Quantitative Goals for Improving Computational Lithography Yield
APR 24, 20269 MIN READ
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Computational Lithography Background and Yield Targets
Computational lithography has emerged as a critical enabler for semiconductor manufacturing as the industry continues to push beyond the physical limits of traditional optical lithography. This field encompasses advanced mathematical and computational techniques that enhance the precision and reliability of pattern transfer processes in semiconductor fabrication. The evolution from simple optical proximity correction to sophisticated machine learning-driven approaches represents decades of continuous innovation aimed at maintaining Moore's Law progression.
The fundamental challenge in modern lithography stems from the increasing disparity between desired feature sizes and the wavelength of available light sources. As semiconductor nodes shrink below 7nm, manufacturers rely heavily on computational methods to predict, correct, and optimize lithographic processes. These techniques include optical proximity correction, source mask optimization, and inverse lithography technology, all designed to achieve precise pattern fidelity on silicon wafers.
Yield improvement in computational lithography directly correlates with manufacturing profitability and technological advancement. Current industry standards demand yield rates exceeding 95% for leading-edge processes, with some applications requiring yields above 99%. The economic impact of yield enhancement is substantial, as each percentage point improvement can translate to millions of dollars in additional revenue for high-volume manufacturing facilities.
Quantitative yield targets in computational lithography focus on several key metrics including critical dimension uniformity, pattern placement accuracy, and defect density reduction. Industry leaders typically aim for critical dimension variations below 2nm across entire wafers, while maintaining overlay accuracy within 1.5nm for multi-layer processes. These stringent requirements necessitate sophisticated computational models that can predict and compensate for various sources of process variation.
The integration of artificial intelligence and machine learning into computational lithography workflows has opened new possibilities for yield optimization. Advanced algorithms can now process vast amounts of manufacturing data to identify subtle correlations between process parameters and yield outcomes, enabling predictive adjustments that prevent defects before they occur.
Future yield targets are becoming increasingly ambitious as the industry approaches fundamental physical limits. Next-generation computational lithography systems must achieve sub-nanometer precision while processing exponentially larger datasets from high-resolution metrology tools, requiring breakthrough innovations in both algorithmic efficiency and computational hardware capabilities.
The fundamental challenge in modern lithography stems from the increasing disparity between desired feature sizes and the wavelength of available light sources. As semiconductor nodes shrink below 7nm, manufacturers rely heavily on computational methods to predict, correct, and optimize lithographic processes. These techniques include optical proximity correction, source mask optimization, and inverse lithography technology, all designed to achieve precise pattern fidelity on silicon wafers.
Yield improvement in computational lithography directly correlates with manufacturing profitability and technological advancement. Current industry standards demand yield rates exceeding 95% for leading-edge processes, with some applications requiring yields above 99%. The economic impact of yield enhancement is substantial, as each percentage point improvement can translate to millions of dollars in additional revenue for high-volume manufacturing facilities.
Quantitative yield targets in computational lithography focus on several key metrics including critical dimension uniformity, pattern placement accuracy, and defect density reduction. Industry leaders typically aim for critical dimension variations below 2nm across entire wafers, while maintaining overlay accuracy within 1.5nm for multi-layer processes. These stringent requirements necessitate sophisticated computational models that can predict and compensate for various sources of process variation.
The integration of artificial intelligence and machine learning into computational lithography workflows has opened new possibilities for yield optimization. Advanced algorithms can now process vast amounts of manufacturing data to identify subtle correlations between process parameters and yield outcomes, enabling predictive adjustments that prevent defects before they occur.
Future yield targets are becoming increasingly ambitious as the industry approaches fundamental physical limits. Next-generation computational lithography systems must achieve sub-nanometer precision while processing exponentially larger datasets from high-resolution metrology tools, requiring breakthrough innovations in both algorithmic efficiency and computational hardware capabilities.
Market Demand for Advanced Lithography Solutions
The semiconductor industry faces unprecedented demand for advanced lithography solutions as device manufacturers push toward smaller node geometries and higher integration densities. The transition to extreme ultraviolet lithography and the continued refinement of deep ultraviolet processes have created substantial market opportunities for computational lithography technologies that can enhance manufacturing yield and process control.
