Thermal Conductivity of Silicon in the Boundary Scattering Regime

Abstract

Thermal-conductivity measurements were made on high-purity silicon samples with both rough-lapped and polished surfaces in the temperature range 1-4°K where boundary scattering of the phonons is dominant. Rough-surfaced rods cut in the [111] and [110] directions gave results in good agreement with the theory for completely diffuse surface scattering, but in the [100] direction there appears to be an appreciable fraction of specular reflection. The latter depends only on the heat-flux direction, not the surface orientations. With polishing, the specularity increases, and can be brought to over 90% at the lowest temperatures. The size-effect variation of the conductivity under such conditions is in excellent agreement with the theory. The thermal conductivity appears to be sensitive tool for detection of surface damage.