Mesh generation and adaption for solving dopant diffusion in process simulation is a difficult task, complicated by both the moving boundaries of oxide growth and the time dependence of the solutions. For both computational and ease of use reasons, automatic mesh generation and discretization error control is desirable. This paper describes an approach based on local error estimates to refine the mesh. The results presented in this paper extend our previous work to two-dimensional problems. The implementation of this approach is done in a process simulator, the Florida Object-Oriented Process Simulator. Several test cases are described to demonstrate the effectiveness of the algorithms.

During simulation of silicidation and oxidation, some layers are consumed (poly, silicon) and other layers grow (oxide, silicide). During these growth processes, grid must be added behind the advancing interface and removed in front of it. In a full integrated circuit process simulator, this has to be performed simultaneously with the transient solution of the diffusion equations for silicon dopants. This paper describes an approach of local adaption that leaves unchanged most of the grid. Robust algorithms are described for handling adaption in two-dimensional process simulation. Examples for etching, deposition, and oxidation are described.>

This work describes the Semiconductor Wafer Representation (SWR) for representing and manipulating wafer state during process and device simulation. The goal of the SWR is to provide an object-oriented interface to a collection of functions designed for developing and integrating Technology CAD (TCAD) applications. By providing functions which can be common across many applications, we aim to greatly reduce tool development and integration time. Corporate, vendor, and university TCAD developers have worked together under the auspices of the CAD Framework Initiative to create an architecture and C++ programming interface for an SWR 1.0 draft standard. Here we describe this architecture and the results of creating and using a prototype implementation of the standard both to integrate existing TCAD tools and to develop simple new tools.>

C++ and object-oriented programming techniques are becoming popular for their modularity, ease of use, and simplicity to maintain and enhance. This paper describes an approach used for device simulation. The object library and organization are described. Specific areas of modularity and enhancement are illustrated in both the areas of physical models and mathematics. Comparisons of both performance and ease of enhancement are made to PISCES-II.>

The authors point out that modern numerical process simulators are becoming increasingly complicated in both physical models and domain shape. Grid generation is difficult for these simulators because of the inherently transient nature of the problems being solved. Here, adaptive grid refinement is considered for use in solving diffusion problems. Higher order approximations to the discretized diffusion flux are also studied. Several methods of both adaptive grid refinement and discretization are investigated and compared in terms of CPU time and final discretization error. All the methods are directly applied to the one-dimensional version of SUPREM-IV.>

The implementation of an improved small-signal AC simulation capability in the general-purpose device simulator PISCES-IIB is described. The preconditioned generalized conjugate residual (GCR) algorithm has been implemented, which allows AC simulations to be performed up to any frequency without convergence problems, although at great computational expense. The current implementation of PISCES-IIB uses the block successive overrelaxation algorithm for AC simulations. This algorithm fails at high frequencies, thus making it impossible to determine accurately the cutoff frequency and switching speed of high-frequency devices. The preconditioned GCR algorithm has been implemented using two different preconditioners. A comparison of the three methods shows that they are most efficient at different frequency ranges, allowing programming of an automatic switching algorithm that chooses the most efficient simulation method.>

Point-defect kinetics is important for understanding and modeling dopant diffusion in silicon. The author describes models for point-defect transport and recombination used in SUPREM-IV, and does extensive fitting for the model parameters. The experimental data used are from experiments on oxidation-enhanced diffusion. Interstitial traps are shown to be critical for consistent agreement with experiment data. Point-defect parameters in lightly doped regions are extracted and fit to Arrhenius expressions.>

Two-dimensional process modeling has been complicated by the increasing complexity of the physical models needed to characterize modern processes. Present physical models for diffusion favor modeling of both the vacancies and interstitials as well as the dopant impurities. these vacancies and interstitials are important in two dimensions since the lateral characteristic lengths are on the order of a few microns, which is comparable to device dimensions. Hence, full two-dimensional solutions of the point defect equations are required to accurately model two-dimensional diffusion. Since the defects diffuse many order of magnitude faster than the impurities, the problem of solving the coupled equations is numerically stiff and the numerical techniques become critical. The numerical methods in SUPREM-IV are described. Since the numerical solutions are time consuming, suitable analytic solutions are considered as an alternative. These analytic solutions are compared to the numerical results to test the limits of the assumptions used in the analytic formulation. The comparison forces the conclusion that analytic solutions are of limited use in prediction of point defect profilesin two dimensions.>