Leading semiconductor foundries and integrated device manufacturers are experiencing increasing pressure to maintain profitability while advancing to next-generation process nodes. The cost of lithography equipment and the complexity of patterning requirements have reached levels where traditional approaches to yield optimization are insufficient. This economic reality drives strong demand for sophisticated computational solutions that can predict, model, and correct lithography-related defects before they impact production wafers.
The market demand extends beyond traditional logic device manufacturers to include memory producers, specialty semiconductor companies, and emerging application areas such as photonics and MEMS devices. Each segment presents unique requirements for lithography yield improvement, creating diverse opportunities for computational solutions. Memory manufacturers particularly value solutions that can address repetitive pattern optimization, while logic device producers focus on complex layout-dependent effects and process variation modeling.
Automotive and industrial electronics sectors are generating additional demand pressure as they require higher reliability standards and longer product lifecycles. These applications cannot tolerate the yield variability that might be acceptable in consumer electronics, necessitating more robust computational lithography approaches that can guarantee consistent manufacturing outcomes across extended production runs.
The emergence of advanced packaging technologies and heterogeneous integration strategies has expanded the addressable market for computational lithography solutions. These applications often involve unique material combinations and non-standard process flows that benefit significantly from predictive modeling and yield optimization algorithms.
Geographic demand patterns show strong concentration in regions with major semiconductor manufacturing capabilities, particularly East Asia and selected locations in North America and Europe. However, the global nature of semiconductor supply chains means that computational lithography solutions developed in one region often find application worldwide, creating opportunities for technology providers to serve diverse market segments simultaneously.
Leading semiconductor foundries and integrated device manufacturers are experiencing increasing pressure to maintain profitability while advancing to next-generation process nodes. The cost of lithography equipment and the complexity of patterning requirements have reached levels where traditional approaches to yield optimization are insufficient. This economic reality drives strong demand for sophisticated computational solutions that can predict, model, and correct lithography-related defects before they impact production wafers.
The market demand extends beyond traditional logic device manufacturers to include memory producers, specialty semiconductor companies, and emerging application areas such as photonics and MEMS devices. Each segment presents unique requirements for lithography yield improvement, creating diverse opportunities for computational solutions. Memory manufacturers particularly value solutions that can address repetitive pattern optimization, while logic device producers focus on complex layout-dependent effects and process variation modeling.
Automotive and industrial electronics sectors are generating additional demand pressure as they require higher reliability standards and longer product lifecycles. These applications cannot tolerate the yield variability that might be acceptable in consumer electronics, necessitating more robust computational lithography approaches that can guarantee consistent manufacturing outcomes across extended production runs.
The emergence of advanced packaging technologies and heterogeneous integration strategies has expanded the addressable market for computational lithography solutions. These applications often involve unique material combinations and non-standard process flows that benefit significantly from predictive modeling and yield optimization algorithms.
Geographic demand patterns show strong concentration in regions with major semiconductor manufacturing capabilities, particularly East Asia and selected locations in North America and Europe. However, the global nature of semiconductor supply chains means that computational lithography solutions developed in one region often find application worldwide, creating opportunities for technology providers to serve diverse market segments simultaneously.
Current Yield Challenges in Computational Lithography
Computational lithography faces significant yield challenges that directly impact semiconductor manufacturing efficiency and profitability. The primary obstacle stems from the increasing complexity of advanced node processes, where traditional optical proximity correction (OPC) and resolution enhancement techniques struggle to maintain acceptable defect rates below 10 parts per million.
Pattern fidelity represents a critical challenge, particularly for sub-7nm processes where edge placement errors (EPE) must be controlled within 1-2nm tolerances. Current computational models often fail to accurately predict resist behavior under extreme ultraviolet (EUV) exposure, leading to systematic pattern distortions that reduce functional yield by 15-25% in high-volume manufacturing.
Stochastic effects pose another fundamental limitation, manifesting as random variations in line edge roughness, contact hole circularity, and via formation. These phenomena become increasingly pronounced at smaller feature sizes, where shot noise and molecular-scale resist interactions create unpredictable pattern variations that current computational frameworks cannot adequately model or compensate for.
Process window limitations further constrain yield optimization efforts. The shrinking overlap between depth of focus and exposure latitude windows leaves minimal margin for process variations, making it extremely difficult to maintain consistent patterning across full wafer areas. This challenge is exacerbated by lens aberrations, illumination non-uniformities, and mask manufacturing tolerances.
