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

1. Micro-Nano Devices Gate Drain Source Nanowire Channel MEMS/NEMS Bio Chip (Wu et al., Berkeley) Microelectronics Si FET (Hu et al., Berkeley) Gate Drain Source Nanowire Channel Consisting of 2D and/or 1D structures

Molecular Electronics Nanotube Nanowire Arrays (Lieber et al., Harvard) TubeFET (McEuen et al., Berkeley) Nanotube Logic (Avouris et al., IBM Research)

Length Scale - + 1 mm Size of a Microprocessor MEMS Devices 1 mm Thin Film Thickness in ICs 100 nm l (Mean free path at RT) 10 nm Nanotube/ Nanowire Diameter 1 nm lF (Fermi wavelength) Atom L W  l: boundary scattering W  lF: quantized effects L  l: ballistic transport - + W 1 Å

2. Thermal Conductivity: k = ke + kp C ~ T d lst lst ~ lum 1 3 kp = C v l Phonon mfp Specific heat Sound velocity lum ~ eQ/ T If T > Q, C ~ constant If T << Q, C ~ T d (d: dimension) Specific heat : Mean free path: Static scattering (phonon -- defect, boundary): lst ~ constant Umklapp phonon scattering: lum ~ eQ/ T

2.1 Measurements of Thin-Film Thermal Conductivity The 3w method -- Cahill, Rev. Sci. Instrum. 61, 802 (1990) Metal line Thin Film I ~ 1w T ~ I2 ~ 2w R ~ T ~ 2w V~ IR ~3w L 2b V I0 sin(wt) Si Substrate

SOI Thin Films Ashegi, Leung, Wong, Goodson, Appl. Phys. Lett. 71, 1798 (1997) 2. Ju and Goodson, Appl. Phys. Lett. 74, 3005 (1999) Courtesy of Ref. 2

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

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)

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)

(ii) Carbon Nanotube Single Wall Multiwall Super high current 109 A/cm2 Single Wall -- Semiconducting or Metallic E k Metal l ic Semiconducting F microns 1-2 nm Multiwall -- Metallic 10 nm

Thermal Conductivity of Nanotubes Carbon Nanotube: high v, long l  high k 3000 ~ 6000 W/m-K at room temperature (e.g. Berber et al., 2000) Theoretical Expectation: Previous Measurement of Nanotube Mats: ~ 200 W/m-K (Hone et al., 2000) Nanotube mat Unknown filling factor Thermal resistance at tube- tube junctions

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 Tested for a 20 mm dia. Pt wire Results for a bundle of MW nanotubes: C ~ linear T dependence, low k ~ 100 W/mK V I0 sin(wt) Electrode Wire Substrate 3w Mechanism: DT~ V2/k and R ~ Ro + aDT Applicable to an individual SW nanotube? -- R4p = Rjunction + Rbulk -- Rjunction  Rjunction,0 + aDT -- Rbulk ~ Rbulk (V) even when DT = 0

Another 1D Method -- A Hybrid Nanotube Microdevice Pt heater line Multiwall nanotube SiNx beam Pt heater line Suspended island

Device Fabrication (c) Lithography Photoresist (a) CVD SiNx SiO2 (d) RIE etch (b) Pt lift-off Pt (e) HF etch

Measurement Scheme Gt = kA/L Thermal Conductance: I Q I R h = h R t R h s VTE Thermopower: Q = VTE/(Th-Ts) T u be Q = IR l l Environment I T 10 nm multiwall tube Island Beam Pt heater line

Measurements Resistance of the Pt line Cryostat: T : 4-350 K P ~ 10-6 torr Resistance of the Pt line Resistance vs. Joule Heat m

Thermal Conductivity  T2 l ~ 0.5 mm 14 nm multiwall tube 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

