graphene: thermal properties and possible applications · alexander a. balandin, university of...

Alexander A. BalandinNano-Device Laboratory

Department of Electrical Engineering and

Materials Science and Engineering Program

University of California – Riverside

Graphene: Thermal Properties

and Possible Applications

IEEE Talk, November 2010

Alexander A. Balandin, University of California - Riverside

2

UCR Bell Tower

City of Riverside

UCR Botanic Gardens

Joshua Tree Park, California

UCR Engineering Building


Nano-Device Laboratory (NDL) Department of Electrical EngineeringUniversity of California – Riverside

Profile: experimental and theoretical research in phonon engineering and nanodevices

Research at NDL was funded

by NSF, ONR, SRC, DARPA,

NASA, ARO, AFOSR, CRDF, as

well as industry, including

IBM, Raytheon, TRW, etc.

Research &

Applications

Raman, Fluorescence

and PL Spectroscopy

Electronic

Devices and

Circuits

Optoelectronics

Direct Energy

Conversion

Bio-

Nanotech

Thermal and Electrical

Characterization

Device Design and

Characterization

Nanoscale Characterization

Theory and

Modeling

PI: Alexander A. Balandin


Outline

Introduction and Motivations

Raman Nanometrology of Graphene

Counting the layers

Temperature effects

Heat Conduction in Graphene

Measurements

2D phonon transport

Graphene Transistors and Communication Applications

Low-noise graphene FETs

Triple-mode graphene amplifier

“Graphene-like” Exfoliation of other Quasi-2D Crystals

Conclusions

4


5

Graphene: The True 2D System

A. Geim and K. Novoselov:

Nobel Prize in Physics, 2010

“Graphene revolution” brought

about by K.S. Novoselov and A.K.

Geim with the help of bulk

graphite and “Scotch” tape.

The first paper was published

by the Manchester, U.K. –

Chernogolovka, Russia group:

Novoselov, et al., Science (2004).

Individual atomic layers of sp2-

hybridized carbon bound in two-

dimensions. Crystalline graphite

is composed of graphene layers.

“Unrolled Carbon Nanotube”


6

The “Unexpected” Discovery

R.E. Peierls (1934) and L.D. Landau (1937):

Strictly 2D crystals cannot exist in the harmonic approximation;

thermal fluctuations should destroy long-range order resulting in

melting 2D lattice at any finite temperature

N.D. Mermin and H. Wagner (1966):

Magnetic long-range order does not exist in 2D

Experimental observations were in agreement:

Below a certain thickness (~10 atomic layers), the films become

thermodynamically unstable and segregate into islands or decompose

“Lost in Translation”:

Theory prohibits perfect 2D crystals but does not prohibit “nearly

perfect” 2D crystals in 3D space

Going beyond harmonic approximation: bending, stretching and

corrugations and microscopic roughening can stabilize 2D crystals


7

Why Should Engineers Care about Graphene?

Exotic physical properties

Electrons as massless relativistic Dirac fermions

Anomalous quantization of Hall conductance

Possible electronic and optoelectronic applications

High electronic mobility

High-speed devices, sensitive detectors, interconnects, etc.

High thermal conductivity

Benefit for electronics, thermal management

Optical transparency

Transparent electrodes for touch-screens and PV cells

Extremely strong and stiff

MEMS/NEMS material, extremely thin resonator


8

How Real are Real-Life Graphene Applications?

Flexible graphene sheet with silver electrodes printed on it can

be used as a touch screen when connected to control software.

Credit: Byung Hee Hong, SKKU.

http://www.technologyreview.com/computing/25633/page1/

http://www.technologyreview.com/computing/25633/page1/


9

Part I: Raman Nanometrology of Graphene


10

Raman Spectroscopy of Graphene

Alternatives:

low-temperature transport study

cross-sectional TEM

few other costly methods

Visualization on Si/SiO2 substrates D band: A1g (~1350 cm-1); G peak: E2g; 2D band

A.C. Ferrari et al., Phys. Rev. Lett. 97, 187401 (2006).

I. Calizo, et al., Nano Lett., 7, 2645 (2007).

Graphene is a single atomic layer of carbon atoms by definition!


11

2D-band features of graphene are reproducible

and can be used to count the number of

graphene layers.

