Piezoresistance Effect inp-Type PbTe

We have measured the piezoresistance effect in 21 samples of $p$-type PbTe taken from single crystals grown by the Czochralski technique. The piezoresistance coefficients ${\pi }_{11}$, ${\pi }_{12}$, and ${\pi }_{44}$ were obtained by application of hydrostatic pressure and of uniaxial stress in the [100], [111], and [110] crystallographic directions. The temperature dependence of these coefficients was investigated in the range 300 to 77°K for hole concentrations between 4.04×${10}^{17}$ and 4.97×${10}^{19}$ ${\mathrm{cm}}^{-3\mathrm{}}$. The temperature and carrier-concentration dependence of the shear coefficient ${\pi }_{44}$ was clearly in qualitative agreement with a $〈111〉$ multivalley model for the principal valence band, and the shear deformation potential ${\Xi }_{\mu }$ was found to be 8.5 eV. The experimental values of ${\pi }_{44}$, however, were much larger at all temperatures and carrier concentrations than those calculated using previously reported band parameters in existing theory. The theory was extended by means of a nonparabolic-band model, and calculations for degenerate statistics were made. This resulted in poorer agreement with experiment. Large values of the hydrostatic coefficient ${\pi }_{11}+2\mathrm{}{\pi }_{12}$ were observed. They are attributed to the volume dependence of the transverse effective mass $m_T$ of the $〈111〉$ band and to the population of a second valence band. The deformation potential $E_2$ of the gap between the two valence bands was found to be -1.0 eV. Large values of the shear coefficient ${\pi }_{11}-{\pi }_{12}$ were also observed. However, the temperature dependence of this coefficient shows that this is not the result of the population of the nearby $〈110〉$ valence band suggested by recent band calculations.