Using Fourier-transform infrared ellipsometry, the authors provide spectroscopic evidence about the valence band (VB) structure of diamond-like α-tin. The mid-infrared dielectric function of α-tin grown pseudomorphically on InSb or CdTe by molecular beam epitaxy shows a strong E¯0 peak near 0.41 eV. This peak is assigned to allowed intravalence band transitions from the Γ7− (electron-like) VB to the Γ8+v heavy hole VB and/or interband transitions from Γ7− to the Γ8+c light “hole” conduction band. The strength of this peak requires a hole density in the mid-1018 cm−3 range at room temperature, which might be caused by unintentional doping, by thermal electron-hole pair generation, or by the possibility that the L6+ conduction band might have an energy slightly lower than the Γ8+ VB maximum. Alternatively, this E¯0 peak might be enhanced by the M-shape of the Γ7− VB caused by interactions with the Γ7+ split-off hole VB. A sum-rule analysis of the dielectric function between 0.16 and 6.5 eV is consistent with a high-frequency dielectric constant of 24, which has at most a weak temperature dependence between 100 and 300 K.
The temperature dependence of the complex pseudodielectric function of bulk InSb (100) near the direct band gap was measured with Fourier-transform infrared ellipsometry between 30 and 500 meV at temperatures from 80 to 725 K in ultrahigh vacuum. Using the Jellison–Sales method for transparent glasses, the thickness of the native oxide was found to be [Formula: see text] Å, assuming a high-frequency dielectric constant of about 3.8 for the native oxide. After this surface correction, the dielectric function was fitted with a Herzinger–Johs parametric semiconductor model to determine the bandgap and with a Drude term to determine the electron concentration and the mobility. We find that the bandgap decreases from 230 meV at 80 K to 185 meV at 300 K, as expected from thermal expansion and a Bose–Einstein model for electron-phonon scattering renormalization of the bandgap. Between 450 and 550 K, the bandgap remains constant near 150 meV and then increases again at even higher temperatures, presumably due to a Burstein–Moss shift resulting from thermally excited electron-hole pairs. The broadening of the direct bandgap increases steadily with temperature. The electron concentration (calculated from the Drude tail at low energies assuming parabolic bands with a constant electron mass of 0.014[Formula: see text]) increases from [Formula: see text] at 300 K to [Formula: see text] at 700 K, in reasonable agreement with temperature-dependent Hall measurements. The electron mobility was found to decrease from [Formula: see text] at 450 K to [Formula: see text] at 700 K, also in good agreement with Hall effect results. We describe a theoretical model that might be used to explain these experimental results.
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