Raman Nanometrology of Graphene:

Counting the Number of Atomic Planes

2300 2400 2500 2600 2700 2800 2900 30000

4000

8000

12000

16000

20000

24000

Inte

nsity (

arb

. u

nits)

Raman Shift (cm-1)

Graphene @ 300K

exc = 488 nm

1 layer

2 layers

3 layers

4 layers

5 layers

Deconvolution of 2D (G’) Band

I. Calizo, et al., Appl. Phys. Lett., 91, 201904 (2007).

I. Calizo, et al., Appl. Phys. Lett., 91, 071913 (2007).


12

Quality Monitoring with Raman Spectroscopy

1250 1300 1350 1400 1450 1500 1550 1600 1650 1700 1750

0

2000

4000

6000

8000

10000

Excitation: 488 nm

G Peak

D Band

1359 cm-1

1582 cm-1

INT

EN

SIT

Y (

AR

BIT

RA

RY

UN

ITS

)

RAMAN SHIFT (cm-1)

Single Layer Graphene

Initial Bulk Graphite

1581 cm-1

Defect or disorder induced D

mode in graphene

D mode is excitation

dependent: 40-50 cm-1/eV

F. Parvizi, et al., Micro & Nano

Letters, 3, 29 (2008).


13

Temperature Coefficients of Graphene

Raman Peaks

-150 -75 0 75

1576

1578

1580

1582

1584

1530 1575 1620

2500

5000

7500

10000

12500

G P

ea

k P

osi

tion

(cm

-1)

Temperature (C)

G Peak Position

Linear Fit of Data

Bi-Layer Graphene

slope = -0.015 cm-1/C

Raman Shift (cm-1

)

Inte

nsi

ty (

arb

. u

nits

)

Bi-layer

Graphene

exc = 488 nm

G Peak

1580 cm-1

Phonon frequency downshift with T is unusual when the bond-bond distances shorten with T since normally

lattice contraction leads to the upward shift of the frequencies.

Note: the sign is negative

Temperature is controlled externally; very low excitation power on the sample surface is used (< 0.5 – 1 mW).


14

Explanation of the Anomalous Sign and

FWHM Behavior of Graphene G Mode

Ab-initio calculations of N. Bonini et al.,

Phys. Rev. Lett., 99, 176802 (2007).


15

Part II: Thermal Conductivity of Graphene

IEEE Spectrum illustration of

the first measurements of

thermal conductivity of graphene

(Spectrum, October, 2009)

The UCR Experiment


Basics of Heat Conduction

16

Fourier’s law:

Definitions and Basic Theory

Phonon vs. electron conduction:

jq

iiNQ,

, ,)(q

qqq

Heat current carried by phonons :

Te

kK Be

22

3

RT thermal conductivity of important materials:

Silicon (Si): 145 W/mK

SiO2: 1-13 W/mK

Copper: 400 W/mK

RT thermal conductivity for carbon materials:

Diamond: 1000 – 2200 W/mK

Graphite: 200 – 2000 W/mK (orientation)

DLC: 0.1 – 10 W/mK

CNTs: 3000 – 3500 W/mK

Very wide range of K for carbon materials

depending on their lattice and dimensionality

TKS

Q


The switch to multi-core

designs alleviates the growth in

the thermal design power (TDP)

increase but does not solve the

hot-spot problem

Non-uniform power densities

leading to hot-spots (>500 W/cm2)

Data is after R. Mahajan et al., Proceed. IEEE (2006)

Why Engineers Need to Worry about

Heat Conduction

IEEE Spectrum illustration of the

thermal issues in the feature

article Chill Out: New Materials

and Designs Can Keep Chips

Cool by A.A. Balandin.

No BIG fan

solutions!


Thermal Transport at Nanoscale: Crystalline Semiconductors and Insulators

300 400 500 600 700 800 0

20

40

60

80

100

120

140

160

TEMPERATURE (K)

TH

ER

MA

L C

ON

DU

CT

IVIT

Y (

W/m

-K) Si Bulk Diffuse Scattering (p=0)

Si Nanowire: A

Si Nanowire: B

Thermal conductivity usually decreases as one goes from bulk

material to nanostructure or thin film

J. Zou and A.A. Balandin, J. Appl. Phys., 89,

2932 (2001).

