Quantum confinement theory of the heat capacity of thin films

TL;DR

This paper presents a quantum confinement theory for thin film heat capacity, predicting a T^4 temperature dependence and a linear increase with thickness, aligning well with experimental data.

Contribution

It introduces a novel quantum confinement model that explains the altered vibrational density of states and heat capacity behavior in nanoscale thin films.

Findings

Heat capacity scales as T^4 instead of T^3 in thin films.

Heat capacity increases linearly with film thickness.

The theory matches experimental data on NbTiN thin films.

Abstract

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 new 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 (VDOS) 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 $\sim T^4$ instead of Debye's $\sim T^3$ law. Furthermore, the new 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.