COMPUTER simulation of integrated circuit fabrication is an invaluable aid in the design of modern integrated circuit devices. Shrinking ULSI geometries have resulted in increasingly nonplanar structures and todays devices are far from former planar geometries. Within the scope of this work modules for the simulation of ion implantation and diffusion in nonplanar two-dimensional structures have been developed. Both modules have been incorporated in the process simulator PROMIS (PROcess Modeling In Semiconductors).
The module for the analytical simulation of ion implantation is an extension of the numerical range scaling technique to arbitrary two-dimensional structures and arbitrary ion beam tilt angles. It provides distribution functions and parameter sets for all usual silicon technologies including point defect calculations and the most common III/V-semiconductor technologies, and a plug-in interface for application specific distribution functions and parameter models.
The module for the simulation of diffusion in two-dimensional nonplanar, and due to oxidation, time-variant domains solves macroscopic transport and continuity equations. The module provides a plug-in interface for a large class of parabolic systems of nonlinear, coupled partial differential equations (PDEs) with fairly general boundary conditions. Thus it allows easy implementation of new physical models and is especially suited as a tool for the model development and prototyping. Physical models implemented and provided in a model library include models for diffusion in silicon considering field coupling, static and dynamic clustering, models for coupled point defect and dopant diffusion under oxidizing conditions, and a pair diffusion model for transient enhanced diffusion of boron.
For the numerical solution of the model equations we apply a coordinate transformation method to map the nonplanar time-variant domain to a stationary rectangle. With this approach the simulation domain is simplified at the expense of complicating the equations and boundary conditions. A reference grid strategy has been developed which is suited for transient adaptive grid methods with heavy changes in grid spacing. Transformation relations for the model equations based on box integration have been introduced in order to satisfy global conservation laws automatically.
The transformed model equations are discretized using finite differences and the resulting system of nonlinear algebraic equations is solved by a damped Newton algorithm. The module is equipped with an adaptive spatial grid and an automatic time step control.
For the calculation of the oxide growth during diffusion in oxidizing ambient analytical models for uniform and local oxidation have been implemented including orientation, pressure and chlorine dependence, and thin dry oxide growth kinetics. For other applications creeping flow equations have been solved.