| This thesis is concerned with methods for calculating scattered fields and aerial images in photolithography. Several improvements to the Finite-Difference Time-Domain code TEMPEST are documented and a vector formulation of optical imaging is presented. The implementation of this theory is then used to study mask effects in EUV lithography, phase defects in alternating phase shift masks and several other lithography-related applications.; The numerics of TEMPEST including the updating equations, domain excitation, convergence checking, and boundary conditions are reviewed. The Fourier Boundary Condition that operates on the Fourier components of the electromagnetic field is introduced and shown to be useful as an efficient and accurate model for the EUV multilayer mirror. An overview and performance analysis of the re-parallelization of TEMPEST for running across a Network of Workstations (NOW) is presented.; A vector model for an optical imaging system that can accommodate the highly oblique plane waves existing in high numerical aperture imaging or inspection is developed. Mathematical models for photomasks are presented and organized by their level of complexity.; A study of EUVL masks is undertaken where the effects of absorber thickness, side wall angle, corner rounding, angle of incidence and substrate defects are investigated. Key observations include a degradation of mask depth of focus due to off-axis imaging, a dependence of CD on absorber feature thickness due to interference, and the ability of a shallow mirror defect to interact strongly with a mask feature.; Phase defects in alternating phase shift masks are investigated from both printability and inspectability points-of-view. Isotropic wet etching was seen to decrease defect printability. Defects with a pre-wet-etch size larger than 200nm were seen to cause greater than 10% CD variation. In simulation studies of defect inspectability annular illumination was observed to yield stronger normalized difference signal than circular illumination.; The breadth of uses for TEMPEST in lithography is demonstrated by overviewing simulations of pinholes, alignment marks, aberration monitors, reflective notching, and two-dimensional phase shift mask topographies. |
