Abstract
A method has been established for calculating the interaction pressures between a half-space consisting of a uniform material and a half-space with a two-dimensional (2D) periodic material distribution in the in-plane directions. The periodic material distribution is expanded as a complex Fourier series and the interaction pressures are derived from the Lennard-Jones potential, which includes both attractive and repulsive terms. The interaction pressures for a general 2D distribution were derived, which is applicable to any periodic distributions of many materials. The equations derived have two contributions: (1) the conventional interaction pressures between half-spaces made of uniform materials and (2) the spatial fluctuation originating from the spatially periodic material distribution. As a typical example of the material distributions, a 2D periodic distribution of two materials is introduced to demonstrate the methods. We present calculation results for parallel and inclined planes, a comparison between 2D and one-dimensional analyses, and the effects of the refractive indices and the duty ratios.
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Matsuoka, H., Kitahama, N. & Fukui, S. Theoretical study of surface interaction pressures of two-dimensional periodic material distributions based on the Lennard-Jones potential. Microsyst Technol 22, 1419–1428 (2016). https://doi.org/10.1007/s00542-016-2881-8
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DOI: https://doi.org/10.1007/s00542-016-2881-8