Exciton and Magneto-Absorption of the Direct and Indirect Transitions in Germanium

Abstract

Low-temperature, high resolution experiments on magneto-absorption effects in germanium have resolved fine structure in the direct interband transition and, in addition, have revealed structure in the indirect transition. In each case, exciton absorption was also observed and the experimental binding energy of the lowest exciton level was measured. The values of the direct-transition energy gap found were (1) at 1.5\ifmmode^\circ\else\textdegree\fi{}K and 4.2\ifmmode^\circ\else\textdegree\fi{}K, 0.898\ifmmode\pm\else\textpm\fi{}0.001 ev; (2) at 77\ifmmode^\circ\else\textdegree\fi{}K, 0.889\ifmmode\pm\else\textpm\fi{}0.001 ev; and (3) at 293\ifmmode^\circ\else\textdegree\fi{}K, 0.805\ifmmode\pm\else\textpm\fi{}0.001 ev. The binding energy of the "direct" exciton was 0.0025\ifmmode\pm\else\textpm\fi{}0.0005 ev. The magneto-absorption at photon energies slightly greater than the indirect energy gap has the appearance of a series of absorption edges unlike the series of absorption maxima observed in the direct case. The experimental findings are consistent with the theoretical predictions described in the following article. The detailed spectra were observed by means of a new low-temperature, high-resolution magneto-spectrophotometric system providing spectral resolution of the order of ${10}^{\ensuremath{-}4}$ electron volt and steady magnetic fields up to 38.9 kilogauss. An accurate measure of the minimum of the conduction band was obtained by extrapolating a plot of the photon energies of the centers of the absorption edges as a function of magnetic field to zero field. The indirect energy gap, 0.744\ifmmode\pm\else\textpm\fi{}0.001 ev at 1.5\ifmmode^\circ\else\textdegree\fi{}K, was then obtained by subtracting the energy of the emitted longitudinal acoustical phonon which is involved in the indirect transition. This accurate value of the energy gap permits the measurement of the exciton binding energy. The "indirect" exciton ground state was found to be split into two components 0.0011 ev apart with a mean value of the binding energy of 0.0025\ifmmode\pm\else\textpm\fi{}0.0004 ev. These values are consistent with preliminary theoretical calculations. The Zeeman effect of both the direct and indirect exciton absorptions has also been measured and found to be quadratic in accordance with theory.