Range Distribution Theory Based on Energy Distribution of Implanted Ions

Abstract

This paper presents a new analysis concerning the range distribution of implanted ions in amorphous substrates. In this analysis, energy distributions of an ion are calculated at steps of collisions in the substrate to determine the range distribution, instead of solving integral equations for the moments of the range which is essential in the theory of Lindhard, Scharff, and Schiott. The validity of this analysis is shown for both single‐ and multiple‐element substrates by assuming a screening function proportional to 1/r and by comparing with the theory of Lindhard et al. The range distribution for the case of multiple‐layer substrates, which cannot be calculated by usual theories, is also considered. The special features obtained for this case are (i) there can be discontinuities in ion concentration at the boundaries of the layers and (ii) for even the same dose, the maximum ion concentration can become higher by depositing an appropriate surface layer on a substrate.