c-v characteristics of mos...

Prof. Yo-Sep Min Electronic Materials: Semiconductor Physics & Devices Chapt. 16 - Lec 19-1

• Measurement of C-V characteristics

– Apply any dc bias, and superimpose a small (15 mV) ac

signal

– Generally measured at 1 MHz (high frequency) or at

variable frequencies between 1KHz to 1 MHz

– The dc bias VG is slowly varied to get quasi-continuous

C-V characteristics

C-V characteristics of MOS capacitors

dV

dQC

thickness

areaKC 0

• C-V measurement is very powerful diagnostic tool for

identifying any deviations from the ideal in both oxide and

semiconductor.


Measured C-V characteristics on an n-type Si

ND = 9.1 1014 cm3

xox = 0.119 m

The measured MOS capacitance (called gate capacitance, CG)

varies with the applied gate voltage


n-MOS capacitor under accumulation

Consider n-type Si under accumulation

(VG > 0).

Thus, for either low or high frequencies, the gate capacitance

under accumulation is equal to the oxide capacitance.

Looks similar to the parallel plate capacitor.

The dc state is characterized by a +Q

charge on the gate and a –Q charge of

majority carriers (electrons) right at the

oxide-semiconductor interface.

The MOS can follow the ac signal quasi-

statically by adding or subtracting a small ΔQ

on the two sides of the oxide. Cox

-

-

ox

GoxoxG

x

AKCaccC 0)(


n-MOS capacitor under depletion

The dc state under the depletion condition

(VG < 0) is characterized by a –Q charge on

the gate and a +Q depletion layer charge

(immobile ions) in the semiconductor.

CG is Cox in series with Cs where Cs can be

defined as “semiconductor capacitance”. Cox Cs

-

- When the ac signal give rise to –ΔQ on the

gate, the depletion layer width (W) widens to

add +ΔQ in the semiconductor.

Cox=Kox0A / xox

Cs = Ks0A / W

In this case, the gate capacitance decreases as the |VG| is

increased. Why?

s

D

S

Nq

KW

)(

2 0

oxs

ox

ox

sox

soxG

xK

WK

C

CC

CCdeplC

1

)(


n-MOS capacitor under inversion (ω 0)

-

The dc state under the inversion condition

(VG << 0) is characterized by more –Q

charge on the gate and more +Q charge

(immobile ions and minority carriers) in the

semiconductor.

If the ac frequency is very low (ω 0), minority carriers (holes)

can be generated or annihilated in response to the applied ac

signal. just as in accumulation,

Note that the depletion layer width is already

maximized to WT in the depletion-inversion

transition point.

ox

GoxoxG

x

AKCinvC 0)(

for ω 0


n-MOS capacitor under inversion (ω ∞)

If the ac frequency is very high (ω ∞),

minority carriers (holes) cannot be generated

or annihilated in response to the applied ac

signal due to the relatively sluggish

generation-recombination process.

The number of minority carriers in the inversion

layer remains fixed at its dc value.

In order to balance the ΔQ change on the gate, the depletion

width fluctuates about the WT.

Similar to the depletion

biasing, oxs

Tox

ox

sox

soxG

xK

WK

C

CC

CCinvC

1

)(for ω ∞

Because WT is a constant independent of the inversion bias,

bias inversion all for constant min)()( deplCinvC GG


C-V characteristics of n-MOS cap (ω 0)

flat band

accumulation

depletion depletion/inversion

transition point

inversion


Example 1

Consider p-type MOS at 300 K with NA=1016 cm3 and xox = 100

nm. Plot the CG versus VG characteristics when VG is varied

slowly from 5 V to +5 V. Assume MOS has an area of 1 cm2.

1) Find Cox.

2) Find Cs (min) (Note that Cs decreases as the depletion layer

width increases. It is minimum when the depletion layer width is

maximum, i.e. when W = WT i.e., ϕs = 2ϕF).

nF cmcm

F/cmox 5.341

101000

1085.89.3 2

8

14

Ct

AKC 0

s

A

S

qN

εKW 02

type-n ...

type-p ...