Phonon - boundary scattering:

Lp

p

B

1

11

Thermal conductivity of bulk Si at room

temperature: K= 148 W/m-K

Thermal conductivity of Si nanowire with

cross section of 20 nm x 20 nm: K=13 W/mK

Phonon spectrum modification

Phonon group velocity changes

Phonon density of states change

18

Thermal transport in crystalline nanoscale

carbon materials will mostly affected by the

phonon - boundary scattering


Measurement of Thermal Conductivity:

Available Experimental Techniques

3-Thermal Conductivity Setup

Transient Plane Source Technique

Laser – Flash Technique

T2 T1

T2>T1

TKS

Q

S

Measurement Principles


Thermal Conductivity Measurements with

Micro-Raman Spectrometer

Importance of the Suspended Portion of Graphene

Formation of the specific in-plane heat front

propagating toward the heat sinks

Reduction in the graphene – substrate coupling

Determining the fraction of the power dissipated in

graphene through callibration procedure

G mode D mode

Idea of the Experiment:

Induce locale hot spot in the middle of the suspended

graphene flake and monitor temperature rise in the middle

with increasing excitation laser intensity.

Graphene Specifics:

Atomic thickness: good for this method

Heat transport: diffusive or partially diffusive thermal transport

In-plane phonon modes: less effect from the substrate and possibility of graphite calibration


2121

Measurement of the Thermal Conductivity

Laser acts as a heater (confirmed by Stoke –

Anti-Stoke intensity ratio): DPG

Raman “thermometer”: DTG=D/cG

Thermal conductivity: K=(L/2aGW)(DPG/DTG)

1( / 2 ) ( / ) .G G GK L a W Pc D D

0 1 2 3 4

-6

-4

-2

0

2

4

SLOPE: -1.292 cm-1/mW

SUSPENDED GRAPHENE

G P

EA

K P

OS

ITIO

N S

HIF

T (

cm-1

)

POWER CHANGE (mW)

EXPERIMENTAL POINTS

LINEAR FITTING

A.A. Balandin, S. Ghosh, W. Bao, I. Calizo, D. Teweldebrhan,

F. Miao and C.N. Lau, Nano Letters, 8: 902 (2008).

Thermal conductivity of rectangular flake (L is

the half-length):

Connect DPD DPG through calibration


22

Thermal Conductivity of Single Layer Graphene:

Comparison with Carbon Nanotubes

Table I: Experimental RT Thermal Conductivity of Graphene and CNTs

Sample K (W/mK) Method Comments Reference

SLG ~ 3000 – 5000 optical individual Balandin et al., Nano Lett. (2008)

MW-CNT ~ 3000 electrical individual Kim et al., Phys. Rev. Lett. (2001)

SW-CNT ~ 3500 electrical individual Pop et al., Nano Lett. (2006)

SW-CNT 1750 – 5800 thermocouples bundles Hone et al., Phys. Rev. B (1999)

SW-CNT 3000 - 7000 thermocouples individual Yu et al., Nano Lett. (2005)

CNTs ~1500 - 2900 electrical individual Fujii et al., Phys. Rev. Lett. (2005)

Sample K (W/mK) Method Comments Reference

CNTs ~6600 MD predicted higher K for graphene Berber et al. PRL (2000)

CNTs ~2980 MD strong defect dependence Che et al., Nanotech. (2000)

graphite ~2000 C-K basal plane (a-plane) Klemens et al., Carbon (1994)

Table II: Theoretical RT Thermal Conductivity of Graphene and CNTs


23

Fundamental Property: Divergence of the Lattice Thermal Conductivity in 2-D Crystals

K ~ log(N) in 2D

K ~ Nα in 1D, α≠1

N – system size[1] K. Saito, et al., Phys. Rev. Lett. 104, 040601 (2010).

[2] A. Dhar. Advances in Physics 57, 457 (2008).

[3] G. Basile et al. Eur. Phys. J. 151, 85 – 93 (2007).

[4] L. Yang et al. Phys. Rev. E 74, 062101 (2006).

[5] L. Delfini et al. Phys, Rev. E 73, 060201R (2006).

[6] S. Lepri et al. Chaos 15, 015118 (2005).

