The effect of crystal size on tunneling phenomena in luminescent nanodosimetric materials

The study of luminescence signals from nanodosimetric materials is an active research area, due to the many possible practical applications of such materials. In several of these materials it has been shown that quantum tunneling is a dominant mechanism for recombination processes associated with luminescence phenomena. This paper examines the effect of crystal size on quantum tunneling phenomena in nanocrystals, based on the assumption of a random distribution of electrons and positive ions. The behavior of such random distributions is determined by three characteristic lengths: the radius of the crystal R, the tunneling length a, and the initial average distance 〈d〉 between electrons and positive ions (which is directly related to the density of charges in the material). Two different cases are examined, depending on the relative concentrations of electrons and ions. In the first case the concentration of electrons is assumed to be much smaller than the concentration of positive ions. Examination of a previously derived analytical equation demonstrates two different types of crystal size effects. When the tunneling length a is much smaller than both R and 〈d〉, the analytical equations show that smaller crystals exhibit a faster tunneling recombination rate. However, when the tunneling length a is of the same order of magnitude as both R and 〈d〉, the opposite effect is observed, with smaller crystals exhibiting a slower tunneling recombination rate. As the crystal size increases, the rate of tunneling in both cases reaches the limit expected for bulk materials. In the second case we examine the situation where the concentrations of electrons and positive ions are equal at all times. In this situation there is no analytical equation available to describe the process, and the crystal size effects are simulated by using Monte Carlo (MC) techniques. The two opposite behaviors as a function of the crystal size are also observed in these MC simulations. The effect of sample temperature is also studied by extending the MC simulations to include thermal characteristics of the defects. The relevance of the simulated results for luminescence dosimetry is discussed.