Weak-Field Magnetoresistance of Impurity Conduction inn-Type Germanium

Abstract

The coefficients $B$, $C$, and $D$ of the weak-field magnetoresistance in $n$-type germanium are calculated in the phonon-induced hopping region at low temperatures. The shrinking of each donor wave function by a magnetic field decreases the transition probability of electrons from a donor site to an unoccupied one and gives rise to a magnetoresistive effect. The phase difference produced by the field between two neighboring donor wave functions contributes to the magnetoresistance to the same order of magnitude as the effect of the shrinking. The results show some characteristic properties of $B$, $C$, and $D$ different from those of electrons in the conduction band: (1) The absolute magnitude of the coefficients is larger for specimens with smaller carrier mobility; (2) the magnitude is much larger than that expected from the usual transport theory of conduction electrons; (3) the isotropic part of the coefficients $B$ is the largest; and (4) the coefficient $D$, which represents the anisotropy of the electronic motion, is the smallest among the three coefficients. These properties are in qualitative agreement with recent experiments in a slightly higher impurity concentration range in $n$-type germanium.