Magnetoresistance Oscillations in Single-Crystal and Polycrystalline Indium Arsenide

Abstract

Measurements of the electrical resistivity of single-crystal and polycrystalline samples of $n$-type InAs have been made as a function of magnetic field strength up to 29 000 gauss at temperatures between 1.25\ifmmode^\circ\else\textdegree\fi{}K and 20.2\ifmmode^\circ\else\textdegree\fi{}K.In both samples oscillations in the resistivity are observed as the magnetic field strength is varied, both when the field is parallel to and when it is perpendicular to the current direction. The oscillations are damped periodic functions of reciprocal field strength. For each sample the period observed in longitudinal and in transverse fields is the same and agrees with that calculated from the electron concentration obtained from the Hall coefficient. The observed phases, at least in the single-crystal sample, agree fairly well with that predicted by theory which is based on a quasi-free electron model.An exponential field dependence of the amplitude of the oscillations is found, indicating the presence of energy-level broadening that can be characterized by a collision-broadening time which is related to the scattering relaxation time obtained from the mobility in a manner consistent with theory. Collision broadening also accounts for the similarity of oscillations observed in transverse and in longitudinal fields and for the absence of higher harmonics in the magnetoresistance oscillations.The temperature dependence of the amplitude of the oscillations has been studied in a range of $\frac{\mathrm{kT}}{\ensuremath{\hbar}\ensuremath{\omega}}$ not usually obtained. Our results for the temperature dependence can be fitted by the theoretically determined form, $\frac{x}{sinhx}$, where $x=\frac{2{\ensuremath{\pi}}^{2}\mathrm{kT}}{\ensuremath{\hbar}\ensuremath{\omega}}$, and thereby allow a value for the effective mass of conduction electrons to be determined.