TWCHDIMEMSICNRL MODELING CF ICN IMPIftNEftTICN

We present a two-dimensional model of ion implantation which accounts for position dependent lateral moments. The lateral standard deviation and the lateral kurtosis as a function of depth have been calculated by two-dimensional Monte Carlo simulations for boron, phosphorus, arsenic and antimony in silicon for energies in the range of 10 to 300 keV. The lateral moments as a function of depth and energy as well as the vertical moments as a function of energy have been fitted by simple formulae. We specify a modification of the Gaussian distribution function in order to include the lateral kurtosis with an analytical expression. 1. INTRODUCTICN For the purpose of describing ion implantation profiles, methods based on distribution functions together with spatial moments are now being used for more than 20 years. The principle of these methods is to assume a functional type for the distribution function and to calculate its free parameters from its spatial mcments. These moments may be obtained either by experiment or by theory. For a long time only the first two mcments, i.e. the mean projected range and the projected range straggling (the standard deviation), could be specified [1], and so the only reasonable distribution function was the Gaussian function. Although this oldest model is still freqently used for sake of simplicity or for lack of higher mcments, it is well established today, that for a realistic description of one-dimensional profiles 4 moments must be taken into account [2]. For this purpose the Pearson IV distribution is commonly used, which was introduced By Hofker in 1975 [3]. The first model including lateral spread was presented by Furukawa in 1972 [4]. It is based > on the statistical distribution function for one ion, i.e. the response to a