High magnetic field dependence of the Hall coefficient in n-type germanium and in other semiconductors with ellipsoidal surfaces of constant energy

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Abstract
The linear dependence of the Hall coefficient on one over the magnetic field squared at high‐field strength has been derived using Boltzmann transport theory results for high‐symmetry‐orientation semiconductor samples with ellipsoidal surfaces of constant energy such as n‐type germanium and silicon. This treatment justifies the practice of linearly extrapolating such Hall coefficient data to infinite fields to obtain the net carrier concentration. Comparison to experimental data taken on n‐type germanium at 77 °K shows that the theory accurately perdicts the slope of this straight‐line variation. A criterion is developed in terms of the conductivity mobility and the anisotropy of effective mass and scattering which specifies how large the magnetic fields must be to allow this extrapolation to be performed accurately. It is shown that up to 90% errors are obtained when a single scattering mechanism correction factor is applied to low‐field Hall coefficient data to estimate carrier concentration in the n‐type germanium samples studied.