Aspherical Lithography Mirror Extension for Curvature-Controlled Polishing
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Solution Overview
Problem
The manufacturing of mirrors for microlithographic lithography systems is hindered by the impairment of surface quality at the edge of the target region due to high-order polynomial descriptions, leading to increased curvature and astigmatism, making accurate polishing difficult.
Innovation Solution
A mirror element with an aspherical target region and an adjoining extension region, where the edge is described by a twice continuously differentiable closed curve, and the extension region has a curvature profile with no more than one local extremum and absolute values less than twice the edge curvature, ensuring a homogeneous surface quality.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Stability of the object's composition
If the mirror surface is extended beyond the target region using high-order polynomial extrapolation, then the mathematical description is continuous, but the surface quality at the edge deteriorates due to increased curvature and astigmatism
Solution Approach 1:
The patent changes the mathematical parameters of the surface profile by limiting the curvature to specific bounds (|κ(s,t)| ≤ 2|κ_edge(s)|) and restricting the number of extrema in the curvature profile (no more than one local extremum). This parameter control prevents the runaway curvature growth inherent in high-order polynomial extrapolation while maintaining surface continuity.
Solution Approach 2:
The patent applies preliminary constraints to the extension region design before manufacturing begins. By pre-defining the curvature bounds and extrema limits in the mathematical model, the design ensures that subsequent polishing operations will not encounter the extreme curvature variations that would compromise surface quality.
2Adaptability or versatility
If the extension region allows free curvature variation, then the mathematical model remains flexible, but the polishing accuracy decreases due to difficult-to-polish high curvature areas
Solution Approach 1:
The patent transforms the flexible but problematic high-order polynomial model into a constrained model where curvature κ(s,t) is bounded by twice the edge curvature and the number of extrema is limited to one. This maintains mathematical flexibility for design while ensuring manufacturability by preventing extreme curvature regions.
3Device complexity
If the curvature in the extension region is allowed to increase with distance from the target region, then the mathematical description is simple, but the surface quality impairment increases
Solution Approach 1:
The patent introduces curvature bounds as a fundamental parameter constraint: |κ(s,t)| ≤ 2|κ_edge(s)| for all points in the extension region. This simple yet effective parameter limitation prevents curvature from increasing indefinitely with distance from the target region, maintaining both mathematical simplicity and surface quality.
Data Source
AI summary
A mirror element (20) having a mirror surface (26) with an aspherical target region (22) and an extension region (28) adjoining an edge (24) of the target region (22) is disclosed, wherein the edge (24) is describable by an at least twice continuously differentiable closed curve (b), wherein the target region (22) has a respective edge curvature at each edge point(s) located on the curve, and wherein, when proceeding from the edge point(s) in a profile direction transverse to the edge (24), the extension region (28) has a curvature profile, which has no more than one local extremum and the absolute values of the curvatures of which are less than twice the absolute value of the edge curvature. Also disclosed are a lithography system (1) including a mirror element (20) and a method for providing a mirror element (20).