An experimental technique for quantitatively characterizing edge effect contributions in transmission through thick photomasks is described and evaluated through electromagnetic simulation. The technique consists of comparing the 0 th order transmission for various duty cycles to the expected experimental behavior from a thin mask model. The real electric field component from the edges is proportional to the shift in the position of the minimum energy in the 0 th order field away from the expected thin mask location. The square root of the minimum 0 th order diffraction energy normalized to a clear mask gives the imaginary edge contribution. The results indicate that Alternating Phase Shifting Masks (ALT-PSM) and Attenuating Phase Shifting Masks (ATT-PSM) technologies have significant edge effects on the order of 0.1λ to 0.2λ per edge respectively, as well as polarization dependence. For periods of 2 wavelengths and larger these edge contribution values are nearly independent of pitch. The existence of an imaginary (or quadrature) phase component is shown to result in an additive linear variation of line edge shortening through focus. This tilt can be interpreted as a focus shift of the normal parabolic behavior and is about 0.5 Rayleigh units (RU). This focus shift depends to some extent on the surrounding layout as well as the feature itself.

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.

Key physical phenomena associated with resists, illumination, lenses and masks are used to show the progress in models and algorithms for modeling optical projection printing as well as current simulation challenges in managing process complexity for manufacturing. The amazing current capability and challenges for projection printing are discussed using the 22 nm device generation. A fundamental foundation for modeling resist exposure, partial coherent imaging and defect printability is given. The technology innovations of resolution enhancement and chemically amplified resist systems and their modeling challenges are overviewed. Automated chip-level applications in pattern pre-compensation and design-anticipation of residual process variations require new simulation approaches.

The variation in the printing of nominally identical contacts with electron-beam exposure is used to quantitatively determine the statistical variation in chemically amplified resists (KRS-XE with and without top coat, TOK) and non-chemically-amplified resists (PMMA and HSQ). Uniform 17×23 arrays of 24 and 32nm contacts were exposed at fixed doses with a 100keV electron beam. By looking at data observed from top view scanning electron microscopy images, a normal distribution was fitted to the fraction of contacts that printed versus dose to determine the standard deviation of the distribution relative to the dose at which 50% of the contacts printed. The top coat on KRS-XE increased contact uniformity and reduced the required dose. Quantitative analysis shows that PMMA contained as much noise as the chemically amplified resist systems, KRS-XE and TOK. Except HSQ, this normalized standard deviation ranged from 0.16 to 0.21 which is indicative that the contact hole printing process may be dominated by less than 40 events. HSQ exhibited lower standard deviation values, corresponding to over 1000 effective events.

Simulation was used to explore boundary layer models for 1D and 2D patterns that would be appropriate for fast CAD modeling of physical effects during design. FDTD simulation was used to compare rigorous thick mask modeling to a thin mask approximation (TMA). When features are large, edges can be viewed as independent and modeled as separate from one another, but for small mask features, edges experience cross-talk. For attenuating phase-shift masks, interaction distances as large as 150nm were observed. Polarization effects are important for accurate EMF models. Due to polarization effects, the edge perturbations in line ends become different compared to a perpendicular edge. For a mask designed to be real, the 90 o transmission created at edges produces an asymmetry through focus, which is also polarization dependent. Thick mask fields are calculated using TEMPEST and Panoramic Technologies software. Fields are then analyzed in the near field and on wafer CDs to examine deviations from TMA.