Chap.1 Physics and Modelling of MOSFETs

반도체 연구실 신입생 세미나

박 장 표

2009 년 1 월 8 일

ContentsContents

Basic MOSFET Characteristics

Current – Voltage Characteristics

p-Channel MOSFETs

Geometric Scaling Theory

Small – Device Effects

Small Device Model

2

1.1 Basic MOSFET Characteristics

The MOS Threshold Voltage

Body Bias

3

Basic MOSFET Characteristics

MOSFET used as a Switch

ID determine by VGS & VDS ( also VSB affects lesser degree )

4

Basic MOSFET Characteristics

W, L are important dimension for electrical characteristics

Aspect ratio : W / L

5

Basic MOSFET Characteristics

VGS < VT : cutoff ( no current flow - ideally ) , VGS > VT : active mode

ID depends on the voltages applied

The MOS Threshold Voltage

: used to enhance the conduction between the drain and source

6

Basic MOSFET Characteristics

MOS system : altering the charge distribution at the surface

soxG VV 7

Basic MOSFET Characteristics

For small values of VG

Create depletion region referred to as bulk charge

The surface charge is made up entirely of bulk charge

Bulk charge consists of ionized acceptor atom, it is immobile

sasiB NqQ 2

BS QQ

8

For VG > VT

initiates thin electron inversion layer when VG = VT

)ln()(22 i

aF

nBS

n

N

q

kT

QQQ

Basic MOSFET Characteristics

9

implantion

adjustment threshold- 221

2

V theiongincorporat - 221

2

ideal - )2(21

2

FB

ox

IFasi

oxFFBT

Fasiox

FFBT

Fasiox

FT

C

qD)φ(Nqε

CφVV

)φ(NqεC

φVV

NqC

V

The MOS Threshold Voltage

Basic MOSFET Characteristics

10

Basic MOSFET Characteristics

Body Bias

asiox

FSBFTT NqεC

γVVV 21

), 22(0

11

1.2 Current – Voltage Characteristics

Square-Law Model

Bulk-Charge Model

12

Current – Voltage Characteristics

Cutoff when VGS < VT

13

Current – Voltage Characteristics

Active when VGS > VT

DSTGSnD

VV dvyVVV

L

WkI

0)]([)('

dx

dVμE, E(x) VvQI

yVVVWCQ

d

TGSoxd

,

)]([

14

Current – Voltage Characteristics

Square-Law Model

Saturation - )(2

Triode - ])(2[2

2

2

TGSD

DSDSTGSD

VVI

VVVVI

15

Current – Voltage Characteristics

)](1[)(2

2satDSTGSD VVVVI

)λVL

ΔL( iprelationsh assuming -

LL

ΔL1

ΔLL

1

L'

1

ΔLLL'

DS

Channel Length Modulation

16

Current – Voltage Characteristics

17

Current – Voltage Characteristics

2

)2

)(2

0 if

](1[)(2

TGSD

SATDSTGSD

VVI

VVVVI

18

Current – Voltage Characteristics

Bulk-Charge Model

)))2()2((3

)2(2(2

0)]([

)2(21

2

)2(21

: ChargeBulk

22

3

2

3

DSFDSFDSox

IFFBGS

DS

TGSD

ox

IFasi

cxFFBT

Fasicx

VVVC

qDVV

V

VdvyVVVI

C

qDVNq

CVV

VNqC

19

1.3 p-Channel MOSFETs

20

p-Channel MOSFETs

p-Channel MOSFETs

21

SpDDBSp

FpBSpFpppTTp

VVV

VVV

) 22(0

p-Channel MOSFETs

22

Cutoff ( VSGp < l VTp l )

Active (VSGp > l VTp l )

Triode - ])(2[2

when

2SDpSDpTpSGp

pDp

SatSDp

VVVVI

VV

2

2

when

)

)(2

Saturation - )](1)[)(2

(

TpSGp

SatSDpTpSGpDp

SatSDp

TpSGpSat

VV

VVVVI

VV

VVV

p-Channel MOSFETs

23

1.4 MOSFET Modelling

Drain-Source Resistance

MOSFET Capacitances

Junction Leakage Currents

24

MOSFET Modelling

25

MOSFET Modelling

Drain-Source Resistance

saturaion - )(

2

triode- ])(2[

2

TGS

DSn

DSTGSn

D

DSn

VV

Vr

VVVr

I

VR

))(('

