https://puma.ub.uni-stuttgart.de/tag/Interference%20diffraction%20algorithm%20diffraction_grating%20gratingPUMA RSS feed for /tag/Interference%20diffraction%20algorithm%20diffraction_grating%20grating2026-04-03T23:11:07+02:00https://puma.ub.uni-stuttgart.de/bibtex/28369a5b0b9c1d5b9bd78f25cc22c6d13/florianbienertflorianbienert2022-06-09T10:04:50+02:00LIL algorithm chirp diffraction diffraction_grating grating interference interference_lithography myown peer therory <span data-person-type="author" class="authorEditorList "><span><span itemtype="http://schema.org/Person" itemscope="itemscope" itemprop="author"><a title="Florian Bienert" itemprop="url" href="/person/1503e2f12069fc6f23a499ccd4bb69f64/author/0"><span itemprop="name">F. Bienert</span></a></span>, </span><span><span itemtype="http://schema.org/Person" itemscope="itemscope" itemprop="author"><a title="Thomas Graf" itemprop="url" href="/person/1503e2f12069fc6f23a499ccd4bb69f64/author/1"><span itemprop="name">T. Graf</span></a></span>, </span> and <span><span itemtype="http://schema.org/Person" itemscope="itemscope" itemprop="author"><a title="Marwan Abdou Ahmed" itemprop="url" href="/person/1503e2f12069fc6f23a499ccd4bb69f64/author/2"><span itemprop="name">M. Abdou Ahmed</span></a></span></span>. </span><span class="additional-entrytype-information"><span itemtype="http://schema.org/PublicationIssue" itemscope="itemscope" itemprop="isPartOf"><em><span itemprop="journal">Optics Express</span>, </em> <em><span itemtype="http://schema.org/PublicationVolume" itemscope="itemscope" itemprop="isPartOf"><span itemprop="volumeNumber">30 </span></span>(<span itemprop="issueNumber">13</span>): <span itemprop="pagination">22410</span></em> </span>(<em><span>June 2022<meta content="June 2022" itemprop="datePublished"/></span></em>)</span>Thu Jun 09 10:04:50 CEST 2022Optics Expressjun1322410Theoretical investigation on the elimination of the period chirp by deliberate substrate deformations302022LIL algorithm chirp diffraction diffraction_grating grating interference interference_lithography myown peer therory 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.https://puma.ub.uni-stuttgart.de/bibtex/28369a5b0b9c1d5b9bd78f25cc22c6d13/ifswifsw2022-06-09T10:04:50+02:00myown chirp diffraction diffraction_grating interference_lithography LIL from:florianbienert grating peer interference therory algorithm <span data-person-type="author" class="authorEditorList "><span><span itemtype="http://schema.org/Person" itemscope="itemscope" itemprop="author"><a title="Florian Bienert" itemprop="url" href="/person/1503e2f12069fc6f23a499ccd4bb69f64/author/0"><span itemprop="name">F. Bienert</span></a></span>, </span><span><span itemtype="http://schema.org/Person" itemscope="itemscope" itemprop="author"><a title="Thomas Graf" itemprop="url" href="/person/1503e2f12069fc6f23a499ccd4bb69f64/author/1"><span itemprop="name">T. Graf</span></a></span>, </span> and <span><span itemtype="http://schema.org/Person" itemscope="itemscope" itemprop="author"><a title="Marwan Abdou Ahmed" itemprop="url" href="/person/1503e2f12069fc6f23a499ccd4bb69f64/author/2"><span itemprop="name">M. Abdou Ahmed</span></a></span></span>. </span><span class="additional-entrytype-information"><span itemtype="http://schema.org/PublicationIssue" itemscope="itemscope" itemprop="isPartOf"><em><span itemprop="journal">Optics Express</span>, </em> <em><span itemtype="http://schema.org/PublicationVolume" itemscope="itemscope" itemprop="isPartOf"><span itemprop="volumeNumber">30 </span></span>(<span itemprop="issueNumber">13</span>): <span itemprop="pagination">22410</span></em> </span>(<em><span>June 2022<meta content="June 2022" itemprop="datePublished"/></span></em>)</span>Thu Jun 09 10:04:50 CEST 2022Optics Expressjun1322410Theoretical investigation on the elimination of the period chirp by deliberate substrate deformations302022myown chirp diffraction diffraction_grating interference_lithography LIL from:florianbienert grating peer interference therory algorithm 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.