Accurate placement of dopants in modern semiconductor devices is mainly performed by ion implantation. The electrical activation and the annealing of the radiation damage requires a thermal process step. The diffusion and reaction processes during this step lead to the desired effects. Additionally, a redistribution of the doping profile is caused by the diffusion.
The complex physical mechanisms during the annealing step are quantitatively determined by numerical solution of the diffusion and reaction equations. The small distances within modern devices cause a significant dependence of the bulk effects on the boundaries and interfaces. In this work a diffusion model describing the behavior of intrinsic point defects in silicon was developed, which considers precipitation effects of silicon self-interstitials. The formation of large immobile complexes of a large number of interstitial atoms limits the super-saturation of the defect density. Thus, the diffusion enhancement of dopants is limited, too. However, the duration of this enhancement is increased due to the slower dissolution of the precipitates. The combination of the point defect model and a pair diffusion model for phosphorus allows modeling of the anomalous pile-up of phosphorus near the silicon/silicon-dioxide interface during implantation-enhanced diffusion, and hence, increases the range of applicability of the pair diffusion model.
For the numerical solution of the diffusion and reaction equations the program AMIGOS ( Analytical Modeling Interface and General Object-oriented Solver) was developed. It utilizes the Finite Element Method, based on an alternatively one, two or three-dimensional discretization of the simulation domain. The program offers the opportunity of splitting up the simulation domain into several segments, each holding a different physical model. The solution quantities on different segments can be coupled by the respective boundary and interface-conditions. Thus, simulation of arbitrary structures is facilitated.
For very small devices three-dimensional simulation is necessary for correct treatment of the boundary influences. However, this requires considerable computational efforts and forces a utilization of the given resources as efficient as possible. A method for automated grid adaptation according to the occuring discretization errors was implemented. This method allows efficient control of the grid density. Additionally, the time step size is chosen according to the errors of the time discretization. Consequently, facilitates highly efficient simulations with defined accuracy.
The power of the program is demonstrated by three-dimensional applications to diffusion processes, which were computed on state-of-the-art workstations within several hours.