PNNL

Abstract

The path from trace doping to solid solution formation involves an intermediate regime in which the doping level is a few to several atomic percent. In this regime, dopant-dopant interactions, which are driven by the spatial arrangement of dopants, are critical factors in determining the resulting properties. Conventional wisdom counts on simple probabilistic methods for predicting dopant distributions. Here, we use Monte Carlo simulations to show that widely used, straightforward statistical models, such as that of Behringer1, are accurate only in the limit of infinitesimally small surface–to-volume ratio. For epitaxial films and nanoparticles, where much of the current interest resides, dopant distributions depend strongly on the surface-to-volume ratio. We present empirical expressions that accurately predict dopant bonding configurations as a function of film or particle size, shape and dopant concentration for doped ZnO, a material of particular interest in semiconductor spintronics.