Two-and three-dimensional analytical solutions for post-anneal implant profiles through arbitrary mask edges

To fill the need for the description of ion-implanted doping profiles for realistic mask edges after annealing or diffusion steps, an analytical solution to the post-anneal implant profile in two and three dimensions for an arbitrary mask edge profile is given here. The technique is applied first to large-area boron implant in Si. The second example is an implant through an ideal 2-µm step window with vertical walls, and the third an implant through a realistic representation of an ion-milled window in SiO
2
. Experimental data for the latter case, derived from SEM analysis of cleaved and selectively etched structures, are also presented. Examples given show that the analytical solution is easily applied to any given implant/anneal conditions in two and three dimensions, and may thus be used as a simple tool for studying the effect of implant, mask, and annealing conditions on the doping profiles of submicrometer structures.