The conduction of heat from a modulated heat source of finite size is analyzed for a semi-infinite solid in contact with the adjacent gas. The solid is a semi-infinite layered composite structure consisting of a superlattice (of thickness Δ) grown on a substrate. Using partitioned matrices that arise naturally from boundary conditions, a closed form solution for the temperature distribution in the solid and gas is found for the limit of conduction-dominated heat transport in the gas. The general case is analyzed in which each layer of a superlattice can have different anisotropic thermal conductivities as well as different thermal boundary resistances between the individual layers due to the growth process. Limits of this most general case are discussed in which all “A” and all “B” layers are themselves the same. The temperature field that arises from the general problem is used to compute probe beam deflections in the gas for the photothermal deflection spectroscopy (PDS) technique for measuring the thermal conductivity. Results are presented to show how probe beam deflection components, and the effective properties of the superlattice, are influenced by the number of periods of the superlattice, thermal properties of the superlattice layers, and the presence or absence of a thermal boundary resistance between the layers.