[7] J. Wang, B. Li. Phys. Rev. Lett. 92, 074302 (2004).

[8] S. Lepri et al. Phys. Rep. 377, 1 (2003).

[9] R. Livi and S. Lepri. Nature 421, 327 (2003).

[10] O. Narayan et al., Phys. Rev. Lett., 89, 20601 (2002).

[11] A. Dhar. Phys. Rev. Lett. 86, 5882 (2001).

[12] A. Lepri and R. Livi, J. Stat. Phys. 100, 1147 (2000).

[13] T. Pozen et al., Phys. Rev. Lett., 84, 2857 (2000).

[14] S. Lepri et. al. Europhys. Lett. 43, 271 (1998).

Thermal conductivity in 2D lattice

vs. Nx. Data is after S. Lepri et al.

(Ref. [8]).

Consensus: The intrinsic thermal conductivity of

2-D or 1-D anharmonic crystals is anomalous.


24

Klemens Theory of the Phonon

Thermal Conductivity of Bulk Graphite

max

min

2

,2 2,

( ) [ ( ) / ]1{( ( ) ) }

4 [ [ ( ) / ] 1]

q

s ss U s

s TA LA qB s

d q exp q kTK q q dq

k T h dq exp q kT

2,max

, 2 2

1 ssU s

s B

M

k T

N. Mounet et al, Phys. Rev. B 71, 205214 (2005). P.G. Klemens, J. Wide Bandgap

Materials, 7, 332 (2000).

Intrinsic Umklapp-Limited Thermal Conductivity:

Umklapp life-time, which defines MFP:

In bulk graphite there is natural low-bound

cut-off at ~4 THz. The heat transport is two-

dimensional only above this frequency.

Klemen’s value for graphite: K=1900 W/mK

2-D: C() ~ K ~T-1-1

3-D: C() ~ 2

jq

iiNQ,

, ,)(q

qqq


25

Theory of the Phonon Heat Conduction

in Graphene

max

min

2

,2 2,

( ) [ ( ) / ]1{( ( ) ) }

4 [ [ ( ) / ] 1]

q

s ss U s

s TA LA qB s

d q exp q kTK q q dq

k T h dq exp q kT

2,max

, 2 2

1 ssU s

s B

M

k T

P.G. Klemens, J. Wide Bandgap Materials, 7, 332 (2000).

Thermal conductivity in graphene:

,max

,min

ss ss

s B

M

k T L

Graphene:MFP = L – physical size of the system

Limitation on MFL: L= vs

Limiting low-bound frequency:


26

Uniqueness of Heat Conduction in Graphene

“Intrinsic” Thermal Conductivity Value is Defined by the Flake Size

The phonon transport in graphene is 2D all the way down to zero frequency

D.L. Nika, S. Ghosh, E.P. Pokatilov, A.A. Balandin,

Appl. Phys. Lett., 94, 203103 (2009).

,max

,min

ss ss

s B

M

k T L

Low-bound cut-off frequency is defined by the

condition that the phonon MFP can not exceed

the physical size of the graphene flake:


27

Phonon Transport in Graphene and FLG:

Accurate Theory vs Experiment

Enhancement of

Umklapp scatterings in

bilayer in comparison with

monolayer due to the two-

fold degeneracy of phonon

energy spectra in bilayer

S. Ghosh, W. Bao, D.L. Nika, S.

Subrina, E.P. Pokatilov, C.N. Lau

and A.A. Balandin, "Dimensional

crossover of thermal transport in

few-layer graphene," Nature

Materials, 9, 555 (2010).


Thermal Management Applications:

Graphene Laterals Heat Spreaders

S. Subrina, D. Kotchetkov and A.A. Balandin, Graphene heat

spreaders, IEEE Electron Device Lett., 30, 1281 (2009).

Significant

reduction of the

hot-spot

temperature due to

incorporation of

graphene layers

US Patent Pending, 2008


Graphene Interconnects and Heat Spreaders

Q. Shao, G. Liu, D. Teweldebrhan and A.A. Balandin,

Applied Physics Letters, 92: 202108 (2008).


