Valence-band energy spectrum of solid solutions of narrow-gap-semiconductor Bi2-xSnxTe3 single crystals.

Abstract

Electrical resistivities along the ${\mathit{C}}_{2}$ and ${\mathit{C}}_{3}$ axes, Hall effect, Shubnikov--de Haas effect, and pulsed-laser-induced transient thermoelectric effect (TTE) have been measured in the temperature range 4.2--300 K for solid solutions of narrow-gap p-type ${\mathrm{Bi}}_{2\mathrm{\ensuremath{-}}\mathit{x}}$${\mathrm{Sn}}_{\mathit{x}}$${\mathrm{Te}}_{3}$ (0\ensuremath{\le}x\ensuremath{\le}0.035) single crystals. We have found systematic variations of the hole concentration, Hall mobility, Dingle temperature, and cyclotron mass with increasing Sn content. By doping Sn atoms, the hole Fermi energy of the upper valence band (UVB) is increased and a Sn-induced impurity band is formed near the top of the lower valence band (LVB) lying by about 15 meV below the top of the UVB. The observed TTE voltages decay exponentially with time, showing a multiple relaxation process with characteristic relaxation times for thermal diffusions of photogenerated carriers. The TTE data show that there are at least four different relaxation times (${\mathrm{\ensuremath{\tau}}}_{1}$--${\mathrm{\ensuremath{\tau}}}_{4}$) due to holes, and two, ${\mathrm{\ensuremath{\tau}}}_{5}$ and ${\mathrm{\ensuremath{\tau}}}_{6}$, due to electrons. Combined with the transport data, as well as the existing band model, we have evaluated the effective masses ${\mathit{m}}_{1}^{\mathrm{*}}$\ensuremath{\simeq}0.033${\mathit{m}}_{0}$ and ${\mathit{m}}_{2}^{\mathrm{*}}$\ensuremath{\simeq}0.060${\mathit{m}}_{0}$ for the many-valley hole Fermi surfaces of the UVB, as well as two effective masses ${\mathit{m}}_{3}^{\mathrm{*}}$\ensuremath{\simeq}0.16${\mathit{m}}_{0}$ and ${\mathit{m}}_{4}^{\mathrm{*}}$\ensuremath{\simeq}0.31${\mathit{m}}_{0}$ for the LVB along the ${\mathit{C}}_{2}$ direction, corresponding to ${\mathrm{\ensuremath{\tau}}}_{1}$--${\mathrm{\ensuremath{\tau}}}_{4}$, respectively. Discussion will be given for the energy spectrum and anisotropy in the UVB and LVB, as well as the lower electron band, in this material system. The thermal conductivities for holes and lattices are also evaluated from the TTE data.