**Publications**(27)

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^{1-5}It has been shown that intensive optimization of the fundamental degrees of freedom in the optical system allows for the creation of non-intuitive solutions in both the mask and the source, which leads to improved lithographic performance. These efforts have driven the need for improved controllability in illumination

^{5-7}and have pushed the required optimization performance of mask design.

^{8, 9 }This paper will present recent experimental evidence of the performance advantage gained by intensive optimization, and enabling technologies like pixelated illumination. Controllable pixelated illumination opens up new regimes in control of proximity effects,

^{1, 6, 7}and we will show corresponding examples of improved through-pitch performance in 22nm Resolution Enhancement Technique (RET). Simulation results will back-up the experimental results and detail the ability of SMO to drive exposure-count reduction, as well as a reduction in process variation due to critical factors such as Line Edge Roughness (LER), Mask Error Enhancement Factor (MEEF), and the Electromagnetic Field (EMF) effect. The benefits of running intensive optimization with both source and mask variables jointly has been previously discussed.

^{1-3}This paper will build on these results by demonstrating large-scale jointly-optimized source/mask solutions and their impact on design-rule enumerated designs.

*Publisher's Note: The author listing for this paper has been updated to include Carsten Russ. The PDF has been updated to reflect this change.*

_{2}O as the immersion medium, non-evanescent propagation and optical design margins limit achievable pitch to approximately 0.53λ/

*n*H

_{2}O = 0.37λ. Non-evanescent images are constrained only by the comparatively large resist indices (typically1.7) to a pitch resolution of 0.5/

*n*resist (typically 0.29). Near-field patterning can potentially exploit evanescent waves and thus achieve higher spatial resolutions. Customized near-field images can be achieved through the modulation of an incoming wavefront by what is essentially an in-situ hologram that has been formed in an upper layer during an initial patterned exposure. Contrast Enhancement Layer (CEL) techniques and Talbot near-field interferometry can be considered special cases of this approach. Since the technique relies on near-field interference effects to produce the required pattern on the resist, the shape of the grating and the design of the film stack play a significant role on the outcome. As a result, it is necessary to resort to full diffraction computations to properly simulate and optimize this process. The next logical advance for this technology is to systematically design the hologram and the incident wavefront which is generated from a reduction mask. This task is naturally posed as an optimization problem, where the goal is to find the set of geometric and incident wavefront parameters that yields the closest fit to a desired pattern in the resist. As the pattern becomes more complex, the number of design parameters grows, and the computational problem becomes intractable (particularly in three-dimensions) without the use of advanced numerical techniques. To treat this problem effectively, specialized numerical methods have been developed. First, gradient-based optimization techniques are used to accelerate convergence to an optimal design. To compute derivatives of the parameters, an adjoint-based method was developed. Using the adjoint technique, only two electromagnetic problems need to be solved per iteration to evaluate the cost function and all the components of the gradient vector, independent of the number of parameters in the design.

_{2}lens elements, which gives rise to intrinsic birefringence at the ppm level. Polarization ray tracing must then contend with the phenomenon of double refraction, wherein a given ray splits into two rays each time it passes through an element, giving rise in principle to an exponentially extended family of rays in the exit pupil. However, we show that it is possible to merge each coherent family of rays into a single plane-wave component of the image. (This is joint work with colleagues at Carl Zeiss SMT.

^{1}) Generalizing beyond the analysis of birefringence, such a plane-wave component can be identified with the particular subset of rays that are converged through a common pupil point and transferred to the image after diffracting from the object points within an isoplanatic patch. Thin-film amplitude transfer coefficients implicitly take into account the prismatic change in beam-width that occurs when such a ray bundle refracts through a lens surface, but these coefficients do not include the focusing effect arising from power in the surfaces; hence polarization ray-tracing by sequential application of thin-film transfer coefficients does not by itself provide the correct amplitude distribution over the pupil.

^{2}can in many cases be considered to decrease roughly as approximately (A*S)

^{0.5}, with the 0.5 exponent representing typical microdisplay operating in a regime that is neither purely brightness-limited nor purely power-limited. Polarization modulation entails a modified scaling approximately (A*S/2)

^{0.5}; color sequential operation, approximately (1/3)*(A*S)

^{0.5}; spatially divided single-light-valve RGB projection, approximately (A*S/3)

^{0.5}. Projection lenses for three-light-valve system must provide an increased working distance to accommodate a color recombiner. Zoom lens are often required in front projectors, and rear projection usually entails a short lens-to-screen distance. It has become cost-effective to use plastic aspherical elements to meet these requirements. Periodic strip-PBS arrays have been widely adopted for polarization recycling, but aperiodic homogenizers are sometimes used to correct the uneven magnification and symmetry limitations of conic reflectors. Bright-state and dark-state beams must occupy distinct etendues in the half space above a reflective light valve, creating a vulnerability to crosstalk. Crosstalk from a polarizing beamsplitter gives rise to a residual background intensity approximately 0.3*NA

^{2}, unless a quarterwave corrector is used. Crosstalk can also arise from stress birefringence in prism substrates. Stray light makes an indirect contribution to background, but can sometimes be corrected by filtering.

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