Computational complexity itself creates yield bottlenecks, as current algorithms require extensive runtime for full-chip verification and correction. The iterative nature of OPC convergence often results in incomplete optimization due to time constraints, leaving residual hotspots that contribute to yield loss during production.
Multi-patterning decomposition introduces additional complexity layers, where pattern conflicts and overlay errors between successive exposures create systematic yield detractors. The computational burden of optimizing multiple mask layers simultaneously while maintaining design rule compliance presents significant algorithmic challenges that current solutions address inadequately.
Mask error enhancement factor (MEEF) amplification at advanced nodes means that even minor mask imperfections translate into significant wafer-level defects, requiring more sophisticated computational correction strategies than currently available methodologies can provide effectively.
Pattern fidelity represents a critical challenge, particularly for sub-7nm processes where edge placement errors (EPE) must be controlled within 1-2nm tolerances. Current computational models often fail to accurately predict resist behavior under extreme ultraviolet (EUV) exposure, leading to systematic pattern distortions that reduce functional yield by 15-25% in high-volume manufacturing.
Stochastic effects pose another fundamental limitation, manifesting as random variations in line edge roughness, contact hole circularity, and via formation. These phenomena become increasingly pronounced at smaller feature sizes, where shot noise and molecular-scale resist interactions create unpredictable pattern variations that current computational frameworks cannot adequately model or compensate for.
Process window limitations further constrain yield optimization efforts. The shrinking overlap between depth of focus and exposure latitude windows leaves minimal margin for process variations, making it extremely difficult to maintain consistent patterning across full wafer areas. This challenge is exacerbated by lens aberrations, illumination non-uniformities, and mask manufacturing tolerances.
Computational complexity itself creates yield bottlenecks, as current algorithms require extensive runtime for full-chip verification and correction. The iterative nature of OPC convergence often results in incomplete optimization due to time constraints, leaving residual hotspots that contribute to yield loss during production.
Multi-patterning decomposition introduces additional complexity layers, where pattern conflicts and overlay errors between successive exposures create systematic yield detractors. The computational burden of optimizing multiple mask layers simultaneously while maintaining design rule compliance presents significant algorithmic challenges that current solutions address inadequately.
Mask error enhancement factor (MEEF) amplification at advanced nodes means that even minor mask imperfections translate into significant wafer-level defects, requiring more sophisticated computational correction strategies than currently available methodologies can provide effectively.
Existing Yield Enhancement Solutions
01 Optical proximity correction (OPC) techniques for yield improvement
Computational lithography methods employ optical proximity correction algorithms to compensate for diffraction effects and process variations in photolithography. These techniques modify mask patterns to ensure that the printed features on wafers match the intended design more accurately. By optimizing the mask layout through iterative simulations and corrections, manufacturing yield can be significantly improved by reducing critical dimension variations and pattern fidelity errors.- Optical proximity correction (OPC) techniques for yield improvement: Computational lithography methods employ optical proximity correction algorithms to compensate for diffraction effects and process variations in photolithography. These techniques modify mask patterns to ensure that the printed features on wafers match the intended design more accurately, thereby improving manufacturing yield. Advanced OPC methods use model-based approaches that simulate the lithography process and iteratively optimize mask shapes to minimize pattern distortions and critical dimension variations.
- Source mask optimization (SMO) for enhanced process windows: Source mask optimization is a computational lithography technique that simultaneously optimizes both the illumination source and mask patterns to maximize the process window and yield. This approach considers the interaction between source shapes and mask features to achieve better imaging performance across various process conditions. The optimization process typically involves iterative algorithms that balance multiple objectives including depth of focus, exposure latitude, and pattern fidelity to improve overall manufacturing yield.
- Lithography hotspot detection and correction: Machine learning and pattern matching techniques are employed to identify potential lithography hotspots that could lead to yield loss. These methods analyze design layouts to detect patterns that are susceptible to printing failures or defects during the lithography process. Once identified, corrective actions such as design rule modifications or localized mask adjustments can be applied to eliminate or mitigate these problematic areas, thereby preventing yield-limiting defects before manufacturing.
