MOS Transistor

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MOS Transistor

E

x


MOS Transistor

E

x


MOS Transistor

-

E

x


MOS Transistor

E

x


MOS Transistor

+

E

x


MOS Transistor

1 2 3 4 576 8

9

kT

E

enn

0

1

1

kT

E

e

n

1

1

kT

EE f

e

n


Boltzmannsche Formel

kT

E

enn

0

kT

mgh

enn

0



kT

E

kT

EEef

enen

0

1

1

kT

EE f

e

n

kT

E

kT

EEhf

epen

01



-Q +Q

/QC

tAC ro /E -Q +Q

E


MOS Transistor

N N


MOS Transistor - Ladungsträgerdichten

aNp

E=eVbi

kT

E

dp eNn

dNn

kT

E

an eNp

aNp

NdNn

dN aN

dN

0gesQ

constpn0gesQ

Warum Sperrzone?


Intrinsischer Halbleiter

kT

E

dp eNn

dNn

kT

E

an eNp

aNp

dN aN

dN

2inpn

a

ip N

nn

2

0 d

in N

np

2

0

TDG

inn

inp

constpn 3101045.1 cmni

31610, cmNN da

32210 cmniatomS


Gate Spannung

N NN N


Gate Spannung - Kanal

N NN N


Gate Spannung

N NN N


Gate Spannung - Valenzband


Gate Spannung - Leitungsband


Gate Spannung – Elektronendichte im Kanal

N N

aip

ap

Nnn

Np

/2

Vox

ψs

N N


Elektronendichte im Kanal

Q‘G

ψsQ‘dep=e Na t

t

Na

Vox

?)(' GBch VQVGB

Q‘ch

oxsGB VV tox

aip

ap

Nnn

Np

/2

depchG QQQ '''

ox

depch

ox

G

ox C

QQ

C

QV

'

''

'

'

ox

oSiOox

tC

2'

?)(' schQ

?)(' sdepQ

Warum so steil?


Gate Spannung – Elektronendichte im Kanal

Q‘G

ψsQ‘dep=e Na t

t

Na

Q‘ch

aip

ap

Nnn

Np

/2


Ladung in verarmter Zone

Q Q+dQ dQ

tC

d

dQ r 0''

teNQ a'

'0

'

Q

eN

d

dQ ar

deNdQQ ar 0'' ar eNQ 0

2'

2

1

ar eNQ 0' 2

a

r

eNt

02

20' ar eN

C

ψ ψ

dψ

dψ

dQ

Q

dQ

t

t

Na

Q


Potential in verarmter Zone

'00

'

'

)( C

dyeN

t

dyeN

dy

teN

dyC

Qd a

r

a

r

a

ψy

y=tdψ dy

teNQ a'

dydyC r 0' )(

20' ar eN

C

dQ beeinflusst nicht


Ladung im Kanal

TU

y

pp eenn)(

0

ydy

dy s

)(

T

a

T

s

UC

yeN

Upp eeenn

'

0

T

s

Up

a

Tch een

eN

UCQ

0

''

s

ar eNC

20'

ψs

y

y=t

'C

eN

dy

d a

t

UC

yeN

Upch dyeeenQ T

a

T

s

0

0' '

chQ '

02 / paip

ap

nNnn

Np


Ladung im Kanal

T

s

U

a

iTsch eN

nUCQ

2

2'' )(

ox

sdepsch

soxsGB C

QQVV

'

'' )()(

sardep eNQ 0' 2

i

aT n

NU ln0

0

02

depQ '

chQ '

ψs

Vo

x

VGB

GBV

s

chQ '

)( fbV

)1(

Vn

NU

i

aT 42.0ln0


Starke Inversion

ox

sdepsch

sGB C

QQV

'

'' )()(

i

aTs n

NU ln22 0

ox

depch

GB C

QQV

'0

''

0

)2(2

THGBoxch VVCQ ''

ox

dep

GBTH C

QVV

'0

'

00

)2(2)2(

0

02

GBV

s

chQ '

i

aT n

NU ln0

T

s

U

a

iTsch eN

nUCQ

2

2'' )(

sardep eNQ 0' 2

TU62 0


Schwache Inversion

ox

sdepsch

sGB C

QQV

'

