Two-stage thermal stimulation of thermoluminescence

A thermoluminescence (TL) model of two-stage stimulation of electrons into the conduction band is discussed. This release of the carriers is assumed to take place via an intermediate localized excited state. Electrons are thermally stimulated from the trap into an excited state and then thermally released into the conduction band from which they may either be retrapped or recombine with holes in centers. The model resembles the previous “semi localized” model, but we concentrate only on recombination of electrons that go through the conduction band. It also bears similarity to the effect of thermally-assisted optically stimulated luminescence (OSL) previously discussed in the literature.The model is studied by solving the set of the relevant four simultaneous differential equations which govern the process during heating or isothermal decay. Using different sets of parameters, we can get pseudo-first-order, pseudo-second-order as well as intermediate cases, which are identified by their symmetry coefficient. Once the effective order is established, different analytical methods are used to determine the effective activation energy and frequency factor. We used the peak-shape methods, the various heating rate (VHR) method and the method based on the change of phosphorescence decay with temperature. The results are compared to the parameters used in the simulation. In many cases, the effective activation energy is equal to E₁ + E₂ where E₁ and E₂ are, respectively, the activation energies for the first and second stage of thermal stimulation. The numerical simulation results are accompanied by an analytical treatment using the usual quasi-steady assumption. Unusual cases, in which the effective frequency factor and the effective retrapping probability coefficient are temperature dependent, are identified. Some cases in which the effective activation energy is close to E₁ rather than E₁ + E₂ are identified and discussed. The relevance of this possible situation to the evaluation of the stability of TL signals is also considered, and a possible effect of anomalous stability is predicted.