Temperature-dependent electrical properties of HgSe

The electrical conductivity and Hall coefficient between 4.2 and 300 K were measured for single-crystalline samples of the zero-gap semiconductor mercury selenide. The samples had extrinsic electron concentrations ranging from 3.6 × ${10}^{16}$ to 4 × ${10}^{18}$ ${\mathrm{cm}}^{-3\mathrm{}}$. The temperature dependences of the band parameters were obtained by fitting to the Hall-coefficient data a band model based upon the full Kane theory with higher-band corrections. The least-squares fit was obtained for a ${\Gamma }_6-{\Gamma }_8$ energy gap which decreased from 0.22 eV at 4.2 K to 0.061 eV at 300 K, an interband-momentum-matrix element which increased slightly from 7.2 × ${10}^{-8\mathrm{}}$ eV cm at 4.2 K to 7.6 × ${10}^{-8\mathrm{}}$ eV cm at 300 K, an effective hole mass of $0.78m_0$, and a valence-band overlap of the conduction band by 5.0 meV. A variational calculation of the electron mobility between 4.2 and 300 K was performed for each HgSe crystal. The limiting scattering mechanisms were taken to be inter- and intraband longitudinal-optical-phonon scattering, electron-hole scattering, acoustic-phonon scattering, and scattering by charged and neutral defects. The calculations included the properly mixed $s$ and $p$ wave functions, the effects of higher bands on the density of states, the temperature dependence of the band parameters, and the anomalous dielectric function associated with the symmetry-induced zero-gap band structure. The results of the calculations for both the temperature and concentration dependences of the electron mobility are in good agreement with experiment for values of the Szigeti effective charge $e_s^{}{}_{}{}^{*}$ (0.76) and the transverse-optic temperature ${\Theta }_T$ (173 K) which were deduced from optical and acoustical data. At temperatures below about 50 K the electron scattering mainly is by ionized donors and neutral defects. At higher temperatures the electron mobility is limited primarily by longitudinal-optical-phonon scattering. Acoustic-phonon scattering is negligible at all temperatures. An anomalous minimum in the electron mobility near 110 K was observed in mercury selenide that was allowed to sit for a few months at room temperature after having been annealed in vacuum.