The direct bandgap of gray α-tin investigated by infrared ellipsometry

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.