The factorized plasmon-phonon polariton description of the infrared dielectric function is generalized to include an additional factor to account for the effects of interband electronic transitions. This new formalism is superior to the usual Drude–Lorentz summation of independent oscillators, especially in materials with large transverse-longitudinal optical phonon splittings, multiple infrared-active phonon modes, or high concentrations of free carriers, if a broadband description of the dielectric function from the far-infrared to the vacuum-ultraviolet spectral region is desired. After a careful comparison of both approaches, the factorized description is applied to the dielectric function of undoped and doped semiconductors (GaAs, GaSb, and InAs) and metal oxides from 0.03 to 9.0 eV. Specifically, the authors find that both descriptions of the far-infrared dielectric function yield the same carrier density and mobility, at least for a single species of carriers. To achieve valid results for moderately high doping concentrations, measurements to lower energies would be helpful.

The temperature dependence of the optical constants of materials (refractive index, absorption and extinction coefficients, and dielectric function) can be determined with spectroscopic ellipsometry over a broad range of temperatures and photon energies or wavelengths. Such results have practical value, for example for applications of optical materials at cryogenic or elevated temperatures. The temperature dependence of optical gaps and their broadenings also provides insight into the scattering of electrons and holes with other quasiparticles, such as phonons or magnons. This review presents a detailed discussion of the experimental considerations for temperature-dependent ellipsometry and selected results for insulators, semiconductors, and metals in the infrared to ultraviolet spectral regions.

No abstract

The dielectric function of bulk Ge is determined between 0.5 and 6.3 eV in a temperature range of 10–738 K using spectroscopic ellipsometry. The authors provide the data in a tabulated format that can be interpolated as a function of photon energy and temperature using commercial software. Another focus of this paper lies on the analysis of critical points, in particular, on the investigation of the temperature dependence of the direct bandgap E0 and the critical point E0+Δ0, where Δ0 is the spin–orbit splitting. To explore the temperature dependence of critical points, the parameters that characterize their line shapes are calculated using three different techniques. First, the common method of numerically calculating and analyzing the second derivatives of the dielectric function works well for critical points at higher energies. Second, an analysis in reciprocal space by performing a discrete Fourier transform and analyzing the resulting Fourier coefficients yields values for the energies of E0 and E0+Δ0. Third, the energy determined from a parametric semiconductor model is shown as a function of temperature. The authors observe a temperature dependent redshift of the E0 and E0+Δ0 critical point energies as well as an increase in the broadening of E0 with temperature.

Using spectroscopic ellipsometry from 0.06 to 6.0 eV at room temperature, the authors determined the optical constants (complex dielectric function, refractive index, and optical conductivity) of bulk cold-rolled polycrystalline Ni. To reduce the thickness of surface overlayers, the sample was heated in ultrahigh vacuum at 750 K for 6 h and then kept in vacuum during measurements. The authors analyze the optical constants using three alternative but mutually exclusive methods: they write the dielectric function as a multiband sum or product of Drude and Lorentz oscillators or with a Drude model with a frequency-dependent scattering rate and plasma frequency. Below 1 eV, they find significant contributions from both d-intraband transitions and free carriers.