Lithographic Mask Design for Arbitrary Wavefronts
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Solution Overview
Problem
Current lithographic technologies face challenges in realizing optimal wavefronts due to limitations in mask manufacturing, particularly with binary or trinary masks, where feature edges must be polygonal and Manhattan, and the finite thickness of mask films causes electromagnetic field (EMF) effects that impact image quality and focus sensitivity, making it difficult to produce specified wavefronts with standard photomask technology.
Innovation Solution
A method is developed to form arbitrary lithographic wavefronts using standard mask technology by designing a manufacturable mask with a Manhattan grid and adjusting gridline positions to maximize transmission discontinuities, compensating for EMF effects through in-phase and quadrature adjustments, allowing for the creation of masks that can diffract specified wavefronts while maintaining manufacturability.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Ease of manufacture
If standard binary or trinary mask technology is used with Manhattan grid constraints, then mask manufacturability is improved, but the ability to form arbitrary wavefronts and achieve optimal image quality deteriorates
Solution Approach 1:
The mask pattern is segmented into rectangular features aligned with a Manhattan grid, where each feature's transmission and position are independently optimized. This segmentation allows the complex wavefront formation problem to be decomposed into manageable discrete elements that can be manufactured with standard technology while still achieving arbitrary wavefront control through collective optimization of all segments.
Solution Approach 2:
The invention optimizes multiple parameters including feature transmission values, positions along grid lines, and grid line spacings. By continuously adjusting these parameters during optimization and then mapping them to discrete manufacturable values, the system achieves near-optimal wavefront formation while maintaining compatibility with standard binary or trinary mask fabrication processes.
2Device complexity
If mask features are constrained to polygonal shapes with Manhattan orientations, then fabrication complexity is reduced, but the flexibility to create complex wavefront patterns deteriorates
Solution Approach 1:
Complex wavefront patterns are constructed by segmenting them into numerous simple rectangular features with Manhattan orientations. While each individual feature is simple, the collective arrangement of many such segments can reproduce complex wavefront shapes and phase distributions, thereby maintaining pattern flexibility despite geometric constraints on individual features.
Solution Approach 2:
The invention introduces the dimension of feature transmission values in addition to positional arrangement. By varying transmission (binary or trinary levels) across the Manhattan-grid-aligned rectangular features, the system gains additional degrees of freedom to create complex wavefront patterns without requiring complex feature geometries, thus maintaining versatility while simplifying fabrication.
3Measurement precision
If the finite thickness of mask films is considered, then electromagnetic field effects are accurately modeled, but the difficulty of compensating for focus sensitivity and image quality degradation increases
Solution Approach 1:
The optimization process performs preliminary compensation for EMF effects by directly incorporating them into the objective function. During the optimization stage, the algorithm anticipates and compensates for the focus sensitivity and image quality degradation that will result from EMF effects, thereby pre-correcting these issues before mask fabrication rather than requiring complex post-fabrication adjustments.
Solution Approach 2:
The optimization algorithm uses feedback from EMF effect calculations to iteratively adjust feature positions and transmissions. By calculating EMF effects at each iteration and using this information to guide subsequent optimization steps, the system automatically compensates for focus sensitivity and image quality issues without requiring manual intervention or complex external compensation mechanisms.
Applied Scientific Principles
This section explains which scientific principles are used to turn an abstract innovation direction into a practical engineering solution.
Function Achieved in This Case
This approach enables the production of high-quality images that would otherwise be impractical with standard masks, improving image quality and focus robustness by effectively addressing EMF-induced issues and allowing for the use of complex patterns and phase-shift imaging.
Implementation Method 1
A method is developed to form arbitrary lithographic wavefronts using standard mask technology by designing a manufacturable mask with a Manhattan grid and adjusting gridline positions to maximize transmission discontinuities
Implementation Method 2
the finite thickness of mask films causes electromagnetic field (EMF) effects that impact image quality and focus sensitivity
Data Source
AI summary
A desired set of diffracted waves using mask features whose transmissions are chosen from a set of supported values are generated. A representation of the mask as a set of polygonal elements is created. Constraints which require that the ratio of the spatial frequencies in the representation take on the amplitude ratios of the desired set of diffracted waves are defined. An optimization algorithm is used to adjust the transmission discontinuities at the edges of the polygons to substantial equality with the discontinuity values allowed by the set of supported transmissions while maintaining the constraints.