Adaptive Meshing Enhances ATHENA Capabilities

Chih Chuan Lin (University of Florida), C.M. Li, D. Lauderback, T. Crandle

 

Version 3.0 of ATHENA will incorporate the results of recent research in the area of adaptive meshing [1]. The new capabilities in ATHENA represent a breakthrough in the usability of the most widely used process simulation tool for both silicon and advanced materials technologies.

Adaptive meshing frees the user of ATHENA from what is arguably the most painstaking aspect of process simulation, namely, mesh specification. With the adaptive meshing module of ATHENA, the simulation begins with an automatically determined base mesh that is refined based on a user controlled error criterion. Thus users can easily run quick simulations with higher error criteria or they can increase the accuracy at the expense of computational speed. The adaptive meshing algorithm, however, generally requires less mesh throughout the simulation since at any given point in the simulation, the mesh that is present is located only where accuracy is needed at that time.

The adaptive meshing capability is tightly coupled with the discretization technique used in ATHENA, (described in a previous issue of the Simulation Standard [2]) that allows accurate simulation with relatively coarse grids. The adaptive meshing capability automatically exploits this discretization technique to produce the optimum combination of grid density for a particular problem.

Figure 1 illustrates the adaptive meshing as applied to a trench structure formed using Elite, implanted and then diffused. The initial structure uses a very coarse base mesh. Following trench formation, the mesh around the surface of the trench has been adapted to accurately represent the etch shape. Implantation results in an enhanced grid in the area of the implant. Subsequent diffusion causes the mesh to relax in the area of the original implant and to move outward, accurately resolving the diffusion front as it widens.

 

Figure 1. A trench structrue that has been adapitely
meshed following implant at 20 degrees tilt angle.

 

 

Figures 2 through 4 illustrate a process simulation sequence that uses the adaptive meshing module to define all of the mesh used for the simulation.

Figure 2 shows a simple MOS structure with a coarse base mesh that has been adapted to resolve the LDD implant in one-dimensional calculation mode.

 

Figure 2. Simple MOS structure with
intial regrid at LDD implant.

 

 

Figure 3 illustrates the refinement of the mesh to accurately represent the source/drain implant. The grid is automatically enhanced to resolve the implant profile in the critical area around the source and drain in both the horizontal and vertical directions.

 

Figure 3. Structure following source/drain
implant and regridding.

 

Figure 4 shows the structure following diffusion. As the impurity distribution changes, the mesh anticipates the advancing diffusion front and captures the full detail of the profile evolution with a minimum of grid.

 

 

Figure 4. Structure following diffusion
and concurretn grid adaption.

 

Acknowledgment

The authors would like to thank Professor Mark Law for many helpful discussions.

 

References

[1] C.C. Lin, M.E. Law, and R.E. Lowther, "Automatic Grid Refinement of Higher Order Flux Discretizations of Diffusion Modeling", IEEE Trans. CAD, Vol. CAD-4, No. 12, p. 436, August 1993.

[2] R.E. Lowther, "New Flux Discretization Technique Enhances SSUPREM4 Efficiency", Simulation Standard, Vol 3, No. 4, September 1992.