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

这项研究的目的是开发一种能力：(1)计算层状硅基衬底上介质或不完美导电特征的边缘的二维光学衍射；以及(2)在用于集成电路的硅晶片和芯片上的线性(线状)特征的形状重建的反演算法中利用衍射二维场。这项研究本质上是数学性质的，是由集成电路行业的关键问题驱动的，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)利用复变量理论中的自相似和矢量边值问题，实现新的矢量绕射理论；(2)考虑到时域和频域数据的优劣和数据采集的可行性，开始初步研究硅衬底边缘特征测量的光学逆散射问题。如果成功，这些衍射解和反演方法将被证明对各种应用问题在技术上是有益的。然而，如果它们能够通过自动化计量手段提高产量，它们的最大潜力最终可能在集成电路行业发挥出来。预计这一系列研究的积极成果最终将有助于IC计量实用、自动化检测仪器的理论研究。这将对集成电路行业的生产率产生重大影响。这里所寻求的矢量绕射解本身对于声纳、雷达和光学应用是有用的。

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.