Nanoscale Investigation of Polycrystalline Ferroelectric Materials via Piezoresponse Force Microscopy

The analytical solution for the displacements of an anisotropic piezoelectric material in the uniform electric field is presented for practical use in the “global excitation mode” of piezoresponse force microscopy. The solution is given in the Wolfram Mathematica interactive program code, allowing the derivation of the expression of the piezoresponse both in cases of the anisotropic and isotropic elastic properties. The piezoresponse’s angular dependencies are analyzed using model lithium niobate and barium titanate single crystals as examples. The validity of the isotropic approximation is verified in comparison to the fully anisotropic solution. The approach developed in the paper is important for the quantitative measurements of the piezoelectric response in nanomaterials as well as for the development of novel piezoelectric materials for the sensors/actuators applications.

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Piezoresponse Force Microscopy

Microscopy Today ◽

10.1017/s1551929509990988 ◽

2009 ◽

Vol 17 (6) ◽

pp. 10-15 ◽

Cited By ~ 2

Author(s):

Roger Proksch ◽

Sergei Kalinin

Keyword(s):

Electromechanical Coupling ◽

Cardiac Activity ◽

Piezoresponse Force Microscopy ◽

Ferroelectric Materials ◽

Inorganic Materials ◽

Active Materials ◽

Force Microscopy ◽

Nanoscale Imaging ◽

Imaging Sensors ◽

Mechanical Phenomena

Coupling between electrical and mechanical phenomena is an important feature of functional inorganic materials and biological systems alike. The applications of electromechanically active materials include sonar, ultrasonic and medical imaging, sensors, actuators, and energy-harvesting technologies, as well as non-volatile computer memories. Electromechanical coupling in electromotor proteins and cellular membranes is the universal basis for biological functionalities from hearing to cardiac activity. The future will undoubtedly see the emergence of broad arrays of piezoelectric, biological, and molecular-based electromechanical systems to allow mankind the capability not only to “think” but also “act” on the nanoscale. The need for probing electromechanical functionalities has led to the development of Piezoresponse Force Microscopy (PFM) as a tool for local nanoscale imaging (Figures 1 and 2), spectroscopy, and manipulation of piezoelectric and ferroelectric materials.

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Observation of the Poling Process in Ferroelectric Ceramics Using Piezoresponse Force Microscopy

Volume 2: Mechanics and Behavior of Active Materials; Integrated System Design and Implementation; Bio-Inspired Materials and Systems; Energy Harvesting ◽

10.1115/smasis2012-8037 ◽

2012 ◽

Author(s):

K. L. Kim ◽

J. E. Huber

Keyword(s):

Electric Field ◽

Domain Structure ◽

Piezoresponse Force Microscopy ◽

Ferroelectric Materials ◽

Ferroelectric Ceramics ◽

Pixel Intensity ◽

Poling Process ◽

Force Microscopy ◽

Domain Evolution ◽

Domain Structures

Evolution of the domain structure in bulk polycrystalline PZT during poling was studied using Piezoresponse Force Microscopy (PFM). For the study, two different experimental methods were employed. First, a trapezoidal PZT specimen was subjected to electric field so as to produce a wide variation of electric field intensity in the specimen. PFM images were then acquired from several different areas that have experienced different field strengths. Histograms of pixel intensity show a distinct difference in the pattern of piezoresponse signal between poled and unpoled areas. The presence of non-180° domain structure in the scanned area significantly affects the histogram pattern. At high levels of electric field the presence of mainly 180° domain structures leads to a bi-modal M-shaped histogram. To illustrate the evolution of the non-180° domain structure, in-plane poling was conducted with the electric field level increased in steps, and the domain evolution process was observed by PFM after each step. The resulting images demonstrate that non-180° domain structures gradually disappear from the specimen surface during the poling process. The PFM data can be exploited to study domain evolution in bulk ferroelectric materials via both qualitative observation and statistical analysis.

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A New Modeling Framework for Piezoresponse Force Microscopy

Volume 10: Mechanics of Solids and Structures, Parts A and B ◽

10.1115/imece2007-42504 ◽

2007 ◽

Author(s):

Amin Salehi-Khojin ◽

Nader Jalili

Keyword(s):

Data Storage ◽

Piezoresponse Force Microscopy ◽

Input Voltage ◽

Ferroelectric Materials ◽

Control Input ◽

Modeling Framework ◽

Contact Mode ◽

Force Microscopy ◽

Wide Range ◽

Tip Mass

Piezoresponse force microscopy (PFM) has evolved into useful tool for measurement of local functionality of ferroelectric materials which shows great potential for applications such as data storage, ferroelectric lithography and nonvolatile memories. Better understanding of current techniques which are applied in the scale of single grain requires a straightforward analytical theory to map the PFM response for a wide range of typical experimental parameters. To this end, a new modeling framework is presented for a PFM which is modeled as a suspended cantilever beam with a tip mass. More specifically, the beam is considered to vibrate in all three directions, while subjected to a bias input voltage. The Hamilton’s principle is used to derive the governing equations. The local electrostatic forces on the tip and distributed forces acting on the cantilever are also taken into account in the current modeling framework. Since the sample and tip are in the contact mode and any changes in the topography of surface will affect the indentation depth of indenter, the boundary control input force is used at the base unit. Moreover, the free end of beam with the equivalent mass of tip is connected to springs in the vertical, longitudinal and lateral directions to represent the resistance of piezoelectric material to tip movement. It is shown that the vertical bending is coupled to longitudinal displacement and lateral bending is coupled to torsion through the friction between tip and sample.

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Frequency-Dependent Electromechanical Response in Ferroelectric Materials Measured via Piezoresponse Force Microscopy

MRS Proceedings ◽

10.1557/proc-784-c11.3 ◽

2003 ◽

Vol 784 ◽

Cited By ~ 8

Author(s):

I. K. Bdikin ◽

V. V. Shvartsman ◽

S-H. Kim ◽

J. Manuel Herrero ◽

A. L. Kholkin

Keyword(s):

Simple Model ◽

Piezoresponse Force Microscopy ◽

Ferroelectric Materials ◽

Piezoelectric Response ◽

Driving Frequency ◽

Polarization Direction ◽

Frequency Dependent ◽

Force Microscopy ◽

Out Of Plane ◽

Frequency Phase

ABSTRACTLocal piezoelectric signal is measured via Piezoresponse Force Microscopy (PFM) in PbZr0.3Ti0.7O3 films and PbZr1/3Nb2/3O3-0.045PbTiO3 single crystals. It is observed that the amplitude of piezoelectric response is almost independent on frequency for vertical (out of plane) signal and strongly decreases with increasing frequency in the range 10–100 kHz for lateral (in-plane) response. Moreover, the in-plane piezoelectric contrast is reversed when the measurements are done at high enough frequency (phase shift exceeds 90°). As a result, the inplane polarization direction can be misinterpreted if the driving frequency exceeds certain level. For the explanation of observed effect a simple model is proposed that takes into account a possible slip between the conductive PFM tip and moving piezoelectric surface. The implications of the observed frequency-dependent contrast for the domain imaging in ferroelectric materials are discussed.

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