Generating ion implantation profiles in one and two dimensions. 1: density functions

In this, the first of two papers, the problem of constructing ion implantation profiles in one and two dimensions from depth-independent spatial moments is discussed. Comparisons are made between Pearson and Johnson curves, constructed from moments produced by a transport equation solver, and profiles obtained directly from Monte Carlo simulations. A set of such comparisons, using consistent input quantities, is performed over a range of ion-target mass ratios and energies. For projected range distributions of the ions B, P and As into a-Si, a single Johnson type (S sub(B)) describes the implants over the energy range 1 keV to 1 MeV. The description using Pearson curves requires two types (I and VI). Also, taking the Monte Carlo data as a reference, the Johnson curves are equivalent, if not superior, to the Pearson curves in terms of fit accuracy. For lateral distributions of the same ion types over the same energy range it is shown that if the depth-dependent lateral kurtosis is less than 3.0, then the Pearson type II (bounded), Johnson type S sub(B) (bounded) and the modified Gaussian (unbounded) curves prove acceptable representations. If the depth-dependent lateral kurtosis is greater than 3.0 then the Pearson type VII (unbounded) and Johnson type S sub(U) (unbounded) curves are good representations.