The quasi-equilibrium approximation and its validity for the thermoluminescence of inorganic phosphors

The validity of the quasi-equilibrium (QE) assumption in the analytical models of thermoluminescence (TL) which assume delocalization of the untrapped charge carriers has often been questioned. In this paper, this problem is further considered using three different physical models of TL emission. The numerically computed glow curves without the QE approximation are compared with those calculated analytically to verify whether the QE condition is satisfied. QE is assessed also by using a mathematical relation between the excitation and relaxation rates. The results lead to the following conclusions. (i) Under a wide variety of parametric combinations QE is attained even when retrapping predomines over recombination. (ii) Glow peaks with first-order character are obtained even when the retrapping rate far exceeds the recombination rate in multiple-trap systems. This is contrary to the premise on which the Randall-Wilkins model is based. These two conclusions contradict also the assertions of Lewandowski and McKeever that QE and fast retrapping are not self-consistent conditions and that the apparent dominance of first-order TL kinetics in nature is due solely to the predominance of recombination over retrapping. (iii) QE depends critically on the product of the trap concentration and the cross section. A new criterion for the validity of the QE assumption is derived, according to which should be greater than , where and are the concentration and the cross section of the traps at the active and deeper levels in a system exhibiting multiple glow peaks. (iv) Evidence from studies of point defects in insulating and semiconducting materials shows that the N and values of the defect centres concerned are high enough to satisfy the QE condition. It is thus inferred that the use of the analytical expressions based on the QE approximation for analysing the glow curves of the common TL phosphors is legitimate.