Massively parallel algorithms for scattering in optical lithography

• Published in: IEEE transactions on computer-aided design of integrated circuits and systems 1991-09, Vol.10 (9), p.1091-1100
• Main Authors: Guerrieri, R., Tadros, K.H., Gamelin, J., Neureuther, A.R.
• Format: Article
• Language: English
• Subjects: Applied sciences; Electromagnetic propagation; Electromagnetic scattering; Electronics; Exact sciences and technology; Finite difference methods; Lithography; Optical propagation; Optical scattering; Parallel algorithms; Semiconductor electronics. Microelectronics. Optoelectronics. Solid state devices; Surfaces; Testing; Time domain analysis
• ISSN: 0278-0070; 1937-4151
• DOI: 10.1109/43.85755

A novel massively parallel technique for rigorous simulation of topography scattering in optical lithography has been developed and tested. The method is equivalent to the time-domain finite-difference method (TDFDM) used in electromagnetic scattering simulations, but exploits the parallel nature of wave propagation and the power of recent massively parallel architectures such as the Connection Machine. A working code called TEMPEST has been implemented on a Connection Machine CM-2 having 1 to 32 K processors with up to 1 M virtual processors. Numerical accuracy comparable with that of other fully rigorous methods was achieved. A very significant finding was that the solution required constant time per iteration for problems ranging from a few thousand unknowns up to one million, provided the ratio between the problem size and the number of processors is kept constant. The suitability of TEMPEST for solving a large class of topography structures important in alignment, metrology, and lithography is illustrated by examples.< >