Pressure and temperature dependence of electronic energy levels in PbSe and PbTe

Abstract

Using recent highly accurate pseudopotential band structures of PbSe and PbTe, the variation of the smallest gap at $L$ with hydrostatic pressure and with temperature has been calculated. The experimental values of the pressure coefficient can well be reproduced assuming reasonable slopes of the pseudopotential-form-factor curves. Combining these values with experimental compressibility and thermal-expansion coefficients, the anharmonic part of the temperature coefficient has been evaluated and found to contribute about 50% to the total experimental temperature coefficient. The remaining contribution arising from electron-phonon interactions has been analyzed using Brooks-Yu and Fan-like scattering theory. While the inclusion of a Debye-Waller factor yields reasonable results for the $L$ gap in PbTe, it fails for the $\Sigma -L$ gap and it predicts a temperature coefficient of the opposite sign for PbSe. A detailed analysis of the PbSe discrepancy is presented. It is proposed that Fan-type intravalley and intervalley scattering can resolve the dilemma. First-order estimates for Fan-type scattering contributions are presented.