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.>

An analytical model for the description of ion-implantation-induced damage profiles is presented. The model is based on extensive Monte Carlo simulations of B-, P-, As-, and Sb-implantations in Si. One-dimensional profiles are described by a Gaussian function and an exponential function joined together continuously with continuous first derivatives. The two-dimensional model has previously been developed by the authors for dopant profiles and is demonstrated to apply well to point defect distributions. Parameters have been obtained for the four ions by fitting the model to the Monte Carlo results, and they are provided in the form of tables for the energy range of 10-300 keV (for the 1D model 1-300 keV). The Monte Carlo simulations are based on the binary collision approximation, the assumption of a random target, and the validity of the linear collision cascade theory. The importance of energy transport by recoils is pointed out.>