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

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 ${\Delta }_P$ 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 $Q_P={\Delta }_P$. A defect reaction with TAE of $E_A$ in thermal equilibrium takes place when another configuration coordinate $Q_R$ exceeds a critical value ${\Delta }_R$. 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 ${\Delta }_P$ at time zero while $Q_R$ reaches ${\Delta }_R$ thereafter, we determine the minimum lattice energy written as $E_P+E_H$. Energy $E_H$ is smaller than $E_A$ when $g\ne 0$ and gives the TAE of the quantum yield of the defect reaction occurring subsequently after carrier capture. We find that $E_H=E_A-E_P$ for $E_P<g^2{E}_A$, $E_H=\frac{{[{\left(E_A\right)}^{\frac{1}{2}}-|g\left|\mathrm{}{\left(E_P\right)}^{\frac{1}{2}}\right]}^2}{(1-g^2)}$ for