3
C1
L1
L2
Lt

CHAPTER 5. GAN HEMT BASED OSCILLATORS
The output is taken on either side of the tank. To keep from loading the tank, and
to match to a 50 Ω output, an L-match (L1 and C2) is used. Bias is provided at the
gate and through the L-matches with the output. This required the use of off-chip
bias-Ts for the RF/DC ports, but not for the gate bias port. The gate uses large square
inductors (L2) as RF chokes. C1 is a DC block that prevents the drain of the HEMTs
from shorting, and C3 isolates the DC of the gate and drain. The lengths of line used
to cross-connect the HEMTs are modeled by the inductors L3. The photograph of the
oscillator in figure 5.3 labels most of the circuit elements found in figure 5.2. Circuit
size is 2 x 1.65 mm 2 .
The circuit was simulated using ADS. Transient and harmonic simulations were
performed. Monitoring these, along with the dynamic load-line at the drain port of the
HEMTs, the circuit was optimized to give as linear an output as possible.
Measurements were performed on-wafer with air-coplanar (Cascade Microtech ACP-
40 GSG) probes. Off-chip bias-Ts were used for both the drains and gates. One side
of the oscillator was terminated in a dummy 50 Ω load. All measurements that follow
(power, linearity, phase noise) were performed using an Agilent E4440 spectrum ana-
lyzer with phase noise personality. Figure 5.4 (a) shows the measured spectrum from
one side providing 22.9 dBm of power at a 4.166 GHz oscillation frequency. The cir-
cuit is biased at Vds 20 V, Ids 233 mA, and Vgs -1 V. The analyzer had a 10 MHz span
and 33 kHz resolution bandwidth for the measurement. How the power and efficiency
137

CHAPTER 5. GAN HEMT BASED OSCILLATORS
(a) (b)
Figure 5.4: Measurements of the oscillator: (a) power spectrum (b) frequency pulling.
(a) (b)
Figure 5.5: Output power (single-sided), second harmonic power, and efficiency (full
circuit) of the high-linearity oscillator for changes in device (a) drain-source voltage
and (b) gate-source voltage.
138

CHAPTER 5. GAN HEMT BASED OSCILLATORS
compare to other oscillators will be discussed in § 5.5.
Of interest is the oscillator pulling, which is the change in oscillation frequency
with DC bias. This was measured for both the gate and drain voltages and plotted in
figure 5.4 (b). It is typical to express the pulling as a ratio of change in frequency to
change in bias. Approximating the data as linear in figure 5.4 (b) gives a pulling of
4.3 MHz/V for the gate and 0.6 MHz/V for the drain. These changes are less than
0.4% of the frequency of oscillation.
The power, 2nd harmonic, and efficiency for changes in bias appear in figure 5.5 (a)
and (b). The third harmonic was so small as to be buried in the noise floor of the spec-
trum analyzer, making it ∼70 dB below the carrier. The 2nd harmonic was typically
better than 30 dBc for all biasings measured. If the output were taken differentially,
even harmonics would cancel and the oscillator would make for an extremely linear
source.
This oscillator was the first GaN differential oscillator to be reported in the litera-
ture, and also the best reported linearity for a GaN oscillator [2]. However, the phase
noise was not impressive, being only -86.3 dBc and -115.7 dBc at best. A second,
similar, oscillator was constructed and is now presented.
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CHAPTER 5. GAN HEMT BASED OSCILLATORS
5.4.2 Low-Phase Noise Oscillator
The previous design was modified to improve phase noise performance. The Q
of the various inductors was reasoned to be a limiting factor, and were replaced. Mi-
crostrip lines, Lt in figure 5.6, were used in place of the tank inductors. The L-matches
were changed to tapped capacitors to help preserve the loaded tank Q. This meant the
drain biasing needed to be applied through the tank microstrip inductors. To provide
an AC ground across Lt, the large blocking capacitor 2C3 was added. The circuit,
shown in figure 5.7, was slightly smaller than the previous at 2 x 1.4 mm 2 .
Load
C 1
C 2
S
2C 3
L t Lt
C 4
L 2
L 1
C t
L 1
C 4
L 2
S
C 2
C 1
Load
Figure 5.6: Circuit schematic of the low-phase noise oscillator (biasing not shown).
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CHAPTER 5. GAN HEMT BASED OSCILLATORS
L 2
L t
C 1
C 2
C 3
C 4
C t
Figure 5.7: Photograph of the low-phase noise oscillator. Passive components are
labeled as in figure 5.6.
Figure 5.8 is a typical measured phase noise spectrum. Above 10 kHz the oscillator
drift obstructs the measurement. From 10 kHz to 1 MHz the spectrum decreases with
a 30 dB per decade slope, similar to figure 5.1 (d). This means the low-frequency
noise (LFN) of the oscillator dominates and hides the 20 dB per decade thermal noise
region. So far, no published GaN-oscillator phase-noise measurements have shown
a strict 20 dB per decade slope below a 1 MHz offset [2, 11–15]. A phase noise
measurement above a 1 MHz offset usually approaches a spectrum analyzer’s noise
floor, hence the lack of phase noise measurements in the literature at larger offsets.
Now to answer the key question: does an increase of oscillator power improve the
phase noise? After the optimal bias for Vgs was determined and set, Vds was varied.
141
C 4
C 3
L t
C 1
C 2
L 2

