atomistic simulation of carbon nanotube fets using non-equilibrium green’s function formalism

Atomistic Simulation of Carbon Nanotube FETsUsing Non-Equilibrium Green’s Function Formalism

Jing Guo1, Supriyo Datta2, M P Anantram3, and Mark Lundstrom2 1Department of ECE, University of Florida, Gainesville, FL

2School of ECE, Purdue University, West Lafayette, IN 3NASA Ames Research Center, Moffett Field, CA

1. Introduction2. NEGF Formalism3. Ballistic CNTFETs4. Summary

2

)nm(8.0 deVEG

22312

kdE

kE G

McEuen et al., IEEE Trans. Nanotech., 1 , 78, 2002.

Introduction: carbon nanotubes

(see also: R. Saito, G. Dresselhaus, and M.S. Dresselhaus, Physical Properties of Carbon Nanotubes, Imperial College Press, London, 1998.)

3

-25

-20

-15

-10

-5

I DS (A

)-0.4 -0.3 -0.2 -0.1 0.0

VDS (V)

Introduction: device performance

Javey, Guo, Farmer, Wang, Yenilmez, Gordon. Lundstrom, and Dai, Nano Lett., 2004

BD GG

mAION /000,3

tube d ~1.7 nm

( W = 2d )

-0.1 V

-0.4 V

-0.7 V

-1.0 V

-1.3 V

VG=0.2Vnanotube diameter ~1.7 nm

Lch ~50nm

Gate

8nm HfO2

SiO2

p++ Si

PdPd CNT

4

1. Introduction2. NEGF Formalism3. Ballistic CNTFETs4. Summary

Outline

5

Nonequilibrium Green’s Function (NEGF)

Gate

molecule or device[H]

S

DSf1 f2

G EI H S 1

device contacts scattering

Datta, Electronic Transport in Mesoscopic Systems, Cambridge, 1995

ID 2q

hT (E) f1(E) f2(E) dE

dEEfEDEfEDN )()()()( 2211

GG2

1)( 2,12,1 ED

]GGTrace[)( 21ET

Charge density (ballistic)

Current

][2,12,1

i

6

1. Introduction2. NEGF Formalism3. Ballistic CNTFETs4. Summary

Outline

7

CNTFETs: real-space basis (ballistic)

DS

Gate

atomistic (pZ orbitals )

c

t

H=

ΣD

ΣS

000

000

00][ S

S

g

][00

000

000

D

D

g

1][ DSr HEIG

Recursive algorithm for Gr: O(m3N)

Lake et al., JAP, 81, 7845, 1997

(m, 0) CNT

8

CNTFETs: real-space results

band gap

interference2nd subband

Confined states

Gate

n+ n+i

9

CNTFETs: mode-space approach (ballistic)

c

t

k

t

The qth mode

Nq

q

q

q

q

ub

b

ut

tub

bu

H

3

2

1

c

qkq

2 S (1,1) and D (N,N)

analytically computed

- Computational cost: O(N)real space O(m3N)

(m,0) CNT

10

CNTFETs: mode-space results

n+ n+i

2 modes

real space

band profile (ON)

coaxial G VD=0.4V

dCNT~1nmcoaxial G

coaxial G

2 modes

real spacecoaxial G

Gate 8nm HfO2

SiO2

p++ Si

PdPd CNT

11

CNTFETs: treatment of M/CNT contacts

M

CE

VE

FE

t

0B

metallic tube band

00

0it

m

:0B band discontinuity

Kienle et al, ab initio study of contacts in progress

12

CNTFETs: treatment of M/CNT contacts

Gate

VD=VG=0.4V

Charge transfer in unit cell: Leonard et al., APL, 81, 4835, 2002

MetalS

metalD

tunneling

13

CNTFETs: 3D Poisson solver

Gate

8nm HfO2

SiO2

p++ Si

PdPd CNT

Method of moments:

')'()'()( rdrrrKrV

Electrostatic kernel:

for 2 types of dielectrics available in Jackson, Classical Electrodynamics, 1962

)'( rrK

)'( rrK

Neophytou, Guo, and Lundstrom, 3D Electrostatics of CNTFETs, IWCE10

14

CNTFETs: numerical techniques

given n: --- > U scf

“Poisson”

given U scf : --- > n

transport equation

Iterate until self -

consistent

given n: --- > U scf

Poisson

given U scf : --- > n

NEGF Transport

Iterate until self -

consistent

- Non-linear Poisson

- Recursive algorithm for

- Gaussian quadrature for doing integral

- Parallel different bias points

- ~20min for full I-V of a 50-nm CNTFET

1][)( DSHEIEG

15

CNTFETs: theory vs. experiment

G

Bp=0

dCNT ~1.7nm

RS=RD~1.7K

VD= -0.3V

-0.2V

-0.1Vexperimenttheory

Gate

8nm HfO2

10 nm SiO2

p++ Si

PdPd CNT

Javey, et al., Nano Letters, 4, 1319, 2004

16

Summary

A simulator for ballistic CNTFETs is developed

- atomistic treatment of the CNT- 3D electrostatics- phenomenological treatment of M/CNT contacts- efficient numerical techniques

Theory is calibrated to experiment