Quantum tunneling recombination in a system of randomly distributed trapped electrons and positive ions

During the past 10 years, quantum tunneling has been established as one of the dominant mechanisms for recombination in random distributions of electrons and positive ions, and in many dosimetric materials. Specifically quantum tunneling has been shown to be closely associated with two important effects in luminescence materials, namely long term afterglow luminescence and anomalous fading. Two of the common assumptions of quantum tunneling models based on random distributions of electrons and positive ions are: (a) An electron tunnels from a donor to the nearest acceptor, and (b) the concentration of electrons is much lower than that of positive ions at all times during the tunneling process. This paper presents theoretical studies for arbitrary relative concentrations of electrons and positive ions in the solid. Two new differential equations are derived which describe the loss of charge in the solid by tunneling, and they are solved analytically. The analytical solution compares well with the results of Monte Carlo simulations carried out in a random distribution of electrons and positive ions. Possible experimental implications of the model are discussed for tunneling phenomena in long term afterglow signals, and also for anomalous fading studies in feldspars and apatite samples.