3-1

CMOSFET

3-2nMOSFET

GS T DSV V V

212D GS T DS DSI V V V V

0DS GS TV V V

2 12D GS T DSI V V V

n oxW CL

2 22 A S F BS

T FB Fox

qN VV V

C

C FiFB M F

E EVq

VB

VS VG VD

VB

VS

VG

VD

p

LW

n n

3-3

0GS TV V

VT

VGS

ID

0 VTVGS

log( ID )

subthreshold

3-40GS TV V

S G D

x

y0n+ n+

p

B

qVBE

E

EC

EV

y

x = 0

MOS MOS (VG, VB

EC

EV-qVG

-q S

x0

EFi-q F

E

-qVB-qVGB

3-50GS TV V

npn

npn2

exp expn i BCBEC

B A B B

qD n qVqVI AW N k T k T

npn nMOS

IC ID

A W d

WB L

NA NA= ni exp(q F /kBT )

VBE S + VBS

VBC S + VBD

dexpi F

B

qn nk T

0

SS S

x S

Qd x xdx

0

0B S

S

ndx k Tdn x qQ

3-6

2S A SQ qN S 2S S

SS S

Q QC

2

exp 2 1 expS DSBD S F BS

ox B B

C qVk T qI VC q k T k T

Bn n

k TDq

2 2S S S F S S FQ Q C

0 1 2S SGS FB S BS T BS S F

ox ox

Q CV V V V VC C

1 S

ox

CnC

2

011 exp 1 exp DSB

D GS T BSB B B

qVk T q n qI n V V Vq nk T n k T k T

subthreshold1

ln(10)kTs nq

, ,

0GS TV V

VT 0 VT VBS = 0

3-7

nJ qR

OFFI q RdV

R :

-R

Jn

source drain

IOFF

R :

VGS [V]

I D[A

]

Subthershold

I D[A

]

EC

EV

3-8Shockley-Read-Hall (SRH)

1n T Tc nN f n T Te N f p T Tc pN f 1p T Te N f

ET

EC

EV

phononET

NT :

n p n pT

n p n p

c c np e eR N

c n c p e e

n n thc v

T Fi BE E k Tn n ie c n e

p p thc v

T Fi BE E k Tp p ie c n e

n, p : vth

E

k

2

T Fi B T Fi B

iE E k T E E k T

p i n i

np nRn n e p n e

1 7~ 10p T pN c s 1 7~ 10n T nN c s

fT :

1n T T n T TR c nN f e N f

1p T T p T Tc pN f e N f

n pT

n p n p

c n ef

c n c p e e

1n T T n T Tc nN f E e N f E1p T T p T Tc pN f E e N f E

/

11F BE E k Tf E

e *3 Bk T m

3-9SRH

OFF

, ~ 0n p

1 1T Fi B T Fi B

i TE E k T E E k T

p n

n NRc e c e

1 1T Fi B T Fi B

i TOFF E E k T E E k T

p n

qn NI dVc e c e

cn ~ cp

2coshi T

OFFT Fi B

qcn NI dVE E k T

1/co

sh(x

)

(ET EFi)/kBT

( EFi )

(deep level)

3-10

EC

EV

trap Coulomb

(trap-assisted band-to-band tunneling)

Acceptor Donor

ep : Dirac wellen : Coulomb well

2

1

T Fi B T Fi B

iAT E E k T E E k T

i iCoul Dirac

p F p n n

np nR Nn n e p n ec c

2

1

T Fi B T Fi B

iDT E E k T E E k T

i iDirac Coul

p p n F n

np nNn n e p n e

c c

fp BE k TF e fp SE q qF

1 5 33 2, , exp 1b

a b K a au Ku b u du

* 34 2, ,

3fp n nCoul n

nn

E m EEkT E q E

* 34 2,0,

3n nDirac n

n

m EEkT q E

* 34 2, ,

3p pp fpCoul

pp

m EE EkT E q F

* 34 2,0,

3p ppDirac

p

m EEkT q F

n C TE E E

p T VE E E

F : E F

ep : Coulomb wellen : Dirac well

3-11

(trap-assisted band-to-band tunneling)