1

)(

1

V V if )(

1

LTI_FETwhen

DD RefRef

TDDnTDD

Tn

D

DSn

VVL

WkVV

VVR

I

VR

26

MOSFET Modelling

MOSFET Capacitances

27

MOSFET Modelling

MOS-Based Capacitances

ooxo

ooxolg

oxG

LCC

WCWLCCC

LWLCC

)(22

2LL' ' o

28

MOSFET Modelling

GGDGGS

GGS

GGB

CCCC

CC

CC

)2/1( and )2/1( : saturation-Non

)3/2( : Saturation

: Cutoff

D

GGD

S

GGS

V

QC

V

QC

29

Depletion Capacitance

00 ),()(0

00

0

1ln ,

1)(

)(

2

RdRd

i

da

d

SIj

R

SI

Rd

SIRj

Vx)(Vxn

NN

q

kT

xC

VVxVC

MOSFET Modelling

30

X)(WCWXC

CCC

Y)(X PPxCPCCWXCC

jswj

sidebotn

jswjjswsidejbot

2

2 ,

0

00

Depletion Capacitance in Drain & Source region

MOSFET Modelling

31

X)(WCWXCC

PWXA

YWCWYCC

YXPWYA

jswjDB

D

jswjSB

SS

2

X)2(W ,

)(2

)(2 ,

00

D

00

Zero-bias source/drain bulk capacitance

MOSFET Modelling

32

Cav using a simpler LTI element

)1(

0

1)1(

0

2

12

2

10

R122,1

213/1212/1

2

13/1

0sw

R

jsw2

12/1

0

R

j0

12

3/1

0sw

R

jsw

2/1

0

R

j0dep

,0

0

0212

112

)1()1())(1(

1

)V

(1

1

)(

1)(

),(),()

V(1

PC

)V

(1

AC{

)(

1

)V

(1

PC

)V

(1

ACC

)1(

)(

),()()(

mmR

mm

jswjoRRav

m

R

mjRj

jRRjav

VV

VVm

V

VdV

VVVVK

PCVVKACVVKdVV

VdV

V

VVVC

VC

VC

ACVVKVV dVVC

VV

AC

General model for voltage-dependent depletion capacitance m : grading coefficient, such that m<1

MOSFET Modelling

33

Device Capacitance Model

DBGDDSBGSS CCCCCC ,

Use the LTI average of the depletion capacitance

MOSFET Modelling

34

Junction Leakage Currents

gengeno

DepqkTV

oR

DepqkTV

o

III

IeIII

IeII

])1([

)1(

)//(

)//(

0

0

0 2 --- 1]- 1[

τ

xqAn I

VII

digo

Rgogen

MOSFET Modelling

35

Drain / Source are always at a voltage greater than or equal to 0v

Bulk is will always exhibit leakage flows regardless of the state of the conduction of the transistor

MOSFET Modelling

36

]1)1[(

]11[

0

0

mRgomgen

RgogenR

VII

φ

VIII

General doping profile ( m : grading coefficient )

MOSFET Modelling

37

1.5 Geometric Scaling Theory

Full-Voltage Scaling

Constant-Voltage Scaling

Second-Order Scaling Effects

38

2 invariant is ratioaspect -

'

' ' ,'

S

A A'

L

W

L

W

S

LL

S

WW

Geometric Scaling Theory

39

Geometric Scaling Theory

invariant is ratioAspect

' , ,'

' ,' SSkk'SC

xC

S

xx ox

ox

oxox

oxox

40

Geometric Scaling Theory

Full Voltage Scaling

S

I

S

V

S

V

S

V

S

VS

VVVVI

S

VV

S

VV

S

VV

VVVVI

SS

DDSDSTGS

DSDSTGSD

TT

GSGS

DSDS

DSDSTGSD

])(2[2

]'')''(2[2

''

,' ,'

])(2[2

flowcurrent saturated-Non

' ,'

2

2

2

2

S

IVVI

DTGSD 2)''(

2

''

flowcurrent Saturated

2'''

Power

SP

SV

SI

VIP

VIP

DSDDSD

DSD

41

Constant-Voltage Scaling

Geometric Scaling Theory

D

TGSD

D

DSDSTGS

DSDSTGSD

SI

VVI

SI

VVVVS

VVVVI

S

)''(2

''

