Nanoelectromechanics of piezoresponse force microscopy

To achieve quantitative interpretation of piezoresponse force microscopy (PFM), including resolution limits, tip bias- and strain-induced phenomena and spectroscopy, analytical representations for tip-induced electroelastic fields inside the material are derived for the cases of weak and strong indentation. In the weak indentation case, electrostatic field distribution is calculated using an image charge model. In the strong indentation case, the solution of the coupled electroelastic problem for piezoelectric indentation is used to obtain the electric field and strain distribution in the ferroelectric material. This establishes a complete continuum mechanics description of the PFM contact mechanics and imaging mechanism. The electroelastic field distribution allows signal generation volume in PFM to be determined. These rigorous solutions are compared with the electrostatic point-charge and sphere-plane models, and the applicability limits for asymptotic point-charge and point-force models are established. The implications of these results for ferroelectric polarization switching processes are analyzed.

[1]  I. Sevostianov,et al.  Penny-shaped and half-plane cracks in a transversely isotropic piezoelectric solid under arbitrary loading , 2000 .

[2]  S. Timoshenko,et al.  Theory of elasticity , 1975 .

[3]  N. M. Miskovsky,et al.  Three‐dimensional electrostatic potential, and potential‐energy barrier, near a tip‐base junction , 1994 .

[4]  G. Temple.  Static and Dynamic Electricity , 1940, Nature.

[5]  Y. Rosenwaks,et al.  Ferroelectric domain breakdown. , 2003, Physical review letters.

[6]  G. Suchaneck,et al.  Scanning force microscopy investigation of the Pb(Zr0.25Ti0.75)O3/Pt interface , 2002 .

[7]  P. Günter,et al.  Higher order ferroic switching induced by scanning force microscopy. , 2001, Physical review letters.

[8]  Steve Dunn,et al.  Atomic Polarization and Local Reactivity on Ferroelectric Surfaces: A New Route toward Complex Nanostructures , 2002 .

[9]  R. Waser,et al.  Piezoresponse force microscopy of lead titanate nanograins possibly reaching the limit of ferroelectricity , 2002 .

[10]  A. Gruverman,et al.  Switching properties of self-assembled ferroelectric memory cells , 1999 .

[11]  M. Molotskii.  Generation of ferroelectric domains in atomic force microscope , 2003 .

[12]  M. Weihnacht,et al.  How to extract spontaneous polarization information from experimental data in electric force microscopy , 1998 .

[13]  M. Hanson.  The Elastic Field for Spherical Hertzian Contact Including Sliding Friction for Transverse Isotropy , 1992 .

[14]  Rosalía Poyato,et al.  Stress-induced suppression of piezoelectric properties in PbTiO3:La thin films via scanning force microscopy , 2003 .

[15]  V. I. Fabrikant,et al.  Mixed Boundary Value Problems of Potential Theory and Their Applications in Engineering , 1991 .

[16]  Jong Up Jeon,et al.  Read/write mechanisms and data storage system using atomic force microscopy and MEMS technology. , 2002, Ultramicroscopy.

[17]  J. Ouyang,et al.  Formation of 90° elastic domains during local 180° switching in epitaxial ferroelectric thin films , 2004 .

[18]  Hiroshi Tokumoto,et al.  Imaging and control of domain structures in ferroelectric thin films via scanning force microscopy , 1998 .

[19]  U. Gösele,et al.  Patterning and switching of nanosize ferroelectric memory cells , 1999 .

[20]  Technology,et al.  Domain wall creep in epitaxial ferroelectric Pb(Zr(0.2)Ti(0.08)O(3) thin films. , 2002, Physical review letters.

[21]  M. Allegrini,et al.  Surface deformation and ferroelectric domain switching induced by a force microscope tip on a La-modified PbtiO3 thin film , 2003 .

[22]  S. Hudlet,et al.  Evaluation of the capacitive force between an atomic force microscopy tip and a metallic surface , 1998 .

[23]  Kenji Kitamura,et al.  Microscale to nanoscale ferroelectric domain and surface engineering of a near-stoichiometric LiNbO3 crystal , 2003 .

[24]  H. Yokoyama,et al.  Nonresonant detection of electric force gradients by dynamic force microscopy , 1994 .

[25]  Sergei V. Kalinin,et al.  Imaging mechanism of piezoresponse force microscopy of ferroelectric surfaces , 2002 .

[26]  Subra Suresh,et al.  THEORY OF INDENTATION OF PIEZOELECTRIC MATERIALS , 1999 .

[27]  J. E. Stern,et al.  Contact electrification using force microscopy. , 1989, Physical review letters.

[28]  D. A. Dunnett.  Classical Electrodynamics , 2020, Nature.

[29]  I. Sevostianov,et al.  The principle of correspondence between elastic and piezoelectric problems , 2002 .

[30]  J. Melngailis,et al.  Scaling of ferroelectric and piezoelectric properties in Pt/SrBi2Ta2O9/Pt thin films , 1999 .

[31]  A. E. Giannakopoulos,et al.  Strength Analysis of Spherical Indentation of Piezoelectric Materials , 2000 .

[32]  U. Böttger,et al.  Differentiating 180° and 90° switching of ferroelectric domains with three-dimensional piezoresponse force microscopy , 2000 .

[33]  R. Waser,et al.  Three-Dimensional Electric Field Probing of Ferroelectrics on the Nanometer Scale Using Scanning Force Microscopy , 2001 .

[34]  N. M. Miskovsky,et al.  A Green's function solution to the image and multiple image interactions for hyperboloidal geometry: Application to metallic pointcontact infrared detectors , 1981 .

[35]  Yuhuan Xu,et al.  Ferroelectric Materials and Their Applications , 2023, Japanese Journal of Applied Physics.

[36]  Mark Kachanov,et al.  Point force and point electric charge in infinite and semi-infinite transversely isotropic piezoelectric solids , 2000 .

[37]  R. Landauer.  Electrostatic Considerations in BaTiO3 Domain Formation during Polarization Reversal , 1957 .

[38]  E. Mele.  Screening of a point charge by an anisotropic medium: Anamorphoses in the method of images , 2001 .

[39]  Nagarajan,et al.  Measurement of internal stresses via the polarization in epitaxial ferroelectric films , 2000, Physical review letters.

[40]  Sergei V. Kalinin,et al.  Ferroelectric Lithography of Multicomponent Nanostructures , 2004 .

[41]  Y. Eugene Pak,et al.  Principle of ferroelectric domain imaging using atomic force microscope , 2001 .

[42]  Warren P. Mason,et al.  Ultrasonic Transducer Materials , 1971 .