Low temperature delayed recombination and trap tunneling

Delayed recombination of charge carriers at an activator is a significant problem for fast scintillators and is usually associated with thermal effects. However, experimental results have shown that this phenomenon can occur even at the lowest temperatures. We here provide evidence in support of the idea that this is due to quantum tunneling between activator and nearby traps, and provide analytic estimates relating the energy levels and locations of those traps to the observed delayed recombination. Several calculations are devoted to showing that deviations from the simplest estimates in fact do not occur. Moreover, these estimates are consistent with lower dimensional numerical calculations for a physically significant range of trap distances. In two examples involving the activator Pr, the formulas developed are used to give the locations of traps based on likely values of trap energy depth.