The wafer flexure technique for the determination of the transverse piezoelectric coefficient (d31) of PZT thin films

J. F. Shepard, P. J. Moses, S. Trolier-McKinstry

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This paper describes a simple and inexpensive method for evaluating the transverse piezoelectric coefficient (d31) of piezoelectric thin films. The technique is based upon the flexure of a coated substrate which imparts an ac two-dimensional stress to the piezoelectric film. The surface charge generated via the mechanical loading is converted to a voltage by an active integrator. Plate theory and elastic stress analyses are used to calculate the principal stresses applied to the film. The d31 coefficient can then be determined from knowledge of the electric charge produced and the calculated mechanical stress. For 52/48 sol-gel lead zirconate titanate (PZT) thin films, the d31 coefficient was found to range from -5 to -59 pC/N and is dependent on poling field.

Original languageEnglish (US)
Pages (from-to)133-138
Number of pages6
JournalSensors and Actuators, A: Physical
Issue number1-2
StatePublished - Nov 1 1998


All Science Journal Classification (ASJC) codes

  • Electronic, Optical and Magnetic Materials
  • Instrumentation
  • Condensed Matter Physics
  • Surfaces, Coatings and Films
  • Metals and Alloys
  • Electrical and Electronic Engineering

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