Revealing the theoretical assumptions of the trap-depth distribution model in the thermoluminescence theory

Abstract

The theoretical assumptions of the analytical expressions characterizing the thermoluminescence glow-peak arising from a continuous trap-depth distribution have been investigated. The sets of the differential equations governing the electrons’ transitions within a continuous trap-depth distribution during the irradiation and heating stages have been numerically solved. The analytical expressions are essentially based on a theoretical assumption that correlates the concentrations of the trapped electrons with the distribution of the trap depths in the bandgap. This correlation could not be considered in the numerical solution, since the irradiation stage is entirely independent of the trap depth. Thus, the final values of the instantaneous trap-filling functions of the irradiation stage do not depend on the trap depth, but rather on the trap capacity and the trapping probability coefficient. Consequently, in the numerical solution, the distribution of the trap depths and the distribution of the trapped electrons are independent. This inconsistency between the numerical solution and the analytical expression has led to differences in the shape of the thermoluminescence glow peaks resulting from the same trap-depth spectrum.