Magnetoresistance of Undoped<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mi>n</mml:mi></mml:math>-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\ifmmode\times\else\texttimes\fi{}${10}^{15}$ and 4.9\ifmmode\times\else\texttimes\fi{}${10}^{15}$ ${\mathrm{cm}}^{\ensuremath{-}3}$ at 77\ifmmode^\circ\else\textdegree\fi{}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 $\frac{H}{(T+\ensuremath{\theta})}$, where $H$ is the magnetic field strength, $T$ is the temperature, and $\ensuremath{\theta}$ has a value close to 2\ifmmode^\circ\else\textdegree\fi{}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.