(image) (image) [ Home ]

Emulation and Simulation of
Microelectronic Fabrication Processes

2.5 Summary

In this chapter, the continuum modelling approach for the description of wafer materials was found to be the most appropriate for the requirements of the developed simulator.

Different numerical representations for continuous materials were introduced and their relative advantages discussed. The sparse-field level set method was deemed appropriate for the description of material interfaces, due to its minimal memory requirements and the ability to extract geometric properties such as the surface normal and the curvature straight-forwardly. Additionally, Boolean Operations can be carried out with optimal efficiency, requiring every defined grid point to only be visited once. For the representation of multiple materials, the layer wrapping scheme was found to be the most appropriate to minimise numerical errors.

Volume-based material descriptions were reviewed and parallels between the level set method and cell-based methods were highlighted. A surface described by the LS can straight-forwardly be converted to cell-based filling fractions. However, due to the latter not storing enough information to generate surface normals, a conversion back to a level set is not possible unambiguously.

Next, the modelling of material evolution was discussed and the level set was deemed the most appropriate for the description of semiconductor fabrication processes. The merger and separation of level set surfaces leads to appropriate results without further considerations, as self-intersections are avoided entirely. Different numerical schemes for level set advection were presented, including the Stencil Local Lax-Friedrichs scheme for the robust advection of non-convex velocity fields. This numerical advection scheme was developed during the course of this work for strongly normal vector dependent material evolution, as encountered during anisotropic wet etching of silicon described in Section 5.1.3.

Next, geometric level set advection was presented and the underlying algorithm, which was developed wihtin the scope of this work, discussed in detail. In this work, for the first time, this efficient modelling approach for material evolution was applied to the level set method. The developed computationally efficient and robust algorithm was presented and limitations shown. It was found that the algorithm is the most appropriate for process emulation, were the geometric outcome of a processing step is known in advance, since it decreases computation time significantly when compared to iterative level set advection.

Finally, the general approach to volume-dependent modelling in the implemented simulator was discussed. A sparse cell-based volume data structure, defined on the same grid as the level set, was developed to achieve compatibility with the surface description. The volume description can then be used to model physical processes deep within materials and it can be combined seamlessly with the level set method to move material interfaces accordingly.