Review of Mesoscopic Thermal Transport Measurements

1. Review of Mesoscopic Thermal Transport Measurements Li Shi IBM Research & University of Texas at Austin IMECE01, New York, November 12, 2001

2. 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

3. 1. Micro-Nano Devices 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

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

5. 1 mm Wl: boundary scattering W  lF: quantized effects Ll: ballistic transport - W + - L Length Scale 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 1 Å

6. 2. Thermal Conductivity: k = ke+ kp 1 3 C ~ T d lst k lst ~ lum T 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: lst ~ constant Static scattering (phonon -- defect, boundary): Umklapp phonon scattering: lum ~ eQ/ T

7. 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

8. 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

9. 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

10. 1. Song, Liu, Zeng, Borca-Tasiuc, Chen, Caylor, Sands, Appl. Phys. Lett. 77, 3154 (2000) Superlattices 2. Huxtable, Majumdar et al., Micro Therm. Eng. (2001)

11. 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)

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

13. ~ 200 W/m-K (Hone et al., 2000) Previous Measurement of Nanotube Mats: Nanotube mat • Unknown filling factor • Thermal resistance at • tube- tube junctions Thermal Conductivity of Nanotubes high v, long l  high k Carbon Nanotube: 3000 ~ 6000 W/m-K at room temperature (e.g. Berber et al., 2000) Theoretical Expectation:

14. 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) evenwhenDT = 0

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

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

17. Thermal Conductance: 10 nm multiwall tube VTE Beam Thermopower: Q = VTE/(Th-Ts) Island Pt heater line Measurement Scheme Gt =kA/L T T T s s h Q I R t R R h = h h s T u be Q = IR l l Environment I T 0

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

19. 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

20. 3000 k(T) (W/m K) 2000 1000 0 100 200 300 T (K) Thermal Conductivity 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

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

22. Single Wall Nanotube 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

23. 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

24. Techniques Spatial Resolution 3. Thermal Microscopy of Micro-Nano Devices 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)

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

26. Ta Rc Rt Tt Rts Ts Q Thermal Probe

27. Pt SiO2 SiO2 tip 200 nm 1 mm Probe Fabrication

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

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

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

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

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

33. 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

34. Thermal Imaging of Nanotubes Thermal 30 10 10 20 5 5 Height (nm) Height (nm) 30 nm 30 nm 10 0 0 0 -400 -200 0 200 400 -400 -400 -200 -200 0 0 200 200 400 400 Distance (nm) Distance (nm) Multiwall Carbon Nanotube Topography Topography 3 V m 88 A m m 1 1 m m Spatial Resolution V) m 30 nm 50 nm 50 nm Thermal signal ( Distance (nm) Shi, Plyosunov, Bachtold, McEuen, Majumdar, Appl. Phys. Lett., 77, p. 4295 (2000)

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

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

37. Multiwall Nanotube Thermal Topographic DTtip A B 3 K 1 mm 0 • Diffusive at low and high biases B A A B

38. Low bias: ballistic contact dissipation High bias: diffusive bulk dissipation Metallic Single Wall Nanotube Optical phonon Topographic Thermal DTtip A B C D 2 K 0 1 mm

39. Thermal DTtip A B 2 K Bulk heating at low and high biases  diffusive 0 Semiconducting Single Wall Nanotube Topographic 1 mm Nanotube field-effect transistor Contact Nanotube Vs Vd = gnd SiO2 Si Gate Vg

40. 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

41. 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