Spin-dependent recombination and hyperfine interaction at deep defects

Abstract

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, ${\ensuremath{\tau}}_{n1}$ and ${\ensuremath{\tau}}_{n2}$, 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 ${\mathrm{log}}_{2}({\ensuremath{\tau}}_{n1})$ and ${\mathrm{log}}_{2}({\ensuremath{\tau}}_{n2})$.