QUANTUM-MECHANICAL CALCULATIONS OF POPULATION-INVERSION AND AMPLIFICATION OF FAR-IR LASER OSCILLATION IN P-GE

Theoretical investigation through quantum-mechanical calculations of far-infrared (FIR) laser oscillation in p-Ge is presented and compared with the experimental results. Analysis on the basis of energy spectra of germanium driven from the Luttinger Hamiltonian under crossed fields is performed for both cyclotron-resonance (CR) and intervalence band (IVB) laser oscillations. The numerical estimations of the population inversion and amplification coefficient for CR-type show that the transition between n = 0 and n = 1 light-hole (LH) Landau levels yields net amplification in the field region that substantially matches the observations. In these calculations, it is clarified that the valence-band mixture and non-equidistant energy spacing of LH-Landau levels play an essential role. As for the IVB-type, it is suggested that the transitions from n = 2-3 LH-Landau levels to the heavy-hole band take part in laser emissions in the shorter-wavelength region. However, the observed gap in the emission wavelength between the shorter- and longer-wavelength regions cannot be explained by our calculations and further investigation based on quantum-mechanical treatments is needed.