: Lorenz, J.; Ryssel, H.; Wierzbicki, R.J.

Abstract
This paper outlines a novel analytical model for the two-dimensional description of ion implantation. Three-dimensional distributions of implanted dopant atoms are calculated using a convolution between an advanced multilayer model for the vertical distribution and a lateral distribution which involves both a depth-dependent lateral range straggling and a depth-dependent lateral kurtosis. For implantations into amarphous materials, the parameters of the lateral model can be taken from tables calculated with the Boltzmann transport program RAMM. Extensive comparisons between results from this model and Monte Carlo simulations have been performed, showing very good agreement for the implantation of various dopants into solicon, oxide and nitride. The model for the depth-dependent lateral kurlosis is applicable for the implantation of heavy ions into silicon, and further improves the accuracy of the analytical model in the tail of the lateral dopant distribution which is important for the simulation of lateral pn-junctions.