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