Graphene - An Experimentalist's Perspective

7/31/2019 Graphene - An Experimentalist's Perspective

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J. AppenzellerPurdue University & Birck Nanotechnology Center

West Lafayette, IN 47907

Purdue Summer School 2009, July 22

Graphene field-effect transistors


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The materials impact

a2

a1

One layer of graphite (graphene)- different from graphite

8

0

-8

kx

ky

( ) FE k v k=


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8

0

-8

kx

ky

Graphene is a gapless semiconductor

2 2 2

2( )

D lin

F

D E Ev

=

E

DOS

( ) FE k v k=


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Material BulkMobility

Bandgap EffectiveMass

cm2/Vs eV m*/mo

GaN 2,0004 3.475 0.25

Si 1,4001,3 1.121,2 0.191,2

Ge 3,9001,3 0.6611,2,3 0.0821,2

GaAs 8,5001,3 1.4241,2,3 0.0671,2,3

InGaAs 12,0006

0.747

0.0418

InAs 40,0001 0.3541,3 0.0231,3

InSb 70,0001,3 0.171,3 0.0141,3

1 Handbook Series on Semiconductor Parameters,Levinshtein et al., 1996.

2 Advanced Semiconductor Fundamentals, Pierret, 2003.3 Compound Semiconductor Bulk Materials and Characterizations,

Oda, 2007.

4 Private communication, T. Sands, 2009.5 Properties of Advanced Semiconductor Materials, Bougrov et al., 2001.

6 J.D. Oliver et al., J. Cryst. Growth, 54, 64 (1981).7 K.-H. Goetz et al., J Appl. Phys., 54, 4543 (1983).8 GaInAsP alloy semiconductors, John Wiley & Sons 1982.



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Material BulkMobility

Bandgap EffectiveMass

cm2/Vs eV m*/mo

GaN 2,0004 3.475 0.25

Si 1,4001,3 1.121,2 0.191,2

Ge 3,9001,3 0.6611,2,3 0.0821,2

GaAs 8,5001,3 1.4241,2,3 0.0671,2,3

InGaAs 12,0006

0.747

0.0418

InAs 40,0001 0.3541,3 0.0231,3

InSb 70,0001,3 0.171,3 0.0141,3


graphene 100,0009

0 09 cond-mat 0805.1830v1 2008.


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2

1d tot

I CL


2 2 *

dddelay

d scatt

totV L L m

I

C

=

*

gL m E const =Direct tunneling probability fromsource to drain (WKB) is constant if:

*

*

1 1

g

delay

g scscat tt at

m

m E E

=


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1delay

g scatt E


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1delay

g scatt E


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The quantum capacitanceimpact:

00 f

gf

0qox CC


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but there is more Cq

Cox

classical limit

quantum capacitance limit

oxtot CC

qtot CC

2~

L

CI totd

2~ L

I

VC

d

ddtot=

2~ L

I

VC

d

ddtot=

LCq ~

oxox t

LC ~

diffusive:

2~

tot

ox

LP C V

t =

2~

totP C V L =

Advantages of the quantum capacitance limit

ox qtottot

g ox q

C CQC e

C C

= =

+


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content not available at this time



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improved electrostatics allows toreduce the device length

bodyox body

ox

t t

=

Advantages of 1D / 2D

Nano allows for improvedelectrostatics

Graphene and graphene nanoribbons are ultra-thin body

devices with a tbody0.5nm


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Advantages of 1D / 2D

Advantages of graphene andgraphene nanoribbons

8

0

-8

kxky

300nm

reduced scattering

top-down approach

ultra-thin body

1:1 band movement

improved scaling


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Switching in graphene versus carbon nanotubes

The energy dependence of the

density of states is the key for

current modulation in G-FETs


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2

1

22ln 1 exp

gsBgs

B

eVek TeI V

h h k T

= + +

Source to drain through conduction band:

(1)

Note: In our calculations, we will consider only one kF-point.

All currents need to be multiplied by 2 for carbon nanotubes.

