Photon-Assisted Magnetotunneling in Germanium in Parallel and Crossed Electric and Magnetic Fields

Abstract

The effects of both a parallel and a transverse magnetic field on the electric-field-induced interband optical absorption (the Franz-Keldysh effect or photon-assisted tunneling) have been studied in germanium for photon energies less than the direct band gap. The effective-mass approximation for simple parabolic bands was used to obtain stationary electron states for parallel fields, and an expression for the interband optical absorption coefficient for direct allowed transitions was calculated. Because parallel fields have independent effects on electron motion, interband transitions take place at these photon energies by means of photon-assisted tunneling between pairs of Landau levels subject to the usual magneto-optical selection rule $\ensuremath{\Delta}n=0$. The expression for the absorption coefficient is valid for photon energies both below and above the direct gap, and in the limit of zero magnetic field it reduces to the expression for the Franz-Keldysh effect. The optical absorption spectra below the direct gap in germanium have been measured for both parallel and crossed fields. The data for parallel fields are shown to be in qualitative agreement with the theoretical absorption coefficient. The data for crossed fields were taken for values of the ratio $\frac{E}{H}$ sufficiently large so that the absorption observed could be interpreted as photon-assisted tunneling. These data are in qualitative agreement with the theoretical results for crossed-field absorption appearing in the following paper.