(band-to-band tunneling)

0F FR BF e= 5/2

F0 = 1.9 x 107 V/cm

B = 4 x 1014 cm-1/2V-5/2s-1

Si :

y

x

x y

p

n+VD

G. A. M. Hurkx, et al., IEEE Trans. Electron Devices vol. 39, p. 331, 1992

3-12

GIDL (Gate Induced Drain Leakage)

VGS [V]

I D[A

/m

] trap-assisted band-to-band tunneling

band-to-band tunneling

total

no electron-hole generation

Simulation (L = 0.13 m, tox = 4 nm)VDS = 3V

3-13

Auger

EC

EV

2 2n i p iR a n np n a p np n

an ~ 8.3 x 10-32 cm6/sap ~ 1.8 x 10-31 cm6/s

3

3-14

EC

EV

- breakdown

Impact ionization

3-15Impact IonizationEC

EV

Egimpact ionization

n n p pG J J

n, p : impact ionization

nb En na e pb E

p pa e

F (V/cm) <2.4x105 5.3x105 <

an (cm-1) 2.6x106 6.2x105 5.0x105

bn (V/cm) 1.43x106 1.08x106 9.9x106

ap (cm-1) 2.0x106 5.6x105

bp (V/cm) 1.97x106 1.32x106

Eg

3-16

DAHCDrain Avalanche Hot Carrier injection

CHEChannel Hot Electron injection

SGHESecondary Generated Hot Electron injection

SHESubstrate Hot Electron injection

VB

VG VD

VG = VD

Source Drain

Gate

VB

VG VD

VG < VD

Source Drain

Gate

VB

Source Drain

Gate VB >> 0

VB

VG VD

Source Drain

GateVG < VD

|VB | > 0

3-17(Breakdown Voltage)Avalanche Breakdown (Bipolar Breakdown)

Impact ionization

Breakdown

+

ISUB

VDS

I D

VGS

1

1 2

2

33

4

4

5

5 6

6

n+ n+

S

B

DG

3-18

EC ~ 104 V/cm~ 5 x 104 V/cm

> (Ep~ 0.063 eV)

*

83

pS

Ev

m

107

106

105

102 103 104 105

(cm

/s)

106

( V/cm)

v = n E v = p E

3-19

0

01

nn

n

sat

EE

v

0n nE

n satv E E v

E

E

n n ox GS TdVI W C V V Vdy

0

01

nn ox GS T

n

sat

dVI W C V V VdV dyv dy

20

0

12

n oxD GS T DS DS

nDS

sat

W CI V V V VL V

v

0D

DS

IV

001 1 11 22 2

GS T GS TDsat

nnGS TGS T

satsat

V V V VVV VV V v Lv L

2012

n oxD Dsat

W CI VL

3-20

RS RD

RG

CGS CGD

CGB

Body

Drain

Gate

CSB CDB

Source

n+ n+

GateSource Drain

Body

3-21

RS RD

RG

CGS CGD

CGBCSB CDB

Body

Source Drain

Gate

DS DS D S DV V I R R

GS GS D SV V I R

VDS

ID

DS D S DV I R R

VGS

ID

GS D SV I R

3/ 22D S DI R I

RDRSRG

3/ 22D S DI R I

3-22

DI

ID

VGS = VDS

0

2 GSV

GS D GSD

V I dVI

=2VT

2GS T D DV V I I

VGS=VDS

RS

RD+RS

1 GS T D SV V I R

DS DV I

= 1/

RS, VT

VDS ~ 0.02V

F. J. G. Sanchez, et al., IEEE Trans. Electron Devices, vol. 49, p. 82, 2002

H. Katto, IEEE Electron Device Lett. vol. 18, p. 408, 1997

3-23

RS RD

RG

CGS CGD

CGBCSB CDB

Body

Source Drain

Gate

N N

P

N N

P

N N

P

Subthreshold

2oxWLC CGS

CGD

VGS > VT

DS

GS T

VV V1

23

oxWLCCGC

VGSVT

2oxWLC

oxWLC

CGB

VDS > 0

CGC

VT+VDS

CGD

CGS

23

oxWLC

CGSO CGDO

CGC

CGC CGSO, CGDO

22 113 2GS ox

XC WLCX

22 113 2GD oxC WLC

X

DS

GS T

VXV V

3-24

factor

tox, L, W 1/KV 1/K Subthreshold

NA KI 1/KC 1/Ktd 1/KPd 1/K2

R K

j K electro-migration

/(ns)