Thermal Interface Materials with Graphene

TIMs are materials with the relatively high thermal conductivity introduced to the joint to fill the air gaps.

http://www.ecnmag.com/tags/products/Materials/

Current TIM based on polymer, grease filled with silver, alumina require 50-70% loading to achieve 1-5 W/mk. F. Sarvar et al. Elect. Sys. Technology Conference (2006)


31

Part III: Graphene Transistors for

Communication Applications


Types of Intrinsic

Electronic Noise:

Thermal noise:

SI=4kBT/R

Shot noise:

SI=2e<I>

Flicker 1/f noise:

SI ~ I2/f

G-R noise:

SI ~ 1/(1+f2t2)

See A.A. Balandin (Ed.), Noise and Fluctuations Control in Electronic Devices (ASP, 2002).

log f

1/f

WHITE

HF

G-R

100 kHz

Electronic Device Noise

No

ise

Sp

ectr

al D

en

sity S

V(V

2/H

z)

Up-conversion

Types of Electronic Noise and their

Practical Importance


Bottom-Gate and Top-Gate Graphene

Field-Effect Transistors

-1.0 -0.5 0.0 0.5 1.012.0u

14.0u

16.0u

18.0u

20.0u

22.0u

I DS

(A

)

VTG (V)

Top Gate Function of Single

Layer Graphene Device

VDS

=0.1V

-60 -40 -20 0 20 40 60

0.0

2.0x10-5

4.0x10-5

Vg

D

Vds

=20 mV

Vds

=40 mV60 mV

80 mVV

ds=100 mV

So

urc

e -

Dra

in C

urr

en

t (A

)

Gate Bias Vg (V)

The fabrication of pads and contact bars was performed using electron beam

lithography Cr/Au metal deposition by electron beam evaporator.

Top gate dielectric of ~20 nm HfO2 is grown by the atomic layer deposition (ALD).

The low-temperature ALD allows for fabrication of the dielectric with low leakage.


Noise Spectrum of Bilayer Graphene

Field-Effect Transistor

1 10 100 1000 1000010

-24

10-23

10-22

10-21

10-20

10-19

10-18

10-17

10-16

Bilayer Graphene Device

13 V

0 V

20 V

-20 V

45 V

1/f

No

ise

Sp

ectr

al D

en

sity S

I (A

2/H

z)

Frequency (Hz)

Vds

=20 mV

Q. Shao, G. Liu, D. Teweldebrhan, A. A. Balandin, S. Rumyantsev, M. Shur and D. Yan, "Flicker noise in

bilayer graphene transistors," IEEE Electron Device Letters, 30, 288 (2009).


S. Vijayaraghavan, et al., J. Appl. Phys. 100, 024315 (2006).

P.G. Collins, et al., App. Phys. Lett. 2000, 76, 894.

A.A. Balandin, Noise in Electronic Devices (ASP, 2002).

fNI

SIH 2

Upper bound: number of carriers equal

to the number of atoms in M-SWNTs.

Different role of contacts

Different exposure to environment

1/f Noise: Graphene vs Carbon Nanotubes

Hooge parameter:

G. Liu, W. Stillman, S. Rumyantsev, Q. Shao, M. Shur and A.A.

Balandin, "Low-frequency electronic noise in the double-gate single-

layer graphene transistors," Appl. Phys. Lett., 95, 033103 (2009).


Where Does The Noise Comes From?

-60 -40 -20 0 20 40 601E-10

1E-9

1E-8

1E-7

f=10Hz

SI/I2

(1/H

z)

Vg (V)

-60 -40 -20 0 20 40 601E-9

1E-8

1E-7

1E-6

f=10Hz

SI/I

2×

W×

Lg (m

2/H

z)

Vg (V)

Noise spectral density SI/Id2 normalized to

channel area results in a much narrower

dispersion: noise originates in graphene layer

Studied devices with a wide range of channel

areas: from 1.5 to 80 mm2

S. Rumyantsev, G. Liu, W. Stillman, M. Shur and A.A.

Balandin, "Electrical and noise characteristics of graphene

field-effect transistors: Ambient effects and noise sources,"

J. Physics: Condensed Matter, 22, 395302 (2010).


The ambipolar electronic

transport in graphene

transistors leads to increased

amplifier functionality

Mode 1

Mode 3

Mode 2

Mode 1: common-drain mode (amplifier is

biased at left branch of the ambipolar curve)

Mode 2: common-source mode (amplifier is

biased at right branch of the ambipolar curve)

Mode 3: frequency multiplication mode

(amplifier is biased at the Dirac point)

Triple-Mode Graphene Amplifier:

The Next “Killer” Application?

