Modeling the Dependence of the Heat Capacity of Metallic Thin Films on Temperature and Thickness

In this paper, we propose a model for the dependence of the heat capacity of thin metal films on temperature and a significant number of atomic layers in films. At the basis of the model presentations, studies of statistical physics of solid state and for the composition of bodies and ideas about the distribution of basic quantities in a set of oscillators distributed in solids at high temperatures, i.e. obtaining Bose-Einstein.

The calculations were performed based on a comparison of the values ​​of the Helmholtz free energy for different film configurations and the number of layers in them. The main tool for implementing the model was the formation and further calculation of the partition function, which was an expression of the distribution of principal quantum numbers in the complex system of a thin film. Calculations have shown that there is an optimal film thickness at which the maximum heat capacity is achieved.

The calculation results show the presence of an increase by 15 - 30% in the heat capacity of thin films corresponding to 300 - 500 atomic layers from the Dulong-Petit law, i.e. exceeding the heat capacity values ​​in comparison with bulk objects for a certain temperature range. The main parameters that were included in the calculations were: Debye temperature, metal density, temperature.