Mathematical Sciences: Optical Diffraction and Inverse Scattering from Features on Silicon Wafers

数学科学：硅片特征的光学衍射和逆散射

• 批准号: 8760089
• 负责人: Gregory Wojcik
• 金额: $ 4.98万
• 依托单位: Weidlinger Associates Palo Alto
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 1988
• 资助国家: 美国
• 起止时间: 1988-02-01 至 1988-07-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=8760089&HistoricalAwards=false
• 关键词: Mathematical; Sciences; Optical; Diffraction; Inverse

The purpose of this research is to develop a capability for: (1) calculating two-dimensional optical diffractions for the edges of dielectric or imperfectly conducting features on layered, silicon-based substrates; and (2) utilizing diffracted two-dimensional fields in an inversion algorithm for shape reconstruction of linear (line-like) features on silicon wafers and chips for integrated circuits. The research is fundamentally mathematical in nature and is driven by critical problems in the integrated circuit industry, although it is important to a wider class of applications. The research objective for Phase I is: (1) to implement a new theory of vector diffraction utilizing self-similarity and vector boundary value problems in complex variable theory; and (2) to begin preliminary study of the inverse optical scattering problem for metrology of edged features on silicon substrates, considering the pros and cons of time domain and frequency domain data, and feasibility of data acquisition. If successful, these diffraction solutions and inversion methods will prove technically beneficial for a variety of applied problems. However, their greatest potential may eventually be reached in the integrated circuit industry if they can contribute to increased yield by means of automated metrology. It is expected that positive results from this line of research could eventually contribute to the theory of a practical, automated inspection instrument for IC metrology. This would have a significant impact on productivity of the integrated circuit industry. The vector diffraction solutions sought here are useful in their own right for sonar, radar, and optics applications.

本研究的目的是开发以下功能：（1）计算分层硅基基板上电介质边缘或不完美导电特征的二维光学衍射； (2) 在反演算法中利用衍射二维场来重建硅晶片和集成电路芯片上的线性（线状）特征。 该研究本质上是数学性的，并且是由集成电路行业的关键问题驱动的，尽管它对于更广泛的应用类别很重要。 第一阶段的研究目标是：（1）利用复变量理论中的自相似性和矢量边值问题实现一种新的矢量衍射理论； (2)开始初步研究用于硅基板边缘特征计量的逆光学散射问题，考虑时域和频域数据的优缺点以及数据采集的可行性。 如果成功，这些衍射解决方案和反演方法将在技术上证明对解决各种应用问题是有益的。 然而，如果它们能够通过自动化计量来提高产量，那么它们最终可能会在集成电路行业发挥最大潜力。 预计这一研究领域的积极成果最终可能有助于建立实用的 IC 计量自动检测仪器的理论。 这将对集成电路行业的生产力产生重大影响。 这里寻求的矢量衍射解决方案本身对于声纳、雷达和光学应用很有用。