Theory of the Magnetoresistive Effect in Semiconductors

Experiments show that the application of a magnetic field increases the resistivity of a semiconductor and produces a decrease in the magnitude of the Hall coefficient. Existing theoretical treatments predict much smaller effects than are actually observed in semiconductors. The present calculation has been carried out to see if theory is brought closer to experiment by considering (1) scattering of conduction electrons by impurity ions as well as by the lattice, and (2) conduction by both holes and electrons at high temperatures. The calculation shows that the presence of impurity scattering decreases the magnitude of the effects produced by a magnetic field and thus increases the gap between theoretical and experimental values. It is noted that the discrepancy decreases with falling temperatures and is no longer present for data measured on a Ge sample at 20^. The calculated magnetic field effects are very much greater for an intrinsic semiconductor than for an impurity semiconductor. The fractional changes in resistivity and Hall coefficient are given, for several different values of the electron-hole mobility ratio, as functions of a parameter containing magnetic field strength and temperature. The absence of experimental values of the magnetic field effects at high temperatures prevents comparison of theory and experiment for the intrinsic semiconductor.