Conductivity, Hall Effect, and Magnetoresistance inn-Type Germanium, and Their Dependence on Pressure

Measurements of the electrical resistance, low-field Hall effect, and low-field longitudinal and transverse magnetoresistance in oriented samples of $n$-type germanium in which the carriers are all of one type have been carried out at 0°C as a function of pressure in the range 1-10 000 kg/${\mathrm{cm}}^2$ by using a nonmagnetic beryllium-copper high-pressure bomb. The experimental results are interpreted in terms of a low-field theory for $n$-type germanium in which the shape parameter $K=\frac{m_1}{m_2}$ of the energy ellipsoids and the dependence of the collision time $\tau$ on energy play a central role. The atmospheric-pressure data indicate that $K$ at 0°C is probably different from the low-temperature cyclotron resonance value. Consideration of several possible forms of the energy dependence of $\tau$ leads to the adoption for lattice scattering of a phenomenological law of the form ${\tau }_L=\left(\frac{a}{\mathrm{kT}}\right){\epsilon }^{-p}$. It is found that the inclusion of the effects of even a small amount of impurity scattering plays a significant role in determining the magnitudes of the galvanomagnetic coefficients. By assuming a reasonable amount of impurity scattering in our samples it is possible to obtain an expression for $\tau \left(\epsilon \right)$ which is capable of producing the magnitudes of the galvanomagnetic coefficients as well as their temperature dependence. The variation of the galvanomagnetic coefficients with pressure is interpreted in terms of changes in $K$ and the form of the dependence of $\tau$ on energy. In particular it is found that $K$ decreases with increasing pressure, indicating that the application of pressure causes the energy ellipsoids to become less prolate. The change in the energy dependence of $\tau$ is interpreted in terms of a change in the exponent of the energy in the lattice scattering law.