Electrical conductivity of germanium as a function of optically injected carrier density and temperature

Abstract

The effects of carrier-carrier scattering on the transport properties of high-density electron-hole plasmas in germanium were studied both experimentally and theoretically. Experimentally, the dc electrical conductivities of nearly uniform optically injected bipolar plasmas in high-purity single crystals of germanium were measured for a broad range of carrier densities (\ensuremath{\sim} ${10}^{14}$ - \ensuremath{\sim} 5 \ifmmode\times\else\texttimes\fi{} ${10}^{17}$ ${\mathrm{cm}}^{\ensuremath{-}3}$) and temperatures (21-298 K). Concurrent measurements of the absorption of 3.39-\ensuremath{\mu}m radiation due to inter-hole-band transitions aided the calibration of the carrier densities at some temperatures. The previous theory of Appel, which used Kohler's variational principle to solve the Boltzmann equation, was generalized with respect to the inclusion of interband hole scattering, electron mass anisotropy, degeneracy, and use of the RPA $\stackrel{\ensuremath{\rightarrow}}{\mathrm{q}}$-dependent screening approximation (although not with respect to all at once). The most crucial generalization was the accounting for the presence of nonconducting excitons in the plasma. The scattering of free carriers by excitons was also considered, using a neutral-impurity scattering theory similar to that of Erginsoy. Incorporation of all the above considerations led to excellent agreement between experiment and theory at densities below the Mott criterion for transition to the exciton-free phase. The transition itself appeared to be gradual, however, and behavior of the conductivity in the high-density region was consistent with the recent assertion by Thomas and Rice that excitons are present at densities significantly above the Mott criterion.