Current Saturated

])(2[2

]'')''(2[2

''

flowcurrent saturated-Non

' ,'

2

2

2

2

SP

VSI

VIP

DSD

DSD

'''

ndissipatioPower

42

Second-Order Scaling Effects

Geometric Scaling Theory

First-Order Scaling Effects deals with MOSFET dimensions, doping level, voltages, and currents

Second-Order Scaling Effects for example of

'

0)(N

by increased impurity scattering

Second-Order Scaling Effects for example of in VT

ox

I

C

qD

)(1

,' oxfox

jj QQ

CS

xx In the flat band voltage as is scaled oxx

43

1.7 Small-Device Effects

Threshold Voltage Modifications

Mobility Variations

Hot Electrons

44

Small-Device Effect

Threshold Voltage Modifications

)2(21

2 VNqC

VV Fasicx

FFBT Basic threshold voltage

)()2(21

2WL

WLVNq

CVV Fasi

cxFFBT Charge – voltage relation by area

Gate voltage does not support all of the bulk char with an area of WL

45

Short-Channel Effect

Small-Device Effect

a

Fsiddm

qNxx

LLL

)2(2

)(21

46

Small-Device Effect

dmjjj

jdmdmj

xxxxL

Lxxxx

2

)()(

2

222

Using Pythagorean theorem

1

]12

1[1)(

1)(

ff

x

x

L

x

L

L

L

LL

WL

WL

j

dmj

47

Small-Device Effect

SCETTSCET

j

dm

ox

BjSCET

Fasicx

FFBSCET

VVV

x

x

C

Q

L

xV

fVNqC

VV

)()(

]12

1[)(

)2(21

2)(

48

Narrow Width Effect

11,)2(21

2

2

,

Wx

AggNq

CVV

AWxAAxqNAQ

dm

NWEFasi

cxFFBT

NWEdmccdmaCB

Small-Device Effect

total area of region

49

Small-Device Effect

Since the area for

W

xg

dm

21

Another approach : empirical factor

)(1W

xg

dm

When W dmx

0)2(2

)(

)()(

WxC

QNqAV

VVV

oxdm

FasiNWENWET

NWETTNWET

4

2dmx

50

Mobility Variations

Small-Device Effect

Evnqu

vJE

J

A

dydR

neIn

ev

c

,

densitycurrent : ,tyconductivi:

)](1[ TGS

nn

VV

Ignore the VGS induces the field effect will alter the local electric field

51

Small-Device Effect

[Exam] L=0.5um, VDS=2V, estimate the Channel electric field

regionnonlinear in V/cm] [ 104105

2 45

L

VE

DS

Electron temperature

For low electric fields : cold electron region

curve goes nonlinear : warm electron region

reaches the : hot electron region

Tkvm B2

3

2

1 2*

by Particle kinetic energy to the thermal energy

)(Ev

v sv

52

Small-Device Effect

Hot Electrons

Particularly important : L < 1 um

Highly energetic particles can leave the silicon and enter the gate oxide

leading to instability of the threshold voltage

Long-term reliability problems may result

May induce leakage gate currents and excessive substrate currents

oxQ

GI SI

The LDD MOSFET

si

ddxqNE

max

Particularly important : L < 1 um

Highly energetic particles can leave the silicon and enter the gate oxide

leading to instability of the threshold voltage

Long-term reliability problems may result

May induce leakage gate currents and excessive substrate currents

Maximum value of the built-in electric field

53

1.7 Small Device Model

54

Small Device Model

)/(1

)/(

1

c

cs

n

sc

s

n

nn

EE

EEvv

vE

v

E

Ev

Critical electric field

)( ],)(1

)()[(

,)/(1

dy

dVE

dydV

v

dydV

VVVWCvWQI

EvEE

s

n

n

TGSoxnnD

NLnC

nNL

Field-dependent velocity

55

Small Device Model

Non-saturated current

)(

]1)(21[

)1(

])(2[ 2

TGSsoxD

TGSs

n

n

sSat

DSs

n

DSDSTGSnD

VVvWCI

VVLv

LvV

Vv

VVVVI

Saturation current for VDS > VSat

56