Negative Magnetoresistance in Impurity Conduction

Negative magnetoresistance is observed at 4.2°K in Cd-doped $p$-type GaAs, vapor deposited $n$-type GaAs, and P-doped $n$-type Ge. In $n$-type GaAs prepared by Czochralski or horizontal-Bridgman techniques, samples with carrier concentrations less than about ${10}^{16}$ show negative magnetoresistance at 4.2°K which goes through a maximum at fields less than 10 000 G and becomes positive at high fields. At concentrations greater than ${10}^{16}$ there is no clear indication of a maximum at fields up to 20 000 G. The ratio of longitudinal to transverse magnetoresistance in the impurity conduction range is a function of temperature and field, but at 1.4°K it exceeds 0.9 both for negative magnetoresistance at low fields and for positive magnetoresistance at high fields. The over-all trends of the data on GaAs and other materials require two competing processes to account for the magnetoresistive behavior. One of these is the effect of the magnetic field in reducing orbital overlap which has been demonstrated by Sladek and Keyes on $n$-Ge and $n$-InSb. A competing process which could operate in the "hopping" region of impurity conduction might be an increase in the population of a set of states of higher energy and mobility than the ground states due to a reduction in the energy separation between them.