We have developed a novel dispersion-related model for monotonic temperature dependencies of fundamental band gaps, E g (T), and the associated excitonic absorption and emission line positions, E gx (T), which is suitable for detailed numerical analyses of experimental data available for a large variety of semiconductor ͑including wide-band-gap͒ materials and quantum-well structures. The present model is distinguished from preceding ones by the following features: ͑i͒ It is applicable to an unusually large span of magnitudes for the phonon dispersion coefficient, ⌬ϵͱ͗(បϪប) 2 ͘/ប , extending from the familiar Bose-Einstein regime of vanishing dispersion, ⌬у0, up to the limiting regime of extremely large dispersion, ⌬р1. ͑ii͒ The resulting analytical E(T) functions approach, in the cryogenic region, quadratic asymptotes, the curvatures of which are throughout significantly weaker than suggested by Varshni's ad hoc model. ͑iii͒ The novel analytical expressions enable direct, straightforward determinations of the T→0 limits of gap widths, the high-temperature limits of slopes, the average phonon temperatures, ⌰ϵប /k B , and the associated dispersion coefficients, ⌬, without requiring preliminary determinations of other ͑auxiliary͒ quantities. Results of least-mean-square fittings for a variety of group IV, III-V, and II-VI materials are given and compared with those obtained in previous studies using less elaborate models. The parameter sets obtained suggest that the physically realistic range of dispersion coefficients is confined to an interval from 0 up to a maximum of about 3/4. Another, qualitatively different, dispersion-related model, which represents the hypothetical regime of extremely large dispersion, ⌬Ͼ1, is also developed in this paper solely for the sake of a detailed dispersion-related analysis of Varshni's model function. Our analytical and numerical study concludes that Varshni's model is associated with a hypothetical case of extremely large dispersion characterized by a dispersion coefficient significantly higher than unity, ⌬ V ϭ(2 /6Ϫ1) Ϫ1/2 ϭ1.245. This is in clear contradiction to empirical ⌬ values that range below unity. The relatively large discrepancy between the upper boundary of about 3/4 for realistic ⌬ values and the high value of ⌬ V Х5/4 for Varshni's model is the fundamental reason for the usual inadequacy ͑large degree of arbitrariness͒ of parameter values resulting from conventional fittings of E(T) data sets using Varshni's formula.

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We have redigitized a large variety of phonon density of states (PDOS) spectra, that have been published by diferent researchers for group IV (diamond, 3C-SiC, Si, and Ge), III–V (BN, BP, BAs, BSb, AlN, AlP, AlAs, AlSb, GaN, GaP, GaAs, GaSb, InN, InP, InAs, and InSb), and II–VI materials (ZnO, ZnS, ZnSe, ZnTe, CdS, and CdTe), including calculations of their moments, ⟨εn⟩, of orders n=−1, 1, 2, and 4. Notwithstanding the obvious differences in concrete shapes of spectra presented for one and the same material by different authors, the respective magnitudes of estimated moments have been found in most cases to be nearly the same (to within uncertainties of some few percent). For most materials under study, the average phonon temperatures of the lower and upper sections of PDOS spectra, ΘL and ΘU, are found to be by factors of order 0.6 lower or 1.4 higher, respectively, than the average phonon temperature, ΘP, of the total PDOS spectra. The estimated high-temperature limits of Debye temperatures, ΘD(∞), are found to be significantly higher (by factors of order 1.4) than ΘP, implying an order-of-magnitude equality, ΘD(∞)≈ΘU (within differences not exceeding an order of ±10%, for all materials under study). The phonon temperatures, Θg, that are effective in controlling the observable temperature dependences of fundamental energy gaps, Eg(T), are found to be usually of the same order as the respective average phonon temperatures, Θg≈ΘP. The existing differences between these two qualitatively different types of characteristic phonon temperatures are seen to be limited, for diamond, 3C-SiC, Si, Ge, AlN, GaN, GaP, GaAs, GaSb, InP, InSb, ZnS, ZnSe, ZnTe, and CdTe, to an order of ±12%. We design an exemplary way for precalculating harmonic parts of isochoric heat capacities on the basis of the estimated quadruplets of PDOS spectra moments. This novel calculation scheme is exemplified for silicon and germanium.

A 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 higherenergy 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 byproducts of these fittings we obtain adequate values for the material-specific PDOS spectra moments for all orders within the range 3 10 n -< £ . 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.

We perform numerical analyses of the temperature dependences of fundamental band gaps, Eg(T), and/or exciton peak positions, Egx(T), for a large variety of group IV, III–V, and II–VI (including wide band gap) materials using a two-oscillator model. This model assumes a fixation of the low-energy oscillator in the vicinity of the dominant TA peak, whereas the location of the high-energy oscillator is taken as an adjustable parameter depending on the relative weights of the contributions of short-wavelength LA and LO/TO phonons. The material-specific sets of empirical parameters have been estimated from fittings of measured E(T) dependences. The results indicate significant changes of the relative contributions of optical versus acoustical phonons from one material to the other. The degree of dispersion is found to increase significantly with contribution of low-energy acoustical phonons.