(Lens) Design For (Chip) Manufacture: Lens tolerancing based on linewidth calculations in hyper-NA, immersion lithography systems

摘要

Tolerancing of lithographic imaging systems is a crucial step in the design of these lens systems. Usually a metric such as maximum RMS wavefront error is specified, and lens surface error budgets (curvature, tilt, decenter,...) are derived to ensure the specification is satisfied. Simple compensation schemes are then used to optimize "yield", that is, to maximize the chances of achieving the designed value of the RMS wavefront error. Software that performs these computations has been available to the lens design community for many years. The concept of tolerancing can be applied to other merit functions as well, but with the advent of hyper-NA, immersion systems for sub-90 nm lithography, questions arise about the efficacy of using RMS wavefront error as an accurate predictor of performance change. For example, nontrivial Jones matrices across the exit pupil give rise not only to scalar phase and transmission variations across the pupil, but also differential changes to transmission ("diattenuation") and phase ("retardance") that are not taken into account in standard wavefront error calculations, and depend upon the incident polarization. However, a merit function based on such quantities is not very useful to the lithographer on the fab floor. For the lithographer, it is desirable to build the system based on more direct metrics, such as across-chip-linewidth-variation (ACLV) or H-V bias, provided the metrics are based on fundamental properties of the imaging system, and are not excessively dependent on process specific information. We have developed software to determine manufacturing and alignment tolerances of a lens using a set of merit functions that are based on linewidth predictions. These include across-chip linewidth variation (ACLV), H-V bias, L-R bias, overlay error and telecentricity error. The calculation of these quantities includes a simple resist development model. In this paper, we will show results of a tolerancing study on a hyper-NA immersion lens that uses this software.