- Process variation modeling and yield prediction: Computational methods for modeling process variations and their impact on lithography yield enable predictive analysis of manufacturing outcomes. These techniques incorporate statistical models of various process parameters such as dose, focus, mask errors, and resist properties to simulate their effects on pattern fidelity. By analyzing the sensitivity of designs to these variations, manufacturers can predict yield rates and identify design weaknesses before committing to production, allowing for proactive optimization.
- Inverse lithography technology (ILT) for optimal mask synthesis: Inverse lithography technology represents an advanced computational approach that directly synthesizes optimal mask patterns by solving inverse imaging problems. Rather than applying rule-based corrections, this method computationally determines the mask pattern that will produce the desired wafer pattern with maximum fidelity under given process conditions. The technique uses optimization algorithms that work backward from the target pattern to generate mask solutions that maximize yield by accounting for all relevant physical effects in the lithography system.
02 Source-mask optimization (SMO) for lithography performance enhancement
Advanced computational methods simultaneously optimize both the illumination source and mask patterns to maximize lithography process windows and yield. This co-optimization approach considers the interaction between source shapes and mask features to achieve better pattern transfer fidelity. The technique enables improved depth of focus, exposure latitude, and overall process robustness, leading to higher manufacturing yields in advanced semiconductor nodes.Expand Specific Solutions03 Machine learning and AI-based lithography optimization
Artificial intelligence and machine learning algorithms are applied to predict and optimize lithography outcomes by analyzing large datasets from previous manufacturing runs. These computational approaches can identify complex patterns and correlations that traditional methods might miss, enabling predictive yield modeling and proactive process adjustments. Neural networks and deep learning models are trained to optimize mask designs and process parameters for maximum yield.Expand Specific Solutions04 Process variation modeling and hotspot detection
Computational lithography tools incorporate sophisticated models to simulate process variations and identify potential yield-limiting hotspots before manufacturing. These methods analyze design layouts to detect areas susceptible to lithographic failures due to factors such as dose variations, focus errors, and mask errors. Early detection and correction of these hotspots through computational analysis prevents costly yield losses in production.Expand Specific Solutions05 Inverse lithography technology (ILT) for mask synthesis
Inverse lithography approaches work backward from desired wafer patterns to computationally synthesize optimal mask designs that maximize yield. Unlike traditional rule-based methods, these techniques use mathematical optimization algorithms to generate mask patterns that may appear counterintuitive but produce superior wafer results. This computational approach enables the creation of complex curvilinear mask shapes that significantly improve process margins and manufacturing yield.Expand Specific Solutions
Key Players in Computational Lithography Industry
The computational lithography yield improvement sector represents a mature yet rapidly evolving market within the semiconductor manufacturing ecosystem, driven by increasing demand for advanced node processing and EUV lithography adoption. The industry is experiencing significant growth with market valuations reaching billions annually, as foundries and IDMs invest heavily in yield optimization technologies. Technology maturity varies significantly across market segments, with established players like ASML Netherlands BV and Taiwan Semiconductor Manufacturing Co. leading in advanced EUV and computational lithography solutions, while companies such as Synopsys and Cadence Design Systems provide critical software infrastructure. Asian manufacturers including Samsung Electronics, SMIC, and Shanghai Huahong Grace Semiconductor are rapidly advancing their capabilities, supported by research institutions like Beijing Institute of Technology. The competitive landscape features a mix of equipment suppliers, foundries, and software providers, with technology readiness levels ranging from production-ready solutions at leading firms to emerging research-stage innovations at specialized companies like D2S and Eulitha AG.
ASML Netherlands BV
Technical Solution: ASML develops advanced computational lithography solutions integrated with their EUV and DUV lithography systems to achieve quantitative yield improvements. Their approach combines machine learning algorithms with optical proximity correction (OPC) and source mask optimization (SMO) to reduce critical dimension uniformity variations by up to 15% and improve overlay accuracy to sub-2nm levels. The company's computational lithography platform utilizes high-performance computing clusters to process complex pattern corrections in real-time, enabling yield improvements of 8-12% for advanced node manufacturing. Their holistic approach integrates scanner hardware feedback with computational models to achieve predictable and measurable lithography performance enhancements.
Strengths: Market-leading lithography equipment with integrated computational solutions, extensive R&D resources, strong customer partnerships. Weaknesses: High system costs, complex integration requirements, dependency on advanced computing infrastructure.
