Acceptor excitation spectra in germanium in a uniform magnetic field.

Abstract

The irreducible-spherical-tensor form of the effective-mass Hamiltonians for acceptors in cubic semiconductors in a homogeneous magnetic field parallel to a 〈001〉 direction or to a 〈111〉 direction has been derived. The Hamiltonians take into account the full structure of the ${\mathrm{\ensuremath{\Gamma}}}_{8}^{+}$\ensuremath{\bigoplus}${\mathrm{\ensuremath{\Gamma}}}_{7}^{+}$ valence-band edge, and they contain a point-charge potential with spherically symmetric q-dependent dielectric screening. The eigenstates have been calculated variationally for the case of acceptors in germanium. For both orientations, the computations have been performed as a function of the magnetic-field strength, in the range from 0 to 5 T. The binding energies of the first 36 odd-parity excited states and of the first 4 even-parity states (which form the ground-state multiplet) are obtained. The oscillator strengths of the electric-dipole transitions from the ground-state sublevels to the excited states are also calculated, and the results are used to simulate theoretical acceptor excitation spectra, which are in excellent agreement with the available experimental far-infrared-absorption and photothermal-ionization-spectroscopy spectra. For the ground state and for the final states of G and D lines, theoretical g factors are obtained which are very close to the experimental ones. In particular, the values ${\mathrm{g}}_{1}^{\ensuremath{'}}$=-0.45 and ${\mathrm{g}}_{2}^{\ensuremath{'}}$=+0.22 are computed for the acceptor ground state. It is found also that for the ground state and for the excited ${\mathrm{\ensuremath{\Gamma}}}_{8}$(T${\mathrm{\ifmmode\bar\else\textasciimacron\fi{}}}_{\mathrm{d}}$) final states of the G, D, and B spectral lines, the ratio r=${\mathrm{g}}_{2}$/${4\mathrm{g}}_{1}$ is always very close to the special values -541, which corresponds to a linear Zeeman splitting of the ${\mathrm{\ensuremath{\Gamma}}}_{8}$ states into a degenerate doublet for B\ensuremath{\Vert}〈111〉 and into an equally spaced quartet for B\ensuremath{\Vert}〈001〉.