Rigorous Coupled-wave Analysis Algorithm Research Articles

Rigorous Coupled Wave Analysis of Radially and Azimuthally-inhomogeneous, Elliptical, Cylindrical Systems

Rigorous Coupled Wave Analysis (RCWA) (used for electromagnetic (EM) analysis of planar diffraction gratings) has been applied to solve EM scattering and diffraction problems for spatially inhomogeneous, cylindrical, elliptical systems. The RCWA algorithm and an appropriate method for matching EM boundary conditions in the elliptical system are described herein. Comparisons of the eigenfunctions determined by RCWA (found in spatially homogeneous elliptical regions) and Mathieu functions are presented and shown to agree closely with one another. Numerical results of scattering from a uniform elliptical shell system (excited by an electrical surface current) obtained by using both a Mathieu function expansion method and by using the RCWA algorithm are presented and also shown to agree closely with one another. The RCWA algorithm was used to study EM scattering and diffraction from an elliptical, azimuthally inhomogeneous dielectric permittivity, step profile system. EM field matching and power conservation were shown to hold for this step profile example. A comparison of the EM fields of the step profile elliptical shell example and that of a uniform profile elliptical shell having the same excitation and bulk material parameters (permittivity and permeability) was made and significant differences of the EM fields of the two systems were observed.

John Dalton

In single patterning, the increase of odd order diffractive power and decrease of even order diffractive power may improve the wafer alignment performance. A Fourier model is given to quantitatively describe the diffractive optical power of grating structures. Four novel alignment mark structures with higher odd order wafer qualities (WQs) have been optimized based on the model. The accuracy of our model has been validated with almost the same results for different alignment marks using our model and rigorous coupled wave analysis (RCWA). Moreover, three dimensions (3D) of alignment mark should be optimized to get higher WQs for self-aligned double patterning (SADP). Our paper proposes a model to simplify the 3D RCWA algorithm where WQs of SADP grating structures could be split into two different one-direction grating structures. The advantage of the equation makes the evaluation of different grating period of SADP mark fast, accurate and simple. The models and structures of all the designed alignment marks will make it easier for engineers to choose the property alignment mark faced with single patterning or SADP process.