––WARREN M. ROHSENOW HEAT AND MASS TRANSFER LABORATORY, MITWARREN M. ROHSENOW HEAT AND MASS TRANSFER LABORATORY, MIT

Gang Chen

Mechanical Engineering DepartmentMassachusetts Institute of Technology

Cambridge, MA 02139

Nanoscale Heat Transfer and Information Technology

Rohsenow Symposium on Future Trends in Heat TransferMay 16, 2003

Response to K.E. Goodson

––WARREN M. ROHSENOW HEAT AND MASS TRANSFER LABORATORY, MITWARREN M. ROHSENOW HEAT AND MASS TRANSFER LABORATORY, MIT

HEAT TRANSFER IN NANODEVICES

1000 Å

Source

Gate

DrainChannel

~10,000 rpm

~50 nm

2mm

MOSFET (IBM, Taur) Laser Diode (S. Pei) Data Storage (IBM)

––WARREN M. ROHSENOW HEAT AND MASS TRANSFER LABORATORY, MITWARREN M. ROHSENOW HEAT AND MASS TRANSFER LABORATORY, MIT

MEAN FREE PATH OF HEAT CARRIERS

• KINETIC THEORY • SPECTRUM EFFECTS

k ≈ CvΛ / 3 ( ) ( ) ( )k = C ω v ω Λ ω∫ dω / 3

101

102

103

104

105

0 50 100 150 200 250 300

PHONON (Dispersive)PHONON (Kinetic Theory)ELECTRONAIR MOLECULE

MEA

N F

REE

PA

TH (n

m)

TEMPERATURE (K)

Silicon

Au Air

––WARREN M. ROHSENOW HEAT AND MASS TRANSFER LABORATORY, MITWARREN M. ROHSENOW HEAT AND MASS TRANSFER LABORATORY, MIT

HEAT CONDUCTION AT NANOSCALE• Phonon Mean Free Path in Silicon: 400-3000 Å• Phonon Wavelength: Lattice Spacing-Crystal Size

Si

Oxide

Nano-Device

• Transport Outside Nanostructures

Phonon Quantization:Surface ModeBoundary Resistance

Phonon Rarefication

Electron-Phonon InteractionThermal Conductivity ReductionHigh Device Temperature

• Phonon Transport Inside NanostructuresPhonon Quantization:

Reflection, Interferene, TunnelingInterface Scattering:

Diffuse vs. Specular

Kang L. Wang M.S. Dresselhaus

––WARREN M. ROHSENOW HEAT AND MASS TRANSFER LABORATORY, MITWARREN M. ROHSENOW HEAT AND MASS TRANSFER LABORATORY, MIT

DOMINANCE OF INTERFACES

0.0

0.5

1.0

1.5

2.0

2.5

0.0 0.1 0.2 0.3 0.4NONDIMENSIONAL COORDINATE

p=0

p=0.5

p=1

INELASTICd

1=d

2=50 Å

AlAsGaAs

NO

ND

IMEN

SIO

NA

L TE

MPE

RA

TUR

E D

ISTR

IBU

TIO

N

100

101

102

103

80 120 160 200 240 280

KX,BULK(FOURIER LAW)KZ,BULK(FOURIER LAW)

KZ,FILM, EXPERIMENTAL

KX,FILM, EXPERIMENTAL

THER

MAL

CO

ND

UC

TIVI

TY (W

/mK

)

TEMPERATURE (K)

Si0.5Ge0.5

BULK ALLOY (300K)

Lines--Fitting with CHen'sModel

P=0.6

P=0.5

P=0.6

Cross-Plane

In-Plane

100

101

102

103

80 120 160 200 240 280

KX,BULK(FOURIER LAW)KZ,BULK(FOURIER LAW)

KZ,FILM, EXPERIMENTAL

KX,FILM, EXPERIMENTAL

THER

MAL

CO

ND

UC

TIVI

TY (W

/mK

)TH

ERM

AL C

ON

DU

CTI

VITY

(W/m

K)

TEMPERATURE (K)

Si0.5Ge0.5

BULK ALLOY (300K)

Lines--Fitting with CHen'sModel

P=0.6

P=0.5

P=0.6

Cross-Plane

In-Plane

––WARREN M. ROHSENOW HEAT AND MASS TRANSFER LABORATORY, MITWARREN M. ROHSENOW HEAT AND MASS TRANSFER LABORATORY, MIT

NONLOCAL AND NONEQUILIBRIUM

Te1 Te2

I1(T )e1+

τ I1(T )e1+

12

I2(T )e2+

I2(T )e2+τ21

r21I2(T )e2+r12I1(T )e1

+Te1 EMITTED

Te2 EMITTED

T1 EQUILIBRIUM

T2 EQUILIBRIUM

TEMPERATURE

T2

T1

r2

r1Diffusive Limit

Ballistic Limit

r2 >> r1

11F 4

34

1RrCvkr Λ

==ππ

Cvr 21

B4

1Rπ

=

T2

T1

r2

r1

––WARREN M. ROHSENOW HEAT AND MASS TRANSFER LABORATORY, MITWARREN M. ROHSENOW HEAT AND MASS TRANSFER LABORATORY, MIT

THERMAL WAVELENGTH

10-2

100

102

104

106

108

101 102 103

THER

MA

L W

AVE

LEN

GTH

(nm

)

TEMPERATURE (K)

