SBIR-STTR Award

We propose to develop fast wavelet and adapted wave form methods for the solution of non-linear hyperbolic and elliptic partial differential equations. A generic example employed will be the PDES that arise in modeling and simulation of micro device fabrication. Current simulations of the various steps of microchip building involve large scale computations time. Wavelet and multiresolution tools are expected to be capable of accelerating some of these computations. We propose to adapt these methods to the fast computation of the optical profiles to be used as boundary conditions for the various PDES involved in the photo lithography process. These include computational solutions of nonlinear Maxwell equations as well as reaction diffusion systems of equations. We expect that they will be handled more efficiently by appropriate wavelet tools. We have currently formed a team of the top experts in the USA in these related areas, in collaboration with top industrial research institutions including IBM, AMD and others. The methods to be developed are expected to assist US industry and DoD labs. In particular the specific PDES considered will aid in the fabrication of 256 Mb DRAM technology.Anticipated

Benefits:
Fast algorithmic methodologies will enable us to reduce substantially the development time for micro device fabrication, by allowing the manufacturer to interactively adjust his process to enhance Line Shape (LS) and Critical Dimension (CD) control of micro fabrications. More generally, the wavelet based numerical tools developed for this purpose will have a broad range of applicability for large scale computation in partial differential equations and simulations of similar industrial processes of interest to DoD.

During Phase I we have identified and investigated the major hurdles for the fast numerical solvability of the nonlinear oscillatory Maxwell equations that arise in modelling and simulation of micro device fabrication. We have developed (see Report Phase I) Fast Algorithmic methodologies that will, in Phase II, enable us to reduce substantially the development time for the micro device fabrication process. We have currently formed a team of the top experts in the USA in these related areas, in collaboration with top industrial research institutions including IBM, AMD and others (see enclosed letters) The coupling of our new algorithms together with advanced spectral element and wavelet tools for this solution of partial differential equations will provide simulation tools running on desktop workstations that will enable device designers to simulate both the manufacturing process and the performance of the manufactured product. The methods to be developed are expected to assist US industry and DOD labs. In particular the specific PDEs considered will aid in the fabrication of 256 MB Dram technology.