Comparison of solutions to the scatterometry inverse problem

Abstract

Scatterometry is a novel optical metrology that has received considerable attention in the silicon industry in the past few years. Based on the analysis of light scattered from a periodic sample, scatterometry technology can be thought of as consisting of two parts known as the forward problem and the inverse problem. In the forward problem, a scatterometer "signature" is measured. The signature is simply the measured optical response of the scattering features to some incident illumination, like laser light. In the inverse problem, the signature is analyzed in order to determine the parameters (such as linewidth, thickness, profile, etc) of the scattering features. Typically a rigorous electrodynamic model is used in the solution to the inverse problem, but due to the complexity of the model there is no direct analytic solution. Instead, a variety of numerical methods to solve the inverse problem have been proposed and utilized.The earliest widely used method of solution to the inverse problem involved the generation of a "library" of scatter signatures corresponding to discrete parameter combinations of the structure being measured. Once the library was generated, it was then searched in order to determine the best match to the measured signature. The parameters of the best match were then reported as the parameters of the measured signature. As the technology matured, other methods such as model optimization techniques also emerged. In fact, a variety of alternate techniques have been explored and reported, but a general study comparing the results (and hence the strengths and weaknesses) of the various techniques has yet to be performed.In this research, we shall report results from using several different solutions to the inverse problem on two applications (patterned resist and etched poly). The solution methods shall include the classic library search method as well as three common optimization methods. The results will show that each technique has strengths and weaknesses. For example, the library search methods are generally the most robust but also the most time consuming, and the optimization methods, while fast, are prone to reporting a local but not global minima.

Development of functional sub-100 nm structures with 3D two-photon polymerization technique and optical methods for characterization

“…Measurement and inclusion of the transfer function of each of these optical elements is desirable and probably will allow getting better agreement in future. As soon as better agreement is reached probably, also other standard optimization algorithms 28 instead of the mentioned library search should be taken into account.…”

Solving the inverse grating problem by white light interference Fourier scatterometry

“…Raymond et al 27 made a helpful comparison of the application of standard optimization algorithms to scatterometry.…”

Simulations of Scatterometry Down to 22 nm Structure Sizes and Beyond with Special Emphasis on LER

“…Besides the measurement technique itself the simulation and reconstruction is of great importance. A simple library search is largely applied, for ID periodic structures a real-time simulation with different techniques for quick scaiming of the parameter space like Recursive Random Search, Genetic Algorithm or Levenberg-Marquardt Regression are apphed [8]. In the recent time, application of scatterometry to 2D periodic structures has been widely investigated.…”