De Haas—van Alphen Oscillations in the Magnetoresistance of Heavily Doped Germanium

Abstract

The existence of de Haas-van Alphen oscillations in the magnetoresistance of degenerately doped $n$- and $p$-type germanium is reported. Transverse and longitudinal magnetoresistance measurements were performed on a number of selected samples of various crystal orientation at 4.2\ifmmode^\circ\else\textdegree\fi{}K in dc magnetic fields up to 110 kOe. In $p$-type germanium distinct oscillations were observed only in the longitudinal magnetoresistance. In $n$-type germanium oscillations could be seen only in the transverse magnetoresistance, the magnitude of the effect being enhanced by the use of antimony as dopant and by aligning $H\ensuremath{\parallel}[111]$. In each sample studied the period of the oscillations can be related to the motion of Landau levels with respect to the Fermi level, when the appropriate cyclotron mass is introduced. The magnetic field dependence of the amplitude of the oscillations yields in each case a value of $\ensuremath{\omega}\ensuremath{\tau}$ in reasonable agreement with that obtained from analysis of conductivity data. As expected, no oscillatory behavior could be detected in the magnetoresistance of degenerately doped silicon.