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Spatially Resolved Measurement of the Stress Tensor in Thin Membranes Using Bending Waves

Reimar Waitz*, Carolin Lutz†, Stephan Nößner‡, Michael Hertkorn§, and Elke Scheer∥

  • Department of Physics, University Konstanz, 78457 Konstanz, Germany

  • *Present address: Rational AG, 86889 Landsberg am Lech, Germany.
  • †Present address: National Institute for Materials Science and Waseda University, 1-2-1 Sengen, Tsukuba Ibaraki, 3050047 Japan.
  • ‡Present address: Robert Bosch GmbH, 71701 Schwieberdingen, Germany.
  • §Present address: ZF Friedrichshafen AG, 88046 Friedrichshafen, Germany.
  • ∥elke.scheer@uni-konstanz.de
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Phys. Rev. Applied 3, 044002 – Published 9 April, 2015

DOI: https://doi.org/10.1103/PhysRevApplied.3.044002

Abstract

The mode shape of bending waves in thin silicon and silicon-carbide membranes is measured as a function of space and time, using a phase-shift interferometer with stroboscopic light. The mode shapes hold information about all the relevant mechanical parameters of the samples, including the spatial distribution of static prestress. We present a simple algorithm to obtain a map of the lateral tensor components of the prestress, with a spatial resolution much better than the wavelength of the bending waves. The method is not limited to measuring the stress of bending waves. It is applicable in almost any situation, where the fields determining the state of the system can be measured as a function of space and time.

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Phys. Rev. Applied 3, 044002– Published 9 April, 2015
  • Received 15 October 2014

© 2015 American Physical Society

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