'' )()(

ox

sdep

ssGB C

QV

'

' )()(

n

VV THGBs

02 n

C

C

ox

'

0' )2(

1

)2()2( 0

2

0

0

ss

GBGBGB d

dVVV

0

02

GBV

s

chQ '

i

aT n

NU ln0

T

s

U

a

iTsch eN

nUCQ

2

2'' )(

sardep eNQ 0' 2

depch QQ ''

s

dep

d

dQC

'

T

THGB

nU

VV

Toxch eUCnQ

'' )1(


Drain Bias

N n=n0=Nd

aip

ap

Nnn

Np

/2

ap Np

eVDB

?pn

N N


Drain Bias

N n=n0=Nd

T

DBbi

U

VV

dp eNn

dNn 0dNn 0

T

bi

U

V

dp eNn

eVDB

?


Drain Bias

N n=n0=Nd

aip

ap

Nnn

Np

/2

ap Np

eVDB

T

DB

U

V

a

ikT

E

dp eN

neNn

2


Drain Bias

T

THGB

nU

VV

Toxch eUCnQ

'' )1(

THGBoxch VVCQ ''

ox

dep

GBTH C

QVV

'0

'

00

)2(2)2(

DBV 00 22

T

DG

U

V

a

i

a

i eN

n

N

n

22

DBTHTH nVVV

DBTHGBoxch nVVVCQ ''

nC

C

ox

'

0' )2(

1

T

DB

T

THGB

U

V

nU

VV

Toxch eeUCnQ

'' )1(

ox

arGBTH C

eNVV

'00

00

222)2(

i

aT n

NU ln0


Drain und Source Bias

N n=n0=Nd

ap Np

T

DB

U

V

pkT

E

dp eneNn

0

eVDB

T

SB

U

V

pkT

E

dp eneNn

0


Ladung im Kanal

xTHGSoxch nVVVCQ ''

T

x

T

THGS

U

V

nU

VV

Toxch eeUCnQ

'' )1(n

C

VC

ox

SB

'0

' )2(1

ox

SBarTH C

VeNV

'00

0

222

),0( DSx VV

ox

arTH C

eNV

'00

00

222

xTHGBoxch nVVVCQ 0''

T

x

T

THGB

U

V

nU

VV

Toxch eeUCnQ

0

'' )1(

),( DBSBx VVV


Gate Bias

N NN N

Q‘G

ψs

Na

Vox

VGB

Q‘ch

tox


Gate Bias

Q‘G

ψs

Na

Vox

VGB

Q‘ch

tox

THGBoxch VVCQ ''

ox

arGBTH C

eNVV

'00

00

222)2(

nC

C

ox

'

0' )2(

1

T

THGB

nU

VV

Toxch eUCnQ

'' )1(


Source Bias

N NN N

Q‘G

ψs

Na

Vox

VGB

Q‘ch

tox

SBs V 02

02 s


Source Bias

Q‘G

ψs

Na

Vox

VGB

Q‘ch

tox

THGSoxch VVCQ ''

T

THGS

nU

VV

Toxch eUCnQ

'' )1(

nC

VC

ox

SB

'0

' )2(1

ox

SBarTH C

VeNV

'00

0

222

ox

arTH C

eNV

'00

00

222

SBTHGBoxch nVVVCQ 0''


Drain Bias

N NN N


Drain Bias

xTHGSoxch nVVVCQ ''

nC

VC

ox

SB

'0

' )2(1

ox

SBarTH C

VeNV

'00

0

222

ox

arTH C

eNV

'00

00

222

xTHGBoxch nVVVCQ 0''

T

x

T

THGS

U

V

nU

VV

Toxch eeUCnQ

'' )1(

T

x

T

THGB

U

V

nU

VV

Toxch eeUCnQ

0

'' )1(

),( DBSBx VVV


Schwache Inversion

N N

eVDB

0chQT

DS

U

V

ch eQ

0

0xE


Starke Inversion

N N

eVDB

0xE


Starke Inversion - Drainstrom

)()( ' xconstdx

dVQWxI x

ch

dxdx

dVQWdxI x

ch '

