Synthetic Quartz Substrate Back Surface Zernike Control
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Solution Overview
Problem
In the imprint mold-forming process, the back surface of synthetic quartz glass substrates experiences deformation due to geometric and pressing stresses, leading to pattern misalignment and low reproducibility, especially when the back surface has a low central symmetry or concave shape, which is critical in fine pattern formation for IC applications where nanometer-level accuracy is required.
Innovation Solution
A synthetic quartz glass substrate with a rectangular shape and a back surface shape defined by Zernike polynomials, where specific coefficients of these polynomials are optimized to minimize deformation and ensure high reproducibility, including a circular region with a coefficient of the 4th term equal to or greater than −(2R/100,000×1) μm and summation of absolute values of coefficients of the 5th to 8th terms equal to or less than 4×(2R/100,000×1) μm, along with stepped or annular regions for improved stability.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Manufacturing precision
If the back surface of the substrate has a conventional shape (flat or simple curvature), then the manufacturing process is simple, but the substrate deforms under pressing stress during imprinting, causing pattern misalignment
Solution Approach 1:
The back surface of the substrate is pre-shaped with a specific complex curvature profile defined by Zernike polynomial coefficients before the imprinting process. This preliminary shaping compensates for the deformation that will occur during pressing, ensuring that the front surface remains flat and the pattern aligns accurately. The pre-shaping includes controlling coefficients a4, a5, a6, a7, and a8 of the Zernike polynomial expansion to achieve the desired deformation compensation.
Solution Approach 2:
The invention changes the geometric parameters of the back surface by precisely controlling the Zernike polynomial coefficients (a4, a5, a6, a7, a8) that describe the surface curvature. By adjusting these parameters within specific ranges, the substrate's deformation behavior under stress is modified to compensate for pattern misalignment, transforming the back surface from a simple flat or curved shape to a complex aspheric profile.
2Manufacturing precision
If the back surface has high central symmetry, then the deformation is more uniform, but the ability to compensate for complex deformation patterns is reduced
Solution Approach 1:
The invention introduces controlled asymmetry into the back surface design by allowing the Zernike polynomial coefficients a5, a6, a7, and a8 to have specific non-zero values within defined ranges. These asymmetric components enable the back surface to generate complex deformation patterns that can compensate for various types of front surface distortion, going beyond what simple symmetric shapes can achieve while maintaining sufficient stability.
3Reliability
If the substrate is held with high clamping force, then the pattern transfer is more stable, but the substrate deformation increases, causing misalignment
Solution Approach 1:
The back surface is pre-shaped with a specific curvature profile that acts in advance to counterbalance the deformation caused by clamping force during imprinting. The Zernike polynomial-based shaping creates a pre-deformation that is opposite to the expected stress-induced deformation, so that when clamping force is applied, the two effects cancel out and the front surface remains flat for accurate pattern transfer.
Data Source
AI summary
In an imprint mold-forming synthetic quartz glass substrate (1) of rectangular shape having dimensions L1 and L2 with L1≥L2, a circular region is delineated on the substrate back surface by a circle of radius R with L2−2R≥10 mm. When approximation analysis is performed from the 1st to 8th term in the Zernike polynomials on the circular region, a coefficient of the 4th term is equal to or greater than −(2R/100,000×1) μm.