Hole concentrations in doped gray α-Sn on InSb and CdTe measured with infrared ellipsometry
Gray tin (α-Sn) layers with 30 nm thickness were grown on InSb (001) substrates using molecular beam epitaxy. The surface preparation of the substrates was adjusted to achieve either n-type or p-type doping in the α-Sn layer. Fourier-transform infrared ellipsometry was used to find the temperature-dependent dielectric function of the α-Sn layers from 0.03 to 0.8 eV and from 10 to 300 K. Because of the inverted band structure of α-Sn, the spectra show a strong absorption peak at 0.45 eV due to transitions from the inverted {Γ_-^7} "electron" valence band to the {Γ_+^8} heavy hole valence band. Applying the Thomas-Reiche-Kuhn f-sum rule, the integrated oscillator strength of this peak was used to calculate the heavy hole concentration as a function of temperature. For a nearly intrinsic α-Sn layer, the heavy hole concentration agrees well with predictions based on degenerate Fermi-Dirac statistics. Deviations from the intrinsic α-Sn carrier concentrations are attributed to substrate surface preparation leading to the diffusion of donor or acceptor ions into the α-Sn layer causing n-type or p-type doping.