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E. P. Shtapenko and Yu. V. Syrovatko
Heat Capacity of Thin Films at High Temperatures
477–493 (2023)

PACS numbers: 05.70.Ce, 63.20.D-, 63.22.Dc, 63.70.+h, 65.40.Ba, 65.80.-g, 68.60.-p

The purpose of this paper is to develop a model, which allows determining the heat capacity of thin films at the temperatures comparable to and exceeding the Debye temperature. The model presented in the paper takes into consideration the anisotropy of vibrations of the corresponding bending waves and wave vibrations in the plane occurring with the decrease in the film thickness. Furthermore, the model is based on the quadratic dispersion law for bending wave vibrations in the normal direction of a thin film and the linear dispersion law for the wave vibrations in the film plane. In order to expand the existing model representations for the heat capacity of thin films at low temperatures, we used the Debye’s method in the integral expression for the free energy. We considered this approach earlier in the model representations of the heat capacity of anisotropic quasi-crystals. Our findings show that the thin-film heat-capacity dependence on the temperature has a maximum and exceeds the heat capacity of a bulk sample. This circumstance confirms the experimental data obtained earlier by other authors. Besides, according to the experimental data collected from the literature, heat capacity of the thin films rises, compared to values of the bulk sample, when the film thickness decreases. This factor is also reflected in the model under consideration, and the calculated dependence of the increase in thin films on the number of atomic layers correlates well with the experimental data. Therefore, the proposed model allows determining the heat capacity of thin films at the temperatures exceeding the Debye temperature with sufficient accuracy without experimental investigation.

Key words: thin films, film thickness, heat capacity, Debye temperature, dispersion law.

https://doi.org/

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