DSV

xch

L

dVQWIdx0

'

0

0

eVDB

LX

eVx

DSV

xchdVQWIL0

'

DSV

xchdVQL

WI

0

' xTHGSoxch nVVVCQ ''


Schwache Inversion - Drainstrom

eVDB

0chQT

DS

U

V

ch eQ

0

0xE

)()('

xconstdx

dQWDxI

ch

T

x

T

THGS

U

V

nU

VV

Toxch eeUCnQ

'' )1(

dxdx

dQWDdxxI

ch'

)(

DSV

xx

chL

dVdV

dQWDIdx

0

'

0

Vx = 0 Vx = Vds

0 L

DSV

xch

T

dVQU

DWLI

0

' DSV

xchdVQL

WI

0

'


Starke und Schwache Inversion

T

x

T

THGS

U

V

nU

VV

Toxch eeUCnQ

'' )1(

DSV

xchdVQL

WI

0

'

xTHGSoxch nVVVCQ ''

2

2' DS

DSGSToxVnVV

L

WCI

TUDSV

T

GST

eeUnL

WCI nU

V

Tox 1)1( 2'

22'DBGBTSBGBTox nVVnVV

L

WCI

0; TGBGBTTGSGST VVVVVV


Schwache Inversion

T

x

T

THGS

U

V

nU

VV

Toxch eeUCnQ

'' )1(

TUDSV

T

GST

eeUnL

WCI nU

V

Tox 1)1( 2'

Ids

Vds

n UT


Starke Inversion

xTHGSoxch nVVVCQ ''

2

2' DS

DSGSToxVnVV

L

WCI

Ids

Vds

n

VV THGS

n

V

L

WCI GST

ox2

2'

+

-


EKV

Ids

Vds

THGS VV

22'DBGBTSBGBTox nVVnVV

L

WCI

0; TGBGBTTGSGST VVVVVV

+

-


BSIM - Drainstrom

xTHGSoxch nVVVCQ ''

satx EE /10

)()( ' xconstdx

dVQWxI x

ch

dxdx

dVQWdx

dx

dV

EI x

chx

sat

'

0

11

satsat Evv20

2

1

2'0 DS

GST

sat

DS

ox VnV

LEV

L

WCI

xEv satx EE

satx EE


BSIM - Sättigung

2

1

2'0 DS

GST

sat

DS

ox VnV

LEV

L

WCI

0

eVDBSAT

L

)(' LWQvI chsatsat

xGSToxch nVVCQ ''

DSSATGSToxsatsat nVVWCEI '0

2

DSSATGSToxsatDSSAT

GST

sat

DSSAT

oxnVVWCE

VnV

LEV

L

WC

'02'

0

221


BSIM - Sättigung

sat

GST

GSTDSSAT

nLE

Vn

VV

1

n

V

nLEV

L

WCI GST

sat

GST

ox

sat 21

2'0

2

2'0 GSTox

sat

V

L

WCI

Ids

Vds

42.1

57.0

/4.6

/4.2

/025.0

/067.0

/3

85.02

11

26

20

20

2'

0

0

n

VV

mVE

mVE

Vsm

Vsm

mfFC

V

mVU

TH

sp

sn

p

n

ox

si

T


Transkonduktanz

n

V

nLE

VL

WCI GST

sat

GST

ox

sat 21

2'0

T

GST

nU

V

Toxsat eUnL

WCI 2' )1(

n

V

L

WCI GSTox

sat 2

2'0

GSToxsatGSToxsatsat VWCvVWCEI ''0

2

gm

I

T

sat

nU

I oxsatWCv '

gm

VGST


BSIM – Early Effekt

n

V

nLEV

L

WCI GST

sat

GST

ox

sat 21

2'0

2

1

2'0 DS

GST

sat

DS

ox VnV

LEV

L

WCI

)( DSSATDS

VDSsat VV

V

III

DSSAT

Ids

Vds

A

DSSATDSsat V

VVII 1

DSSATsatA VLEV

sat

sat

I

LE

MOS Transistor

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Transcript of MOS Transistor