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Authors: Bienert, Florian
Graf, Thomas
Abdou Ahmed, Marwan
Title: Theoretical investigation on the elimination of the period chirp by deliberate substrate deformations
Issue Date: 2022 Zeitschriftenartikel 11 Optics express 30 (2022), pp. 22410-22420
ISSN: 1094-4087
Abstract: We present a theoretical investigation on the approach of deliberately bending the substrate during the exposure within laser interference lithography to compensate for the period chirp. It is shown that the yet undiscovered function of the surface geometry, necessary to achieve the zero-chirp case (i.e. having a perfectly constant period over the whole substrate) is determined by a first-order differential equation. As the direct analytical solution of this differential equation is difficult, a numerical approach is developed, based on the optimization of pre-defined functions towards the unknown analytical solution of the differential equation by means of a Nelder-Mead simplex algorithm. By applying this method to a concrete example, we show that an off-center placement of the substrate with respect to the point sources is advantageous both in terms of achievable period and substrate curvature and that a fourth-order polynomial can greatly satisfy the differential equation leading to a root-mean-square deviation of only 1.4 pm with respect to the targeted period of 610 nm.
Appears in Collections:07 Fakultät Konstruktions-, Produktions- und Fahrzeugtechnik

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