F

i

D

i

A

n

N

q

kT

n

N

q

kT

ln

ln


Example 1 (continued)

nF cm

cm F/cm(min)

2

s 3.3410066.3

11085.89.11

5

14

0

T

sW

AKC

cmV/cmC

F/cm

3

T

5

2/1

1619

14

0

10066.3357.0210106.1

1085.89.112

22

F

A

S

qN

εKW

VC

K eV/KF 357.0

10

10ln

1061

30010617.8ln

10

16

19

5

.n

N

q

kT-

i

A

nF

nF

nF nF (min)G 2.17

3.345.34

3.345.34

sox

sox

CC

CCC


Example 1 (continued)

34.5 nF

VG

CG

p-type

2.14 V

17.2 nF

34.5 nF

low-f

high-f

)2(2

20

F

S

Aox

ox

SFT

εK

qNx

K

KV

VVF/cm

/cmCcmV

3

14.2)357.02(1085.89.11

10106.12101000

9.3

9.11357.02

14

16198

TV


Delta-depletion analysis for C-V curve of MOS

)( inv

0)( inv

depl

acc

oxs

Tox

ox

ox

oxs

ox

ox

ox

G

xK

WK

C

C

xK

WK

C

C

C

1

1ND = 1015 cm3

xox = 0.1 m

T = 300 K

oxG CC /

)(voltVG

oxGT CCV /, min,

According to the delta-depletion approximation, the CG can

varies only at the depletion biases.



s

S

Aox

ox

SSG

εK

qNx

K

KV

0

2

FS 20

GsA

ox

oxSS VN

εK

xqK

0

2

22 2

0

Rewriting the equation to obtain ϕs,

2

422

0

2

2

0

2

2

GA

ox

oxSA

ox

oxS

s

VNεK

xqKN

εK

xqK

GA

ox

oxSA

ox

oxS VNεK

xqKN

εK

xqK

0

2

2

0

2

2

22

bulk-p for ... A

ox

oxs NK

xKqV

0

2

2

2 Setting and bulk-n for ... D

ox

oxs NK

xKqV

0

2

2

2


biases) (depletion

V

V

CC

G

oxG

1

11

V

Vx

K

KW G

ox

ox

s

s

A

S

qN

εKW 02

Because and for p-type ,

111

V

VV

V

VVVVVV GG

Gs


A

ox

oxs NK

xKqV

0

2

2

2

11

2

211

2

0

2

2

00

V

VN

K

xKq

qN

εK

V

VV

qN

εKW G

A

ox

oxs

A

SG

A

S

Therefore and 11 V

V

xK

WK G

oxs

ox

Substituting the equation of the depletion biases,

oxs

ox

oxG

xK

WK

CC

1


ND = 1015 cm3

xox = 0.1 m

T = 300 K

oxG CC /

)(voltVG

biases) (depletion

V

V

CC

G

oxG

1

V

/cmF/cm

cmC

3

071.0

101085.89.3

1010009.11

2

106.1

2

15

142

2819

0

2

2

A

ox

oxs NK

xKqV


For the given n-MOS capacitor,


C-V curve of n-MOS from exact-charge theory See the Appendix B & C

xox = 0.1 m

T = 300 K

The significant increase in the high-frequency inversion

capacitance and the substantial widening of the depletion bias

region with increased doping.



ND = 1015 cm3

T = 300 K

An increase in the oxide thickness also widens the depletion

bias region and also affect the high-frequency inversion

capacitance.



ND = 5 x 1014 cm3

xox = 0.1 m


Practical C-V curves: Deep depletion

The previous discussions pertain to the condition when the

gate voltage is ramped slowly, from accumulation condition to

depletion and then to inversion condition.

When the ramp rate is fast, the inversion layer does not form

and does not have time to equilibrate.

This is called “deep depletion” condition. In this case, W will

continue to increase beyond WT and CG will continue to

decrease.

partial deep depletion total deep depletion


MOS-capacitor under deep depletion

n-type Si

type)-n for type;-p for (

depletion deep total Under

V

V

CC

VVVV

G

oxG

TGTG

1


Announcements

• Next lecture: p. 611 ~ 620

• Homework (due to Dec. 3): 16.9; 16.13, 16.14

• Final EXAM: Dec. 15, 13:00 ~ 15:00, 별 232

Everything studied after the Mid-Term EXM

c-v characteristics of mos...

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