Prospects and limits of the Rayleigh Fourier approach for diffraction modelling in scatterometry and lithography

Joerg Bischoff

doi:10.1117/12.833489

17 June 2009 Prospects and limits of the Rayleigh Fourier approach for diffraction modelling in scatterometry and lithography

Joerg Bischoff

Author Affiliations +

Proceedings Volume 7390, Modeling Aspects in Optical Metrology II; 73901E (2009) https://doi.org/10.1117/12.833489
Event: SPIE Europe Optical Metrology, 2009, Munich, Germany

Abstract

With ever shrinking feature sizes in semiconductor and photonics industry, the demand and the challenges for optical modelling in terms of accuracy has increased dramatically over the last decade. Rigorous modal diffraction methods such as the RCWA, the Differential method or the C-method provide sufficient accuracy, however, they are rather costly particularly for 3D patterns. In this paper, we are suggesting an approach which is based on the so-called Rayleigh hypothesis. The basic idea of this method is to extend the expansion of the electromagnetic field components into Rayleigh modes inside the grating grooves as opposed to the RCWA where the expansion within the slices is done in so-called Bragg modes. Therefore, the Rayleigh-Fourier method does not need a diagonalization for the decoupling of the modes. It requires only the formation of an interface transition matrix, the elements of which can be computed analytically. As a consequence, it is very fast both for 2D as well as for 3D. Here, we discuss the details of the method and show how it can be combined with other modal methods into one framework. The application limits are discussed in terms of the corrugation depth of the grating, the shape of the grating profile, the pitch and the refraction index contrast. Surprisingly, the method can be applied far beyond the Rayleigh limit in a sort of semi-convergent regime when implemented and utilized carefully. Due to its speed, the method might be an appropriate choice for real time regression particularly for only slightly corrugated multilayer stacks.

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Joerg Bischoff "Prospects and limits of the Rayleigh Fourier approach for diffraction modelling in scatterometry and lithography", Proc. SPIE 7390, Modeling Aspects in Optical Metrology II, 73901E (17 June 2009); https://doi.org/10.1117/12.833489

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