Special Topics in Nanodevices

2007. 1. Special Issues on Nanodevices 1

Special Topics in Nanodevices

3rd Lecture: Nanowire MOSFETs

Byung-Gook Park


Nanowire MOSFETs

MOSFET Scaling and Issues

Evolution of MOSFET Device Structure

Double Gate Structures

Multiple Gate Structures

Ballistic Electron Transport in Nanowires

Effect of Scattering – Landauer’s Formula

Ref : H.S. Min, Y.J. Park, B.G. Park, H.C. Shin, Semiconductor Devices with NANOCAD, Ch. 8

S. Datta, Electronic Transport in Mesoscopic Systems, Ch. 2


MOSFET Scaling - The Grand View

1

10

100

1960 1980 2000 2020

Year

0.1

0.01

Ave

rage

Des

ign

Ru

le ( m

)

SIA Roadmap ’94

SIA Roadmap ’97

ITRS (DRAM) ’05

ITRS (MPU) ’05

D.R. = 20e - 0.116(Y-1960)

~ 3 yrs : 2-1/2 reduction ~ 20 yrs : 10-1 reduction

ITRS Roadmap (’05)

2016 : 9 nm (MPU Lphy)

2019 : 6 nm (MPU Lphy)


Short Channel Effects (1)

Phenomenon : roll-off of VT as a function of gate length L

VT

L

Cause : charge sharing


Short Channel Effects (2)

L'

S D

L

B

G L'

w s

w p

x j

w c

x D

)]1/21)(/(1[2 jDjox

dFFBT xxLx

C

QVV

V VQ

CT FB Fd

ox

2

Q L QL L

d d 2 w c = x D 로 두 고 공 핍 층

모 양 을 S / 과 동 심 원 으 로 가 정 하 면

( ) ( )x x x w xj D j s D 2 2 2 w x x x x

x x x

s j D D j

j D j

( )

/( )

2 2

1 2 1

Q Q w L

Q x L x x

d d s

d j D j

( / )

[ ( / )( / )]

1

1 1 2 1


Number of dopants in the depletion region :- The number of dopant atoms in the depletion region decreases as the device dimension decreases.- As the number of dopants decreases, the statistical fluctuation of the number of dopants becomes more important.

Example : L = W = 50 nm, Na = 1018 cm-3

Wdm = 35 nm N = Na LWWdm = 87.5

sN = N1/2 = 9.35 (~ 10.7%)

Threshold voltage variation due to dopant number fluctuation :

NN

N

NN 1

LW

WN

C

q dma

oxVT 3

Dopant Number Fluctuation and VT


Evolution of Device Structure (1)

Tightness of gate control over the channel

SiO2

Double gateSOIBulk


Evolution of Device Structure (2)

Tightness of gate control over the channel


Short Channel Effects

<Single gate> <Double gate>

Design guideline

SG: tsi Lchannel/3

DG: tsi 2Lchannel/3

NW: tsi Lchannel


Various Double Gate Structures

S D

S

D

S

D

L: horizontalW: horizontal

L: verticalW: horizontal

L: horizontalW: vertical

Type I Type II Type III


FinFETs

G

SD

LG

tSOI

Wfin

G

SD

LG

SOI

Wfin

S DG

G

G

G

S D

FinFET Schematic FinFET Issue

Hfin=tSOI

Wfin<LG


Electric Field and Charge Distribution

Electric Field

Charge

Eof

Eob

qNA Qnf Qnb

Eof

Eob

VG>VTVG<VT


Basic Equations for DGMOSFETs

oobof ttt

Due to symmetry

oobof CCC

obobobofofof VtEtEV

Voltage, electric field, and channel charge

so

sobof QEE

2

1

bcfs QQQ 2


Threshold Voltage and Drain Current

Threshold voltage

o

bFFBT C

QVV

2

12

Drain current

2

2

12DDTGonD VVVVC

L

WI

* Usually, Qb 0 to suppress the dopant # fluctuation effect

negative threshold voltage for n-channel

work function engineering required

* Two devices in one!


Inversion Charge in the Channel

Charge distribution :

- assumption: Charge distribution is dominated by the ground state.

Surface inversion – two channels are separated

<Thick channel>

<Thin channel>

Bulk inversion – two channels are merged


VT vs. Channel Thickness

VT

Tch

Threshold voltage for

thicker channel :

o

bFFBT C

QVV

2

12

Threshold voltage for

thin channel :

- dominated by the energy

level quantization

- higher for thinner body


MG MOSFETs and Corner Effects

Gate

Oxide

Channel

Gate

Oxide

Channel

Quadruple gate MOSFET

- The gate surrounds the

channel.

Corner effect :

- Field concentration at

corners.


Coaxial Gate MOSFETs

Gate

Oxide

Channel

Ideal shape for NW MOSFET

- No corner effect

- 2D analysis with cylindrical coordinates


Carbon Nanotube FETs

CNT FETs

- Schottky contact at S/D junction- High dielectric for gate

insulator


Ballistic Transport in Nanowire (1)

Contact 1 Contact 2

W

LBallistic Conductor

x

y

Large conductor (L >> mean free path): G = W/L (Ohmic scaling)

G for L 0?

Ballistic conductor (L << mean free path): G Gc for L 0 Gc

“contact” resistance


Assumption : ‘reflectionless contacts’Electrons can enter a wide contact from a narrow conductor without suffering reflections.=> +k states : occupied by electrons originating in the left contact k states : occupied by electrons originating in the right contact

Quasi-Fermi levels :

Dispersion relation :

N : transverse mode number N : cut-off energy for mode N

2, eVEeVE ff 1

Nmk

kNE *

22

2),(

k

E N = 3 2 1

1

2

3

eV1eV2



Number of transverse modes :

Current by a single transverse mode : +k states are occupied according to the function f(EEf

+)

N

NEEM )()(

kf

kf

EEfkE

Le

EEvfLe

envI

)(1

)(

k

dkL2

spin)2(for

dEEEfhe

I f )(2



Current by multiple transverse modes :

dEEMEEfhe

I f )()(2

Total current :

dEEMEEfEEfhe

III

ff )()]()([2

At low temperature : )()( EEEEf ff

MVVhe

MEEhe

I ff )(2

)(2

12

2

Mhe

Gc

22

MMe

hGc

k9.12

2 21



Landauer’s Formula (1)

Contact 1 Contact 2Conductor

x

yTLead 1 Lead 2

)1( TMVVhe

I

MTVVhe

I

MVVhe

I

)(2

)(2

)(2

12

2

1

12

2

2

12

2

1


Landauer’s Formula (2)

MTVVhe

IIII )(2

12

2

211

MThe

G22

Contact 1 Contact 2Conductor

x

yTLead 1 Lead 2

Special Topics in Nanodevices

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