Theoretical predictions of the lateral spreading of implanted ions

The theoretical model and computer program (AAMPITS-3D) of Ashworth and coworkers (1985) for the calculation of three-dimensional distributions of implanted ions in multielement amorphous targets are extended to show that the lateral rest distribution is gaussian in a form with a lateral standard deviation (lateral-spread function) which is a function of depth beneath the target surface. A method is given whereby this function may be accurately determined from a knowledge of the projected range and chord range rest distribution functions. Examples of the lateral-spread function are given for boron, phosphorus and arsenic ions implanted into silicon and a detailed description is given of how the lateral-spread function may be used in conjunction with the projected range rest distribution function to provide a fully three-dimensional rest distribution of ions implanted into amorphous targets. Examples of normalised single ion isodensity contours computed from AMPITS-3D are compared with those obtained using the previous assumption of a lateral standard deviation which was independent of distance beneath the target surface.