Coupled eigenmode theory applied to thick mask modeling of TM polarized imaging

Coupled eigenmode (CEM) theory for TM polarized illumination is presented and applied to the 3D modeling of a line-space reticle. In this approach, the electric and magnetic field inside a line-space reticle is described in terms of an orthogonal set of eigenmodes of Maxwell's equations. The diffraction of light by the reticle can then be expressed as a coherent sum of diffraction orders produced by each eigenmode independently. Fresnel transmission, overlap of eigenmodes with diffraction orders and propagation through the mask are shown to be the interactions that determine the complex amplitude of the diffraction orders produced by each mode. We further shown that only a small number of eigenmodes are needed to accurately calculate image contrast under TM polarized illumination.