The operation time of an ideal reliable wafer scanner model is defined at the die level where the actual exposure process takes place as the time unit per die, or at the wafer substrate level as the time unit per wafer substrate. Therefore, the machine throughput is given as the reciprocal of the operation time. The involved motion profiles of a machine, namely the step-and-scan trajectories, function as the heartbeats that drive its multidisciplinary elements, which suggests that a multidisciplinary design optimization should be involved when such profiles are selected or designed. This is also true when considering the traverse motion profiles among rows and columns within the wafer substrate. The step-and-scan trajectories affect the machine throughput, performance, and die yield. The effects of tracking such profiles appear as structural vibration, tracking errors, and thermal loading at various machine elements such as the actuators, the reticle, the wafer, and the projection elements specifically when the exposure high-energy duration and frequency are not taken into consideration while designing the reference motion. From the dynamics perspective, having a reference motion with nonzero and bounded higher-order derivatives is recommended since it enhances the tracking performance of the machine, however, its ability to increase the operation time is usually overlooked. In an attempt to understand such effects, we present a case study that outlines the aforementioned aspects using three step-and-scan profiles of mainly $3^{rd}$ -order. Taking the dynamics of the driven stage into consideration through input shaping, both the step-and-scan and traverse motion profiles are analyzed. We provide analytical expressions that can be used to generate both types of motion profiles on the fly without additional optimization. A simulation example of a simplified wafer scanner machine shows the usefulness of the proposed framework. Note to Practitioners—Choosing the most suitable operating conditions of a lithography machine is challenging. These conditions affect machine productivity, profit margin, and maintenance. In this paper, we reveal the relation between the selection of operating conditions based on several decision variables- and the kinodynamic step-and-scan trajectory generation based on specific machine parameters and clients’ requirements. Being chart-based, the selection process of an operating point can be less practical at some points. However, using appropriate curve fitting tools, the information provided in the optimal operating charts can be put into suboptimal closed-form expressions that facilitate the selection process. Therefore, the designed trajectories parameters can be easily saved in lookup tables for ease of evaluation and future use. This helps in accommodating changes in the operation plans and flexible manufacturing systems. Also, starting with a given set of machine parameters, it is possible to calculate the optimal machine operating point when the input shaping technique is used, as illustrated in this paper.

中文翻译：

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半导体制造中使用的晶圆扫描仪轨迹的动力学生成


理想的可靠晶圆扫描仪模型的操作时间在实际曝光过程发生的芯片级定义为每个芯片的时间单位，或者在晶圆衬底级定义为每个晶圆衬底的时间单位。因此，机器吞吐量以操作时间的倒数给出。机器所涉及的运动轮廓，即步进扫描轨迹，充当驱动其多学科元素的心跳，这表明在选择或设计此类轮廓时应涉及多学科设计优化。当考虑晶片衬底内的行和列之间的横向运动轮廓时也是如此。步进扫描轨迹影响机器的吞吐量、性能和芯片产量。跟踪此类轮廓的影响表现为各种机器元件（例如致动器、光罩、晶圆和投影元件）的结构振动、跟踪误差和热负载，特别是在不考虑曝光高能持续时间和频率时设计参考运动时的考虑。从动力学角度来看，建议使用具有非零且有界高阶导数的参考运动，因为它可以增强机器的跟踪性能，但是，它增加操作时间的能力通常被忽视。为了理解这种影响，我们提出了一个案例研究，使用主要为 $3^{rd}$ 阶的三个步进扫描配置文件概述了上述方面。通过输入整形考虑驱动级的动力学，分析步进扫描和横向运动曲线。 我们提供解析表达式，可用于动态生成两种类型的运动曲线，无需额外优化。简化晶圆扫描仪的模拟示例显示了所提出框架的有用性。从业者须知——选择光刻机最合适的操作条件是一项挑战。这些条件会影响机器的生产率、利润率和维护。在本文中，我们揭示了基于多个决策变量的操作条件选择与基于特定机器参数和客户要求的运动动力学步进扫描轨迹生成之间的关系。由于基于图表，操作点的选择过程在某些时候可能不太实用。然而，使用适当的曲线拟合工具，可以将最佳操作图表中提供的信息放入次优封闭式表达式中，以促进选择过程。因此，设计的轨迹参数可以轻松保存在查找表中，以便于评估和将来使用。这有助于适应运营计划和灵活制造系统的变化。此外，从一组给定的机器参数开始，使用输入整形技术时可以计算最佳机器工作点，如本文所示。