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.
@article{arxiv.2604.15553,
title = {Hole concentrations in doped gray {\alpha}-Sn on InSb and CdTe measured with infrared ellipsometry},
author = {Jaden R. Love and Carlos A. Armenta and Atlantis K. Moses and Haley B. Woolf and Jan Hrabovsky and Stefan Zollner and Aaron N. Engel and Christopher J. Palmstrøm},
journal= {arXiv preprint arXiv:2604.15553},
year = {2026}
}