Single spherical mirror optic for extreme ultraviolet lithography enabled by inverse lithography technology

Abstract

Traditionally, aberration correction in extreme ultraviolet (EUV) projection optics requires the use of multiple lossy mirrors, which results in prohibitively high source power requirements. We analyze a single spherical mirror projection optical system where aberration correction is built into the mask itself, through Inverse Lithography Technology (ILT). By having fewer mirrors, this would reduce the power requirements for EUV lithography. We model a single spherical mirror system with orders of magnitude more spherical aberration than would ever be tolerated in a traditional multiple mirror system. By using ILT, (implemented by an adjoint-based gradient descent optimization algorithm), we design photomasks that successfully print test patterns, in spite of these enormous aberrations. This mathematical method was tested with a 6 plane wave illumination source. Nonetheless, it would have poor power throughput from a totally incoherent source.

Diffractive Spectral-Splitting Optical Element Designed by Adjoint-Based Electromagnetic Optimization and Fabricated by Femtosecond 3D Direct Laser Writing

“…In this section, we show that the adjoint method in electromagnetics can reduce the cost of the gradient calculation to just two simulations per iteration; we call these the forward and adjoint simulations, as shown in Figure a. These methods have been successful in designing electromagnetic structures of various types. − Similarly to Scranton et al, we specifically analyze the case of optical diffraction to the far field (distance much greater than a wavelength). A more general treatment of the adjoint method for the optimization of electromagnetic structures can be found in refs and .…”

“…These methods have been successful in designing electromagnetic structures of various types. 16−20 Similarly to Scranton et al, 18 we specifically analyze the case of optical diffraction to the far field (distance much greater than a wavelength). A more general treatment of the adjoint method for the optimization of electromagnetic structures can be found in refs 16 and 17.…”

Efficient inverse design of large-area metasurfaces for incoherent light

“…We also find that the angular dependence of optimizing average performance can be very different from optimizing the worst-angle performance as in some earlier concentrator work, 2,3 except for very large angular ranges (> 40 • ). Although previous designs sampled only 6-20 angles, [2][3][4] we find that simulations for ∼ 10 3 angles would be required to obtain an accurate brute-force average over ±20 • , corresponding to a three-order-of-magnitude speedup for our reciprocal approach. (Even larger speedups will occur in 3D, where two incident angles must be considered in general.)…”

Efficient Inverse Design of Large-Area Metasurfaces for Incoherent Light

“…(Even larger speedups will occur in 3D, where two incident angles must be considered in general.) We believe that this technique will be crucial to developing metasurfaces and photomasks for incoherent-light applications ranging from lithography 4 to bioluminescence sensing (as discussed in section 5).…”

“…We also find that the angular dependence of optimizing average performance can be very different from optimizing the worst-angle performance as in some earlier concentrator work, , except for very large angular ranges (>40°). Although previous designs sampled only 6–20 angles, − we find that simulations for ∼10 3 angles would be required to obtain an accurate brute-force average over ±20°, corresponding to a three-order-of-magnitude speedup for our reciprocal approach. (Even larger speedups will occur in 3D, where two incident angles must be considered in general.)…”