Review of Mesoscopic Thermal Transport Measurements Li Shi IBM Research & University of Texas at Austin IMECE01, New York, November 12, 2001 Outline 1. Thermal Transport in Micro-Nano Devices 2. Thermal Property Measurements of Low-Dimensional Structures: -- 2D: Thin Films -- 1D: Nanotubes, Nanowires -- Quantized Thermal Conductance 3. Thermal Microscopy of Micro-Nano Devices 2 1. Micro-Nano Devices Microelectronics MEMS/NEMS Bio Chip (Wu et al., Berkeley) Si FET (Hu et al., Berkeley) Gate Drain Source Nanowire Channel • Consisting of 2D and/or 1D structures 3 Molecular Electronics Nanotube Nanowire Arrays (Lieber et al., Harvard) TubeFET (McEuen et al., Berkeley) Nanotube Logic (Avouris et 4al., IBM Research) 1 mm Length Scale Size of a Microprocessor MEMS Devices 1 mm Thin Film Thickness in ICs 100 nm 10 nm Nanotube/ Nanowire Diameter W lF: quantized effects L l: ballistic transport 1 nm l (Fermi F 1Å wavelength) Atom W l: boundary scattering - l (Mean free path at RT) W - + L 5 2. Thermal Conductivity: k = ke + kp kp= 13 C v l Specific heat Phonon mfp Sound velocity If T > Q, Specific heat : If T << Q, k lst C ~Td C ~ constant lst ~ lum C ~ T d (d: dimension) lum ~ eQ/ T T 1 1 1 Mean free path: l lst lum Static scattering (phonon -- defect, boundary): lst ~ constant Q / T Umklapp phonon scattering: lum ~ e 6 2.1 Measurements of Thin-Film Thermal Conductivity The 3w method -- Cahill, Rev. Sci. Instrum. 61, 802 (1990) Metal line L Thin Film 2b V I0 sin(wt) • I ~ 1w • T ~ I2 ~ 2w • R ~ T ~ 2w • V~ IR ~3w Si Substrate P 1 Ds 1 i Pd T (2w ) ln 2 ln2w Lk s 2 b 2 4 2 Lbk f 7 SOI Thin Films 1. Ashegi, Leung, Wong, Goodson, Appl. Phys. Lett. 71, 1798 (1997) 2. Ju and Goodson, Appl. Phys. Lett. 74, 3005 (1999) Courtesy of Ref. 2 8 Anisotropic Polymer Thin Films Ju, Kurabayashi, Goodson, Thin Solid Films 339, 160 (1999) • By comparing temperature rise of the metal line for different line width, the anisotropic thermal conductivity can be deduced 9 Superlattices 1. Song, Liu, Zeng, Borca-Tasiuc, Chen, Caylor, Sands, Appl. Phys. Lett. 77, 3154 (2000) 2. Huxtable, Majumdar et al., Micro Therm. Eng. (2001) 10 2.2 1D Nanostructure: (i) Nanowires • Si Nanowires for Electronic Applications • Bi Nanowires for TE Cooling (Dresselhaus et al., MIT) Top View Al2O3 template • Boundary scattering + modified phonon dispersion (group velocity): Suppressed thermal conductivity Volz and Chen, Appl. Phys. Lett. 75, 2065 (1999) 11 (ii) Carbon Nanotube Super high current 109 A/cm2 Single Wall -- Semiconducting or Metallic microns 1-2 nm Multiwall -- Metallic E Semiconducting EF E Metallic EF k k 12 Thermal Conductivity of Nanotubes Carbon Nanotube: high v, long l high k 3000 ~ 6000 W/m-K at room temperature Theoretical Expectation: (e.g. Berber et al., 2000) Previous Measurement of Nanotube Mats: ~ 200 W/m-K (Hone et al., 2000) Nanotube mat • Unknown filling factor • Thermal resistance at tube- tube junctions 13 The 3w method for 1D Structures -- Lu, Yi, Zhang, Rev. Sci. Instrum. 