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

本研究的目的是开发一种能力：(1)计算层状硅基衬底上介电或不完全导电特征边缘的二维光学衍射；(2)在反演算法中利用衍射二维场对集成电路硅片和芯片上的线性（线状）特征进行形状重建。这项研究基本上是数学性质的，是由集成电路工业中的关键问题驱动的，尽管它对更广泛的应用类别很重要。第一阶段的研究目标是：(1)利用复变理论中的自相似问题和矢量边值问题实现新的矢量衍射理论；(2)对硅衬底边缘特征测量的逆光学散射问题进行初步研究，考虑时域和频域数据的优缺点，以及数据采集的可行性。如果成功的话，这些衍射解和反演方法将在技术上证明对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提高产量，它们的最大潜力可能最终在集成电路工业中得到实现。预计这条研究路线的积极结果最终可能有助于集成电路计量实用的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。这里所寻求的矢量衍射解决方案对声纳，雷达和光学应用本身是有用的。

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.