Nonradiative multiphonon capture of free carriers by deep-level defects in semiconductors: Adiabatic and nonadiabatic limits

The rate of multiphonon capture with thermally activated temperature dependence is formulated with the semiclassical approximation for phonons. It bridges the nonadiabatic (weak-coupling) and the adiabatic (strong-coupling) limits when the interaction to induce capture is strengthened. Except in the nonadiabatic limit it is important that once-captured carriers can be reemitted into free states in a very short time (much shorter than an average phonon period) after capture. In the adiabatic limit, the preexponential factor ${\sigma }_{\infty }$ of the capture cross section, being proportional to $T^{-2\mathrm{}}$ at a temperature $T$, reaches a maximum of the order of ${10}^{-14\mathrm{}}$ ${\mathrm{cm}}^2$, while that of the carrier-emission rate reaches a constant of the order of an average phonon frequency. Moreover, in this limit ${\sigma }_{\infty }$ does not include defect parameters any more and depends only on the effective mass of free carriers. These features of the adiabatic limit explain well Henry and Lang's observation that ${\sigma }_{\infty }$ being of the order of ${10}^{-14\mathrm{}}$-${10}^{-15\mathrm{}}$ ${\mathrm{cm}}^2$ is apparently a universal quantity independent of defects within GaAs and GaP. The strength of the interaction is determined by the bandwidth of free carriers for defects with only one bound state, and a parameter distinguishing between the adiabatic and the nonadiabatic limits is given.