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

这项研究的目的是发展以下能力： (1)计算二维光学衍射， 电介质或不完全导电特征的边缘， 分层的硅基衬底;以及（2）利用衍射 形状反演算法中的二维场 硅晶片上的线性（线状）特征的重构 和用于集成电路的芯片。 这项研究从根本上 数学的性质，并由关键问题驱动， 集成电路产业，虽然它是重要的， 类的应用。 第一阶段的研究目标是：（1）实施一个 利用自相似性的矢量衍射新理论， 复变量理论中的向量边值问题; (2)开始对逆光散射的初步研究 对于硅衬底上的边缘特征的计量的问题， 综合考虑时域和频域的优缺点 数据和数据采集的可行性。 如果成功，这些衍射解和反演 这些方法将证明在技术上有益于各种 应用问题。 然而，它们最大的潜力可能 最终在集成电路行业达到，如果他们 可以通过自动化的方式提高产量， 计量学 预计这一系列产品将产生积极的结果， 研究最终可能有助于理论的一个 用于IC计量的实用自动化检测仪器。 这将对生产力产生重大影响。 集成电路产业。 矢量衍射解 在这里寻求的是有用的，在自己的权利，声纳，雷达， 光学应用

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.