Monte Carlo simulation of ion implantation into two- and three-dimensional structures

Until now, rigorous Monte Carlo simulations of ion implantation into 3-D structures have been prohibited by the large amount of computer time required, and 2-D simulations have been restricted to simple structures like linear mask edges or rectangular trenches. Methods are presented which made 2-D simulations with arbitrary geometries as well as 3-D simulations with simple geometries feasible. First, an auxiliary grid is used to reduce the time required to check whether an ion crosses a boundary. Second, each ion trajectory is used several times to determine the history of ions entering the target at different positions. The methods are demonstrated by three examples: implantation into a rectangular trench, implantation into a 2-D trench with nonplanar sidewalls, and implantation into a 3-D trench with quadratic cross section