Ultrafast laser-based metrology for micron-scale measurements of thermal transport, coefficient of thermal expansion, and temperature

Transcription

1 Ultrafast laser-based metrology for micron-scale measurements of thermal transport, coefficient of thermal expansion, and temperature David G. Cahill, Xuan Zheng, Chang-Ki Min, Ji-Yong Park Materials Research Lab and Department of Materials Science, U. of Illinois J.-C. Zhao Department of Materials Science and Engineering, The Ohio State University supported by DOE and ONR

2 Time domain thermoreflectance since 2003 Improved optical design Normalization by out-ofphase signal eliminates artifacts, increases dynamic range and improves sensitivity Exact analytical model for Gaussian beams and arbitrary layered geometries One-laser/two-color approach tolerates diffuse scattering Clone built at Fraunhofer Institute for Physical Measurement, Jan

3 psec acoustics and time-domain thermoreflectance Optical constants and reflectivity depend on strain and temperature Strain echoes give acoustic properties or film thickness Thermoreflectance gives thermal properties

4 Time-domain Thermoreflectance (TDTR) data for TiN/SiO 2 /Si TiN SiO 2 Si reflectivity of a metal depends on temperature one free parameter: the effective thermal conductivity of the thermally grown SiO 2 layer (interfaces not modeled separately)

5 Windows software author: Catalin Chiritescu, users.mrl.uiuc.edu/cahill/tcdata/tdtr_m.zip

6 TDTR: Flexible, convenient, and accurate...with 3 micron resolution

7 Thermal conductivity map of a human tooth 100 μm ΛC/C0 (W m -1 K -1 ) dentin enamel Distance from the DEJ (μm)

8 High throughput data using diffusion couples

9 Mapping of a metallurgical diffusion couple SEM (backscattered) thermal conductivity

10 Carbon nanotubes Evidence for the highest thermal conductivity any material (higher conductivity than diamond) Yu et al. (2005) Maruyama (2007)

11 Can we make use of this? Fischer (2007) Much work world-wide: thermal interface materials so-called "nanofluids" (suspensions in liquids) polymer composites and coatings Lehman (2005)

12 Thermal conductivity and interface thermal conductance Thermal conductivity Λ is a property of the continuum Thermal conductance (per unit area) G is a property of an interface

13 Nanotubes in surfactant in water Nanotubes in surfactant in water: Transient absorption Optical absorption depends on temperature of the nanotube Assume heat capacity is comparable to graphite Cooling rate (RC time constant) gives interface conductance G = 12 MW m -2 K -1

14 Critical aspect ratio of a fiber composite Critical aspect ratio for a fiber composite Isotropic fiber composite with high conductivity fibers (and infinite interface conductance) But this conductivity if obtained only if the aspect ratio of the fiber is high Troubling question: Did we measure the relevant value of the conductance? "heat capacity G" vs. "heat conduction G"

15 Interface thermal conductance: Factor of 60 range at room temperature W/Al 2 O 3 Au/water PMMA/Al 2 O 3 nanotube/alkane L = Λ/G Λ = 1 W m -1 K -1

16 Time-domain probe beam deflection (TD-PBD) for CTE measurements Probe Sample Bi-cell photodiode θ Al (~100 nm) V(t) = V in (t) + iv out (t) Lock-in amplifier Vin/Vout t (ps) spatial resolution ~ laser spot size (~ 4 μm)

17 Model for the beam deflection Al Substrate L 100 nm Thermal expansion of Al film Bi-axial stress of Al film g g Substrate Thermal expansion and bi-axial stress of substrate Substrate Z 1 L 1+ υ Al = αt, AlTAldz g 0 1 υ Al = L Y Y BAlαT, AlTAldz 2 U+ ( U) 0 2(1 + υ) 2(1 + υ)( 1 2υ ) = T + ρu Y Y 2 U+ ( U) 2(1 + υ) 2(1 + υ)( 1 2υ ) = ρu Z 2 Z 3

18 Model for the beam defection (continued) Temperature gradient on surface Al Heated air Al φ r r Z air = 2 0 dn dt T dz air n + ik 1 r = = n + ik + 1 r0 exp( iφ) Z = T SurfaceTemp surface dφ λ dt 4π Z = Z1 + Z2 + Z3 + Z + SurfTemp Z air

19 Validation of CTE measurements 100 Vin/Vout Al(100 nm)/si t (ps) Measured CTE (10-6 K-1) 10 1 Ni35Fe65 Invar Mg Mn Zn Cu Al Co Sn CaF Ti Ni 2 Zr SrTiO 3 Rh Si Cr Accuracy: ±6% Accepted CTE (10-6 K -1 )

20 CTE of Fe-Ni diffusion couple SEM Fe Ni Ni concentration (at.%) CTE (10-6 K-1) CTE (10-6 K-1) Present experiment Guillaume Ni concentration (at.%) Position (μm)

21 Use ion bombardment to reduce atomic short range order 16 5 CTE (10-6 K-1) dpa 0.03 dpa dpa Before ion bombardment CTE (10-6 K-1) Fe 65 Ni Ni concentration (at.%) Ion Dose (dpa)

22 Er:fiber-laser pump-probe system at UIUC

23 Transient absorption below the band gap of Si Pump-probe measurements of twophoton absorption Ф is the normalized absorption λ=1.55 μm pump probe Si wafer

24 Two-photon (+one phonon) absorption is strongly temperature dependent 470 cm -1 (670 K) phonon population controls the optical absorption Simple calibration based on well-known physics

25 Thermometry by two-photon absorption Volume probed is μm 3 Sensitivity is < 1 K in a 1 khz bandwidth Control of Heat Transfer at Interfaces

26 Conclusions Time domain thermoreflectance (TDTR) is now a robust and routine method for measuring the thermal conductivity of almost anything (that has a smooth surface). Difficult to take advantage of superlative properties of carbon nanotubes because of "thermally weak" interfaces. Time domain probe beam deflection (TD-PBD) provides micron-scale measurements of coefficient of thermal expansion Transient absorption by below band-gap (1.56 μm) twophoton absorption provides a fast, spatially resolved thermometer in Si