Effect of Uniaxial Compression on Impurity Conduction inp-Germanium

The effect of uniaxial compression along [100] and [111] on impurity conduction has been investigated in Ga-doped $p-\mathrm{G}\mathrm{e}$ in the concentration range $3\times {10}^{15}<N_A<9\mathrm{}\times {10}^{16}$ ${\mathrm{cm}}^{-3\mathrm{}}$ for compensation $K=0.04\mathrm{}$ and in the range $9\times {10}^{14}<N_A<4\mathrm{}\times {10}^{16}$ ${\mathrm{cm}}^{-3\mathrm{}}$ for $K=0.40\mathrm{}$. The experiments were performed between 300 and 1.2°K. The largest stress applied was 6.8×${10}^9$ dyn ${\mathrm{cm}}^{-2\mathrm{}}$. The analysis of the experimental results deals primarily with the high-stress region ($X>\mathrm{}4\mathrm{}\times {10}^9$ dyn ${\mathrm{cm}}^{-2\mathrm{}}$) in which the two valence bands, which in the absence of stress are degenerate at k = 0, are nearly decoupled so that the effect of the lower band on the acceptor wave function is treated as a perturbation. In the low-concentration region ($N_A<5\mathrm{}\times {10}^{15}$ ${\mathrm{cm}}^{-3\mathrm{}}$) the extension of Miller and Abrahams' theory to include nonspherical charge distributions, together with the acceptor wave functions calculated from the effective-mass approximation, accounts for the observed stress dependence of the resistivity. At intermediate concentrations ($2\times {10}^{16}<N_A<9\mathrm{}\times {10}^{16}$ ${\mathrm{cm}}^{-3\mathrm{}}$) a linear relation between the impurity-conduction activation energy ${\epsilon }_2$ and the acceptor ionization energy ${\epsilon }_1$ is established. Although the experimental results are not able to distinguish between Mikoshiba's and Frood's theories of the ${\epsilon }_2$ process they are clearly in disagreement with the predictions of Mycielski's theory. The investigation of the stress dependence of the transition from nonmetallic to metallic conduction yields the stress dependence of the effective Bohr radius. The form of this stress dependence indicates the importance, at high concentrations, of the potential-energy term in the effective-mass Hamiltonian. This term can be neglected at low concentrations.