Magnetoresistance of Undopedn-Type Gallium Arsenide at Low Temperatures

Abstract

The magnetoresistance of undoped $n$-type GaAs has been measured at liquid-helium temperatures employing magnetic field strengths up to 140 kOe. The samples had electron concentrations between 1.7×${10}^{15}$ and 4.9×${10}^{15}$ ${\mathrm{cm}}^{-3\mathrm{}}$ at 77°K. At low magnetic fields, negative magnetoresistance is observed. It is analyzed into a positive and a negative component. The latter is a function of $\frac{H}{(T+\theta )}$, where $H$ is the magnetic field strength, $T$ is the temperature, and $\theta$ has a value close to 2°K for each sample. In high magnetic fields, above 30 kOe, the resistivity increases very strongly with magnetic field strength, in a manner similar to that when conduction is due to quantum-mechanical resonance jumping of electrons between donor impurities. To account for both the low-field and high-field magnetoresistance, we suggest that conduction takes place in a set of excited impurity states which are delocalized in zero or low magnetic field but become localized because of shrinkage of the wave functions when a high magnetic field is present.