Nanoelectromechanics of Piezoresponse Force Microscopy: Contact Properties, Fields Below the Surface and Polarization Sw
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Nanoelectromechanics of Piezoresponse Force Microscopy: Contact Properties, Fields Below the Surface and Polarization Switching S.V. Kalinin,1 Junsoo Shin,1,2 M. Kachanov,3 E. Karapetian,3 and A.P. Baddorf1 1
Condensed Matter Sciences Division, Oak Ridge National Laboratory, Oak Ridge, TN 37831 Department of Physics and Astronomy, The University of Tennessee, Knoxville, TN 37996 3 Department of Mechanical Engineering, Tufts University, Medford, MA 02155 2
ABSTRACT To achieve quantitative interpretation of Piezoresponse Force Microscopy (PFM), including resolution limits, tip bias- and strain-induced phenomena and spectroscopy, knowledge of elastic and electrostatic field distributions below the tip is required. The exact closed form solution of the coupled electroelastic problem for piezoelectric indentation is derived and used to obtain the tip-induced electric field and strain distribution in the ferroelectric material. This establishes a complete continuum mechanics description of the PFM imaging mechanism. These solutions are reduced to the point charge/force behavior for large separations from contact, and the applicability limits and charge/force magnitude for these models are established. The implications of these results for ferroelectric polarization switching processes are analyzed. INTRODUCTION Multiple applications of ferroelectric materials as actuators, electrooptical materials, and nonvolatile memory components has motivated a number of studies of local ferroelectric behavior using PFM [1,2]. Applications including ferroelectric domain imaging and studies of temporal and thermal evolution of domain structures require qualitative interpretation of the PFM image in terms of ferroelectric domain morphology. In recent years, significant attention was attracted to quantitative studies of local ferroelectric behavior, including hysteresis loop measurements, depth dependence of ferroelectric properties [3], and ferroelectric size effects [4]. Another set of applications is related to the PFM engineering and control of domain structures. This can be used as potential high-density ferroelectric storage [5,6]; alternatively, polarization dependent reactivity in the acid etching [7] or metal photodeposition processes [8] can be used to engineer nanoscale structures (ferroelectric lithography). It is recognized that PFM imaging and polarization switching mechanisms are governed by the interplay of the electrostatic and elastic fields induced by the tip. Examples of this behavior include local polarization suppression by the stress [9] or ferroelectroelastic polarization switching [10]. Here we extend Hertzian contact mechanics for ferroelectric materials and analyze the structure of the electroelastic fields below the tip using an exact closed form solution of the piezoelectric indentation problem. THEORETICAL DEVELOPMENT Hertzian mechanics for spherical indentation To describe PFM mechanism, we consider a transversely isotropic piezoelectric halfspace pressed upon by a spherical indenter. General elast
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