The primary focus of this work is on two-dimensional simulation of ion implantation and diffusion in nonplanar, and due to oxidation, time-variant structures with special attention on high flexibility in physical models and easy model implementation. The latter has been addressed already in the initial version of PROMIS (PROcess Modeling in Semiconductors) [Pic85b], though just for planar structures and with more restrictions in the model equations. Simulation of ion implantation into arbitrary two-dimensional structures has been possible in PROMIS by the Monte Carlo method [Hob88a].
For analytical simulation of ion implantation a convolution method is used. Angled implants and irregular geometries, including undercuts, are allowed. The geometry is cut into thin slices parallel to the incident ion beam, for each slice a one-dimensional profile is calculated using the numerical range scaling technique. The two-dimensional profile is calculated by a convolution perpendicular to the incident ion beam using a lateral distribution function to account for the the lateral scattering effects.
We simulate diffusion on the macroscopic level of transport and continuity equations. A transformation method is used to solve the model equations in nonplanar structures. The nonplanar time-variant physical domain is mapped onto a stationary rectangle, where the solution of the differential equations is sought.
This work is structured as follows: In Chapter 2 we describe the Analytical Ion Implantation Module of PROMIS. We survey physically based simulation techniques which may provide parameter values for our analytical models. We give an overview of vertical and lateral distribution functions which are the basis for two-dimensional profiles. We explain the implementation details for treating arbitrary structures and the generation of the spatial grid to resolve the profiles sufficiently accurate. In the applications we point out the limitations of the analytical approach by comparing its results to Monte Carlo simulations. Additionally we study the feasibility of knock-in implantation for the production of ultra shallow profiles.
The major part of the work is devoted the Diffusion Module of PROMIS. Chapter 3 discusses the modeling of diffusion in silicon and the numerical solution of the model equations. We commence with a review of physical models we have implemented. For the numerical solution a transformation method is applied, motivated by its computational efficiency and good experience with grid adaption using rectangular grids. For coupling the transformation method to an adaptive grid scheme a reference mapping strategy is introduced. The curvilinear coordinate system, which establishes the transformation, is obtained by algebraic, elliptic, or variational methods. The transformed form of the physical equations in the curvilinear coordinates is got from box integration. The transformed equations are discretized using finite differences, including upwind spatial differencing, and the resulting system of nonlinear algebraic equations is solved by a damped Newton method. In the applications we use the implemented physical models to simulate a trench isolation for a twin-tub process, a p-channel transistor design for a 16Mb static RAM, a field oxide isolation, and RTA-experiments.
In Chapter 4 we briefly present the models applied for the oxide growth during diffusion in oxidizing ambient and, finally, Chapter 5 suggests future activities.