(V)( m)

tox (nm)

103

251210

120

5 x 104

15550

106

0.053.55-5

115

5 x 107

0.010.9-1.8

0.255

1970 1980 1990 2000

1/K

3-25

L

VT

VDS

VT

Drain Induced Barrier Lowering (DIBL)

n+ n+

n+ n+

punchthroughL

VDS

3-26

W

VT

W

2 BTT fb F

ox

QV VC

B W WBT B

Q WL Q L QQ QWL W

QBT , QB , QW < 0

QBT (QBT < 0 (nMOS

3-27(lightly doped drain)

SiO2

SiO2

SiO2

n+n+

n

GIDL

n+n+

N N

LDD

LDD

E y[V

/cm

]

y [ m]

LDDLDD

3-28(Halo)

n+n+

n n

p+

p

p+

V T/

V DS

H.-S. Huang, et al. International Symposium on Nano Science and Technology, 2004

3-29

thermionic emission (RLD:Richardson-Laue-Dushman)

Fowler-Nordheim

3 24 22 23

216

b

ox

mqEox

b

q Ej e

b Vox

oxox

ox

VEt

2 2

2 32

b

Bk TBmqk Tj e

bVox

EF

EF

3 23 24 22 2 1 1

3216

box b

ox

mqV

Eox

b

q Ej e

3-30

A. Gupta, et al. IEEE Electron Device Lett. vol.18, p. 580, 1997

tox

3-31High-k

tox

oxox

ox

Ct

tox

S. H. Lo et al., IEEE Electron Device Lett. Vol. 18, No. 5, p. 209, 1997

10-12A0.1 mx0.1 m

3-32

Sitox

pMOSFET

EC

EV

4.05eV

5.17eV

Nb 3.99-4.3Al 4.06-4.2Ta 4.12-4.25Mo 4.3-4.6Zr 3.9-4.05V 4.12-4.3Ti 3.95-4.33TaN 4.2-3.9

Re 4.72-5.0Ir 5.-5.7Pt 5.32-5.5RuO2 4.9-5.2

nMOS

pMOS

Co 4.41-5.0W 4.1-5.2Os 4.7-4.83Cr 4.5-4.6Ru 4.60-4.71Rh 4.60-4.71Au 4.52-4.77Pd 4.8-5.22Ni 4.5-5.3

WNx, TNxp+ polySi

n+ polySin+ polySiGe

p+ polySiGe0-0.51

High-k Si

3-33(silicon on insulator)

n+ n+ D < Wmax = Fully-depleted

D > Wmax Partially-depleted

D

subthreshold(W/Km)

Si 140SiO2 1.1

3-34SOI

N+ N+

A. Wei, M. Sherony, and D. A. Antoniadis, IEEE Trans. Electron Devices, vol. 45, p. 430, 1998.

3-35SOI Dynamic Pass Gate Leakage

n+ n+

0 VVCC VCC

n+ n+

0 VVCC0 V

VS = VCC 0

Ip

In

MOS subthreshold

Bipolar ID ~ hFE Ip

MOS

1~10 ns

VGS = VCC

3-36SiSi

SiGe SiGe

n+ n+

p- relaxed Si1-xGex

p- graded buffer Si1-yGey

P-Si substrate

strained Si

y = 0 x

SiO2

Si

Si

SiO2

http://www.miraipj.jp/ja/result/030704/06.pdf

3-37

Double-gate FIN-FET Surrounding gate

UC Berkeley

SiO2

Si

n+

n+

Si

LDD

W(