Decay of Phosphorescence from a Distribution of Trapping Levels

Abstract

In a previous paper it was shown that the usual model for second-order decay predicted the correct form for the decay in many thermoluminescent crystals but gave the wrong behavior for the parameters involved. Specifically, it was shown that $b$ and $m$ in the decay expression, $I=I_0{\left[\frac{b}{\mathrm{}(b+t)\mathrm{}}\right]}^m$, should behave differently as functions of the decay temperature and the degree of trap filling than is observed experimentally at temperatures near or below the glow peak. In the present paper it is shown that the discrepancies can be accounted for by assuming a first-order decay from a distribution of trapping levels. Most of the results are based on a Gaussian distribution but it is shown that other distributions can produce similar results. The first-order mechanism is justified by considering the relative magnitudes of the rate constants for trap emptying, retrapping, and recombination. At temperatures well above the glow peak this assumption is no longer justified, but in this range the second-order decay predicts the observed results for $b$ and $m$. The effects of retrapping and of crystal dimensions are considered. Also, the effect on the glow peak of having a distribution of levels rather than a set of discrete levels is worked out and it is shown that the peak is broadened appreciably even for relatively narrow distributions.