31 March 2014 Critical assessment of the transport of intensity equation as a phase recovery technique in optical lithography
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Proceedings Volume 9052, Optical Microlithography XXVII; 90521D (2014); doi: 10.1117/12.2048278
Event: SPIE Advanced Lithography, 2014, San Jose, California, United States
Photomasks are expected to have phase effects near edges due to their 3D topography, which can be modeled as imaginary boundary layers in thin mask simulations. We apply a modified transport of intensity (TIE) phase imaging technique to through-focus aerial images of photomasks in order to recover polarization-dependent edge effects. We use AIMS measurements with 193nm light to study the dependence of recovered phase on mask type and geometry. The TIE is an intensity conservation equation that quantitatively relates phase in the wafer plane to intensity through-focus. Here, we develop a modified version of the TIE for strongly absorbing objects, and apply it to recover wafer plane phase of attenuating masks. The projection printer blurs the fields at the wafer plane by its point spread function, hence an effective deconvolution is used to predict the boundary layers at the mask that best approximate the measured thick mask edge effects. Computation required for the inverse problem is fast and independent of mask geometry, unlike FDTD computations.
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Aamod Shanker, Martin Sczyrba, Brid Connolly, Franklin Kalk, Andy Neureuther, Laura Waller, "Critical assessment of the transport of intensity equation as a phase recovery technique in optical lithography", Proc. SPIE 9052, Optical Microlithography XXVII, 90521D (31 March 2014); doi: 10.1117/12.2048278; http://dx.doi.org/10.1117/12.2048278


Semiconducting wafers

Imaging systems

3D modeling


Phase imaging

Phase shifts


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