The Size effect on the specific heat and Debye temperature of thin-film semiconductors

A theoretical model is proposed in this work for an evaluation of the specific heat and Debye temperature of thin-film semiconductors. In the model, the specific heat contributed by the confined acoustic phonons is calculated first. An effective Debye temperature is then defined by fitting the conventional Debye model to the calculated specific heat. It is found that the so-defined Debye temperatures of both the dilatational and flexural polarizations are about 25% smaller than the bulk longitudinal Debye temperature. When the temperature is so low that there are only a few phonon modes excited, the temperature-dependence of the specific heats shows two-dimensional behavior, except the one associated with flexural polarization which shows one-dimensional behavior instead due to its parabolic dispersion relation at small wave numbers.