Principles of Semiconductor Devices-L34

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Alam ECE-606 S09 1

www.nanohub.org

NCN

ECE606: Solid State DevicesLecture 34: MOSCAP Frequency Response

Muhammad Ashraful [email protected]



Outline

Alam ECE-606 S09 2

1. Background

2. Small signal capacitances

3. Large signal capacitance

4. Conclusion

Ref: Sec. 16.4 of SDF



Topic Map

Alam ECE-606 S09 3

Equilibrium DC Small

signal

Large

Signal

Circuits

Diode

Schottky

BJT/HBT

MOSCAP



Small Signal Equivalent Circuit

Alam ECE-606 S09 4

p

G0

CD

CJ

CJ/Co

1

VG

For insulated devices,consider only majority carrier

junction capacitance CJ

High

frequency

Low

frequency



Junction Capacitance

Alam ECE-606 S09 5

p-Si

+-~

sinG S

V t υ ω + C G ≡

dQ G

dV G

=d −Q S ( )dV

G

SGS

OC

V Qψ = −

( ) ( )

1G

S

S

OSC

dV d

d Q d Q

ψ = +

− −

11 1

S OG C C C = +



Junction Capacitance

Alam ECE-606 S09 6

1 1 1

SG OC C C = +

( )S

S

S

Q

d C

d

ψ

−≡

V G

O

C

SC

( )SSQ ψ

which we already

understand!



Definition of m for later use

Alam ECE-606 S09 7

( )1 S Om C C = + V

G

OC

C S

ψ S

O GS G

O S

C V V

C C mψ ≡=

+

‘body effect coefficient’

( )01 S O T m x W κ κ = +

1.1 ≤ m ≤ 1.4

in practice:



Outline

Alam ECE-606 S09 8

1. Background



4. Conclusion



Junction Capacitance in accumulation

Alam ECE-606 S09 9

0

, 00

ox

j accC C x

κ ε ≈ ≡

,

,

0

, ,

s acc

s

s

j acc s acac a

o

o cc

cc

C C W C

C

C

C κ ε = ≡

+

Wacc

-Q

+Q

Low frequencyC/Co

1

+Q



Junction Capacitance in depletion

Alam ECE-606 S0910

+Q

VG -Q

0 0

0,

01 j d s

e

s

s p

C

C

C C

C C C C = =+ +

0

1 1o G

s

W

x

V

V δ

κ

κ = + −

2

0 0

02

A AG

o s

qN qN W V x

W

κ ε κ ε

= +

1

o

G

C

V

V δ

=

+

Low frequencyC/Co

V G

1

0

0

0

01 so

W

C

x

ε κ κ ε =

+



Junction capacitance in inversion

Alam ECE-606 S09 11

-Q

+Q

Electrons

Exposed

Acceptors

VG

VG’ >VT’

0, 0

0

s j invC C x

κ ε

≈ ≡

0

,

o inv s j inv inv

o inv inv

C C C C

C C W

κ ε = ≡

+

Low frequency

C/Co

VG

1



Equivalent Oxide Thickness

Alam ECE-606 S09 12

Q i = −C G V G −V T ( )

,

ino

G j inv o

v

v oin

C

C

C C C C

C = = <

+

s onv

inv

iC W

κ ε ≡

0

o ooC

x

κ ε =

ox O

e c

G

le EOT C κ ε = ox O

O Oinelec

s

v

O

x x E W OT κ ε

κ ε = + >

‘Equivalent oxide thickness - electrical ’

Low frequency

C/C ox

1

V G



High frequency curve at inversion

Alam ECE-606 S09 13

-ΔQ

ΔQ

WT

What about high frequency part of the curve?

0, 0

0

s j invC C

xκ ε ≈ ≡

High frequency

C/Co

1

V GV TH



Response Time

Alam ECE-606 S09 14

VG

VG’ >VT’

VGVG

Dielectric Relaxation

0s

στ =

κ ε

SRH Recombination-Generation

2

1 1( ) ( )

i i

n p n p

np n n R

p p n n

− −= →

τ + + τ + τ + τ

Ref. Lecture no. 15



High frequency response in MOS-C

Alam ECE-606 S09 15

High frequency

Low frequency

C/Co

1

VG

-ΔQ

ΔQ

WT

Low Frequency

-ΔQ

ΔQ

WT

High Frequency



Ideal vs. Real C-V Characteristics

Alam ECE-606 S09 16

Flat band voltage …

Threshold voltage …

C/CoC/Co



Outline

Alam ECE-606 S09 17

1. Background



4. Conclusion



Topic Map

Alam ECE-606 S09 18

Equilibrium DC Small

signal

Large

Signal

Circuits

Diode

Schottky

BJT/HBT

MOS



Large Signal Deep Depletion

19

0 0

,

0

0

1

s j dep

oxs

s

C C C C

W C C

x

κ

κ

= =+ +

1

o

G

C

V

V δ

=

+

(even beyond threshold)High frequency

Low frequency

C/Co

VG

-ΔQ

ΔQ

Wdm

NA

x0

ρ(x)

-ΔQ

ΔQ Wdm

NA



Relaxation from Deep Depletion

20

High frequency

Low frequency

C/C ox

1

Deep depletion

-ΔQ

ΔQ

Wdm

NA

x0

ρ(x)

-ΔQ

ΔQ

Wdm

NA

x0

ρ(x)

-ΔQ

ΔQ

Wdm

ρ(x)

Depending on the measurementfrequency, it will either merge

with low-freq. or high-freq. curve.



Ideal vs. Real C-V Characteristics

Alam ECE-606 S09 21

Flat band voltage …

Threshold voltage …

C/CoC/Co

VGVG



Low or High frequency?

Alam ECE-606 S09 22

typically observe hi-

frequency CV

G = n i 2τ

p-Si

typically observe low-frequency CV

No deep-depletion as well

p-Si

n+-Si n+-Si

What happens if I shine light on a MOS capacitor?



Summary

Alam ECE-606 S09 23

1) Since current flow through the oxide is small, we are

primarily interested in the junction capacitance of the

MOS-capacitor.

2) High frequency of MOS-C is very different than low-

frequency C-V. In MOSFET, we only see low frequency

response.

3) Deep depletion is an important consideration for MOS-

capacitor that does not happen in MOSFETs.

Principles of Semiconductor Devices-L34

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