A Kinetic Theory of Incoherent Exciton Annihilation

Abstract

The properties of an exciton system with the high concentration are investigated on the basis of microscopical equations for the density matrix of the type of BBGKY hierarchy. A new recipe for decoupling a chain of equations is proposed, which takes into account the effect of three-particle collisions on the definition of a two-particle distribution function of an exciton sub-system. Using this decoupling procedure and making no assumption about the smallness of the quadratic concentration effects the set of equations for density matrix reduced to the known phenomenological equation describing exciton annihilation under steady-state excitation. The kinetic equations applicable to an essentially larger concentration region are also derived taking into account high concentration effects. There use for the case of excitons with a great diffusion length permits us to predict a new effect of additional luminescence quenching at high excitation levels. This effect turns to be very appreciable in two-, and particularly, in one-dimensional systems and may manifest itself in the kinetics of nonlinear luminescence quenching. A qualitatively new-behaviour of the quantum yield dependence on excitation intensity is predicted, which gives reasonable explanation of recent experimental results. The limits on concentration and intensity values where the present theory is good are pointed out. The results of the paper may be applied to other quantum many-particle systems where the coordinates of a quasi-particle are good quantum numbers, and also to chemical reaction theory, to coagulation and the related problems.