Chapter 6: MOS Capacitors 6.3. MOS analysis

SMFBV Φ−Φ= (6.3.1)

)ln(

i

at

gMSM n

NV

q

E−−−Φ=Φ−Φ χ

(6.3.2)

gaten polysilico type-n )ln(

gaten polysilico type-p )ln(

,

2

,

,,

apolyd

itSpolySpoly

a

polyatSpolySpoly

NNn

V

N

NV

=Φ−Φ=Φ

=Φ−Φ=Φ

(6.3.3)

∫−−Φ=oxt

oxoxox

iMSFB dxxx

CQ

V0

)(1

ρε

(6.3.4)

0)(

=−=

inv

TGoxinv

QVVCQ

for TG

TG

VVVV

≤>

(6.3.5)

dad xNqQ −= (6.3.6)

s

das

xNqε

=E and ox

daox

xNqε

=E (6.3.7)

s

das

xNq

εφ

2

2=

(6.3.8)

i

atF n

NV ln=φ

(6.3.9)

Fs

a

ssd Nq

x φφφε

20for ,2

≤≤= (6.3.10)

TdaTd xNqQ ,, −= (6.3.11)

a

FsTd Nq

x)2(2

,

φε=

(6.3.12)

)( invdM QQQ +−= (6.3.13)

ox

invdsFB

ox

MsFBG C

QQV

CQ

VV+

−+=++= φφ (6.3.14)

Fs

ox

sassFBG C

NqVV φφ

φεφ 20for ,

2≤≤++=

(6.3.15)

ox

invT

ox

inv

ox

FasFFBG C

QV

CQ

C

qNVV −=−++=

∆φεφ

42

(6.3.16)

ox

FasFFBT C

qNVV

φεφ

42 ++=

(6.3.17)

FBGoxHFLF VVCCC ≤== for , (6.3.18)

TGFB

s

d

ox

HFLF VVVx

C

CC ≤≤+

== for ,1

1

ε

(6.3.19)

d

ssd qN

xφε2

= (6.3.20)

Fs

ox

sassFBG C

NqVV φφ

φεφ 20for ,

2≤≤++=

(6.3.15)

TG

s

Td

ox

HFoxLF VVx

C

CCC ≥+

== for ,1

1 and

,

ε

(6.3.21)

ts

a

s

aa

s VqN

eqN

pNq

dxd

tV φεεε

φ φ

≅−=−=−+ )1()(

2

2

(6.3.22)

a

tsDs qN

VLe DL

x εφφ ==

− with ,

(6.3.23)

D

s

s

D

ss

s

sFBs Ld

Ld

ddQ

Cε

φ

φε

φ===

)(

,

(6.3.24)

s

D

ox

FB LC

C

ε+

=1

1

(6.3.25)

)2

(2

)()(

||

,,ntn

a

ddssi

TGox

nddd

inv

VqN

qn

VVCLxqG

Qtime

τµφε

τ+

−=

+=

(6.3.26)

n

tn

ox

iG VCqn

dtdV

τµ

2>

(6.3.27)