CHAPTER 5. GAN HEMT BASED OSCILLATORS
Figure 5.8: Measured phase noise of the oscillator.
Figure 5.9: Phase noise at 100 kHz and 1 MHz offsets versus drain-source bias for a
few oscillators.
142

CHAPTER 5. GAN HEMT BASED OSCILLATORS
The power of the oscillators increases from 15 dBm to 18 dBm as Vds increased from
6 V to 35 V. Below Vds 5 V the power drops quickly (it was typically 7 dBm at Vds
4 V). Phase noise for devices with different Vds is plotted in figure 5.9. The phase
noise does not improve with an increase in signal power, but actually increases. This
agrees with measurements in [12]. Of interest is that the general shape of figure 5.9 is
similar to the measured LFN bias dependence in figure 4.6. While proper design can
help to lower the offset frequency where the 30 dB/decade and 20 dB/decade slopes
meet, only Hajimiri’s model [5] addresses how this can be accomplished and its ability
to do this is still debated. With these results in mind, we now compare GaN oscillators
to other material systems for phase noise and for other oscillator measurements.
5.5 Comparison to Other Oscillators
A summary of measurements of several oscillators is found in table 5.1. Listed are
the measured frequency of oscillation (or range if the oscillator is tunable), the total
device (or devices) width, the oscillator power at its resonance frequency in addition
to second and third harmonics, the best efficiency of which the oscillator was capable,
phase noise measurements at 100 kHz and 1 MHz offsets, and the reference for each
work.
The table is separated into four parts depending on oscillator type. All oscillators in
the table are either HEMT or MESFET-based (no BJTs or HBTs) and integrated (no
143

CHAPTER 5. GAN HEMT BASED OSCILLATORS
Desc. Carrier Device Fund. 2nd 3rd Best Phase Noise Ref.
Freq. Width Power Harm. Harm. Eff. 100 kHz,1 MHz
GHz mm dBm dBm dBm % dBc/Hz
GaN HEMT Oscillators
Colpitts 5.3 0.2 20.5 -11.5 – 14.1 -105 -123 [12]
Hartley 9.56 1.5 32.3 – – 16 -87 -115 [16]
VCO 9 ± 0.5 1.5 31.8 10.8 4.8 21 -77 – [14]
Colpitts,
1.1 µm FP
5.02 0.5 30 ∼8 – 24 -104 -132 [11]
GaAs MESFET Oscillator
GaAs
VCO
11.5±0.3 – 9 >20 – – -91 -119 [17]
Differential Oscillators (Fixed Frequency), This Work
§ 5.4.1 4.16 0.4 22.9 -19.2

