Empirical cluster modeling revisited

Impurities being present in a semiconductor in high concentrations may form agglomerates. Agglomeration usually demobilizes the impurities and, in case of dopants, also renders them electrically inactive. A standard approach in continuum process simulation assumes the formation of energetically favorable small clusters of size m. High numbers of m are used to mimic an often desired saturation of the concentration of unclustered impurity atoms with increasing total concentration. However, for systems far from equilibrium, potentiated high concentrations may lead to numerical problems. In this work, an alternative formulation is presented which features a saturation of the unclustered impurity concentration while introducing only one equation derived from Waite's theory of diffusion-limited reactions.