PHOTON

WIEN'S DISPLACEMENT LAW

ELECTRON

PHONON

AIR MOLECULE

v(PHONON)=5000 m/s• de Broglie Wavelength

λ =hp

E=hν

• Average Thermal Energy

kBT2

=p2

2m

• Optical Coherence Length

Lc=c

∆ν~ ∆λ

• Thermal Spreading∆E~kBT

––WARREN M. ROHSENOW HEAT AND MASS TRANSFER LABORATORY, MITWARREN M. ROHSENOW HEAT AND MASS TRANSFER LABORATORY, MIT

WAVE vs. PARTICLE DESCRIPTION

2a

dΛ

0

10

20

30

40

50

60

70

101 102 103 104

Bulk, In-Plane

Bulk, Cross-Plane

k (W

/mK

)

Period Thickness (Å)

SL,Cross-Plane

SL,In-PlaneP=0.95

2

6

10

10 100

Interface Scattering

––WARREN M. ROHSENOW HEAT AND MASS TRANSFER LABORATORY, MITWARREN M. ROHSENOW HEAT AND MASS TRANSFER LABORATORY, MIT

RADIATION HEAT TRANSFER

Total Reflection

0

5 10-12

1 10-11

1.5 10-11

2 10-11

2.5 10-11

3 10-11

0 5 1013 1 1014 1.5 1014 2 1014 2.5 1014 3 1014

Flux

(Wm

-2/ra

d s-1

)

Angule Frequency ω (rad s-1)

10 nm

100 nm

1 µm

10 µm

Blackbody

Surface Waves

103

104

105

106

107

108

109

1010

1011

0.05 0.1 0.15 0.2 0.25 0.3 0.35

Flux

(Wm

-2eV

-1)

Energy (eV)

d = 10nm

d = 1µmd = 1mm

blackbody

ImmersionLens

d

Cold

Hot

––WARREN M. ROHSENOW HEAT AND MASS TRANSFER LABORATORY, MITWARREN M. ROHSENOW HEAT AND MASS TRANSFER LABORATORY, MIT

ISSUES AND OPPORTUNITIES• Nonequilibrium among phonons

What does the equivalent temperature mean to lattice?• Nonequilibrium between electrons and phonons

Not fully explored, potential energy conversion applications• Transport at a single interface

Limiting the predicative power of all simulations.• Spectral-dependent relaxation time of heat carriers

Relaxation time in bulk materials not accurate• Wave vs. particle descriptions of heat carriers• Predicative power from nano to macroscales• Coupled phonon, electron, and photon transport• Creating new applications in energy conversion,

information storage, and thermal management

––WARREN M. ROHSENOW HEAT AND MASS TRANSFER LABORATORY, MITWARREN M. ROHSENOW HEAT AND MASS TRANSFER LABORATORY, MIT

MAJOR RESEARCH ACTIVITIES

1.0

1.5

2.0

2.5

3.0

3.5

4.0

4.5

5.0

50 100 150 200 250 300 350 400

TH

ER

MA

L C

ON

DU

CT

IVIT

Y (

W/m

K)

TEMPERTURE (K)

p=0.81

p=0.83

13x9 Si/Ge

23x13 Si/Ge

LINES CURRENT MODEL

DOTS FROM LEE ET AL. 7

Phonon Dynamics &Phonon Engineeringin Nanostructures for

- +

I N P

I I

HOT SIDE

COLD SIDE

Nanostructured Thermoelectrics Materials, Measurement,

Theory, and Devices

Micro and NanofabricationNanostructured Materiuals

Microelectrons/Photonics/Thermoelectrics

Nanoscale Thermal Radiation,Thermophotovoltaic Devices, andElectromagnetic Metamaterials

Bi Nanowires

Silver Nanowire Arrays

Nanotweezer SurfaceMetamaterials

––WARREN M. ROHSENOW HEAT AND MASS TRANSFER LABORATORY, MITWARREN M. ROHSENOW HEAT AND MASS TRANSFER LABORATORY, MIT

ACKNOWLEDGMENTS• Current Members

D. Borca-Tasciuc (Nanowires&Arrays)C. Dames (Thermoelectrics&Nanowires)J. Cybulski (Guided Self Assembly)J.P. Fu (Thermal Management and Phononics)T. Harris (Thermoelectrics&Nanomaterials)F. Hashemi (Nano-Device Fabrication)W.L. Liu (Thermoelectrics, Superlattices)H. Lu (Metamaterials&TPV)A. Narayanaswamy (Metamaterials, TPV)A. Shah (TPV Device Fabrication)A. Schmidt (Nanofabrication&Photonics)D. Song (Nanoporous Materials, Monte Carlo)B. Yang (Phonon Dynamics, Thermoelectrics)R.G. Yang (Phonon and Electron Transport)

Dr. Dekui Qing (Metamaterials&Nanofabrication)Prof. J.B. Wang (Microfabrication&Refrigeration)Mr. M. Takashiri (Thermoelectric Devices)Prof. K. Kar (Thermoelectric Materials)

• Collaborators

R. DiMatteo (TPV, Draper Lab)M.S. & G. Dresselhaus (MIT, Bi Nanowire, Theory)J.-P. Fleurial (JPL, Thermoelectric Devices) J. Freund (UIUC, MD Simulation)J. Joannopoulos (MIT, Photonic Crystals)K.L. Wang (MBE of Si/Ge Superlattices)X. Zhang (UCLA, Metamaterials)

• Past MembersProf. S.G. Volz (MD, Ecole de Paris)Prof. T. Borca-Tasciuc (Thermoelectrics,RPI)Prof. T. Zeng (Thermionics, NCSU)Dr. R. Kumar (Thermoelectric Device Modeling)Dr. A. Jacquot (Device Fabrication)

Sponsors: DOE, DOD/ ONR MURI, Draper, Lincoln Lab, JPL, NASA, NSF