Extensions of boundary layer modeling of photomask topography effects to fast-CAD using pattern matching

Abstract

In lithography for the 45nm node and beyond, phase errors introduced through electromagnetic field (EMF) effects at photomask openings are significant sources of error in calculating on-wafer images. These edge effects create distortion in both real and imaginary field transmission, which leads to a tilt in the process window, and must be addressed in mask design to avoid loss of process latitude. This study presents a new formulation for pattern matching, which allows EMF effects to be included via boundary layer modeling to facilitate extremely fast assessment of EMF impact on imaging. Boundary layers are first used to model these edge effects, by adding additional transmission features to a layout to represent the error transmissions caused by edges. Pattern matching is then used to determine susceptibly to various pre-existing perturbations, in the presence of defocus. This process can be extremely fast and hotspot detection can be run on an entire chip in hours, compared to days for aerial imaging. Correlation between pattern matching and full aerial imaging can be as high as 0.97 for coherent imaging, and ≈ 0.75 for off-axis dipole illumination. This pattern matching framework is extremely flexible and can be used for fast assessment of any series of effects which can be described as a path difference in the pupil or as a transmission on the mask.

Modeling Optical Lithography Physics

“…(Color online) Kernel convolution method with simulationgenerated kernels for estimating through-focus behavior of mask edge effects. 37)…”

“…Mask edge effects that alter the real part of the transmitted electric field change the effective width of the opening and can be corrected by a bias but effects that alter the imaginary part of the transmitted electric field tilt the through-focus behavior and degrade the process window. 28) Multilayer Mo and Si masks for extreme ultra violet (EUV) lithography at 13.5 nm use a smoothing deposition process that reduces the bump height to a few nm but spreads the bump to a diameter of about 60 nm. Michael Lam used FDTD to first carefully characterize the nearly undeflected forward scattering, the ray like tilted surface scattering in the backward direction and the resonate like effects for new waves created at various heights within the multilayer stack.…”

“…Kernel convolution is also useful for estimating the impact of EM mask edge effects. 37) Polarization dependent in phase and out of phase boundary layers are first attached to every edge of every feature in a layout. Spillover kernels for the in phase and out of phase spillover are then determined automatically through use of an image simulator.…”

Automatic numerical determination of lateral influence functions for fast-CAD

“…6 Here we summarize and revise this theory. The algorithm is based on using the point response of a single mask pixel to estimate the intensity at a specific location.…”