Birefringence issues with uniaxial crystals as last lens elements for high-index immersion lithography

Abstract

We discuss the birefringence issues associated with use of crystalline sapphire, with uniaxial crystal structure, as a last lens element for high-index 193 nm immersion lithography. Sapphire is a credible high-index lens material candidate because with appropriate orientation and TE polarization the ordinary ray exhibits the required isotropic optical properties. Also, its material properties may give it higher potential to meet the stringent optical requirements compared to the potential of the principal candidate materials, cubic-symmetry LuAG and ceramic spinel. The TE polarization restriction is required anyway for hyper-NA imaging, due to TM-polarization contrast degradation effects. Further, the high uniaxial-structure birefringence of sapphire may offer the advantage that any residual TM polarization results in a relatively-uniform flare instead of contrast degradation. One issue with this concept is that spatial-dispersion-induced effects should cause some index anisotropy of the ordinary rays, in a way similar to the intrinsic birefringence (IBR) effects in cubic crystals, except that there is no ray splitting. We present the theory of this effect for the trigonal crystal structure of sapphire and discuss its implications for lithography optics. For this material the spatial-dispersion-induced effects are characterized by eight material parameters, of which three contribute to index anisotropy of the ordinary rays. Only one gives rise to azimuthal distortions, and may present challenges for correction. To assess the consequences of using sapphire as a last element, neglecting any IBR effects, we use lithography simulations to characterize the lithographic performance for a 1.7 NA design, and compare to that for LuAG.