Dispersion‐related theory for heat capacities of semiconductors

Abstract

AbstractA reasonable analytical basis for dispersion‐related descriptions of the temperature dependences of harmonic parts of isochoric heat capacities is given by a three‐oscillator model for phonon density of states (PDOS) spectra of semiconductors with a relatively large degree of phonon dispersion. Within this model, a combination of two lower‐energy oscillators substitutes the lower (acoustical) part, and a single higher‐energy oscillator represents the upper (optical) part of PDOS spectra. This model provides good simulations of T ‐dependences of harmonic parts of isochoric heat capacities from moderately low to high temperatures. The incorporation of continuous (quadratic and quartic) power function components into the low‐energy tail region enables a very fine description of temperature dependences also throughout the cryogenic region. Deviations of experimentally measured heat capacities from their harmonic parts are quantified by a conveniently designed low‐order anharmonicity term. The corresponding analytical model provides excellent numerical simulations of isobaric heat capacities of Si and Ge from absolute zero up to room temperature on the basis of least‐mean‐square fittings involving total sets of 6 model‐specific parameters in combination with known zero temperature values of Debye temperatures. As important by‐products of these fittings we obtain adequate values for the material‐specific PDOS spectra moments for all orders within the range –3 < n ≤ 10. The extended version of this dispersion‐related description, which involves a power series expansion for anharmonic components of heat capacities, represents an unprecedented analytical tool for adequate numerical representations of isobaric heat capacities of Si and Ge throughout the whole experimentally relevant temperature region, i.e. from absolute zero up to the respective melting points.Supporting information for this acticle (Appendices on “Self‐sufficient scheme for estimations of even moments” and “Direct use of heat capacity data for determinations of lower moments”) is provided online at www.pss‐b.com.(© 2007 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)