Anisotropic Hall Coefficients in n-Type Germanium

Abstract

Precise measurements of Hall effect have been made at 77°K, 90°K, 195°K, and 298°K up to 11,000 gauss on oriented single crystals of n-type germanium containing 5×10 ¹⁴ antimony per cm ³ as donor centers. The results should principally indicate the variations of µ _H /µ with the magnetic field and with the temperature, since the carrier concentration may be practically constant under the present conditions. Absolute values of µ _H /µ have been deduced from R _∞ and R ₀ . R _∞ for which µ _H /µ always equals unity is fortunately obtained by extraporating R _H ^< 001> (77°K) vs 1/ H ² data. Then R _H ^< 001>/ R _∞ will straightway give µ _H /µ· _H . On the other hand, µ _H /µ for other orientations may be indirectly estimated from their extraporated R ₀ for which µ _H /µ is independent of the orientation and should be equal to R ₀ ^< 001>/ R _∞ at respective temperatures, neglecting the effect due to slightly different impurity concentration between specimens. Values of µ _H /µ thus determined are always smaller than unity, while those of _H approach to unity most rapidly with increasing field and those of _H most slowly. They are of course temperature dependent and the zero magnetic field values are equal to 0.83 at 77°K, 0.84 at 90°K, 0.90 at 195°K and 0.92 at 298°K respectively. Numerical evaluation of the Boltzmann's equation taking account of ellipsoid model and mixed scatterings can give the observed values fairly well. It appears, however, preferable to introduce some correction term, e.g., reasonable amount of optical phonon scattering for the best agreement.