Representation of two-dimensional ion implantation rest distributions by Pearson distribution curves for silicon technology

Abstract

This is the second of two papers concerned with fitting Pearson curves to Monte Carlo simulations of implants into amorphous targets. In the first paper [ Solid-St. Electron. 35, 1151 (1992)] it was shown that accurate Pearson curve fitting to projected range profiles is possible when implant profiles are available for which optimised moments can be generated. In the present paper we extend the fitting to simulations of two-dimensional rest distributions. Comparisons are made between Pearson curve fits and the original high-resolution implant profiles, in two-dimensions, for the ions B and As implanted into amorphous silicon. The profiles were derived from Monte Carlo simulations, each of one million ion trajectories. Fit coefficients are provided that allow the regeneration of the moment surfaces for the depth and implantation energy dependent lateral straggle and lateral kurtosis for the ions B, P, As and Sb implanted, with energies in the range 25–300 keV, into targets of amorphous silicon, silicon dioxide and silicon nitride. The depth-dependent lateral distribution is then constructed using symmetrical Pearson curves driven by analytical formulae for the moment surfaces. The two-dimensional rest distribution is then reconstructed from the product of this depth-dependent lateral distribution and the projected range distribution derived in the first paper.