Algorithms for simulation of three-dimensional etching

A three-dimensional optical lithography simulator has been developed based on a new ray-string algorithm for dissolution etch-front advancement. In developing the new algorithm, performance studies of cell, string and ray algorithms were carried out in two dimensions. A key finding was that a recursive ray method for the calculation of the surface-advancement vector produced numerically stable and highly accurate results. The optimum algorithm was found to be one that combines the recursive-ray method with the string approach, in which etch-rate-dependent rays are used to advance the points, segments and triangles which make up the etching boundary. This algorithm has been implemented in 3-D in the C programming language, using a linked-list data structure to represent the etching boundary mesh. Recursive time-step selection, mesh modification, and clipping and delooping of the etch boundary surface have been implemented. The 3-D ray-string etch simulator has been coupled to 2-D imaging and 3-D resist-exposure simulators to form SAMPLE-3D, a complete fast and accurate 3-D photolithography simulator. The complete simulator has been used to investigate various issues in 3-D lithographic pattern transfer.>