Contribution of surface roughness of an isotropic solid to low-temperature surface heat capacity

Abstract

The effect of roughness of the free surface of a semi-infinite isotropic solid on the low-temperature surface heat capacity is studied. The method of modified Green’s function (as compared with that used by Maradudin, Wallis, and Equiluz (1977) and perturbation theory are used for deriving an analytic expression for the contribution of weak roughness to the low-temperature surface heat capacity, which is a correction to the well-known result obtained by Dupuis, Mazo, and Onsager (1960) for the surface heat capacity of a semi-infinite isotropic solid with a plane free boundary. It is proved that the inclusion of roughness of isotropic crystals with optical surfaces increases the surface heat capacity in a wide temperature range (of the order of several kelvins).