Quantum confinement theory of the heat capacity of thin films

A theory and mechanistic understanding of the thermal properties of solids under nanoscale confinement are currently missing. We develop a theoretical quantum confinement description of thin films which predicts a quantitative physical law for the heat capacity. In particular, due to the suppression of vibrational modes caused by the thin-film confinement, the vibrational density of states deviates from the Debye quadratic law in frequency and is, instead, cubic in frequency. This leads to a temperature dependence of the heat capacity which is - T 4 instead of Debye's - T 3 law. Furthermore, this theory predicts a linear increase of the heat capacity upon increasing the nanometric film thickness. Both dependencies are found in excellent agreement with recent experimental data on NbTiN thin films.