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 σ_∞ of the capture cross section, being proportional to T^-2 at a temperature T, reaches a maximum of the order of 10^-14 cm², while that of the carrier-emission rate reaches a constant of the order of an average phonon frequency. Moreover, in this limit σ_∞ 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 σ_∞ being of the order of 10^-14-10^-15 cm² 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.