Determination of the Orientation Distribution Function of PZT Ceramics by Piezoresponse Force Microscopy

Michael Lasnik

Research output: ThesisDiploma Thesis


Ferroelectric ceramics like lead zirconate titanate (PZT) offer a large potential for applications such as actuators, transducers, sensors, integrated microelectronics, and memory storage. Such materials consist of regions of uniform polarization, which are called ferroelectric domains. The change in orientation of these domains under the influence of electric field or mechanical stress is at the basis of the outstanding electro-mechanical performances of these materials. Hence, the orientation distribution function (ODF) of the ferroelectric domains is an important figure of merit for analyzing and improving the behavior of ferroelectrics. The first part of this thesis is dedicated to establish a proper measurement setup and data evaluation procedure to obtain the ODF of ferroelectric domains using piezoresponse force microscopy (PFM), it includes a thorough explanation of the whole measurement procedure and required parameters. By measuring the out-of-plane (vertical) and in-plane (lateral) components of the polarization vectors of domains using PFM, a three-dimensional (3D) reconstruction of the domain polarization can be obtained, which is called Vector PFM. Such a 3D reconstruction requires at least one vertical and two lateral (0° and 90° sample rotation) PFM measurements. The measured data is then analyzed and evaluated with the help of a program code developed during this thesis using Wolfram Mathematica 10. The program combines all data of a scan area and performs several image correlation as well as data correction steps. After all these steps, and taking the piezoelectric coefficients of PZT into account, the two solid angles describing the polarization vector orientation (polar angle θ and azimuthal angle φ) are calculated. As a final result the ODF is obtained. Further calculations and a more detailed illustration allows showing the actual analyzed scan area, whereof each pixel is colored according to the polarization vector orientation. The second part of this thesis includes the practical application of the developed PFM setup and evaluation procedure. Here, three differently polarized PZT ceramics (unpoled, in-plane poled, and out-of-plane poled) were investigated by means of Vector PFM. The ODF for each sample was determined by averaging the ODFs of seven independent scan areas from the same sample. The obtained ODFs were generally in good agreement with the expected results. The unpoled sample exhibits a homogeneous distribution of all polarization vector directions. The measurements on the in-plane poled sample result in polarization vectors in the range from 0° to 90° and 270° to 360° φ, as well as 0° to 180° θ. The results from the out-of-plane poled sample reveal that the polarization vector directions are in the range from 0° to 360° φ, as well as 0° to 90° θ. Furthermore, the more detailed illustration displays the domains and provides information about their shape and size. The measured domains appear lamellarly ordered with a length in the range of a few µm and a width of a few hundred nm depending on the sample. In order to verify the data evaluation procedure, two further poling experiments with different DC voltages (25V and 50V) were conducted. Therefore, two smaller areas within each of these two scan areas were poled. One area was poled with a positive voltage, whereas the other was poled with a negative one. Both scan areas were then also investigated by means of Vector PFM. From the results of the poling experiments the actual out-of-plane direction of the polarization vector could be derived.
Translated title of the contributionErmittlung der Orientierungsverteilungsfunktion von PZT-Keramiken mittels Piezoresponse-Rasterkraftmikroskopie
Original languageEnglish
  • Deluca, Marco, Co-Supervisor (external)
  • Kratzer, Markus, Co-Supervisor (internal)
  • Teichert, Christian, Supervisor (internal)
Award date21 Oct 2016
Publication statusPublished - 2016

Bibliographical note

embargoed until 01-09-2021


  • lead zirconate titanate
  • PZT
  • ferroelectric domains
  • polarization vector
  • orientation distribution function
  • ODF
  • piezoresponse force microscopy
  • PFM
  • vector piezoresponse force microscopy
  • Vector PFM

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