72, 2996 (2001) • Low frequency: V(3w) ~ 1/k • High frequency: V(3w) ~ 1/C V Wire I0 sin(wt) • Tested for a 20 mm dia. Pt wire Electrode Substrate • Results for a bundle of MW nanotubes: C ~ linear T dependence, low k ~ 100 W/mK • 3w Mechanism: T~ V2/k and R ~ Ro + aT • Applicable to an individual SW nanotube? -- R4p = Rjunction + Rbulk -- Rjunction Rjunction,0 + aT -- Rbulk ~ Rbulk (V) even when T = 0 14 Another 1D Method -- A Hybrid Nanotube Microdevice Multiwall nanotube Pt heater line SiNx beam Pt heater line Suspended island 15 Device Fabrication (c) Lithography Photoresist (a) CVD SiN x SiO2 (d) RIE etch Si (b) Pt lift-off Pt (e) HF etch 16 Measurement Scheme Gt = kA/L Thermal Conductance: Ts Th Qh=IRh Rh Qh Ql Ts T0 Gt Th Ts 2T0 Th Ts Ql=IRl I t Tube Ts Rs Environment T0 10 nm multiwall tube VTE Beam Island Pt heater line Thermopower: Q = VTE/(Th-Ts) 17 Cryostat: T : 4-350 K P ~ 10-6 torr Resistance (k ) Measurements 6 4 Resistance of the Pt line 2 0 0 Resistance vs. Joule Heat m 100 200 300 Temperature (K) 18 k (103 W/m K) Thermal Conductivity T2 3 2 l ~ 0.5 mm 1 0 14 nm multiwall tube 100 200 300 Temperature (K) • Room temperature thermal conductivity ~ 3000 W/m-K • k ~ T2 : Quasi 2D graphene behavior at low temperatures • Umklapp scattering ~ 320 K , l ~ 500 nm • Nearly ballistic phonon transport Kim, Shi, Majumdar, McEuen, Phy. Rev. Lett, in press 19 Thermal Conductivity -7 Interlayer phonon mode filled – 2D 14 nm individual MW tube -8 10 2.0 3000 k(T) (W/m K) Thermal Conductance (W/K) 10 -9 10 80 nm bundle 2000 Junctions in bundles reduce k and lst 1000 2.5 Interlayer phonon mode unfilled – 3D 0 2 10 3 4 5 100 200 300 T (K) 200 nm bundle 6 7 8 9 100 Temperature (K) 2 3 4 20 Thermopower (mV/K) Thermopower 100 For metals w/ hole-type majority carriers: 80 Q 2 k B 2T 6eEF 60 40 Ts 20 T 0 50 100 150 200 Temperature (K) 250 300 21 More on 1D Measurements • Short lst and suppressed k found for Si nanowires (D. Li et al.) • Bi and Bi2Te3 wires to be measured • Challenges of measuring single wall nanotube Single Wall Nanotube 22 2.3 Quantized Thermal Conductance Electron thermal conductance quantization (Molenkamp et al., 1991) Quantum point contact Phonon thermal conductance quantization (Schwab et al., 1999) Quantum of Thermal Conductance 23 3. Thermal Microscopy of Micro-Nano Devices Techniques Spatial Resolution Infrared Thermometry 1-10 mm* Laser Surface Reflectance [1] 1 mm* Raman Spectroscopy 1 mm* Liquid Crystals 1 mm* Near-Field Optical Thermometry [2] < 1 mm Scanning Thermal Microscopy (SThM) < 100 nm *Diffraction limit for far-field optics 1. Ju & Goodson, J. Heat Transfer 120, 306 (1998) 2. Goodson & Asheghi, Microscale Thermophysical Eng. 11, 225 (1997) 24 Scanning Thermal Microscope Atomic Force Microscope (AFM) + Thermal Probe Laser Deflection Sensing Cantilever Temperature Sensor Thermal Sample Z Topographic X X-Y-Z Actuator T X 25 Thermal Probe Ta Rc Cantilever Mount Cantilever Tip Rt Substrate Sample Solid-Solid Conduction Pt Liquid-Film Conduction Tt Rts Ts SiO2 Cr Liquid Air Conduction Radiation Sample Q 26 Probe Fabrication Cr SiO2 SiO2 SiO2 tip Pt Si SiNx 100~500 nm Photoresist 1 mm Photoresist Cr Pt Pt SiO2 SiO2 Pt RIE+HF Etch Cr 200 nm 27 Microfabricated Probes Pt Line Pt-Cr Junction Tip Laser Reflector SiNx Cantilever Cr line 10 mm Shi, Kwon, Miner, Majumdar, J. MicroElectroMechanical Sys., 10, p. 370 (2001) 28 Locating Defective VLSI Via Tip Temperature Rise (K) Topography 19 21 Via Metal 1 28 25 20 mm Cross Section Passivation Metal 2 Dielectric Metal 1 23 • Collaboration: TI 0.4 mm • Shi et al., Int. Reli. Phys. Sym., p. 394 (2000) 29 Via Topography Thermal 0 Au line 10 8 I S = 0.46 K/K 6 W 4 2 Lead 0 R 5 10 22 mm 20 15 Sample temperature rise (K)40 W(mm) S(K/K) 50 0.56 6 0.46 0.2 0.06 0.1 20 0 0 2 4 6 X (mm) 8 10 0 2 4 6 X (mm) 8 0.0 10 30 T (au) 0 Height (nm) Junction temperature rise (K) Calibration Tip-Sample Heat Transfer •W , air •W = 0.2 mm, Air ~ Solid + Liquid W •W < 0.1 mm, Air << Solid + Liquid 0.06 Approaching 0 Solid Retracting 0.04 -100 Liquid 0.02 Air -200 Why saturated? 0.1 0.2 Temperature response (K/K) Jump to contact Snapped out of contact 100 Deflection (nm) 0.08 0.00 0.3 Sample vertical position (mm) 0.4 31 Why GSol Saturated? Elastic-Plastic Contact of an Asperity and a Plane Tip end 90 nm 10 nm Liquid Sample Asperity What is the thermal conductance at the nano contact? 32 Temperature response (K/K) Thermal Transport at Nano Contacts Modeling results: GLiq ~ 7 nW/K, GSol ~ 0.8 W/m2-K-Pa 0.06 Model L < Mean free path of air orfitphonon Measured Solid 0.04 Liquid 0.02 0.00 0.1 Air 0.2 0.3 0.4 Sample vertical position (mm) Shi and Majumdar, J. Heat Transfer, in press 33 Thermal Imaging of Nanotubes Multiwall Carbon Nanotube Topography Thermal 3V 88 mA 1 mm Height (nm) 10 30 nm 30 nm 5 0 -400 -200 0 200 Distance (nm) 400 Thermal signal ( m V) Spatial Resolution 30 20 50 nm nm 50 10 0 -400 -200 0 200 400 Distance (nm) Shi, Plyosunov, Bachtold, McEuen, Majumdar, Appl. Phys. Lett., 77, p. 4295 (2000) 34 Electron Transport in Nanotube Ballistic (long mfp) + Diffusive (short mfp) + mfp: electron mean free path Ballistic (Frank et al., 1998) Multiwall Diffusive (Bachtold et al., 2000) Single Wall Semiconducting Diffusive (McEuen et al., 2000) Ballistic at low bias (Bachtold ,et al.) Single Wall Metallic Diffusive at high bias (Yao et al., 2000) E Low Bias E High Bias Short mfp Long mfp k Acoustic Phonon Optical Phonon 35 k Dissipation in Nanotube Electrode Nanotube bulk Electrode Junction Diffusive – Bulk Dissipation T X T profile diffusive or ballistic Ballistic – Junction Dissipation T X 36 Multiwall Nanotube Topographic Thermal B A Ttip 3K 1 mm 0 20 •Diffusive at low and high biases 0 B A -20 -40 Ttip (K) Current (mA) 40 20 A 10 B 0 -1000 0 1000 Bias voltage (mV) 0 1 2 Distance (mm) 37 Current (mA) Metallic Single Wall Nanotube 20 Optical phonon 0 A B C D -20 -2000 -1000 0 1000 2000 Low bias: ballistic contact dissipation High bias: diffusive bulk dissipation Bias voltage (mV) Topographic Thermal A B C D Ttip 2K 1 mm 0 38 Semiconducting Single Wall Nanotube Topographic A Thermal B Ttip 2K Bulk heating at low and high biases diffusive 1 mm Nanotube field-effect transistor Contact Nanotube Vs Vd = gnd SiO2 Si Gate Current (mA) 0 10 A 5 0 -5 2 5 1 Vg 0 -9 -1000 Vg B 0 1000 Bias voltage (mV) 39 More on Thermal Microscopy • UHV and low-temperature thermal and thermoelectric microscopy • Near-field radiation and solid conduction through a point contact, e.g. in thermally-assisted magnetic writing and thermomechanical data storage 40 • Nanotube Thermal Conductivity --Majumdar, McEuen Summary • Thin film Thermal Conductivity --Cahill, Goodson, Chen, Majumdar L 2b V I0 sin(wt) • Thermal Conductance Quantum --Roukes • Thermal Microscopy of Nanotubes -- Majumdar 41