The theory of diffusion-limited recombination of donor-acceptor pairs

The asymptotics of the quasi-steady kinetics of diffusion-limited recombination of donor-acceptor (DA) pairs has been developed. The theory is based on the probability of DA pair recombination according to the relation w₀ exp [-(r/r_B)], where w₀ is constant, r is the separation between defects and r_B is the half Bohr radius of the more diffuse wavefunction. The reaction rate equation (for the thermal activation mechanism) includes the reaction constant as follows: k = 4πr_B[E_a/kT + ln (w₀r^2_B/D₀) + 1.54 + 2 K₀ (α)], α = 2r₀(w ₀/D) 1 2, where E_a is the activation energy, and K₀, I₀ are the modified Bessel functions. The quasi-steady recombination radius is introduced. The theory developed has been compared with the zone one. The interpretation of the activation energy and frequency factor have been presented for the diffusion model. An extension of the theory developed by taking into account Coulomb interaction between defects has also been presented. The applicability of the theory to the recombination of V_k centers with electronics centers is alkali halides has been shown. It is assumed that the theory is applicable to other centers of hole nature (H, proton, low symmetry exciton i.e. V_k + electron).