Nanoscale Heat Transfer and Information Technology
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1 Response to K.E. Goodson Nanoscale Heat Transfer and Information Technology Gang Chen Mechanical Engineering Department Massachusetts Institute of Technology Cambridge, MA Rohsenow Symposium on Future Trends in Heat Transfer May 16, 2003
2 HEAT TRANSFER IN NANODEVICES Gate Source Channel Drain ~10,000 rpm 2mm ~50 nm 1000 Å MOSFET (IBM, Taur) Laser Diode (S. Pei) Data Storage (IBM)
3 MEAN FREE PATH OF HEAT CARRIERS KINETIC THEORY SPECTRUM EFFECTS k CvΛ /3 k = C( ω) v( ω) Λ( ω) dω /3 MEAN FREE PATH (nm) Au PHONON (Dispersive) PHONON (Kinetic Theory) ELECTRON AIR MOLECULE Silicon Air TEMPERATURE (K)
4 HEAT CONDUCTION AT NANOSCALE Phonon Mean Free Path in Silicon: Å Phonon Wavelength: Lattice Spacing-Crystal Size Oxide Si Nano-Device 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
5 DOMINANCE OF INTERFACES THERMAL CONDUCTIVITY (W/ mk) K X,BULK (FOURIER LAW) K Z,BULK (FOURIER LAW) K Z,FILM, EXPERIMENTAL K X,FILM, EXPERIMENTAL In-Plane Si 0.5 Ge 0.5 BULK ALLOY (300K) P=0.6 P=0.5 Cross-Plane Lines--Fitting with CHen'sModel P= TEMPERATURE (K) NONDIMENSIONAL TEMPERATURE DISTRIBUTION p=0 GaAs p=0.5 p=1 INELASTIC d 1 =d 2 =50 Å AlAs NONDIMENSIONAL COORDINATE
6 NONLOCAL AND NONEQUILIBRIUM + r 12 I 1 (T e1 ) + r 21 I 2 (T e2 ) T e1 EMITTED TEMPERATURE T e1 T e2 τ + 21 I 2 (T e2 ) + 12 τ I 1 (T e1) T 1 EQUILIBRIUM + I 1 (T e1) + I 2 (T e2 ) T 2 T e2 EQUILIBRIUM EMITTED T 2 r 2 T 1 r 1 r 2 >> r 1 Diffusive Limit R F = 1 4πkr 1 = 3 4πCvΛr 1 Ballistic Limit R B = 1 4πr 2 Cv 1
7 THERMAL WAVELENGTH de Broglie Wavelength λ = E=hν h p Average Thermal Energy k B T 2 = p2 2m Thermal Spreading E~k B T THERMAL WAVELENGTH (nm) v(phonon)=5000 m/s PHOTON WIEN'S DISPLACEMENT LAW ELECTRON PHONON Optical Coherence Length L c = c ν ~ λ 10-2 AIR MOLECULE TEMPERATURE (K)
8 WAVE vs. PARTICLE DESCRIPTION d Λ 2a k (W/mK) Bulk, In-Plane Bulk, Cross-Plane P=0.95 SL,In-Plane SL,Cross-Plane Period Thickness (Å) Interface Scattering
9 RADIATION HEAT TRANSFER Cold Hot Immersion Lens Total Reflection d Flux (Wm -2 ev -1 ) Flux (Wm -2 /rad s -1 ) d = 10nm d = 1mm 1 µm 10 nm 100 nm d = 1µm Surface Waves Blackbody 10 4 blackbody 10 µm Angule Frequency ω (rad s -1 ) Energy (ev)
10 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
11 5.0 MAJOR RESEARCH ACTIVITIES COLD SIDE THERMAL CONDUCTIVITY (W/mK) x13 Si/Ge TEMPERTURE (K) 13x9 Si/Ge LINES CURRENT MODEL DOTS FROM LEE ET AL. p=0.81 p= Phonon Dynamics & Phonon Engineering in Nanostructures for Microelectrons/Photonics/Thermoelectrics I I - + I N P HOT SIDE Bi Nanowires Nanostructured Thermoelectrics Materials, Measurement, Theory, and Devices Nanotweezer Surface Metamaterials Silver Nanowire Arrays Micro and Nanofabrication Nanostructured Materiuals Nanoscale Thermal Radiation, Thermophotovoltaic Devices, and Electromagnetic Metamaterials
12 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 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
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