Nonradiative capture and recombination by multiphonon emission in GaAs and GaP

Abstract

Data are presented for 9 capture cross sections of deep levels in GaAs and 4 in GaP which can be interpreted as capture by multiphonon emission (MPE). At high temperatures the cross sections have the form $\ensuremath{\sigma}={\ensuremath{\sigma}}_{\ensuremath{\infty}}{e}^{\frac{\ensuremath{-}{E}_{\ensuremath{\infty}}}{\mathrm{kT}}}$ where ${\ensuremath{\sigma}}_{\ensuremath{\infty}}={10}^{\ensuremath{-}14}\ensuremath{-}{10}^{\ensuremath{-}15}$ ${\mathrm{cm}}^{2}$ and ${E}_{\ensuremath{\infty}}=0\ensuremath{-}0.56$ eV. A simple theory of MPE capture is presented in which vibrations of a single lattice coordinate modulate the depth of the potential well binding the carrier. In this model capture results from lattice vibrations causing the crossing of free- and bound-carrier levels. The breakdown of the adiabatic approximation near the crossing is discussed. The calculated cross sections have the form $\ensuremath{\sigma}=Af(0)$ where $f(h\ensuremath{\nu})$ is the normalized line shape for radiative capture. The lattice relaxation properties of the center determine $f(0)$. The temperature dependence of $f(0)$ correctly accounts for the thermally activated behavior of the cross sections at high temperatures. Classical and quantum treatments of the lattice motion give the same expression for $\ensuremath{\sigma}$ at high temperature. A detailed calculation of $A$ is made for the capture of a carrier by an attractive neutral impurity in the case where both the free-carrier and bound-carrier wave functions are describable in a one-band effective-mass approximation. The theoretical value of $A$ leads to ${\ensuremath{\sigma}}_{\ensuremath{\infty}}\ensuremath{\approx}6\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}15}$ ${\mathrm{cm}}^{2}$, the same order of magnitude as the experimental values. However, many of the experimental cross sections involve complexities not accounted for in this simple model such as charged impurities and transitions between free states and bound states of different symmetry. The lattice relaxation parameters are experimentally determined for the Zn-O and O centers in GaP. Lattice relaxation is found adequate to explain the large cross sections for electron capture by the Zn-O center and hole capture by the two-electron state of O. The studies of the O and Zn-O centers also provide evidence for nonlinear changes in the impurity energy level with lattice displacement which decrease the electron capture cross sections and greatly enhance the hole recombination cross sections. The source of this nonlinearity is discussed.