Experiments on the Kapitza Resistance

Abstract

The Kapitza resistances of samples of copper, gold, tungsten, single-crystal lithium fluoride, and single-crystal silicon have been measured in the temperature range from 1.25 to 2.10°K. We find that a clean copper surface prepared by machining under liquid helium exhibits a Kapitza resistance whose magnitude and temperature dependence are considerably greater than that which a dirty copper surface exhibits. The Kapitza resistances which these samples exhibited can be represented by a power law as follows: Au, $8T^{-3\mathrm{}}$; LiF, $23T^{-3.75\mathrm{}}$; Cu (clean), $19T^{-3.6\mathrm{}}$; Si (unetched, 7 dislocations/${\mathrm{cm}}^2$), $21T^{-3.2\mathrm{}}$; Cu (dirty), $7T^{-2.6\mathrm{}}$; Si (etched, 7 dislocations/${\mathrm{cm}}^2$), $35T^{-4.15\mathrm{}}$; W, $39T^{3.5}$; Si (etched, 800 dislocations/${\mathrm{cm}}^2$), $35T^{-4.15\mathrm{}}$ (units are deg ${\mathrm{W}}^{-1\mathrm{}}$ ${\mathrm{cm}}^2$). The interfacial surface of the lithium fluoride crystal was a (100) cleavage plane. The interfacial surfaces of the silicon crystals were (111) planes which were ground, polished, and in some cases, etched. We have considered these results in relation to the theories of Khalatnikov, Little, and a modification of the Khalatnikov theory by Challis, Dransfeld, and Wilks. These theories failed to predict both the absolute magnitude and temperature dependence of the Kapitza resistances and the relative magnitude of the resistances for different samples. In addition, we have found no evidence in our experiments on cleaned copper of the mechanism proposed by Bloch involving the conduction electrons.