Numerical solutions to the rate equations governing the simultaneous release of electrons and holes during thermoluminescence and isothermal decay

The usual, simple model for the analysis of thermoluminescence (TL) curves deals with just one trapping level and one recombination level and assumes that only one recombination pathway exists for the production of luminescence (e.g., the thermal release of trapped electrons to recombine with thermally stable, trapped holes). In this paper we examine a more complex model which allows for the thermal release of both charge carriers in the same temperature range. Known as the Schön-Klasens model, this charge-transfer scheme has been often suggested as a cause of the thermal quenching of luminescence in insulators. The set of four simultaneous differential equations which describe the flow of charge between the energy levels in the Schön-Klasens model is solved numerically without the use of approximations. The TL curve shapes so generated are then analyzed with use of the usual Randall-Wilkins, Garlick-Gibson, or general-order formalisms i.e., the so-called three-parameter form of equations. In the cases examined, good fits between the generated TL curves and the curves expected using these approximate formulations were obtained. We conclude that a fit of an experimental glow curve to a three-parameter form of equation cannot be used to indicate that the simple three-parameter model is necessarily valid. Additional to curve fitting, the curves were also analyzed using the conventional initial-rise and heating-rate methods. The parameters calculated from these analyses were compared with the original parameters inserted into the model and conclusions drawn regarding the interpretations of the calculated values. Finally, with use of these calculated parameters the isothermal stabilities of the TL curves were predicted and compared with the stabilities calculated from the numerical solution to the differential equations. We conclude that a three-parameter type of analysis is not a reliable means of estimating the thermal stability of the TL when the Schön-Klasens model is applicable. © 1985 The American Physical Society