X. Yang, G. Liu, A.A. Balandin and K. Mohanram, “Triple-mode graphene amplifier,” ACS Nano (2010).

Collaboration with Rice University


38

Enhanced Functionality of

Graphene Amplifier

a) The schematic for triple-

mode graphene amplifier. (b)

The I-V characteristics of the

graphene transistor. (c), (d), (e)

are the output of the amplifier at

different biasing points

Binary phase shift keying (BPSK)

modulation with graphene

amplifiers: (a) biasing points and

(b) experimental results.

The graphene circuit can realize the

modulation necessary for phase shift

keying and frequency shift keying, which

are widely used in wireless applications

such as Bluetooth, RFID, and ZigBee.


39

Part IV: “Graphene-Like” 2D Crystals


40

A.A. Balandin and K.L. Wang, Phys. Rev. B (1998).

A.A. Balandin and K.L. Wang, J. Appl. Phys. (1998).

The thermoelectric figure of merit: ZT=S2T/(Ke+Kp)

S is the Seebeck coefficient, is the electrical conductivity and K is the thermal conductivity.

Electron Quantum Confinement Acoustic Phonon Confinement

M.S. Dresselhaus, et al. Phys. Solid State (1999).

L.D. Hicks and M.S. Dresselhaus, Phys. Rev. B (1993).

Low potential barrier in Bi2Te3/Bi2Se3; Bi2Te3/Sb2Te3

Thermoelectric Motivation for “Graphene-Like” Exfoliation of Bi2Te3


Topological Insulators: Benefits of Few-Quintuple Exfoliated Films

41

Improved gating for tuning the

Fermi level position

Reduce the volume component

of transport

Band-gap modulation

Better quality of materials with

less unintentional doping

FQL can be better than SGL

For review see

M.Z. Hasan and C.L. Kane, arXiv: 1002.3895

X.-L. Qi and S.-C. Zhang, arXiv: 1008.2026.

J. Moore, Nature Physics, 5, 378 (2009).


“Graphene-Like” Exfoliation of Different Type

of Dirac Materials: Topological Insulators

D. Teweldebrhan, V. Goyal and

A.A. Balandin, "Exfoliation and

characterization of bismuth

telluride atomic quintuples and

quasi-two-dimensional crystals,"

Nano Letters, 10, 1209 (2010).


Raman Spectroscopy of the Atomically Thin Films of Bi-Te Topological Insulators

43

K.M.F. Shahil, M.Z. Hossain, D. Teweldebrhan and A.A.

Balandin, "Crystal symmetry breaking in few-quintuple

Bi2Te3 films: Applications in nanometrology of topological

insulators," Appl. Phys. Lett., 96, 153103 (2010).


Room-Temperature Electrical Characterization Bi-Te Atomic Films

44

Weak gating at RT

Resistivity is ~10-4 Wm

D. Teweldebrhan, V. Goyal, M. Rahman and

A.A. Balandin, "Atomically-thin crystalline films

and ribbons of bismuth telluride," Appl. Phys.

Lett., 96, 053107 (2010). - Issue's Cover


Thermoelectric Topological Insulators

V. Goyal, D. Teweldebrhan

and A.A. Balandin,

“Mechanically exfoliated

stacks of thin films of Bi2Te3

topological insulator films”,

Appl. Phys. Lett. (2010).

ZT increase by ~140 – 250% at room

temperature

The enhancement is expected to be

larger at low T


46

Outlook: “The Carbon World”

IEEE Spectrum artistic rendering of the hybrid silicon – carbon 3D chip with

graphene heat spreaders, graphene interconnects and graphene transistors.

Graphene Applications

Transparent electrodes

Touch screens

Heat spreaders

Sensors

Interconnects

High-Frequency

Analog, RF, Mixed Signal


47

Acknowledgements

Nano-Device Laboratory (NDL) research group, UCR 2010.

graphene: thermal properties and possible applications · alexander a. balandin, university of...

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