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 ΔP of a configuration coordinate QP, the total energy of the induced vibrations is larger than EP of the minimum lattice energy obtained under QP=ΔP. A defect reaction with TAE of EA in thermal equilibrium takes place when another configuration coordinate QR exceeds a critical value ΔR. Both QP and QR are a linear combination of many normal-mode coordinates in general. Energy flow from QP to QR 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 QP started from ΔP at time zero while QR reaches ΔR thereafter, we determine the minimum lattice energy written as EP+EH. Energy EH is smaller than EA when g≠0 and gives the TAE of the quantum yield of the defect reaction occurring subsequently after carrier capture. We find that EH=EA-EP for EP<g²EA, EH=[(EA)1/2-|g|(EP)1/2]²(1-g²) for g²EA<EP<EAg², and EH=0 for EP>EAg². The TAE of the defect reaction observed is given by EH plus the TAE of carrier capture, which is shown to explain experimental data quite well.