CHAPTER 5. GAN HEMT BASED OSCILLATORS
in its circuit and [11] used a FP on the devices in the oscillator, providing astonish-
ing improvements in phase noise (∼10 dB over the same circuit using devices with
no FP). The oscillators in Si and GaAs technologies all used varactors for frequency
tuning. This will degrade the tank Q and lead to poorer phase noise performance. As
a safe assumption, assume that the phase noise would be -10 dBc/Hz lower (better)
than what is stated in the table. With this adjustment, we see that GaN has better or
comparable phase noise at a 1 MHz offset, but by offsets ≤ 100 kHz the phase noise
is worse. Work by Rice [15] agrees with these measurements. The reason for this
difference is because GaN oscillators are dominated by their LFN and never show the
20 dB/decade slope from thermal noise. This is better-explained by figure 5.10. Here
the phase noise is displayed comparatively for a GaN oscillator and a typical low-noise
oscillator in GaAs or Si. Note that the magnitudes of the phase noise are not the same,
as phase noise is expressed relative to the carrier. The measured absolute power of the
phase noise sidebands for the GaN oscillator will be much larger than in GaAs or Si.
GaN oscillators provide at least an order of magnitude more power than the other
technologies. For the total device width of the HEMTs, the oscillators in this work
provide an average amount of power compared to the other GaN oscillators. The
standout is the FP HEMT oscillator, with 2 W/mm. The linearity of the first oscillator
in this work is second to none. The efficiencies of the GaN oscillators appears to be
much higher than GaAs and Si.
145

CHAPTER 5. GAN HEMT BASED OSCILLATORS
Figure 5.10: Relative comparison of GaN oscillator to a typical oscillator with low
phase noise (figure courtesy of Dr. Robert York).
5.6 Summary
Two GaN HEMT-based differential oscillators were presented. The first displayed
very good harmonic suppression but poor phase noise. This oscillator was also the first
GaN differential oscillator to appear in the literature [2]. The second oscillator showed
excellent phase noise performance at a 1 MHz offset of -132 dBc/Hz. However, be-
cause GaN oscillator phase noise appears to be dominated by very large amounts of
LFN, the noise performance is worse at offsets closer to the carrier. The hoped-for
benefit of better phase noise with more oscillator power is shattered by measurements
that show that more power actually increases the phase noise. This could be expected
because of the HEMT drain LFN bias dependence with Vds. Because of these two
146

CHAPTER 5. GAN HEMT BASED OSCILLATORS
problems, GaN does not appear to have an advantage over GaAs or Si oscillators for
phase noise.
References
[1] H. Xu, “MMICs using GaN HEMTs and Thin-Film BST Capacitors,” Ph.D. dissertation,
University of California, Santa Barbara, 2005.
[2] C. Sanabria, H. Xu, S. Heikman, U. Mishra, and R. York, “A GaN Differential
Oscillator With Improved Harmonic Performance,” IEEE Microwave Components
Lett., vol. 15, pp. 463–465, Jul. 2005.
[3] A. N. Riddle, “Oscillator Noise: Theory and Characterization,” Ph.D. dissertation,
North Carolina State University, 1986.
[4] W. P. Robins, Phase Noise in Signal Sources. London, UK.: Peter Peregrinus
Ltd., 1982.
[5] A. Hajimiri and T. Lee, The Design of Low Noise Oscillators. Boston: Kluwer
Academic Publishers, 1999.
[6] S. A. Maas, Noise in Linear and Nonlinear Circuits. Boston: Artech House, 2005.
[7] M. J. Buckingham, Noise in Electronic Devices and Systems. New York: John
Wiley & Sons, 1983.
[8] T. H. Lee, The Design of CMOS Radio-Frequency Integrated Circuits, 2nd ed.
New York: Cambridge University Pess, 2004.
[9] D. Leeson, “A Simple Model of Feedback Oscillator Noise Spectrum,” Proc. IEEE,
vol. 54, no. 2, pp. 329–330, 1966.
[10] V. Manan and S. Long, “A Low Power and Low Noise p-HEMT Ku Band VCO,”
Microwave and Wireless Components Letters, IEEE [see also IEEE Microwave
and Guided Wave Letters], vol. 16, no. 3, pp. 131–133, 2006.
[11] H. Xu, C. Sanabria, S. Heikman, S. Keller, U. Mishra, and R. York, “High Power
GaN Oscillators Using Field-Plated HEMT Structure,” in Microwave Symposium
Digest, 2005 IEEE MTT-S International, 2005, pp. 1345–1348.
[12] H. Xu, C. Sanabria, A. Chini, S. Keller, U. Mishra, and R. A. York, “Low Phase-
Noise 5 GHz AlGaN/GaN HEMT Oscillator Integrated with BaxSr1−xTiO3 Thin
Films,” IEEE Microwave Theory and Tech. Symp., pp. 1509–1512, 2004.
147

