Weak-field magnetoresistance of hopping conduction in simple semiconductors

Abstract

The weak-field magnetoresistance of phonon-induced hopping conduction is calculated for simple semiconductors, in which the impurity state is represented by the hydrogenic wave function. Emphasis is placed upon the angular dependence of the magnetic perturbation on the wave function, of the elementary transition probability from one to the other impurity sites and of the magnetoresistance coefficients. The quadratic Zeeman perturbation gives rise to an increase of the wave function near the impurity site and a decrease at large distances from the site. Critical distances at which the wave function remains unchanged are given by ɣ c = 3.32 a ( a: Bohr radius) in the direction parallel to the field and ɣ c = 1.63 a in the perpendicular direction. It is shown that the ratio of the contribution to the magnetoresistance from the shrinkage of each impurity-wave function to the contribution from the phase difference between two neighboring impurity sites is 1.22 at a sufficiently low concentration of impurities. The two magnetoresistance coefficients B and C have the interrelation C = − B 2 .