Massively parallel electromagnetic simulation for photolithographic applications

The two-dimensional massively parallel electromagnetic simulation program TEMPEST has been generalized to extend its applicability to many of the difficult problems in photolithography, metrology, and alignment. TEMPEST, which has been made available on the NCSA and other computing centers, combines together techniques for analysis of the transverse electric (TE) and the transverse magnetic (TM) polarizations, oblique incidence, highly dispersive materials, and a technique for synthesis of partially coherent optical images. The solution is based on the time-domain finite-difference method, but exploits the power of massively parallel computer architectures. Equations suitable for massively parallel implementation are given for oblique incidence, both polarizations and dispersive materials. Computer time per iteration cycle is constant irrespective of the polarization and angle of incidence. However, the total simulation time for convergence was found to be dominated by physical scattering phenomena. Convergence for the TM polarization is 1.5 times slower than the TE polarization because of edge currents, and oblique incidence is 2 times slower than normal incidence owing to artificial reflection from the domain boundaries. A typical simulation time is three to five minutes with 256 k (1 k=1024) simulation nodes on a CM-2 with 8 k processors. The effectiveness of the program for photolithographic applications is demonstrated by considering the effects of subtle changes in phase-shifting mask topography on the optical images