CHAPTER 5. GAN HEMT BASED OSCILLATORS
[13] J. B. Shealy, J. A. Smart, and J. R. Shealy, “Low-Phase Noise AlGaN/GaN FET-
Based Voltage Controlled Oscillators (VCOs),” IEEE Microwave Components
Lett., vol. 11, no. 6, pp. 244–245, Jun. 2001.
[14] V. Kaper, R. Thompson, T. Prunty, and J. R. Shealy, “Signal Generation, Control
and Frequency Conversion AlGaN/GaN HEMT MMICs,” IEEE Microwave Theory
and Tech. Symp., pp. 1145–1148, 2004.
[15] P. Rice, R. Sloan, M. Moore, A. R. Barnes, M. J. Uren, N. Malbert, and N. Labat,
“A 10 GHz Dielectric Resonator Oscillator Using GaN Technology,” IEEE
Microwave Theory and Tech. Symp., pp. 1497–1500, 2004.
[16] V. S. Kaper, V. Tilak, H. Kim, A. V. Vertiatchikh, R. M. Thompson, T. R. Prunty,
L. Eastman, and J. R. Shealy, “High-Power Monolithic AlGaN/GaN HEMT Oscillator,”
IEEE J. Solid-State Circuits, vol. 38, no. 9, pp. 1457–1461, Sept. 2003.
[17] C.-H. Lee, S. Han, B. Matinpour, and J. Laskar, “A Low Phase Noise X-band
MMIC GaAs MESFET VCO,” Microwave and Guided Wave Letters, IEEE [see
also IEEE Microwave and Wireless Components Letters], vol. 10, no. 8, pp. 325–
327, 2000.
[18] P. Kinget, “A Fully Integrated 2.7 V 0.35 m CMOS VCO for 5 GHz Wireless
Applications,” ISSCC Dig. Tech. Papers, p. 226227, 1998.
[19] M. Soyuer, K. Jenkins, J. Burghartz, and M. Hulvey, “A 3-V 4-GHz nMOS
Voltage-Controlled Oscillator with Integrated Resonator,” Solid-State Circuits,
IEEE Journal of, vol. 31, no. 12, pp. 2042–2045, 1996.
[20] S.-W. Yoon, E.-C. Park, C.-H. Lee, S. Sim, S.-G. Lee, E. Yoon, J. Laskar, and
S. Hong, “5 6 GHz-Band GaAs MESFET-Based Cross-Coupled Differential Oscillator
MMICs With Low Phase-Noise Performance,” IEEE Microwave Components
Lett., vol. 11, no. 12, pp. 495–497, Dec. 2001.
148

6
Summary, Conclusions, and Future
Directions For Noise Studies
6.1 Summary and Conclusions
THIS dissertation has looked at several aspects of the noise performance of
GaN HEMTs: noise figure, low-frequency noise, and phase noise. The noise
figure of GaN HEMTs is comparable to GaAs HEMTs. However, the gate leakage
needs to be well-controlled. Source resistance might also be too large a contributor for
small devices. At high biasings, self-heating causes the gain to drop, and an increase
in source resistance quickly degrades the noise figure performance.
A simple model, that included device scaling, was put together that not only pre-
dicts the minimum noise figure well, but also the other noise parameters: |Γopt|,� Γopt,
and rn. It is useful for hand and Matlab calculations to predict and understand noise
without the need for noise parameter measurements beforehand. It was successfully
used to understand how gate leakage and a field plate influence noise figure. The
model does not work when the gain of the transistor drops, such as at high biasings
149

