Exponential series representation for heat capacities of semiconductors and wide‐bandgap materials

Abstract

AbstractThe Thirring series expansion is used as the starting point for the design of a structurally novel, dispersion‐related analytical model for descriptions of the temperature dependences of harmonic parts of isochoric heat capacities, CVh (T). The notorious problem of slow convergence of this conventional series expansion is satisfactorily resolved here by its transformation into an associated exponential series representation, which shows up markedly better convergence properties than the original Thirring expansion. Combining this unprecedented analytical CVh (T) model in a physically adequate way with the recently introduced power series expansion for contributions of lattice expansion and anharmonicity effects to the observable isobaric heat capacities, we get a novel effective tool for numerical simulations and analyses of corresponding Cp (T) data sets, which is suitable for applications to the practically important regions of intermediate to high temperatures. This model is usable, among other things, as a physically consistent substitution for various types of ad hoc chosen polynomials that are hitherto still frequently used, especially in the field of thermochemistry. In order to illustrate the considerable usefulness of the novel analytical tool, especially for the technologically important class of wide‐bandgap materials, we perform simultaneous least‐mean‐square fittings of combined sets of available high‐ and low‐temperature Cp (T) data for diamond, SiC‐3C, the III‐nitrides BN, AlN, and GaN, and the zinc chalcogenides ZnO, ZnS, and ZnSe. For a comparison with results obtained recently for Si and Ge on the basis of a three‐oscillator model, we have re‐examined the respective Cp (T) data sets. As interesting byproducts of present fittings we evaluate several even‐order moments of the respective phonon density of states spectral functions. The discussion of numerical results reveals, among other things, the basic physical cause of the obvious inappropriateness of the conventional Debye model with respect to the majority of the materials under study. (© 2008 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)