Lattice Model of Nonphonon Donor–Acceptor Photoluminescence in Germanium Crystals

A formula is proposed for calculating the spectral position of the peak of the nonphonon line (zero phonon line, ZPL) of donor–acceptor (DA) photoluminescence in p- and n-type covalent semiconductors with hydrogen-like impurities at low temperatures and low levels of steady-state interband photoexcitation. The model uses a nonstoichiometric simple cubic impurity lattice formed jointly by doping (majority) and compensating (minority) impurity atoms in the crystal matrix. It is assumed that the distribution densities of energy levels of donors forming the D0-band and energy levels of acceptors forming the A0-band in the band gap of the crystal are Gaussian with equal root-meansquare fluctuations of the ionization energy. Nonphonon radiative DA-recombination is considered to occur only between nearest neighbors in the impurity lattice upon a nonequilibrium electron transition from the energy level of the first excited state of donor to the acceptor energy level in the A0-band, which coincides with the Fermi level in this band in a p-type semiconductor or upon a nonequilibrium hole transition from the energy level of the first excited state of acceptor to the donor energy level in the D0-band, which coincides with the Fermi level in the band in an n-type semiconductor. The calculated dependence of the maximum of DA-photoluminescence nonphonon line on the concentration and degree of compensation of majority impurities by minority impurities is consistent with known experimental data for neutron-transmutation doped germanium crystals.