Taiwan Semiconductor Manufacturing Co., Ltd.
Technical Solution: TSMC implements comprehensive computational lithography strategies focused on quantitative yield optimization across their advanced node processes. Their approach combines proprietary OPC algorithms with machine learning-based hotspot detection to achieve measurable improvements in pattern fidelity and manufacturing yield. The company has developed statistical process control methods that integrate computational lithography feedback to maintain critical dimension variations within ±2nm for 5nm and 3nm processes. TSMC's computational lithography framework includes advanced mask synthesis techniques and real-time process correction algorithms that have demonstrated yield improvements of 10-15% for complex logic designs. Their systematic approach to computational lithography optimization has enabled consistent achievement of industry-leading yield targets.
Strengths: Leading-edge process technology, extensive manufacturing data for algorithm training, strong computational resources. Weaknesses: High development costs, complex process integration, requires continuous algorithm updates for new technologies.
Core Innovations in Lithography Yield Optimization
Method for evaluating the effects of multiple exposure processes in lithography
PatentInactiveUS6777147B1
Innovation
- A method is developed to determine composite aerial images by simulating individual exposure steps and combining them with weighted images from subsequent steps, allowing for process window analysis and yield prediction using a focus-exposure matrix and Monte Carlo analysis.
A method for optimization of a lithographic process
PatentWO2018077651A1
Innovation
- A method that determines parameter and process window fingerprints to assess uncertainty and probability of performance parameters being outside acceptable ranges, allowing for optimized placement of metrology targets and modification of performance parameter data to enhance yield, incorporating uncertainty and process window metrics for improved control strategies.
Semiconductor Manufacturing Standards and Regulations
The semiconductor manufacturing industry operates under a comprehensive framework of standards and regulations that directly impact computational lithography yield optimization. International standards organizations such as SEMI (Semiconductor Equipment and Materials International) and IEEE establish critical guidelines for lithography processes, equipment specifications, and measurement protocols. These standards define acceptable tolerances for critical dimensions, overlay accuracy, and defect density levels that computational lithography systems must achieve to meet industry requirements.
Regulatory compliance in computational lithography encompasses multiple dimensions including environmental safety, equipment certification, and process validation. The International Technology Roadmap for Semiconductors (ITRS) and its successor, the International Roadmap for Devices and Systems (IRDS), provide quantitative targets for lithography performance metrics including resolution enhancement, pattern fidelity, and throughput requirements. These roadmaps establish benchmark standards that drive the development of computational lithography algorithms and optimization techniques.
Quality management systems such as ISO 9001 and semiconductor-specific standards like IATF 16949 mandate rigorous documentation and traceability requirements for lithography processes. These regulations necessitate comprehensive data collection and analysis capabilities within computational lithography systems, enabling real-time monitoring of yield-impacting parameters and automated corrective actions when deviations occur.
Export control regulations, particularly those governing advanced semiconductor manufacturing technologies, significantly influence the development and deployment of computational lithography solutions. The Wassenaar Arrangement and various national export control regimes impose restrictions on the transfer of advanced lithography technologies, affecting global supply chains and technology development strategies.
Emerging regulations addressing cybersecurity and data protection are increasingly relevant to computational lithography systems, which rely heavily on proprietary algorithms and sensitive manufacturing data. Compliance with frameworks such as NIST Cybersecurity Framework and industry-specific security standards requires robust data protection measures and secure communication protocols within lithography control systems.
Environmental regulations governing semiconductor manufacturing, including restrictions on chemical usage and waste disposal, directly impact the selection and optimization of computational lithography processes. These regulatory constraints influence the development of environmentally sustainable lithography techniques while maintaining yield performance targets.
Regulatory compliance in computational lithography encompasses multiple dimensions including environmental safety, equipment certification, and process validation. The International Technology Roadmap for Semiconductors (ITRS) and its successor, the International Roadmap for Devices and Systems (IRDS), provide quantitative targets for lithography performance metrics including resolution enhancement, pattern fidelity, and throughput requirements. These roadmaps establish benchmark standards that drive the development of computational lithography algorithms and optimization techniques.
