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