Hole concentrations in doped gray {\alpha}-Sn on InSb and CdTe measured with infrared ellipsometry

TL;DR

This study measures hole concentrations in doped gray {\

Contribution

It introduces infrared ellipsometry to quantify doping levels in {\

Findings

Heavy hole concentration matches Fermi-Dirac predictions in intrinsic {\

Doping caused by substrate surface preparation affects carrier types.

Infrared spectra reveal strong absorption at 0.45 eV due to band transitions.

Abstract

Gray tin ({\alpha}-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 {\alpha}-Sn layer. Fourier-transform infrared ellipsometry was used to find the temperature-dependent dielectric function of the {\alpha}-Sn layers from 0.03 to 0.8 eV and from 10 to 300 K. Because of the inverted band structure of {\alpha}-Sn, the spectra show a strong absorption peak at 0.45 eV due to transitions from the inverted {\Gamma_-^7} "electron" valence band to the {\Gamma_+^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 {\alpha}-Sn layer, the heavy hole concentration agrees well with predictions based on degenerate Fermi-Dirac statistics. Deviations from the intrinsic {\alpha}-Sn carrier concentrations are attributed to substrate surface preparation leading to the diffusion of donor or acceptor ions into the {\alpha}-Sn layer causing n-type or p-type doping.