www.c2s2.org

1 2 3

MSD Annual Review May 1-2, 2012

Task 6.1: Atomistic Simulation of Graphene Transistors

1S. Kim, 2M. Luisier, 3T. B. Boykin, 1J. Geng, 1J. Fonseca, 1G. Klimeck1Purdue University, 2ETH Zürich, 3University of Alabama in

Huntsville

NEMO5- https://engineering.purdue.edu/gek

cogrp/software-projects/nemo5/

S D

G

GS D

Bulk

Graphene

Efield

Excellent high field transport/mobility

Problem: No bandgap

http://en.wikipedia.org/wiki/Graphene

Akturk, JAP2008Shishir, JPCM2009

Wang, PRL2008

Experimental realization

Confinement

Betti, ITED2011

Simulation (pz-TB)

• Experimental realization of GNRFETs• Edge roughness is very important at small width (w<2.5 nm)

Why Graphene?

Graphene Nanoribbon

Graphene Nanoribbon Transistors

pz vs p/d Tight-binding Model

Bandgap Id-Vgs Characteristics

p/d better match with DFTpz-wrong bandgap

pz-wrong off-current

OMEN: Boykin, et al., JAP2011

Edge Roughness and Hydrogen Passivation Roughness

• Atomistic study of edge roughness and hydrogen passivation roughness

• Reproducing experimentally possible situation

inv

1

eff

1

qNdL

dR

densityelectron :

length scattering:

inv

eff

N

L

d

d

I

VR

Edge roughness

Hydrogen passivation roughness

S D

Vd

Id

S D

Vd

Id

CH

Mobility vs Experiment

• Edge roughness limited mobility much smaller than hydrogen passivation limited mobllity

Experiment: Wang, PRL2008

Hydro. Pass.

Edge roughness

n~ 0.95x1013/cm2

2

Bandstructure Effects

Hydrogen Passivation Roughness Edge Roughness

Second subband

First subband

Ef Ef

AGNR-13 AGNR-12

P=50 %

CH

CH

DIBL suppressed

Graphene Nanomesh

Experiment: Liang et al., NanoLett 2010

NEMO5 Simulation Structure

33 nm

138x138 uc33 nm

Bandgap vs. Neckwidth

Graphene

Bandgap BandgapZero bandgap

w = 26 nm w = 19 nm w = 11 nm

Bandgap

Flat bands are ignored in bandgap calculation

(crieterion: dE/dk<0.53 eV )

w

Bandgap Comparison with Experiment

• Trend of experimental data captured

• Overestimation of bangap at a small neck width < 10 nm

Effects of Edge States

• Bandgap uncertainty due to edge roughness

• Electron Localization

Eg

Edge states

D=24 nm

w=9.7 nm

Γ Γ

Edge states criterion: dE/dk<0.53 eV

o Conclusion

• Importance of p/d model in graphene modeling

• Significant effects of edge roughness on electron mobility via bandstructure modification in GNRs

• Relatively less effective hydrogen passivation effects in GNRs

• GNM bandgap prediction through NEMO5 simulation

o Future Work

• GNR width dependent mobility and ON/OFF-current

• GNM effects of edge roughness, different shape of holes

• GNM transmission/mobility calculation

• GNR, GNM self-consistent transport simulation

A

A

Conclusion / Future Work

pz vs p/d Tight-binding Model

• p/d model necessary to reproduce the asymmetry at Dirac point

Graphene Bandstructure

OMEN- https://engineering.purdue.edu/gek

cogrp/software-projects/omen/

OMEN: Boykin, et al., JAP2011