Analytical Model for Ion Implantation Profiles

In the design of VLSI devices, accurate prediction of the doping profiles resulting from ion implantation, a standard method for doping impurities in VLSI (very-large-scale integrated circuit) processes, is essential. This is done by obtaining analytical expressions for the SIMS (secondary ion mass spectrometry) data of ion implantation profiles, and these analytical formulas are used to compile an ion implantation profile database. The profiles of arbitrary implantation conditions can be generated using interpolated parameter values. Various analytical models have been developed for expressing ion implantation profiles. The functions used to express these ion implantation profiles include Gaussian, joined half Gaussian, Pearson, and dual Pearson functions. In addition to these, a tail function was proposed. This tail function has fewer parameters than the dual Pearson function, and it is better able to specify an arbitrary profile using a unique set of parameters.

Keywords: Ion implantation, skewness, kurtosis, Gaussian, joined half Gaussian, Pearson, Pearson IV, Pearson family, dual Pearson, tail function, SIMS, database, Monte Carlo, projected range, dose, amorphous substrate, damage, differential channel dose.