CHAPTER 6. SUMMARY, CONCLUSIONS, AND FUTURE DIRECTIONS
or frequencies close to fτ. It was shown that the Pospieszalski and correlated noise
models can be successfully applied to GaN HEMTs, even for noise versus bias.
Summarizing the other noise figure studies, devices on either SiC or sapphire sub-
strates can have the same minimum noise figure as long as the bias is low. Thick-cap
devices show low noise at high biasings. However, their noise at lower biasings is
sub-par because of a very large amount of gate leakage.
A low-frequency noise setup that works at biasings typically needed for GaN HEMTs
was constructed and thoroughly explained. Unlike many other setups, this allowed
bias dependent studies well into the device saturation region. From this, a strong Vds
dependence for the drain was discovered and a scalable, bias dependent, model that
could be entered in a circuit simulator was introduced. The gate was found to follow
the low-frequency noise modeling for a diode, as could be expected for a Schottky
contact.
Low-frequency noise studies were performed. Passivation was found to improve the
low-frequency noise by an order of magnitude. An unpassivated thick-cap device has
the same low-frequency noise performance as a passivated standard HEMT. A field-
plate does not appear to help LFN, unlike noise figure. GaN HEMT low-frequency
noise is worse than that of GaAs HEMTs because the slope of the noise is much larger.
The phase noise of two GaN HEMT-based differential oscillators were explored.
The first had poor phase noise, but very good harmonic suppression, and was the
150

CHAPTER 6. SUMMARY, CONCLUSIONS, AND FUTURE DIRECTIONS
first GaN HEMT differential oscillator in the literature. The second oscillator showed
excellent phase noise performance at large offsets, but poor performance at closer
offsets because of the phase noise being dominated by the low-frequency noise. The
GaN power advantage that was hoped would improve the oscillator signal-to-noise,
and thus phase noise, was more than offset by the increase of low-frequency noise
with power. Because of these problems with low-frequency noise, GaN oscillators do
not perform better - they do not even meet the performance typically seen by GaAs
and Si oscillators.
6.2 Future Paths
Trying to make progress in an entire field of study which is not completely under-
stood and making three difficult-to-use measurement systems work allows room for
improvement. To improve noise figure, gate leakage needs to be controlled, but first
it needs to be understood. This is no doubt the pursuit of many champions of GaN
research because of its implications for reliability and power performance. It would
also be of interest to look at bias dependence of ion-implanted GaN HEMTs to see
if it improves the curve typically seen for minimum noise figure versus drain-source
current. As thick-cap HEMTs do not need passivation, they are an interesting device
with possible industry applications. Their noise figure performance at large current
biasings was better than any other measured by the author. A better understanding
151

CHAPTER 6. SUMMARY, CONCLUSIONS, AND FUTURE DIRECTIONS
could be pursued.
The work on low-frequency noise studies was only started and could be greatly
expanded upon. In particular, while few researchers have even reported the drain low-
frequency noise Vds dependence, none have attempted to explain it. As this seems to
be directly linked to the measured phase noise of oscillators, it is strongly suggested
it be studied in depth.
There are many ways to try to improve phase noise. The oscillators presented here
were relatively simple. More-sophisticated circuits should be undertaken and with
smaller devices than those presented here or in other works. The researchers whose
work has been discussed were designing with high power in mind. Before these cir-
cuits can be attempted, the circuit model needs to be improved. There are several
shortcomings. First, the ADS circuit model predicts that minimum noise figure ver-
sus drain source current is flat, which is a glaring problem (see figure 3.7). Dynamic
source and drain resistances must be included along with self-heating effects. Gate
leakage is not included in the model and should be added. The attempt at using
an ADS symbolically-defined device to generate a voltage-controlled low-frequency
noise current source was not successful, as the simulator appeared to use the DC bias
instead of the varying large-signal voltage of the oscillation. A custom ADS compo-
nent might be required, which could involve a few hundred lines of code. With these
deficiencies corrected, it might be possible to more closely simulate phase noise and
152

CHAPTER 6. SUMMARY, CONCLUSIONS, AND FUTURE DIRECTIONS
possibly better understand why a field plate helps the phase noise performance.
153

An ADS project that contains files used in this work can be downloaded at
http://my.ece.ucsb.edu/sanabria/research/ADSNoiseTemplate.zap
A
ADS Files
or by contacting the author at sanabria@ece.ucsb.edu. The downloaded file will need
to be unarchived in ADS. The project contains files necessary to:
1. Extract and optimize the small-signal parameters, as well as to simulate a smallsignal
model of the transistor for S-parameters
2. Simulate noise figure with either the correlated noise or Pospieszalski model
3. Extract the noise variables for the correlated noise model
Steps explaining how to do each of these functions with the project are presented in
the next three sections. Example files for each are provided in the project.
154

