Spin-dependent recombination and hyperfine interaction at deep defects

We present a theoretical study of optical electron-spin orientation and spin-dependent Shockley-Read-Hall recombination in the longitudinal magnetic field, taking into account the hyperfine coupling between the bound-electron spin and the nuclear spin of a deep paramagnetic center. The master rate equations for the coupled system are extended to describe the nuclear spin relaxation by using two distinct relaxation times, tau(n1) and tau(n2), respectively, for defect states with one and two (singlet) bound electrons. The general theory is developed for an arbitrary value of the nuclear spin I. The magnetic-field and excitation-power dependencies of the electron and nuclear spin polarizations are calculated for the value of I = 1/2. In this particular case the nuclear effects can be taken into account by a simple replacement of the bound-electron spin relaxation time by an effective time dependent on free-electron and hole densities and free-electron spin polarization. The role of nuclear spin relaxation is visualized by isolines of the electron spin polarization on a two-dimensional graph with the axes log(2)(tau(n1)) and log(2) (tau(n2)).