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

The validity of the quasi-equilibrium (QE) assumption in the analytical mod els 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. Th e numerically computed glow curves without the QE approximation are compare d 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 conclus ions. (i) Under a wide variety of parametric combinations QE is attained ev en when retrapping predomines over recombination. (ii) Glow peaks with firs t-order character are obtained even when the retrapping rate far exceeds th e recombination rate in multiple-trap systems. This is contrary to the prem ise on which the Randall-Wilkins model is based. These two conclusions cont radict also the assertions of Lewandowski and McKeever that QE and fast ret rapping are not self-consistent conditions and that the apparent dominance of first-order TL kinetics in nature is due solely to the predominance of r ecombination over retrapping. (iii) QE depends critically on the product of the trap concentration and the cross section. A new criterion for the vali dity of the QE assumption is derived, according to which Sigma(i) N(i)sigma (i) should be greater than 10(-1) m(-1), where N-i and sigma(i) are the con centration and the cross section of the traps at the active and deeper leve ls in a system exhibiting multiple glow peaks. (iv) Evidence from studies o f point defects in insulating and semiconducting materials shows that the N and sigma values of the defect centres concerned are high enough to satisf y the QE condition. It is thus inferred that the use of the analytical expr essions based on the QE approximation for analysing the glow curves of the common TL phosphors is legitimate.