Thermal Conductivity Interlayer phonon mode filled – 2D k(T) (W/m K) T (K) 3000 2000 1000 300 200 100 Interlayer phonon mode filled – 2D 14 nm individual MW tube 2.0 80 nm bundle Junctions in bundles reduce k and lst 2.5 Interlayer phonon mode unfilled – 3D 200 nm bundle

Thermopower For metals w/ hole-type majority carriers:  T

More on 1D Measurements Single Wall Nanotube 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

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

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)

Scanning Thermal Microscope Atomic Force Microscope (AFM) + Thermal Probe Laser Deflection Sensing Cantilever Temperature Sensor Thermal X T Sample Topographic X Z X-Y-Z Actuator

Thermal Probe Rts Rt Ts Ta Tt Rc Q

Probe Fabrication 200 nm Pt SiO2 1 mm SiO2 tip

Microfabricated Probes Pt Line Tip Laser Reflector Pt-Cr Junction SiNx Cantilever Cr line 10 mm Shi, Kwon, Miner, Majumdar, J. MicroElectroMechanical Sys., 10, p. 370 (2001)

Locating Defective VLSI Via Topography Tip Temperature Rise (K) 19 21 40 mA Via Metal 1 23 28 25 Metal 2 20 mm Cross Section Passivation Metal 2 Collaboration: TI Shi et al., Int. Reli. Phys. Sym., p. 394 (2000) Dielectric 0.4 mm Via Metal 1

Calibration S = R W(mm) S(K/K) 0.56 6 0.46 0.2 0.06 W

Tip-Sample Heat Transfer Why saturated? W W , air  W = 0.2 mm, Air ~ Solid + Liquid W < 0.1 mm, Air << Solid + Liquid

Why GSol Saturated? Elastic-Plastic Contact of an Asperity and a Plane What is the thermal conductance at the nano contact?

Thermal Transport at Nano Contacts Modeling results: GLiq ~ 7 nW/K, GSol ~ 0.8 W/m2-K-Pa L < Mean free path of air or phonon Shi and Majumdar, J. Heat Transfer, in press

Thermal Imaging of Nanotubes Multiwall Carbon Nanotube Distance (nm) Height (nm) 30 nm 10 5 400 200 -200 -400 Thermal Topography Topography 3 V 88 m A 1 1 m m m m Spatial Resolution V) 30 20 10 400 200 -200 -400 m 30 nm 50 nm 50 nm Thermal signal ( Distance (nm) Shi, Plyosunov, Bachtold, McEuen, Majumdar, Appl. Phys. Lett., 77, p. 4295 (2000)

Electron Transport in Nanotube Ballistic (long mfp) Diffusive (short mfp) - - + + - - mfp: electron mean free path Multiwall Ballistic (Frank et al., 1998) Diffusive (Bachtold et al., 2000) Single Wall Semiconducting Diffusive (McEuen et al., 2000) Single Wall Metallic Ballistic at low bias (Bachtold ,et al.) Diffusive at high bias (Yao et al., 2000)

Dissipation in Nanotube bulk Electrode Electrode Junction Diffusive – Bulk Dissipation T T profile  diffusive or ballistic X Ballistic – Junction Dissipation T X

Multiwall Nanotube Thermal Topographic DTtip A B 3 K 1 mm Diffusive at low and high biases B A A B

Metallic Single Wall Nanotube Low bias: ballistic contact dissipation High bias: diffusive bulk dissipation Optical phonon Topographic Thermal DTtip A B C D 2 K 1 mm

Semiconducting Single Wall Nanotube Topographic Thermal Bulk heating at low and high biases  diffusive A B DTtip 2 K 1 mm Nanotube field-effect transistor Contact Nanotube Vs Vd = gnd SiO2 Si Gate Vg

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

Summary Nanotube Thermal Conductivity --Majumdar, McEuen Thin film Thermal Conductivity --Cahill, Goodson, Chen, Majumdar L 2b V I0 sin(wt) Thermal Conductance Quantum --Roukes Thermal Microscopy of Nanotubes -- Majumdar