Sublinear dose dependence of thermoluminescence and optically stimulated luminescence prior to the approach to saturation level

In the use of thermoluminescence (TL) and optically stimulated luminescence (OSL) for dosimetry and for geological and archaeological dating, the nature of the dose dependence of the luminescence signal is of great importance. Non-linear dependence has been shown to result either from non-linear filling of the relevant traps or recombination centers during excitation, or by a combined effect of the linear filling of traps and centers due to processes taking place during the read-out stage. Sublinearity, which had been found in several materials, was usually attributed to saturation effects during excitation of either the relevant traps or centers. Sometimes, the competition effects during the excitation between traps result in superlinearity of some TL peaks and sublinearity of others. In the present work, we show that sublinear dose dependence may take place even in the simplest possible case of one trap-one recombination center (OTOR), even when the traps and centers are far from saturation. Analytical derivations as well as simulations consisting of the numerical solution of the relevant sets of coupled differential equations show the occurrence of the sublinear dose dependence under these circumstances. The filling of the traps is shown to behave like D^1/2 where D is the excitation dose, for an appropriate choice of the trapping parameters. This, in turn, may result in a similar dose dependence of the TL and OSL signals.