APPENDIX A. ADS FILES
A.1 Small-Signal Extraction
To extract the small-signal model, three S-parameter measurements are needed:
those of the device, a shorted-pads version of the device, and an open channel version
of the device. For more details, refer to § 2.3. It may also be useful to measure
extrinsic parasitic resistances through another means (such as Hall measurements).
The S-parameter measurements will then need to be imported into individual ADS
data sets.
Once the data is correctly in the ADS project, open the data display file
template small signal parameter extraction.dds
The middle of the first page of the dds file should look like figure A.1. This is where
the S-parameters for the device, open, and short are entered. Example data sets are
currently entered (Hongtao open, Hongtao short, d021218FC1...). Once these are en-
tered, turn to the next page in the data display (its shortcut key combination is Alt,
p, e). Plots for the small-signal extrinsic capacitances are displayed, along with two
markers per graph. The plots should be relatively flat, except maybe at very low fre-
quencies (less than 1 GHz). Move the markers to a suitable range of values for each
parameter. An average will be calculated for these (and the rest of the small-signal
parameters). Continue through the next two pages for the parasitic resistance and in-
ductances. Then advance two pages to the intrinsic parameters graphs page. Here
there may be larger variations in the parameters. Choose values that make sense, and
155

APPENDIX A. ADS FILES
Figure A.1: First page of template small signal parameter extraction.dds.
narrow the range close to the target frequency. Advancing to the next page shows the
calculated small-signal parameters. These can be entered into a small-signal model of
the transistor. Two have already been provided in the project:
template HEMT smallsignal and PospieszalskiNoise model.dsn
156

APPENDIX A. ADS FILES
template HEMT smallsignal and PucelNoise model.dsn
Simply substitute your values into one of these and save it as a new file. Once the
small-signal parameters have been entered, the sub-circuit containing the network can
be simulated for S-parameters. Open the schematic file
template Sparameters extraction optimization.dsn
Here there is one of the small-signal files in a subnetwork, an S-parameter simulation
block, optimization blocks, and a Data Access Component for identifying an ADS
data set. This is shown in figure A.2. Leave the deactivated components out of the
simulation. Exchange the subnetwork with the circuit to be simulated, and simulate.
This will call the previous data display window. If ADS asks to change the data set,
answer “yes.” Go to the verification page. Here, S-parameters for the simulation are
compared to the data set used for extraction. The fit should be good, but not excellent.
The parameters can be optimized to the data. In the schematic window, enter the
ADS data set into the Data Access Component that was used for the extraction. Ac-
tivate all components in the schematic, then simulate. The simulation window will
display the final optimized small-signal parameters. The verification page of the data
display window will show S-parameters for both the initial and optimized values. En-
ter the optimized values in the circuit sub-network. Deactivate the optimization blocks
again, and simulate. The agreement on the verification page of the data display win-
dow of the simulated and measured S-parameters should be excellent.
157

APPENDIX A. ADS FILES
Figure A.2: Schematic used for simulating S-parameters of the small-signal circuit
and for optimization.
A.2 Noise Figure Simulation
Open the project, and then open the circuit schematic file
template noise figure measure.dns
You should now be at the window shown in figure A.3. The subnetwork
template HEMT smallsignal and PucelNoise model
contains a small-signal model for a HEMT that includes noise sources and noise vari-
158

APPENDIX A. ADS FILES
ables for a Correlated Noise (CN) model. How to obtain the noise variables from
noise parameter measurements and small-signal parameter values is discussed in the
next section. This subnetwork can also be substituted with
template HEMT smallsignal and PospieszalskiNoise model.dsn
which contains a small-signal model of a HEMT and noise sources and noise vari-
ables for the Pospieszalski model. The Pospieszalski noise variables are obtained from
noise parameter measurements and small-signal parameters with the Matlab code in
Figure A.3: Schematic used for simulating noise parameters.
159

