Use of the integer and non-integer n-dimensional Debye functions in computing thermal expansivity, with applications to Si and Ge semiconductors

In the present study, a novel method is proposed to accurately calculate the thermal expansivity of semiconductors using the analytical expression obtained for the integer and non-integer n-dimensional Debye functions. The proposed approach is novel as it uses the non-integer n-dimensional Debye functions for the accurate calculations of the thermal expansivities of semiconductors. As an example of the application, the calculation is performed for the thermal expansivities of the Si and Ge semiconductors. Analysis using computer simulation proved that the formula was in excellent agreement with the results reported in the literature.

► The paper provides a novel method to calculate the thermal expansivity.
► This method is validated by calculating the thermal expansivity of Si and Ge semiconductors.
► The proposed analytical expression is simple to use and allows obtaining accurate results.
► The analytical formula is suitable for the integer and non-integer n-dimensional Debye functions.