The Fourier modal method (FMM), also referred to as Rigorous Coupled-Wave Analysis (RCWA), is based on Fourier-mode expansions and is inherently built for periodic structures such as diffraction gratings. When the infinite periodicity assumption is not realistic, the finiteness of the structure has to be incorporated into the model. In this paper we discuss the recent extensions of the FMM for finite structures. First, we explain how an efficient FMM-based method for finite structures is obtained by a reformulation of the governing equations and incorporation of perfectly matched layers (PMLs). Then we show that the computational cost of the method can be further reduced by employing an alternative discretization instead of the classical one. Numerical results demonstrate the characteristics of the discussed FMM-based methods and include a discussion of computational complexities.
This paper extends the area of application of the Fourier modal method from periodic structures to aperiodic
ones, in particular for plane-wave illumination at arbitrary angles. This is achieved by placing perfectly matched
layers at the lateral sides of the computational domain and reformulating the governing equations in terms of a
contrast field which does not contain the incoming field.
The wafer alignment system plays a key role in the reduction of product overlay. This reduction allows shrink of current products and tighter overlay design rules on next generation products. Further reduction of product overlay numbers requires continuous research in the field of interaction between wafer mark and alignment sensor. We explain how this research and various IC manufacturing requirements drive wafer alignment system design and how these requirements are met in two new phase-grating based wafer alignment concepts. This paper describes and compares these two new concepts that extend ASML's current ATHENATM alignment system. The first concept we describe is an extension of ATHENATM which uses a smaller alignment illumination beam. The second concept adds a self-referencing interferometer, combined with a high numerical aperture objective. Each concept targets a specific range of performance parameters, such as greater mark layout flexibility and the possibility to use more than two illumination wavelengths. We will show how both concepts clearly add to the existing ATHENATM sensor performance; focus-tilt sensitivity reduces with a factor of 5 to 20 for concept A and B respectively. Both concepts will be further developed.
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