One-dimensional transport in the QCL limit

( ) ( ) ( )( )1 1 ,gs

D s

eV

I e dE D E v E f E T

=


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2

122 ln 1 exp

gsBgs

B

eVek TeI Vh h k T

= + +

Source to drain through conduction band:

2 2

2

22 2ln 1 exp

gsdsBds gs

B B

eVeVek Te eI V V

h h h k T k T

= +

Drain to source through conduction band:

(1) (2)



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2 2

3

2 2 2

2 ln 1 exp

ds gs

gs dsB

B

g

B B

g

e e eI V V

h h h

eV eVek T

h k

E

T k T

E

T k

=

+ + +

Drain to source through valence band:

Source to drain through valence band:

2

4

22 2ln 1 exp

gsBgs

B

g

B

geVek Te e

I Vh h h k

EE

T k T

= + + +

(1) (2)

(3)(4)



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Contributions from I1 to I4


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2 2

3

2 2 2

2 ln 1 exp

ds gs

gs dsB

B

g

B B

g

e e eI V V

h h h

eV eVek T

h k

E

T k T

E

T k

=

+ + +

Drain to source through valence band:

Source to drain through valence band:

2

4

22 2ln 1 exp

gsBgs

B

g

B

geVek Te e

I Vh h h k

EE

T k T

= + + +

(1) (2)

(3)(4)



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Eg-dependence of output characteristics


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CNFET with Eg=0.1eV


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1D and 2D transport in the QCL limit

CNFET with Eg=0.1eV G-FET with Eg=0eV


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( )21

tot g dss ThdC V

LVI V=

On the operation of different FETs

Silicon MOSFET (with gap)( )d gsQI V

[ ]1 ( , ) ( ,( )) ( ) sd D dVgs

fI e dE D E T f E T E v E =

Carbon nanotube FET (with gap)

[ ]( , ) ( , )dV

s dgs

f E T fI EE Td Graphene FET (without gap)

[ ]2 ( ) ( , ) ( ,( ) )Dd s dVgs

I e L dE v ED f EE T f E T =

2

( )Dd Vgs

D EI dE


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Silicon nanowire FET Carbon nanotube FET(with gap)

Graphene FET(without gap)

( )d gsQI V [ ]( , ) ( , )dV

s dgs

f E T fI EE Td

2( )Dd

VgsD EI dE

On the operation of different FETs


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The quantum capacitance

Large area graphene devices

for quantum capacitance

characterization


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Sample fabrication

AFM height: 0.4nm

1m

Single layer graphene through peeling

IEDM Technical Digest, 509 (2008)


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Graphene capacitance measurements

Similar Id-V

gsare obtained for single and multi-layer graphene



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Cq ~ DOS

E

2 2

2graphene

F

EDOS

=

22

multi graphenemDOS

=

However, C-Vgs characteristics are very different


G h i


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Including a trap capacitance contribution allows to

G h i


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extract the quantum capacitance Cq


G h i


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Scaled graphene devices will operate in the QCL!

Cox (2nm Al2O3)

G h bilit


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Graphene mobility

Intrinsic and extrinsic

contributions in graphene

devices

G h d i h t i ti


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Graphene device characteristics

short channel characteristics long channel characteristics

mobility extraction from gm

carrier concentration in gm- region: ns~1012cm-3

G h d i h t i ti


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2

0

ds m ox

gs ox ds ds r

I g dL

V C V WV

L

= =


Mobility decreaseis evidence of

transition into the

ballistic transport

regime

G h d i h t i ti


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( )1 ) (ox oxgs th ds gs th injC CI V V V VL L

VL L

= = +

0

L

L

=

+


( )0 ( )ds oxball gs th injball

V CI L V V

R L

= =

G h d i h t i ti


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Graphene de ice characteristics


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00 /(1 )

caLL L

R

= +

+ +

300c

R m=

( )o gs thox

Wa V Vd

=

300nm =


Summary


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Summary

Graphene devices can operate in thequantum capacitance regime

Graphene offers a number of intrinsicmaterials related properties that makeit particularly suited for electronic applications

Contact effects need to be considered ingraphene even in the absence of a bandgap

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Graphene - An Experimentalist's Perspective