General solution for the complex frequency shift in microwave measurements of thin films

D.-N. Peligrad, B. Nebendahl, M. Mehring, A. Dulčić, M. Požek, and D. Paar
Phys. Rev. B 64, 224504 – Published 20 November 2001
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Abstract

Perturbation of a microwave cavity by a small sample with variable dielectric, magnetic, or conducting properties is considered. The complex frequency shift is derived in terms of a volume integral, or equivalently, in terms of a surface integral. These are used to obtain a general formula for thin films in the microwave electric field maximum. The complex frequency shift depends on the depolarization factor of the film and on its thickness in a nontrivial way. The previously known expressions for the complex frequency shift are shown to be good approximations of the present solution in the low and high conductivity limits. Our formula is applied to calculate the signal shapes in superconducting films of various geometric parameters and conductivities. It is shown that a diversity of signal shapes can result, and experimental support of those shapes is provided. The role of the dielectric substrate on which the thin film is grown is simply reduced to an asymmetry effect.

  • Received 30 May 2001

DOI:https://doi.org/10.1103/PhysRevB.64.224504

©2001 American Physical Society

Authors & Affiliations

D.-N. Peligrad*,†, B. Nebendahl, and M. Mehring

  • 2. Physikalisches Institut, Universität Stuttgart, D-70550 Stuttgart, Germany

A. Dulčić, M. Požek, and D. Paar

  • Department of Physics, Faculty of Science, University of Zagreb, POB 331, 10002 Zagreb, Croatia

  • *Present address: Philips Research Laboratories, Weisshausstrasse 2, D-52066, Aachen, Germany.
  • To whom correspondence should be addressed. Electronic address: dulcic@faust.irb.hr; Electronic address: dragos.peligrad@philips.com
  • Present address: Agilent Technologies, Herrenberger Str. 130, D-71034, Böblingen, Germany.

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Issue

Vol. 64, Iss. 22 — 1 December 2001

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