Quantum confinement theory of the heat capacity of 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.

References in corpus (6)

• Nonlinear viscoelastic dynamics of nano-confined water
• Explaining the low-frequency shear elasticity of confined liquids
• The ${\omega }^3$ scaling of the vibrational density of states in quasi-2D nanoconfined solids
• Extended analytical BCS theory of superconductivity in thin films
• Universal $L^{-3}$ finite-size effects in the viscoelasticity of confined amorphous systems
• Analytical theory of enhanced Bose-Einstein condensation in thin films

Cited by in corpus (4)

• Low-Temperature Heat Transport under Phonon Confinement in Nanostructures
• Quantum confinement theory of ultra-thin films: electronic, thermal and superconducting properties
• Phonon-confinement theory of thermal conductivity in ultrathin silicon films
• Temperature crossovers in the specific heat of amorphous magnets