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CV Measurements
Diode junction capacitance Cj = A/w
Depletion depth aod
VVqN
w 2
np+
w
Va
reverse bias:
= ro (static dielectric constant). For Si, r = 11.7.
for Na >> Nd
Differential Capacitance
What is actually being measured is the differential capacitance C = dQ/dVa as a function of Va.
~
n-typep-type
w + dw
Va dVa
dc adjusted by user ac supplied by C- meter
dQ = Nd(w+w) – Nd(w)
Measurement of Nd
Boonton meter: dVa = 1 MHz, 15 mV
dQ: ionized dopants in depletion region w
C is determined by Nd in the region dw. The depth w is determined by Va. So a measure of the capacitance at Va corresponds to a measurement of Nd at w.
~
n-typep-type
w + dw
Va dVa
1/Cj2 – Va Plot
aod
VVqN
w 2
dao
j NVV
qA
wC
2
2
Depletion depth
Junction capacitance
d
a
j Nq
VV
AC
022
21
If Nd is constant, we can plot a straight line to find Vo and Nd.
Diode CV Data
Capacitance vs. Voltage
0
2E-12
4E-12
6E-12
8E-12
1E-11
1.2E-11
1.4E-11
1.6E-11
1.8E-11
2E-11
-9 -8 -7 -6 -5 -4 -3 -2 -1 0
Voltage (V)
Ca
pa
cita
nce
(F
)
The “raw” CV data looks something like the following. The capacitance C ~ Va
-1/2 if the doping density is constant.
Doping a Semiconductor
n-type semiconductor (in cross-section)
Addition of p-type dopants (B)• diffusion• implantation
BB
B
B
B
B
B
B
B
BB
B B
B
B
B
BB
BB
B
B
NA
x
Doping Density ProfileDoping Profile (Simulation)
0.0E+00
5.0E+17
1.0E+18
1.5E+18
2.0E+18
2.5E+18
3.0E+18
3.5E+18
4.0E+18
4.5E+18
5.0E+18
0.0E+00 5.0E-05 1.0E-04 1.5E-04 2.0E-04 2.5E-04
Distance (cm)
Do
pin
g C
on
ce
ntr
ati
on
(/c
m^
3)
n-type background concentration
Net Doping Density |NA – ND|
Doping Profile (Simulation)
1.0E+15
1.0E+16
1.0E+17
1.0E+18
1.0E+19
0.0E+00 5.0E-05 1.0E-04 1.5E-04 2.0E-04 2.5E-04
Distance (cm)
Do
pin
g C
on
ce
ntr
ati
on
(/c
m^
3)
n-type background concentration
p-type n-type
p-type dopant
Data Analysis
1/C^2 vs. V
0
5E+21
1E+22
1.5E+22
2E+22
2.5E+22
-10 -8 -6 -4 -2 0 2
Voltage (V)
1/C
^2
(1/F
^2)
Vo
Slope ~ 1/ND
For doping density ND constant with depth, 1/C2 vs. Va is a straight line. The doping density in this sample is not constant.
General Doping Density
We can show that the doping profile NB(x) is given by…
…and that the distance x is…
22 1
2
ja
d
CdV
dAq
xN
jC
Ax
Data Analysis
There is “noise” from the numerical differentiation, but we can do some “curve fitting”.
0.00E+00
1.00E+16
2.00E+16
3.00E+16
4.00E+16
5.00E+16
6.00E+16
7.00E+16
0.E+00 1.E-05 2.E-05 3.E-05 4.E-05 5.E-05 6.E-05 7.E-05
x (cm)
NB
(x)
(/c
m3
)
Curve-fitting RegionDoping Profile (Simulation)
0.0E+00
1.0E+17
2.0E+17
3.0E+17
4.0E+17
5.0E+17
6.0E+17
7.0E+17
8.0E+17
9.0E+17
1.0E+18
0.0E+00 5.0E-05 1.0E-04 1.5E-04 2.0E-04 2.5E-04
Distance (cm)
Do
pin
g C
on
ce
ntr
ati
on
(/c
m^
3)
p-type n-type
This plot shows where in the sample we are “looking”.
Diode Connection
The diagram shows how to connect the diode to the capacitance meter. Connecting with the wrong polarity will forward-bias the diode, resulting in a very large capacitance.
Test Place device to be measured here.Diff (difference) A capacitance placed here will be subtracted from “Test”.
High Low
Test
Diff
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