MAGNETOPIEZOTRANSMISSION STUDIES OF INDIRECT TRANSITION IN GERMANIUM

The indirect transition in germanium at T∼20°K has been examined with magnetic fields up to 90 kG, using the high-sensitivity piezotransmission technique. Samples were in the Voigt configuration in which the Poynting vector of the radiation field is perpendicular to the applied magnetic field. The spectra recorded with light polarized either parallel or perpendicular to the magnetic field applied along a [001], [111], or [110] direction exhibit a series of sharp peaks, in contrast to the corresponding series of less distinct steps which are observed in the conventional magnetoabsorption spectra for the indirect edge. At high magnetic fields the piezotransmission peaks have been resolved over a spectral range of more than 0.1 eV which extends from the zero-field edge at 0.77 eV to photon energies at which the direct transition dominates. From the energy spacings of the peaks, we have deduced the cyclotron effective mass mc for the L1 conduction band and its variation as a function of the energy E measured from the bottom of the band. For large E, mc is found to vary linearly with E, in agreement with the results of the k•p perturbation analysis. But the observed slope of the mc-versus-E curve is greater than that expected from theory. Linear extrapolation of the experimental curve gives for the effective mass at the bottom of the band mc(0)=(0.129±0.002)m0 for H[001]. Similarly, for H[111] and [110], we obtain for the light electron mass at the bottom of the conduction band mle(0)=(0.079±0.001)m0 and (0.095±0.001)m0, respectively. Assuming that the ratio of the longitudinal to the transverse effective masses is ml(0)mt(0)20, the above values for mc(0) and mle(0) give the transverse effective mass mt(0)=(0.078±0.002)m0, (0.079±0.001)m0, and (0.079±0.001)m0 for H[001], [111], and [110], respectively. ml has been estimated from the series of peaks due to the heavy electron mass. Using an average value for mhem0=0.352 with H[110], we find that mlm0=1.54±0.06. © 1969 The American Physical Society.