Abstract
Anisotropic lamellar sub-wavelength gratings (nanogratings) are described by Effective Medium Approximation (EMA). Analytical formulas for effective medium optical parameters of nanogratings from arbitrary anisotropic materials are derived using approximation of zero-order diffraction mode. The method is based on Rigorous Coupled Wave Analysis (RCWA) combined with proper Fourier factorization method. Good agreement between EMA and the rigorous model is observed, where slight differences are explained by the influence of evanescent higher Fourier harmonics in the nanograting.
Highlights
Traditional optical characterization methods propose considerable instrumental advantages, for example, non-destructive and non-invasive character, fast response for monitoring of real-time processes, and relatively simple and cheap experimental setups
We show that the sub-wavelength gratings can be described by an effective medium with parameters slightly different from those obtained from the simple Effective Medium Approximation (EMA)
The main result of this article is the proposition of the general method of obtaining analytical EMA formulas for arbitrary permittivity tensor element
Summary
Traditional optical characterization methods (reflection and transmission spectroscopy, ellipsometry) propose considerable instrumental advantages, for example, non-destructive and non-. The optical methods become standards of process monitoring and quality control in semiconductor technology. There are several rigorous methods that differ by solution approach, numerical implementation, applicability, and computation time. Effective Medium Approximation (EMA) provide efficient description of sub-wavelength structures as surface roughness [6], nanocomposite and polycrystalline materials [7, 8, 9], and periodic structures [10, 11, 12]. This article deals with effective permittivity tensor of arbitrary anisotropic sub-wavelength lamellar gratings. We show that the sub-wavelength gratings can be described by an effective medium with parameters slightly different from those obtained from the simple EMA. The differences are explained as effects of the higher evanescent Fourier harmonics in the nanograting
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