Phonon-Drag Thermomagnetic Effects inn-Type Germanium. I. General Survey

In a magnetic field H and a thermal gradient $\nabla T$, a conductor develops a Nernst field $-B\mathrm{H}\times \nabla T$ and its thermoelectric power $Q$ depends on H. These two effects have been measured for a number of single-crystal six-armed samples of high-purity $n$-type germanium, with various orientations, at fields up to 18 000 gauss and at a number of temperatures from the liquid-hydrogen range to the onset of intrinsic conduction; the most detailed measurements were made near liquid air temperature. Both the Nernst coefficient $B$ and the quantity $\Delta Q=Q\left(\mathrm{H}\right)-Q\left(0\right)\mathrm{}$ are compounded additively out of terms arising from diffusion of the electrons and terms arising from their anisotropic scattering by the phonons moving from hot to cold. The latter "phonon-drag" terms are strongly predominant at low temperatures. They give rise to a positive contribution $B_p$ to the low-field $B$ which outweighs the negative electron-diffusion contribution for $T<\mathrm{}175\mathrm{}°$K, and which can be expressed in terms of Hall mobility ${\mu }_H$ and phonon-drag thermoelectric power $Q_p$ by $B_p=\frac{{\zeta }_p\left|Q_p\right|{\mu }_H}{c}$ with ${\zeta }_p\approx 0.25$ over most of the range. Theoretically and experimentally, $\mathrm{BH}\to 0$ as $H\to \infty$. As expected, $\Delta Q\left(\mathrm{H}\right)$ resembles the magnetoresistance both in its anisotropy and in its variation with H. All the results are understandable theoretically in terms of a model which assigns to each ellipsoidal energy shell in crystal-momentum space an anisotropic phonon-drag Peltier tensor with principal components ${\Pi }_{p\mathrm{II}}$ in the high-mass direction, ${\Pi }_{p\perp }$ in the low-mass direction. The data show that $\frac{{\Pi }_{p\mathrm{II}}}{{\Pi }_{p\perp }}\gg 1$ but < the mass-relaxation-time anisotropy $\frac{{m_{\mathrm{II}}}^{*}{\tau }_{\perp }}{{m_{\perp }}^{*}{\tau }_{\mathrm{II}}}\approx 17$. The effective average of ${\Pi }_{p\mathrm{II}}$ and ${\Pi }_{p\perp }$ increases slightly with decreasing energy of the shell, as it should if the relaxation times of the phonons vary with wave number $q$ at a rate between $q^{-1\mathrm{}}$ and