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Identification of Probabilistic Input Data for a Glue-Die-Package Problem

  • Roland Pulch
  • Piotr Putek
  • Herbert De Gersem
  • Renaud Gillon
Conference paper
Part of the Mathematics in Industry book series (MATHINDUSTRY, volume 26)

Abstract

In mathematical models, physical or geometrical parameters often involve uncertainties due to measurement errors, estimations or imperfections of an industrial production. An uncertainty quantification can be performed by a stochastic description, where parameters are substituted by random variables or random processes. The probability distributions of the parameters have to be predetermined as an input to the stochastic model. However, the variability of input parameters often cannot be measured directly, whereas the output quantities are available. We consider a test problem from nanoelectronics, where a piece of glue connects a die and a package. The geometrical parameters as well as the material parameters are uncertain for the piece of glue. We fit the input probability distributions of the random parameters to measurements of the output, which represents a kind of inverse problem. For this purpose, a minimization problem is defined including a piecewise linear approximation of the cumulative distribution functions. We present numerical results for this test problem.

Notes

Acknowledgements

This work is part of the project nanoCOPS (nanoelectronic COupled Problems Solutions) supported by the European Union in the FP7-ICT-2013-11 program (grant agreement no. 619166). The authors are indebted to Dr. Jan ter Maten (Bergische Universität Wuppertal, Germany), Prof. Volkmar Liebscher (Ernst-Moritz-Arndt-Universität Greifswald, Germany) and Dr. Tanja Clees (Fraunhofer-Institut SCAI, Sankt-Augustin, Germany) for helpful discussions.

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Copyright information

© Springer International Publishing AG, part of Springer Nature 2017

Authors and Affiliations

  • Roland Pulch
    • 1
  • Piotr Putek
    • 2
  • Herbert De Gersem
    • 3
  • Renaud Gillon
    • 4
  1. 1.Institute for Mathematics and Computer ScienceErnst-Moritz-Arndt-Universität GreifswaldGreifswaldGermany
  2. 2.Chair of Applied Mathematics and Numerical AnalysisBergische Universität WuppertalWuppertalGermany
  3. 3.Computational Electromagnetics Laboratory (TEMF)Technische Universität DarmstadtDarmstadtGermany
  4. 4.ON SemiconductorOudenaardeBelgium

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