The band structure of semimagnetic ${\mathrm{Hg}}_{1\ensuremath{-}y}{\mathrm{Mn}}_{y}\mathrm{Te}∕{\mathrm{Hg}}_{1\ensuremath{-}x}{\mathrm{Cd}}_{x}\mathrm{Te}$ type-III quantum wells (QW's) has been calculated using an eight-band $\mathbit{k}∙\mathbit{p}$ model in an envelope function approach. Details of the band structure calculations are given for the Mn-free case $(y=0)$. A mean-field approach is used to take the influence of the $sp\text{\ensuremath{-}}d$ exchange interaction on the band structure of QW's with low Mn concentrations into account. The calculated Landau level fan diagram and the density of states of a ${\mathrm{Hg}}_{0.98}{\mathrm{Mn}}_{0.02}\mathrm{Te}∕{\mathrm{Hg}}_{0.3}{\mathrm{Cd}}_{0.7}\mathrm{Te}$ QW are in good agreement with recent experimental transport observations. The model can be used to interpret the mutual influence of the two-dimensional confinement and the $sp\text{\ensuremath{-}}d$ exchange interaction on the transport properties of ${\mathrm{Hg}}_{1\ensuremath{-}y}{\mathrm{Mn}}_{y}\mathrm{Te}∕{\mathrm{Hg}}_{1\ensuremath{-}x}{\mathrm{Cd}}_{x}\mathrm{Te}$ QW's.

https://arxiv.org/pdf/cond-mat/0409392.pdf

Band structure of semimagnetic Hg 1 − y Mn y Te quantum wells

High-quality ZnS, ZnSe, and ZnTe epitaxial films were grown on (001)-GaAs-substrates by molecular beam epitaxy. The 1s-exciton peak energy positions have been determined by absorption measurements from 2 K up to about room temperature. For ZnS and ZnSe additional high-temperature 1s-exciton energy data were obtained by reflectance measurements performed from 300 up to about 550 K. These complete E1s(T) data sets are fitted using a recently developed analytical model. The high-temperature slopes of the individual E1s(T) curves and the effective phonon temperatures of ZnS, ZnSe, and ZnTe are found to scale almost linearly with the corresponding zero-temperature energy gaps and the Debye temperatures, respectively. Various ad hoc formulas of Varshni type, which have been invoked in recent articles for numerical simulations of restricted E1s(T) data sets for cubic ZnS, are discussed.

Temperature dependence of exciton peak energies in ZnS, ZnSe, and ZnTe epitaxial films

vanishing dispersion, D>0, up to the limiting regime of extremely large dispersion, D 5/4 for Varshni’s model is the fundamental reason for the usual inadequacy ~large degree of arbitrariness! of parameter values resulting from conventional fittings of E(T) data sets using Varshni’s formula.

/pdf/dispersion-related-description-of-temperature-dependencies-2hc3o550zl.pdf

Dispersion-related description of temperature dependencies of band gaps in semiconductors

We have investigated the temperature dependence of the fundamental absorption edge of a series of Hg1−xCdxTe alloys (with composition x ranging from 0.5 to 1). Analyzing our data in the light of the three‐dimensional theory of direct‐allowed excitons, we find precise values for the fundamental Γ8‐Γ6 interband transition energy in a temperature range extending from 0 to 300 K. All experimental results, including previous data for HgTe and mercury‐rich Hg1−xCdxTe alloys, are well accounted for using a simple empirical formula: Eg (eV)=−0.303(1−x)+1.606x−0.132x(1−x)+[6.3(1−x) −3.25x −5.92x(1−x)]10−4T2/[11(1−x)+78.7x+T]. This expression, which is valid for all compositions 0≤x≤1 and temperatures 0≤T≤500 K, predicts an alloy composition such that the band‐gap energy is temperature independent: We find x=0.505. Finally, it can be used for technological application purpose (far‐infrared detection as well as optical‐fiber communications performed at realistic values of the temperature) and gives accurate values f...

Temperature dependence of the fundamental absorption edge of mercury cadmium telluride

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.

Temperature dependence of fundamental band gaps in group IV, III–V, and II–VI materials via a two-oscillator model

The composition dependence of the ${\ensuremath{\Gamma}}_{8}$-${\ensuremath{\Gamma}}_{6}$ transition in mercury cadmium telluride (MCT) has long been classified apart among all disordered alloy systems. The nonconstant bowing parameter reported in this case could only be accounted for in terms of a finite departure from the virtual-crystal approximation but was not clearly reflected in the properties of carriers and/or the characteristics of the alloys. Moreover this nonconstant bowing appears to be a unique feature of MCT. First, it departs from all reports concerning standard II-VI and III-V materials which, even for structurally disordered systems like In-Ga-As, still exhibit a constant bowing and a parabolic dependence of the fundamental absorption edge on alloy composition. Second, it is not easily reflected in many band-structure calculations. Most of the time, even if they have been performed in the light of the coherent-potential approximation (CPA), they fail to reproduce such a complicated scheme.As a matter of fact, because of the closer lattice matching achieved in Hg-Cd-Te than in Hg-Zn-Te, these calculations suggest that less deviation (or bowing) from the straight-line average between the two binary compounds should exist in Hg-Cd-Te than in Hg-Zn-Te. In both cases, they predict a parabolic (or nearly parabolic) behavior. This rather large discrepancy between the experimental results and the theoretical calculation is one of the characteristics of MCT. To clear up this point, we have investigated a series of samples with concentrations in the range x=0.5--1 (where x=1 corresponds to CdTe). We resolve a series of excitonic features and get a clear, unambiguous determination of the first interband transition at different alloy compositions. This gives a constant bowing parameter (i.e., a simple parabolic dependence) with a maximum departure from linearity of 33 meV at x=0.5. We discuss these results in the light of the virtual-crystal approximation, using the empirical pseudopotential method, and compare them with recent CPA predictions where both diagonal and off-diagonal disorder terms had been included. We find a surprisingly good agreement which demonstrates, on a purely experimental basis, the near-cancellation of disorder effects expected at the band edge in mercury cadmium telluride.

B. Toulouse

Papers

Temperature dependence of the fundamental absorption edge of mercury cadmium telluride

Composition dependence of the Γ 8 - Γ 6 transition in mercury cadmium telluride: A reexamination