Surface State Density Calculations

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Surface State Density Calculations
Step 1 – screen diodes
Perform IV measurement to find “good diodes”, those with low leakage current and highest
breakdown voltage.
Step 2 – perform CV
Use IV curve results to find voltage range that does not have significant leakage current that may
damage diode. This is important because there is no current limiting mechanism on CV machine
(compliance setting). Incidentally, the compliance used for IV graphs was 0.1 µA/cm 2 .
Step 3 – doping concentration estimation
Use CV curve to calculate doping concentration
For p type silicon, here is a typical cv curve
A) Plot 1/C 2 vs. V
*NOTE – curvature in this region may represent nonuniform doping in the semiconductor.

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B) Calculate the doping concentration, N
ε s = semiconductor dielectric constant
A = diode area
q = magnitude of electronic charge
N = doping concentration (acceptor/donor)
STEP 4 – Calculate Debye length, L D
STEP 5 – Calculate the semiconductor flat band capacitance, C FBS
STEP 6 – Calculate dielectric layer capacitance C i
Calculate or experimentally measure dielectric layer (insulating layer) capacitance (C i )
Calculate by
Ci
i
d
A
A = diode area
d = insulating layer thickness
ε i = insulating layer dielectric constant
Experimentally obtain by …
*Maximum capacitance with minimal
leakage current (as ascertained by IV
curves from semiconductor parameter
analyzer HP 4145A) is equal to insulator
capacitance, because depletion layer
thickness is essentially 0.

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The depletion layer thickness increases as the capacitance decreases due to effectively increasing
distance, d, (remember C = εA/d). Therefore, at max capacitance, the depletion layer thickness
is essentially 0, so d = insulator thickness. So, you can back calculate ε i (insulator dielectric
constant) if you know d = insulator thickness …
STEP 7 – Calculate the overall flat band capacitance C FB
Once C i is calculated, you can calculate overall flat band capacitance….
And the ratio C FB /C i
Supplemental
If you know the dielectric layer thickness, the ratio can also be found by….
C
FB
/ C
i
1
iL
1
d
s
D
i
STEP 8 – calculating V shift
The “standard” method is to regraph the CV curve as C/C i v.s. V

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Then use the ratio C FB /C i to estimate the flat band voltage shift V shift or ΔV. Basically, in an ideal
diode, the flat band voltage condition/capacitance ΔV = 0. So, the attached paper attributes the
voltage shift to interfacial states.
Charges
Q m – mobile charges – bias dependent location
Q ot – oxide trapped – distributed in oxide
Q f – fixed oxide – located near surface charge
Q it – interface traps – at interface
From discussion of
SiO 2 /Si diode in
“Semiconductor
Devices Physics and
Technology” by SZE,
Pgs 197‐200
Effect of charge
Q m, Q ot, Q f – shifts curves to left or right (negative charges shift curve to right)
Q it – charge or discharge over range of bias (
change slope)

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V
FB
ms
Q
f
Q
c
m
i
Q
ot
ms
= work function of metal – work function of semiconductor
STEP 9 – Find ms
P-type
N-type
ms
m
s
m
[ x Eg
B
/ 2
]
Eg/2= intrinsic Fermi level
m
= metal work function
X = electron affinity of
semiconductor
ms
m
s
m
[ x Eg
/ 2
B
]
= Fermi level difference
between Fermi level and intrinsic
Fermi level
STEP 10
X, E g – can be found from reference tables
– may be found from reference tables or calculated
Calculate surface STATE density by….
N f = number/cm 2
N f = surface state density
Method 1
A) Do steps 1 – 4 as described; skip step 5
B) Do step 6 by using reference vale for ε i , use experimental C i to calculate “d”
C) Do step 7 using
C
FB
/ C
i
1
iL
1
d
s
D
i
Method 2
D) Do step 8 graphing C/C i vs. V
Use calculated C FB /C i to get V shift
E) Do steps 9 and 10
A) Do steps 1-5 as stated
B) Use experimental value of C i found in step 6

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Example
C) Do step 7 using and C FB /C i
D) Do steps 8,9, 10
A) Calculating Doping Concentration
(slope) = 2.53 x 10 19
E srelative = E s /E o = 9.7 SiC
A = .005026548 cm 2
B) Calculate debye Length (L D )
T = 300k
K = 1.3806x10 ‐23 J/k (or kgm 2 /s 2 k)
Ε o = 8.85418 x 10 ‐12 F/m
C) Calculating C FBS
Unit Check
D) Get C i from experimental CV curves
F

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C i = 1/760 x 10 -12 F
E) Calculate C FB
Incidentally…
C
/ 0.998 1
fB C i
F) From this I found V shift (by reading the curves) to be
V shift = – 3.95V
G) Calculate P type Fermi Level distance from intrinsic Fermi level…
Variables
The equations to be solved are…
1)
2)
effective density of states in
valence band
acceptor cone
effective hole mass
= electron rest mass
= .91095 x 10 ‐30 kg
Back to Fermi Level calculation….
= 1 for SiC

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E i = intrinsic Fermi level
E g = band gap
H) Now to find
m
ms
m
s
m
[ x Eg
B
/ 2
]
E g = 2.996 eV for SiC
For SiC at 300k
E g = 2.996
X = 4.1 eV (used value for GaN!)
estimated
For Pt metal contact
m
=5.65eV
ms
5.65
4.1
(2.996 / 2) 1.32
1.
27eV
Calculate Surface state density….