Semiconductor Workpiece Shape Modeling for Warp-Aware Focus Maps

The patent applies preliminary action by generating a shape model of the semiconductor workpiece before the imaging process. The system collects displacement data across the workpiece surface, fits mathematical functions (such as Zernike polynomials) to characterize warp and bow, and creates a predictive shape model that is used to pre-adjust the focusing behavior of the imaging device. This preliminary characterization eliminates the need for complex real-time focusing adjustments during imaging, thereby improving imaging accuracy without proportionally increasing system complexity.

The patent implements continuity of useful action by performing multiple line scans across different regions of the workpiece surface in a continuous manner without interruption. The system systematically moves the imaging device or workpiece to collect displacement data along multiple scan lines, fitting mathematical functions to each set of data points. This continuous data collection approach efficiently captures the three-dimensional shape characteristics across the entire workpiece surface, achieving high shape characterization accuracy while minimizing idle time between measurements.

The patent applies parameter changes by utilizing Zernike polynomials, which are mathematical functions defined by specific parameters (radial and angular degrees) that can flexibly represent various surface shapes. The system selects appropriate polynomial orders based on the observed workpiece characteristics, adjusting the model complexity to match the actual shape variations. This parameter-based approach allows the system to achieve high model accuracy for complex warp and bow patterns while avoiding unnecessary computational overhead by not using excessively high-order polynomials for simple surfaces.

The patent implements segmentation by dividing the workpiece surface into multiple scan regions and collecting displacement data along discrete line scans across these regions. The system systematically moves through different areas of the workpiece, fitting mathematical functions to data from each scanned line. This segmented approach ensures comprehensive coverage of the entire workpiece surface, creating a complete shape model that captures local variations in warp and bow, while maintaining efficient measurement throughput by processing each segment independently and in sequence.