Localized transition models in luminescence: A reappraisal

Localized energy levels within the forbidden energy band are the source of various stimulated luminescence phenomena. The present study deals with the case of electrons stimulated from localized levels and recombining with a hole at a luminescence center, without the mediation of the conduction band. Previous research was based on three different assumptions as follows. Firstly, it was assumed that the recombination rate is independent of the concentration of recombination centers, and is proportional only to the concentration of electrons in the excited state of the trap. Secondly, it is assumed that the principle of detailed balance holds for these localized transitions. A third common assumption is that the system is in quasi-equilibrium condition. When these three conditions are applied to the system of differential equations describing the localized transitions, it was shown that the resultant thermoluminescence (TL) signals follow first order kinetics. This paper examines the assumptions used in these previous studies, and extensive simulations are carried out for a wide range of parameters in the localized transitions model. The results of the simulations show that the TL peaks in the localized model have very similar characteristics with TL peaks derived from delocalized models, including non-first order kinetic characteristics. The differential equations describing the localized transition model are solved analytically using the Lambert W function, and the resulting analytical master equation can describe a variety of optically and thermally stimulated phenomena.