Interband Optical Absorption in Crossed Electric and Magnetic Fields in Germanium

Abstract

The theory for interband optical absorption in semiconductors in crossed electric and magnetic fields is developed for the case of low electric field strengths by considering the electric potential as a perturbation on the magnetic level structure. For simple parabolic valence and conduction bands the results agree with those of Aronov, obtained from an exact solution of the effective-mass Schr\"odinger equation in crossed fields, but the present method has the advantage that it can be applied to complicated bands, such as the degenerate valence bands in germanium, whenever the energy levels and eigenfunctions in the absence of an electric field are known. Actual calculations are presented for the case of germanium. Experimentally, the optical absorption in crossed fields was studied using a modulation technique in which both the transmission in the absence of an electric field and the modulation of this transmission by an ac electric field are measured to obtain the electric-field-induced change in absorption coefficient $\ensuremath{\Delta}\ensuremath{\alpha}$. Strain-free as well as strained thin germanium samples were used in magnetic fields up to 96 kOe and electric fields up to 1000 V/cm. Both allowed transitions ($\ensuremath{\Delta}n=0, \ensuremath{-}2$ for germanium) and electric-field-induced forbidden transitions ($\ensuremath{\Delta}n=\ensuremath{-}3, \ensuremath{-}1, +1$) can be observed in these differential spectra. A good agreement between theory and experiment is obtained. It is shown that under favorable conditions the electron and hole masses can be determined separately from the differential spectra. It is also found that the electric-field-modulation technique can sometimes be used to study the allowed transitions with greater sensitivity than in the normal magnetoabsorption experiments.In zero magnetic field the Stark broadening of the low-energy direct exciton line in a strained germanium sample was studied up to 1000 V/cm. The linewidth was found to vary linearly with electric field, increasing at a rate of about 160 \ifmmode\times\else\texttimes\fi{} ${10}^{\ensuremath{-}8}$ eV/V ${\mathrm{cm}}^{\ensuremath{-}1}$. This phenomenon is tentatively explained in terms of an electric dipole moment of the short-lived exciton state.