Response to K.E. Goodson
Nanoscale Heat Transfer and
Information Technology
Gang Chen
Mechanical Engineering Department
Massachusetts Institute of Technology
Cambridge, MA 02139
Rohsenow Symposium on Future Trends in Heat Transfer
May 16, 2003
–WARREN M. ROHSENOW HEAT AND MASS TRANSFER LABORATORY, MIT
HEAT TRANSFER IN NANODEVICES
Gate
Source
Channel
~10,000 rpm
2mm
Drain
~50 nm
1000 Å
MOSFET (IBM, Taur)
Laser Diode (S. Pei)
Data Storage (IBM)
–WARREN M. ROHSENOW HEAT AND MASS TRANSFER LABORATORY, MIT
MEAN FREE PATH OF HEAT CARRIERS
• SPECTRUM EFFECTS
• KINETIC THEORY
k = ∫ C( ω ) v ( ω ) Λ ( ω )dω / 3
k ≈ Cv Λ / 3
MEAN FREE PATH (nm)
10
10
5
PHO NO N (Dispersive)
PHO NO N (Kinetic Theory)
ELECTRO N
AIR M O LECULE
4
Silicon
10
3
10
2
10
1
Au
0
50
Air
100
150
200
TEM PERATURE (K)
250
300
–WARREN 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
Nano-Device
Oxide
Si
Kang L. Wang
M.S. Dresselhaus
• Phonon Transport Inside Nanostructures
Phonon Quantization:
Reflection, Interferene, Tunneling
Interface Scattering:
Diffuse vs. Specular
• Transport Outside Nanostructures
Phonon Quantization:
Surface Mode
Boundary Resistance
Phonon Rarefication
Electron-Phonon Interaction
Thermal Conductivity Reduction
High Device Temperature
–WARREN M. ROHSENOW HEAT AND MASS TRANSFER LABORATORY, MIT
THERMAL CONDUCTIVITY (W/ mK)
103
KX,BULK(FOURIER LAW)
KZ,BULK(FOURIER LAW)
102
KZ,FILM, EXPERIMENTAL
KX,FILM, EXPERIMENTAL
101
Si0.5Ge0.5
BULK ALLOY (300K)
In-Plane
P=0.6
P=0.5
Cross-Plane
Lines--Fitting withCHen'sModel
P=0.6
0
10
80
120 160 200 240
TEMPERATURE (K)
280
NONDIMENSIONAL TEMPERATURE DISTRIBUTION
DOMINANCE OF INTERFACES
2.5
p=0
INELASTIC
d 1=d 2=50 Å
2.0
1.5
GaAs
AlAs
1.0
p=0.5
0.5
p=1
0.0
0.0
0.1
0.2
0.3
0.4
NONDIMENSIONAL COORDINATE
–WARREN M. ROHSENOW HEAT AND MASS TRANSFER LABORATORY, MIT
NONLOCAL AND NONEQUILIBRIUM
Te1
Te2
r12I1+(Te1 )
r21I2+(Te2 )
τ21I+2(Te2 )
τ12I+1(Te1)
+
I1(Te1)
Te1 EMITTED
TEMPERATURE
T1 EQUILIBRIUM
T2 EQUILIBRIUM
+
I2(Te2 )
Te2 EMITTED
T2
r2
T1r1
r2 >> r1
1
3
R
=
=
F
Diffusive Limit
4πkr1 4πCvΛr1
Ballistic Limit
RB =
1
4πr12 Cv
–WARREN M. ROHSENOW HEAT AND MASS TRANSFER LABORATORY, MIT
THERMAL WAVELENGTH
• de Broglie Wavelength
h
λ=
p
E=hν
• Average Thermal Energy
p2
kBT
=
2
2m
• Thermal Spreading
∆E~kBT
• Optical Coherence Length
c
~ ∆λ
Lc=
∆ν
THERMAL WAVELENGTH (nm)
10 8
v(PHONON)=5000 m/s
10 6
10 4
PHOTON
WIEN'S DISPLACEMENT LAW
10 2
10 0
ELECTRON
PHONON
AIR MOLECULE
10 -2
1
10
2
10
TEMPERATURE (K)
3
10
–WARREN M. ROHSENOW HEAT AND MASS TRANSFER LABORATORY, MIT
WAVE vs. PARTICLE DESCRIPTION
d
Λ
2a
70
k (W/mK)
60
50
Bulk, In-Plane
Interface Scattering
Bulk, Cross-Plane
40 P=0.95
SL,In-Plane
30
SL,Cross-Plane
20
6
10
0
10
2
1
10
2
10
10
100
3
10
10
Period Thickness (Å)
4
–WARREN M. ROHSENOW HEAT AND MASS TRANSFER LABORATORY, MIT
RADIATION HEAT TRANSFER
Immersion
Lens
11-11
103 10
10
10
2.5 10
-11
d = 10nm
Cold
d
Hot
10
Flux (Wm /rad s )
Total
Reflection
Flux (Wm-2-2eV-1
)
-1
9
Surface Waves
10 nm
-11
100 nm
2 10
8
10
7-11
1.5 10
10
6
10
1 10
d = 1mm
d = 1µm
1 µm
-11
5
10
-12
5 10
4
Blackbody
10
30
10 0
0.05
blackbody
10 µm
13
5 10
0.1
14
1 10
14
1.5 10
14
2 10
0.15 0.2 0.25
-1
Energy (eV)
Angule Frequency ω (rad s )
14
2.5 10
0.3
14
3 10
0.35
–WARREN 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, MIT
MAJOR RESEARCH ACTIVITIES
COLD SIDE
5.0
THERMAL CONDUCTIVITY (W/mK)
4.5
p=0.81
23x13 Si/Ge
I
4.0
-
I
+
3.5
Bi Nanowires
13x9 Si/Ge
3.0
I
p=0.83
2.5
2.0
Phonon Dynamics &
Phonon Engineering
in Nanostructures for
Microelectrons/Photonics/Thermoelectrics
P
HOT SIDE
LINES CURRENT MODEL
1.5
DOTS FROM LEE ET AL.
1.0
50
N
100
150
200
250
300
350
7
400
TEMPERTURE (K)
Nanotweezer
Nanostructured Thermoelectrics
Materials, Measurement,
Theory, and Devices
Surface
Metamaterials
Silver Nanowire Arrays
Micro and Nanofabrication
Nanostructured Materiuals
Nanoscale Thermal Radiation,
Thermophotovoltaic Devices, and
Electromagnetic Metamaterials
–WARREN M. ROHSENOW HEAT AND MASS TRANSFER LABORATORY, MIT
ACKNOWLEDGMENTS
• Current Members
• Collaborators
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)
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 Members
Prof. 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
–WARREN M. ROHSENOW HEAT AND MASS TRANSFER LABORATORY, MIT