Phonon-Drag Thermomagnetic Effects in<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mi>n</mml:mi></mml:math>-Type Germanium. I. General Survey

Abstract

In a magnetic field H and a thermal gradient $\ensuremath{\nabla}T$, a conductor develops a Nernst field $\ensuremath{-}B\mathrm{H}\ifmmode\times\else\texttimes\fi{}\ensuremath{\nabla}T$ 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 $\ensuremath{\Delta}Q=Q(\mathrm{H})\ensuremath{-}Q(0)$ 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 $T&lt;175\ifmmode^\circ\else\textdegree\fi{}$K, and which can be expressed in terms of Hall mobility ${\ensuremath{\mu}}_{H}$ and phonon-drag thermoelectric power ${Q}_{p}$ by ${B}_{p}=\frac{{\ensuremath{\zeta}}_{p}|{Q}_{p}|{\ensuremath{\mu}}_{H}}{c}$ with ${\ensuremath{\zeta}}_{p}\ensuremath{\approx}0.25$ over most of the range. Theoretically and experimentally, $\mathrm{BH}\ensuremath{\rightarrow}0$ as $H\ensuremath{\rightarrow}\ensuremath{\infty}$. As expected, $\ensuremath{\Delta}Q(\mathrm{H})$ 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 ${\ensuremath{\Pi}}_{p\mathrm{II}}$ in the high-mass direction, ${\ensuremath{\Pi}}_{p\ensuremath{\perp}}$ in the low-mass direction. The data show that $\frac{{\ensuremath{\Pi}}_{p\mathrm{II}}}{{\ensuremath{\Pi}}_{p\ensuremath{\perp}}}\ensuremath{\gg}1$ but the mass-relaxation-time anisotropy $\frac{{{m}_{\mathrm{II}}}^{*}{\ensuremath{\tau}}_{\ensuremath{\perp}}}{{{m}_{\ensuremath{\perp}}}^{*}{\ensuremath{\tau}}_{\mathrm{II}}}\ensuremath{\approx}17$. The effective average of ${\ensuremath{\Pi}}_{p\mathrm{II}}$ and ${\ensuremath{\Pi}}_{p\ensuremath{\perp}}$ 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 ${q}^{\ensuremath{-}1}$ and ${q}^{\ensuremath{-}2}$. A more quantitative analysis is possible and will be given in a forthcoming paper.