Quality management systems such as ISO 9001 and semiconductor-specific standards like IATF 16949 mandate rigorous documentation and traceability requirements for lithography processes. These regulations necessitate comprehensive data collection and analysis capabilities within computational lithography systems, enabling real-time monitoring of yield-impacting parameters and automated corrective actions when deviations occur.
Export control regulations, particularly those governing advanced semiconductor manufacturing technologies, significantly influence the development and deployment of computational lithography solutions. The Wassenaar Arrangement and various national export control regimes impose restrictions on the transfer of advanced lithography technologies, affecting global supply chains and technology development strategies.
Emerging regulations addressing cybersecurity and data protection are increasingly relevant to computational lithography systems, which rely heavily on proprietary algorithms and sensitive manufacturing data. Compliance with frameworks such as NIST Cybersecurity Framework and industry-specific security standards requires robust data protection measures and secure communication protocols within lithography control systems.
Environmental regulations governing semiconductor manufacturing, including restrictions on chemical usage and waste disposal, directly impact the selection and optimization of computational lithography processes. These regulatory constraints influence the development of environmentally sustainable lithography techniques while maintaining yield performance targets.
Cost-Benefit Analysis of Yield Enhancement Strategies
The economic evaluation of yield enhancement strategies in computational lithography requires a comprehensive assessment of implementation costs versus expected returns on investment. Initial capital expenditures typically include advanced software licensing fees, high-performance computing infrastructure upgrades, and specialized personnel training programs. These upfront investments can range from several hundred thousand to multiple millions of dollars, depending on the scale and sophistication of the enhancement solutions deployed.
Operational cost considerations encompass ongoing software maintenance, increased computational resources, and extended processing times for complex correction algorithms. While these strategies may initially increase per-wafer processing costs by 15-30%, the economic benefits become apparent through reduced defect rates and improved manufacturing yields. Enhanced optical proximity correction and source mask optimization techniques demonstrate particularly strong cost-effectiveness ratios in high-volume production environments.
The quantifiable benefits manifest primarily through reduced scrap rates, decreased rework requirements, and improved first-pass yield percentages. Industry data indicates that comprehensive yield enhancement implementations can achieve 3-8% improvements in overall manufacturing yield, translating to substantial cost savings in high-volume semiconductor production. For advanced node processes, where wafer costs exceed $10,000 per unit, even modest yield improvements generate significant financial returns.
Return on investment calculations must account for the cumulative impact across multiple product generations and process nodes. Advanced computational lithography solutions typically achieve payback periods of 12-18 months in production environments, with ongoing benefits extending throughout the technology lifecycle. The cost-benefit ratio becomes increasingly favorable as production volumes scale, making these investments particularly attractive for foundries and high-volume manufacturers.
Risk mitigation factors further enhance the economic proposition, as improved yield predictability reduces manufacturing variability and associated costs. The integration of machine learning algorithms and advanced process modeling capabilities provides additional long-term value through continuous optimization and reduced development cycle times for future technology nodes.
Operational cost considerations encompass ongoing software maintenance, increased computational resources, and extended processing times for complex correction algorithms. While these strategies may initially increase per-wafer processing costs by 15-30%, the economic benefits become apparent through reduced defect rates and improved manufacturing yields. Enhanced optical proximity correction and source mask optimization techniques demonstrate particularly strong cost-effectiveness ratios in high-volume production environments.
The quantifiable benefits manifest primarily through reduced scrap rates, decreased rework requirements, and improved first-pass yield percentages. Industry data indicates that comprehensive yield enhancement implementations can achieve 3-8% improvements in overall manufacturing yield, translating to substantial cost savings in high-volume semiconductor production. For advanced node processes, where wafer costs exceed $10,000 per unit, even modest yield improvements generate significant financial returns.
Return on investment calculations must account for the cumulative impact across multiple product generations and process nodes. Advanced computational lithography solutions typically achieve payback periods of 12-18 months in production environments, with ongoing benefits extending throughout the technology lifecycle. The cost-benefit ratio becomes increasingly favorable as production volumes scale, making these investments particularly attractive for foundries and high-volume manufacturers.
Risk mitigation factors further enhance the economic proposition, as improved yield predictability reduces manufacturing variability and associated costs. The integration of machine learning algorithms and advanced process modeling capabilities provides additional long-term value through continuous optimization and reduced development cycle times for future technology nodes.
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