APPENDIX A. ADS FILES
appendix C.
Returning to the circuit schematic, simulating brings up the data display
template noise figure viewer.dds
Page 3 of this data display (use the shortcut Alt, p, e to navigate through the pages)
contains noise and gain circles on Smith Charts, the noise parameters, stability factor,
and noise figure for a 50 Ω termination compared to NFmin versus frequency. The
other pages of the display also contain useful information for design.
A.3 Correlated Noise Model Extraction
To extract the noise variables for this type of noise model, the small-signal param-
eters need to be determined and entered into a circuit as explained in the first section
of this appendix. In particular, have all the small-signal parameters entered into the
variable (VAR) block of the circuit network
template HEMT smallsignal and PucelNoise model.dsn
Measured noise parameters are also needed to determine the noise variables. Once
setup, open the circuit schematic
template parasitic matrix for correlation extraction.dsn
which is shown in figure A.4. Here, there are two networks simulated for S-parameters.
They correspond to the intrinsic and extrinsic parameters, respectively. If the small-
signal network listed above was used, its VAR block can just be pasted into this design
160

APPENDIX A. ADS FILES
and the previous one deleted.
Simulating should bring up the data display
template noise correlation extraction.dds
A screen shot of it is shown in figure A.5. The noise parameters will need to be entered
into the equations inside the Change These box. Once this is done, the Cpd unnorm
box and Cext will be the desired results: Cpd unnorm(1,1) is the gate noise in units
of A 2 /Hz, Cpd unnorm(2,2) is the drain noise in units of A 2 /Hz, Cpd unnorm(1,2)
and Cpd unnorm(2,1) are the cross-correlation terms (not used here), and Cext is the
correlation between the gate and drain noise. Entering these back into the second VAR
block in
template HEMT smallsignal and PucelNoise model.dsn
will allow for simulation of the noise parameters.
161

APPENDIX A. ADS FILES
Figure A.4: Schematic used for extracting correlated noise model noise variables.
Figure A.5: Data display used for extracting correlated noise model noise variables.
162

B
Matlab Code for Noise
Parameter Modeling
THIS Matlab script computes all four of the noise parameters as developed in § 2.6,
displays them in different formats, and plots minimum noise figure versus frequency.
This should facilitate the model’s use for other researchers. A copy of the file
can be obtained by contacting the author at sanabria@ece.ucsb.edu.
% NF.m
% NF and other noise parameters including gate leakage, but not Cgd.
% Chris Sanabria, 12/03/04
clear all;
close all;
% Variables (change)
163

APPENDIX B. MATLAB CODE FOR NOISE PARAMETER MODELING
Igs = 6e-6; % Gate leakage
rge = 3.03; % Gate resistance
rs = 6;
gmi = 0.033;
ri = 8;
cgsi = 0.21e-12;
rds = 1000; % Drain-source resistance. Only used for a gain calculation
% and not for noise prediciton.
G = 2/3; % Gamma, use 2/3
f = [5e9 10e9]; % Operating frequency or frequencies
Zo = 50; % Reference impedance for calculating reflection coefficient
Ta = 290; % Kelvin. This is the input temp., NOT the channel temp.!
% Constants
q = 1.6022e-019;
k = 1.3807e-023;
w = 2*pi*f;
% Intermediates that may change
rin = rge + ri + rs;
gm = gmi./(1+gmi.*rs);
cgs = cgsi./(1+gmi.*rs);
% Intermediate variables (no changing)
wt = gm./cgs; % That’s right, no 2pi.
a = gm.*G.*(w./wt).ˆ2;
b = q.*Igs./(2.*k.*Ta);
xgs = -1./(2.*pi.*f.*cgs);
% Optimum input impedance (reflection coefficient) for noise
Xopt = 1./(w.*cgs).*a./(a+b);
Ropt = sqrt(rin./(a+b) + a./(a+b).*rin.ˆ2 + a.*b./((a+b).ˆ2.*(w.ˆ2.*cgs.ˆ2)));
Zopt = Ropt + j.*Xopt;
Gamopt = (Zopt-Zo)./(Zopt+Zo);
% Minimum Noise Figure
164

