Generalized description of thermally stimulated processes without the quasiequilibrium approximation

Abstract

An alternative mathematical description of thermally stimulated luminescence (TL) and thermally stimulated conductivity (TSC) is presented without the restrictions of the quasiequilibrium (QE) and kinetic-order (KO) approximations. The development is carried out within the framework of a model consisting of a single active trap in the presence of a large concentration of deep, thermally disconnected traps and recombination centers. The QE and KO approximations are removed and replaced by two new functions, Q(T) and P(T), both rigorously defined in terms of trap emptying and filling processes. The resulting generalized equations are capable of continuously describing the behavior of systems over a wide range of kinetic cases and very far from QE. From these, generalized initial-rise and Hoogenstraaten equations are derived from which previously unknown correction terms are identified. In addition, a modified version of the initial-rise analysis is presented and its range of validity addressed. The formalism presented provides much insight in that one may describe clearly the effects of common approximations and estimate if such approximations are warranted. Other results include a physical justification for why first-order (slow-retrapping) processes dominate in nature, a general TL-TSC relationship, the realization that the QE approximation is only valid at the temperature of the TSC peak maximum, and an experimental method for determining the shape of the Q(T) function. The applicability of this analysis is illustrated using numerical solutions of the differential rate equations.