Auxiliary Pattern Positioning via Differential PSF Extrema
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Solution Overview
Problem
The challenge in semiconductor manufacturing is determining the optimal placement of auxiliary patterns on photomasks to ensure sufficient lithography margins, especially when dealing with fine line widths and resolution limits, as conventional methods are time-consuming and rely heavily on exhaustive or exploratory techniques.
Innovation Solution
A method involving the extraction of a linearly treatable portion from the transmission cross coefficient (TCC) of the exposure optical system, followed by inverse Fourier transformation and calculation of a second-order differential of the point spread function (PSF) index, to identify positions on the photomask where the differential PSF index assumes extremal values, which are used to determine the placement of auxiliary patterns.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Reliability
If exhaustive or exploratory techniques are used to determine auxiliary pattern placement, then the lithography margin is improved, but the design time increases significantly
Solution Approach 1:
The patent transforms the auxiliary pattern placement problem from a spatial arrangement problem into a parameter optimization problem by using the differential PSF index as a quantitative criterion. By calculating the differential PSF index at each candidate position and selecting positions with extremal values, the method provides a systematic parameter-based approach that replaces time-consuming exhaustive search while ensuring optimal lithography margin.
Solution Approach 2:
The patent replaces the manual or trial-and-error exploratory technique with an automated computational method based on optical physics principles. By using the differential PSF index calculation derived from the exposure optical system's transmission cross coefficient, the method substitutes human judgment and iterative adjustment with a deterministic mathematical model that automatically determines optimal positions.
2Manufacturing precision
If the illumination condition is adapted to the finest pattern, then the resolution of the closest pattern is improved, but the lithography margin for other patterns deteriorates
Solution Approach 1:
The patent applies local quality by placing auxiliary patterns at specific locations where the differential PSF index has extremal values. These locally optimized positions are determined based on the interaction between the auxiliary pattern and each main pattern, allowing the illumination condition to be effectively adapted for each local region while maintaining overall system performance.
Solution Approach 2:
The patent performs preliminary action by pre-calculating the differential PSF index map before actual photomask fabrication. This advance calculation identifies all optimal auxiliary pattern positions in advance, allowing the photomask to be designed with predetermined auxiliary patterns that will improve lithography margins for all patterns during exposure, rather than adjusting illumination conditions during the actual manufacturing process.
Data Source
AI summary
According to one embodiment, a method is disclosed for determining position of an auxiliary pattern on a photomask. The method can include generating a first set for each of three or more imaging positions of an exposure optical system. The method can include generating a second set for each of the three or more imaging positions by inverse Fourier transforming each of the first set. The method can include calculating a second order differential with respect to the imaging position of an index indicating amplitude of light belonging to the second set. In addition, the method can include extracting a position where the second order differential assumes an extremal value on an imaging plane of the exposure optical system. At least part of positions on the photomask each corresponding to the position assuming the extremal value on the imaging plane is used as a formation position of the auxiliary pattern.