Thermal conductance of interfaces between highly dissimilar materials

Understanding the thermal conductance of interfaces G is important for improving our knowledge about interlayer heat transport in multi-layer thermoelectric devices. Previously G for interfaces between highly dissimilar materials such as Pb/diamond and Pb/Al$_{2}$O$_{3}$ was measured by Stoner and Maris and found to be much higher than the radiation limit; the radiation limit G=$\frac{\pi }{3}\frac{k_B \nu _{\max }^3 }{c^2}$ is the maximum thermal conductance predicted by theory, where $\nu _{\max } $is the cutoff vibrational frequency of the metal and $c$ is the Debye velocity of the substrate. We report data for G between Pb or Bi and several substrates; diamond, hydrogen(H)-terminated diamond, sapphire, SiO$_{2}$/Si, H-terminated Si, and BeO/Be. The thermal conductance G is obtained by analyzing in-phase and out-of-phase signals from pump-probe measurements of thermoreflectance using a mode-locked Ti:sapphire laser. Measured values at room temperature are 16-29 MW/m$^{2}$/K for Pb (a factor of 2 smaller than previously reported) and 15-20 MW/m$^{2}$/K for Bi; i.e, the measured values of G exceed the radiation limit by a factor of 3-7, and are nearly independent of the substrate.