GENERATING ION-IMPLANTATION PROFILES IN ONE AND 2 DIMENSIONS .1. DENSITY-FUNCTIONS

In this, the first of two papers, the problem of constructing ion impl antation profiles in one and two dimensions from depth-independent spa tial moments is discussed. Comparisons are made between Pearson and Jo hnson curves, constructed from moments produced by a transport equatio n solver, and profiles obtained directly from Monte Carte simulations. A set of such comparisons, using consistent input quantities, is perf ormed over a range of ion-target mass ratios and energies. For project ed range distributions of the ions B, P and As into a-Si, a single Joh nson type (S-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 cur ves are equivalent, if not superior, to the Pearson curves in terms of fit accuracy. For lateral distributions of the same ion types over th e same energy range it is shown that if the depth-dependent lateral ku rtosis is less than 3.0, then the Pearson type II (bounded), Johnson t ype S-B (bounded) and the modified Gaussian (unbounded) curves prove a cceptable representations. If the depth-dependent lateral kurtosis is greater than 3.0 then the Pearson type VII (unbounded) and Johnson typ e S-U (unbounded) curves are good representations.