Lundstrom ECE 305 F16

ECE-305: Spring 2016

MOS Capacitance vs. Voltage

Professor Mark Lundstrom Electrical and Computer Engineering

Purdue University, West Lafayette, IN USA lundstro@purdue.edu

4/5/16

Pierret, Semiconductor Device Fundamentals (SDF) pp. 584-599

MOS capacitor

2

p-Si

vS sinωt

+ VG

+

-

-

VG + vS sinωt

~

Lundstrom ECE 305 F16

MOS capacitor in depletion

3

VG

p-Si

W φS( ) W VG( )

Lundstrom ECE 305 F16

4

MOS capacitor in depletion

xo

W φS( )

KO

KS

C = ?

Gate

Undepleted P-type semiconductor

CS =KSε0W φS( )

Cox =KOε0xo

1C

=1Cox

+1CS

C =CSCox

CS + Cox

C =Cox

1+ Cox CS

result

xo

W φS( )

κ ox

κ Si

C = Cox

1+KOW φS( )KSxo

VG

Cox

CS

φS

Lundstrom ECE 305 F16 5

6

s.s. gate capacitance vs. d.c. gate bias

C

VG′

C = Cox

1+KOW φS( )KSxo

accumulation depletion

inversion

VT′

flat band

Cox

Lundstrom ECE 305 F16

7

s.s. gate capacitance vs. d.c. gate bias

C

VG′C = Cox

1+KOW φS( )KSxo

accumulation

depletion

inversion

VT′

flat band

Cox

high frequency

Lundstrom ECE 305 F16

8

capacitance vs. gate voltage

C

VG

C = Cox

1+KOW φS( )KSxo

accumulation

depletion

inversion

VT

flat band

Cox

VFB = φms

Lundstrom ECE 305 F16

9

high frequency vs. low frequency

C

VG′

C = Cox

1+KOW φS( )KSxo

accumulation depletion

inversion

VT′

flat band

Cox

high frequency

low frequency

Lundstrom ECE 305 F16

10

high frequency vs. low frequency

p-Si

n+-Si n+-Si

MOS capacitor

11

CV measurements as an analysis tool

C

VG

C = Cox

1+KOW φS( )KSxo

accumulation

depletion

inversion VT

Cox

C = Cox =K0ε0xo

C = Cox

1+KOW 2φF( )

KSxo

flat band

VFB = φms

Lundstrom ECE 305 F16

12

CV measurements as an analysis tool

source drain S

iO2

Si

S DG

(Texas Instruments, ~ 2000)

•  Oxide thickness •  Flatband voltage •  Doping density