Coupled eigenmode theory applied to thick mask modeling

Gary Allen; Paul Davids

doi:10.1117/12.729019

15 May 2007 Coupled eigenmode theory applied to thick mask modeling

Gary Allen, Paul Davids

Proceedings Volume 6607, Photomask and Next-Generation Lithography Mask Technology XIV; 660730 (2007) https://doi.org/10.1117/12.729019
Event: Photomask and Next-Generation Lithography Mask Technology XIV, 2007, Yokohama, Japan

Abstract

Coupled eigenmode (CEM) theory is presented and applied to the 3D modeling of a line-space reticle. In this approach, the electric 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. CEM is then applied to the cases of a binary mask and an att-PSM under dipole illumination. It is shown that the behavior of contrast with pitch and mask bias is primarily affected by the propagation loss of the eigenmodes, which increases for smaller trench widths. In the case of the binary mask, this attenuation causes one eigenmode to become dominant and the resultant image approaches the perfect imaging of a single eigenmode. In the case of att-PSM, this attenuation causes a detuning of the transmission and phase, and thus, the image contrast is degraded.

Citation Download Citation

Gary Allen and Paul Davids "Coupled eigenmode theory applied to thick mask modeling", Proc. SPIE 6607, Photomask and Next-Generation Lithography Mask Technology XIV, 660730 (15 May 2007); https://doi.org/10.1117/12.729019

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