Exciton-exciton “collisions” in crystals

Abstract

The paper represents a theoretical examination of the process of the creation of a free electron in the conduction band and a free hole in the valence band from two excitons of the Wannier-Mott type under the influence of an electrostatic correlation interaction of valence electrons in dielectric and semi-conducting crystals. It can be seen that such a process can take place in two ways: by a direct non-radiative transfer of energy, released by the annihilation of one exciton, to a second exciton dissociating thereafter — which will be called “collision” with an energy transfer — or by a non-radiative recombination of the electron of one exciton with the hole of a second exciton, whereby the remaining electron-hole pair is decomposed by the energy released at the recombination and forms a free hole and a free electron — a so-called exchange “collision”. The probabilities par second of these processes are computed and are finally compared with the probabilities of other processes connected with the formation, the annihilation or the dissociation of excitons in crystals.