Efficient Rigorous Coupled-Wave Analysis Simulation of Mueller Matrix Ellipsometry of Three-Dimensional Multilayer Nanostructures

Abstract

Mueller matrix ellipsometry (MME) is a powerful metrology tool for nanomanufacturing. The application of MME necessitates electromagnetic computations for inverse problems of metrology determination in both the conventional optimization process and the recent neutral network approach. In this study, we present an efficient, rigorous coupled-wave analysis (RCWA) simulation of multilayer nanostructures to quantify reflected waves, enabling the fast simulation of the corresponding Mueller matrix. Wave propagations in the component layers are characterized by local scattering matrices (s-matrices), which are efficiently computed and integrated into the global s-matrix of the structures to describe the optical responses. The performance of our work is demonstrated through three-dimensional (3D) multilayer nanohole structures in the practical case of industrial Muller matrix measurements of optical diffusers. Another case of plasmonic biosensing is also used to validate our work in simulating full optical responses. The results show significant numerical improvements for the examples, demonstrating the gain in using the RCWA method to address the metrological studies of multilayer nanodevices.

Sensitivity analysis of optical scatterometry technique for high-aspect ratio trench measurement

“…We develop a method to evaluate the sensitivity using the Mueller matrix (MM) formalism on periodic trenches. All the study is based on simulated spectra based on an optimized RCWA code developed in-house to simulate the 2D gratings scattering spectra [5].…”

“…❖ Mueller matrix Spectroscopic Ellipsometry OCD (SE-OCD) scatterometry configuration gives us Rss and Rpp, but it is possible to extract even more information. Having more points and more coefficients can increase the accuracy and statistical robustness of our study [5][6][7]. A complete description of the polarization state can be obtained through polarimetry with the use of Mueller matrix (MM-OCD configuration) which takes into consideration the cross-polarization effects of the light.…”

“…Those correspond to the same diffraction orders but different polarization states. [5,7] The elements can be normalized according to M11 [8]. Thus nine elements in bold in Eq.8, can describe the Mueller matrix, since: m11= 1,m12= m21, m13= -m31,m14= m41,m32= m23,m42= m24 ,m43= -m34 .…”

“…Their values are chosen according to the multiplication of a factor and the ratio of the period of the structure over the wavelength of the incident light. By choosing the number of diffraction orders to include in the simulation, we can control the level of accuracy of the simulation results and the computation time [5,9,10]. By increasing the factor, the simulation will be more accurate, but it will also be more computationally demanding [11].…”

Condition-number-based measurement configuration optimization for nanostructure reconstruction by optical scatterometry

“…First, the operation of the forward model is usually time-consuming in optical scatterometry. Rigorous coupled wave analysis (RCWA) is more effective in calculating periodic structures compared to other methods [19]. However, as the architectures become more complex, the computational efficiency significantly decreases due to the frequent invocation of RCWA with a greater number of slicing layers and higher truncated orders.…”