Theory of Heat Transport in a Dielectric Slab and Its Applications to CVD Diamond Films

Abstract

Subject classification: 44.10+i; 66.70+f; 68.60Dv; S5The problem of heat transport across a slab of dielectric material is treated within the frame of a model where the phonon scattering processes are described in terms of mean free paths. The conservation of the phonon flux through any plane parallel to the slab, as required for any frequency by the assumption that the above processes are elastic, leads to an integral equation which is solved through a variational procedure. The result is a general formula for the corresponding thermal conductivity k ? , which can thus be studied as a function of the slab thickness. The theory is helpful when discussing size effects for the thermal conductivity of CVD diamond films. These effects are particularly important in the part of the conductivity curve which contains information on phonon scattering by grain boundaries: as a consequence, the formula for k ? could be used to extract, from low temperatures measurements of this parameter, the frequency dependence of the grain boundary scattering rate.