Dynamic defect reactions induced by multiphonon nonradiative recombination of injected carriers at deep levels in semiconductors

Abstract

Violent lattice vibrations, induced by nonradiative capture of a free carrier by a deep-level defect in semiconductors, enhance greatly defect reactions such as movement of the defect itself or production of a new one, through reduction of the thermal activation energy (TAE). A theory of this phenomenon is presented. When capture takes place at a critical value ${\ensuremath{\Delta}}_{P}$ of a configuration coordinate ${Q}_{P}$, the total energy of the induced vibrations is larger than ${E}_{P}$ of the minimum lattice energy obtained under ${Q}_{P}={\ensuremath{\Delta}}_{P}$. A defect reaction with TAE of ${E}_{A}$ in thermal equilibrium takes place when another configuration coordinate ${Q}_{R}$ exceeds a critical value ${\ensuremath{\Delta}}_{R}$. Both ${Q}_{P}$ and ${Q}_{R}$ are a linear combination of many normal-mode coordinates in general. Energy flow from ${Q}_{P}$ to ${Q}_{R}$ occurs through the direction cosine $g$ between them in the phonon space, and $g$ is nonvanishing when there exist normal-mode components common between them. Under the condition that ${Q}_{P}$ started from ${\ensuremath{\Delta}}_{P}$ at time zero while ${Q}_{R}$ reaches ${\ensuremath{\Delta}}_{R}$ thereafter, we determine the minimum lattice energy written as ${E}_{P}+{E}_{H}$. Energy ${E}_{H}$ is smaller than ${E}_{A}$ when $g\ensuremath{\ne}0$ and gives the TAE of the quantum yield of the defect reaction occurring subsequently after carrier capture. We find that ${E}_{H}={E}_{A}\ensuremath{-}{E}_{P}$ for ${E}_{P}<{g}^{2}{E}_{A}$, ${E}_{H}=\frac{{[{({E}_{A})}^{\frac{1}{2}}\ensuremath{-}|g|{({E}_{P})}^{\frac{1}{2}}]}^{2}}{(1\ensuremath{-}{g}^{2})}$ for ${g}^{2}{E}_{A}<{E}_{P}<\frac{{E}_{A}}{{g}^{2}}$, and ${E}_{H}=0$ for ${E}_{P}>\frac{{E}_{A}}{{g}^{2}}$. The TAE of the defect reaction observed is given by ${E}_{H}$ plus the TAE of carrier capture, which is shown to explain experimental data quite well.