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 Ē0 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 Ē0 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.