Thermal conductance of solid-solid and solid-liquid interfaces

1. Thermal conductance of solid-solid and solid-liquid interfaces David G. Cahill, Zhenbin Ge, Ho-Ki Lyeo, Xuan Zheng, Paul Braun Frederick Seitz Materials Research Lab and Department of Materials Science University of Illinois, Urbana

2. Interfaces are critical at the nanoscale 50 nm • Low thermal conductivity in nanostructured materials • improved thermoelectric energy conversion • improved thermal barriers • High thermal conductivity composites and suspensions

3. Interfaces are critical at the nanoscale • High power density devices • solid state lighting • high speed electronics • nanoscale sensors Micrograph of tunneling magnetoresistive sensor for 120 GB drives, M. Kautzky (Seagate)

4. Interface thermal conductance • Thermal conductivity L is a property of the continuum • Thermal conductance (per unit area) G is a property of an interface

5. Interface thermal conductance (2001) • Observations (2001) span a very limited range • Al/sapphire  Pb/diamond • no data for hard/soft • lattice dynamics (LD) theory by Stoner and Maris (1993) • Diffuse mismatch (DMM) theory by Swartz and Pohl (1987)

6. Acoustic and diffuse mismatch theory • Acoustic mismatch (AMM) • perfect interface: average transmission coefficient <t> given by differences in acoustic impedance, Z=rv • lattice dynamics (LD) incorporates microscopics • Diffuse mismatch (DMM) • disordered interface: <t> given by differences in densities of vibrational states • Predicted large range of G not observed (2001) • For similar materials, scattering decreases G • For dissimilar materials, scattering increases G

7. 2005: Factor of 60 range at room temperature W/Al2O3 Au/surfactant/water PMMA/Al2O3 nanotube/alkane

8. Modulated pump-probe apparatus f=10 MHz rf lock-in

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

10. Modulated pump-probe • four times scales: • pulse duration, 0.3 ps • pulse spacing, 12.5 ns • modulation period, 100 ns • time-delay, t t Bonelloet al. (1998)

11. Analytical model for modulated time-domain thermoreflectance • frequency domain solution for heat flow in cylindrical coordinates using gaussian beams. • G(k) given by iterative solution (transfer matrix) • In-phase and out-of-phase signals by series of sum and difference over sidebands

12. Iterative solution for layered geometries

13. Two basic types of experiments on solid samples • thermal conductivity of thin films • thermal conductivity of bulk samples and thermal conductance of interfaces

14. Flexible, convenient, and accurate technique... • ...with 3 micron resolution thermal conductivity map of cross-section of thermal barrier coating, with J.-C. Zhao (GE)

15. Interfaces between highly dissimilar materials DOS MaterialA (Pb, Bi) w MaterialB (diamond, BeO) w • high temperature limit of the radiation limit R. J. Stoner and H. J. Maris, Phys.Rev.B48, 22, 16373 (1993)

16. Thermoreflectance data for Bi and Pb interfaces

17. Room temperature thermal conductance • Pb and Bi show similar behavior. Electron-phonon coupling is not an important channel. • Weak dependence on Debye velocity of the substrate. • Pb/diamond 50% smaller than Stoner and Maris but still far too large for a purely elastic process.

18. Temperature dependence of the conductance • Excess conductance has a linear temperature dependence (not observed by Stoner and Maris). • Suggests inelastic (3-phonon?) channel for heat transport

19. Application: can we use interfaces to beat the minimum thermal conductivity? • If the small thermal conductance of Bi/diamond could be reproduced in a multi-layered film, then placing interfaces every 10 nm would give an incredibly low thermal conductivity of 0.1 W/m-K (factor of 2 smaller than a polymer).

20. W/Al2O3 nanolaminates 50 nm • room temperature data • sputtered in pure Ar • atomic-layer deposition at 177 and 300 °C, S. George (U. Colorado) • G = 220 MW m-2 K-1

21. Unexpected advance: Thermal conductivity imaging • At t=100 ps, • in-phase signal is mostly determined by the heat capacity of the Al film • out-of-phase signal is mostly determined by the effusivity (LC)1/2 of the substrate

22. ZrO2:Y thermal barrier • after 500 thermal cycles (1 h) 25 °C —>1135 °C—>25 °C

23. ZrO2:Y thermal barrier • after 500 thermal cycles (1 h) 25 °C —>1135 °C—>25 °C

24. Solid-liquid interfaces: Two approaches • Transient absorption measurements of nanoparticles and nanotubes in liquid suspensions. • Measure the thermal relaxation time of a suddenly heat particle. If the particle is small enough, then we have sensitivity to the interface • limited to interfaces that give good stability of the suspension • Thin planar Al and Au films. Same as before but heat flows both directions: into the fluid and into the solid substrate.

25. Transient absorption • Optical absorption depends on temperature of the nanotube • Cooling rate gives interface conductance G = 12 MW m-2 K-1 • MD suggests channel is low frequency squeezing and bending modes strongly coupled to the fluid.

26. Application: 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

27. Hydrophilic metal nanoparticles: 4 nm diameter Au:Pd nanoparticles in water G = ∞ (a) ∆αl (ppm) EG4 G = 2.0108 t (ps) (b) G = ∞ ∆αl (ppm) Tiopronin G = 1.8108 t (ps) • transient absorption data

28. 22 nm diameter Au:Pd nanoparticles in water; CTAB surfactant G = ∞ ∆αl (ppm) G = 1.8  108 t (ps)

29. Nanoparticle summary In Toluene In water G ~ 200 MW m-2 K-1 G ~ 15 MW m-2 K-1

30. Application: Critical particle radius for nanocomposite • Interface conductance and thermal conductivity of the fluid determine a critical particle radius rc = L/G • For particles in water, rc = 3 nm. • For high thermal conductivity particles, dilute limit of effective medium theory r >> rc DL = (1+3f)L r << rcDL = (1-1.5f)L

31. Thermoreflectance of solid-liquid interfaces hydrophobic 37 MW/m2-K no water • hydrophilic • 150 MW/m2-K

32. Conclusions • Much to learn about transport of heat across interfaces but we now have good tools. • Pb/diamond, Bi/diamond interfaces show a temperature dependent conductance far above the radiation limit. What is the correct description of this inelastic channel? • Can circumvent the “minimum thermal conductivity” with high densities of interfaces. • Conductance of hydrophilic nanoparticle/surfactant/water interfaces is essentially independent of the surfactant layer. • Heat transfer is reduced by a factor of 4 at hydrophobic interfaces with water.