APPENDIX B. MATLAB CODE FOR NOISE PARAMETER MODELING
rg = Ropt;
xg = Xopt;
Fmin = 1 + rin./rg + b./rg.*(rg.ˆ2+xg.ˆ2) + a./rg.*(abs(rin+rg+j.*(xg - 1./(w.*cgs)))).ˆ2;
% Noise resistance
% First calculate NF at Zo, then use NFmin and NF @ Zo to get rn
rgzo = real(Zo);
xgzo = imag(Zo);
Fzo = 1 + rin./rgzo + b./rgzo.*(rgzo.ˆ2 + xgzo.ˆ2) + a./rgzo.*(abs(rin+rgzo+j.*(xgzo -
1./(w.*cgs)))).ˆ2;
Rn = Zo.*(Fzo - Fmin).*(abs(1 + Gamopt)).ˆ2./(4.*abs(Gamopt)); % noise resistance
(not normalized)
% Gain av @ NFmin. Will not be accurate because Cgd is not included
Gav = abs(-(rds./2).*(wt./w).*j./((rg+rin) + j.*(xgs + xg))).ˆ2;
% Display outputs
disp([’Fmin = ’ num2str(Fmin)])
disp(’ ’)
NFmin = 10*log10(Fmin);
disp([’NFmin (dB) = ’ num2str(NFmin)])
% disp([’|Zopt| = ’ num2str(abs(Zopt))])
% disp([’|Zopt| = ’ num2str(abs(Zopt))])
% disp(’ ’)
% disp([’phase Zopt = ’ num2str(angle(Zopt)/pi*180)])
% disp(’ ’)
disp([’r n = ’ num2str(Rn./Zo)])
disp([’|Gamma opt| = ’ num2str(abs(Gamopt))])
disp([’phase Gamma opt = ’ num2str(angle(Gamopt)/pi*180)])
disp([’Gain av [dB] = ’ num2str(10.*log10(Gav))])
% Some plotting
figure;
plot(f./1e9,NFmin,’r’)
xlabel(’Frequency [GHz]’)
ylabel(’NF {min} [dB]’)
165

C
Matlab Code for Pospieszalski Noise
Parameter Modeling
THIS Matlab script calculates the two noise temperatures for the Pospieszalski
noise model as discussed in § 2.5.3. Because this involves solving a pair of
quadratic equations, it returns two sets of noise temperatures. The temperatures that
are negative in value are non-physical and should not be used.
% noise temps.m
% Uses Pospieszalski’s model to get the two noise temperatures. You need to
% have taken noise figure measurements and have extracted a small signal
% model. Because the solving is for a pair of quadratic equations, there
% are two sets of solutions. Ignore the negative temperature pair.
% Chris Sanabria, March 2003
clc;
format compact
%Input these:
freq = 10e9; % Hz
NFmin = 2.03; % dB
rn = .755; % NOT ohms, the normalized value
gam opt= 0.609*exp(j*54.4/180*pi); % Complex Reflection Coefficient
ft = 22.1e9; % In Hz. Pospieszalski defines this as gm/(Cgs*2*pi), but the
% author finds that the measured ft can work better.
Cgs = .258e-12; % Farads
rgs = 7.46; % Same as Ri
166

APPENDIX C. MATLAB CODE FOR POSPIESZALSKI NOISE PARAMETER MODELING
rds = 1155; % Ohms
gm = .032; %S
To = 290; % Kelvin
% Intermediate Equations
gds = 1/rds;
Rn = rn*50;
gn = 1/Rn;
Zopt = (1+gam opt)/(1-gam opt)*50;
Xopt = imag(Zopt);
Ropt = real(Zopt);
Tmin = (10ˆ(NFmin/10)-1)*To;
N = Ropt/Rn;
% Solve the equations
[Td Tg] = solve(’Roptˆ2 = (ft/freq)ˆ2*rgs/gds*Tg/Td+rgsˆ2’,...
’Tmin = 2*freq/ft*sqrt(gds*rgs*Tg*Td+(freq/ft)ˆ2*rgsˆ2*gds...
ˆ2*Tdˆ2) + 2*(freq/ft)ˆ2*rgs*gds*Td’,’Td’,’Tg’);
% Values are currently in Kelvin
disp(’Values in Kelvin’);
Td = eval(Td)
Tg = eval(Tg)
disp(’ ’);
disp(’ ’);
% Values are now in degrees C
disp(’Values in Celcius’);
Td C = Td - 273.15
Tg C = Tg - 273.15
% Check the validty
disp(’ ’)
disp(’ ’)
disp(’Validity Check’)
167

APPENDIX C. MATLAB CODE FOR POSPIESZALSKI NOISE PARAMETER MODELING
check = 4*N*To/Tmin;
(1