Temperature Dependence of the HgTe Band Gap

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Abstract
Hg and Te Debye-Waller factors in HgTe have been measured using x-ray diffraction. These have been combined with a previously published pseudopotential to calculate the temperature dependence of the band gap within the Brooks-Yu theory. The calculated value has approximately one-half the magnitude and the opposite sign of the experimental value. A detailed analysis indicates the Debye-Waller factors are not likely to be the cause of the discrepancy, but that the pseudopotential may be. A further analysis shows that when interband matrix elements are included for normal electron-phonon processes in a rough self-energy calculation, the correct sign is obtained. The magnitude has not, however, been determined. It is also shown, though, that a self-energy band calculation neglects significant terms if only the bands closest to the gap are included. We conclude that our understanding of the temperature dependence of semiconductor band gaps is somewhat weaker than many are claiming on the basis of moderate agreement with experiment.