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

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Abstract
In a magnetic field H and a thermal gradient ∇T, a conductor develops a Nernst field −BH×∇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 ΔQ=Q(H)−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 Bp to the low-field B which outweighs the negative electron-diffusion contribution for T<175°K, and which can be expressed in terms of Hall mobility μH and phonon-drag thermoelectric power Qp by Bp=ζp|Qp|μHc with ζp≈0.25 over most of the range. Theoretically and experimentally, BH→0 as H→∞. As expected, ΔQ(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 ΠpII in the high-mass direction, Πp⊥ in the low-mass direction. The data show that ΠpIIΠp⊥≫1 but < the mass-relaxation-time anisotropy mII*τ⊥m⊥*τII≈17. The effective average of ΠpII and Πp⊥ 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 and