Parameter-oriented reduction strategies for a thermo-mechanical model of extreme ultraviolet reticles

C. Bikcora, S. Weiland

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Abstract

With the demands for shrinkage in feature sizes becoming more than ever, the extreme ultraviolet (EUV) lithography is the route pursued by the industry's leading authorities. Leaving the strive for achieving a high source power aside, we hereby consider one of the most prominent disrupters of imaging quality: heating induced deformation of EUV reticles. To diminish its detrimental effect, a model-based prediction scheme is ideally used for steering certain actuators in an EUV tool. To enable such a solution in practice, computationally fast models are required. Along this direction, we use the POD and DEIM reduction methods on finite-element-based thermal and mechanical equations that relate to a recent geometry where cooling channels are placed nearby the reticle. Several sensor measurements approximating the initial thermal state of this model are treated as parameters, and two parameter-oriented reduction methods are designed which we refer to as local reduction (LR) and decomposed reduction (DR), respectively. The former builds local simplified models based on clustering of the parameters, whereas the latter expands the terms in the model so that the reduction is independent of the parameters. The results indicate that only two sensors are sufficient for an accurate characterization of the initial condition. Furthermore, among the evaluated methods, similar accuracies were observed for various tested scenarios, and therefore, it is concluded that the LR is more suitable for this application due to its less intricate structure.
Original languageEnglish
Title of host publication2016 IEEE Conference on Control Applications, CCA 2016
Place of PublicationPiscataway
PublisherInstitute of Electrical and Electronics Engineers
Pages1149-1154
Number of pages6
ISBN (Electronic)978-1-5090-0755-4
ISBN (Print)978-1-5090-0756-1
DOIs
Publication statusPublished - 10 Oct 2016
Event2016 IEEE Conference on Control Applications (CCA 2016) - Buenos Aires, Argentina
Duration: 19 Sep 201622 Oct 2016
http://www.msc2016.org/

Conference

Conference2016 IEEE Conference on Control Applications (CCA 2016)
Abbreviated titleCCA2016
CountryArgentina
CityBuenos Aires
Period19/09/1622/10/16
Internet address

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