Nanoscale electromechanics of paraelectric materials with mobile charges: Size effects and nonlinearity of electromechanical response of SrTiO3films

Nanoscale enables a broad range of electromechanical coupling mechanisms that are forbidden or negligible in the materials. We conduct a theoretical study of the electromechanical response of thin paraelectric films with mobile vacancies (or ions) paradigmatic for capacitor-type measurements in X-ray scattering, piezoresponse force microscopy (PFM), and electrochemical strain microscopy (ESM). Using quantum paraelectric SrTiO3 film as a model material with well known electromechanical, electronic and electrochemical properties, we evaluate the contributions of electrostriction, Maxwell stress, flexoelectric effect, deformation potential and compositional Vegard strains caused by mobile vacancies (or ions) and electrons to the electromechanical response. The local electromechanical response manifests strong size effects, the scale of which is determined by the ratio of the SrTiO3 film thickness and PFM/ESM tip size to the carriers screening radius. Due to the strong dielectric nonlinearity effect inherent in quantum paraelectrics, the dependence of the SrTiO3 film electromechanical response on applied voltage demonstrates a pronounced crossover from the linear to the quadratic law and then to the sub-linear law with a factor of 2/3 under the voltage increase. The temperature dependence of the electromechanical response as determined by the interplay between the dielectric susceptibility and the screening radius is non-monotonic and has a pronounced maxima, the position and width of which can be tuned by film thickness. This study provides a comparative framework for analysis of electromechanical coupling in the non-piezoelectric nanosystems.

[1]  Sergei V. Kalinin,et al.  Nanoelectromechanics of piezoresponse force microscopy , 2004, cond-mat/0408223.

[2]  S. Kalinin,et al.  Local probing of ionic diffusion by electrochemical strain microscopy: Spatial resolution and signal formation mechanisms , 2010 .

[3]  Weidong Luo,et al.  Atomic-scale compensation phenomena at polar interfaces. , 2010, Physical review letters.

[4]  J. F. Stoddart,et al.  Molecular, Supramolecular, and Macromolecular Motors and Artificial Muscles , 2009 .

[5]  V. Nagarajan,et al.  Film thickness versus misfit strain phase diagrams for epitaxial PbTiO 3 ultrathin ferroelectric films , 2008 .

[6]  Sergei V. Kalinin,et al.  Nanoelectromechanics of piezoelectric indentation and applications to scanning probe microscopies of ferroelectric materials , 2005 .

[7]  T. Elsaesser,et al.  Coupled ultrafast lattice and polarization dynamics in ferroelectric nanolayers. , 2007, Physical review letters.

[8]  Ilan Riess,et al.  Properties of solid state devices with mobile ionic defects. Part I: The effects of motion, space charge and contact potential in metal|semiconductor|metal devices , 2007 .

[9]  M. Glinchuk,et al.  Ferroelectric thin films phase diagrams with self-polarized phase and electret state , 2006 .

[10]  Rainer Waser,et al.  Nanoelectronics and Information Technology: Advanced Electronic Materials and Novel Devices , 2003 .

[11]  Anna N. Morozovska,et al.  Resolution-function theory in piezoresponse force microscopy : Wall imaging, spectroscopy, and lateral resolution , 2007 .

[12]  Anna N. Morozovska,et al.  Nanoscale Electromechanics of Ferroelectric and Biological Systems: A New Dimension in Scanning Probe Microscopy , 2007 .

[13]  J. Scott,et al.  Strain-gradient-induced polarization in SrTiO3 single crystals. , 2007, Physical review letters.

[14]  A. Tagantsev,et al.  Effect of mechanical boundary conditions on phase diagrams of epitaxial ferroelectric thin films , 1998 .

[15]  R. Moos,et al.  ELECTRONIC TRANSPORT PROPERTIES OF SR1-XLAXTIO3 CERAMICS , 1996 .

[16]  S. Kalinin,et al.  Electromechanical Probing of Ionic Currents in Energy Storage Materials , 2010 .

[17]  Y. Tsur,et al.  Eliminating chemical effects from thermal expansion coefficient measurements , 2009 .

[18]  Materials contrast in piezoresponse force microscopy , 2006, cond-mat/0603010.

[19]  C. Eom,et al.  Nanosecond domain wall dynamics in ferroelectric Pb(Zr, Ti)O(3) thin films. , 2006, Physical review letters.

[20]  Amit L. Sharma,et al.  Structural characteristics of ferroelectric phase transformations in single-domain epitaxial films , 2004 .

[21]  Sergei V. Kalinin,et al.  Nanoscale mapping of ion diffusion in a lithium-ion battery cathode. , 2010, Nature nanotechnology.

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

[23]  R. Bell,et al.  Dielectric Constant in Paraelectric Perovskites , 1964 .

[24]  Z. Ban,et al.  Fundamentals of graded ferroic materials and devices , 2003 .

[25]  H. Uwe,et al.  Raman-scattering study of stress-induced ferroelectricity in KTaO 3 , 1977 .

[26]  Nava Setter,et al.  Interferometric measurements of electric field-induced displacements in piezoelectric thin films , 1996 .

[27]  Mark A. Ratner,et al.  Molecular electronics , 2005 .

[28]  L. E. Cross,et al.  Laser interferometer for the study of piezoelectric and electrostrictive strains , 1988 .

[29]  James S. Speck,et al.  DOMAIN CONFIGURATIONS DUE TO MULTIPLE MISFIT RELAXATION MECHANISMS IN EPITAXIAL FERROELECTRIC THIN FILMS. I: THEORY , 1994 .

[30]  Granino A. Korn,et al.  Mathematical handbook for scientists and engineers , 1961 .

[31]  A. Tagantsev,et al.  Phase transitions and strain-induced ferroelectricity in SrTiO3 epitaxial thin films , 2000 .

[32]  V. Kharton,et al.  Thermal and chemical induced expansion of La0.3Sr0.7(Fe,Ga)O3−δ ceramics , 2003 .

[33]  S. Hsieh,et al.  Nanomechanics of Materials and Structures , 2006 .

[34]  M. Glinchuk,et al.  The internal electric field originating from the mismatch effect and its influence on ferroelectric thin film properties , 2004 .

[35]  S. Kalinin,et al.  Thermodynamics of electromechanically coupled mixed ionic-electronic conductors: Deformation potential, Vegard strains, and flexoelectric effect , 2011 .

[36]  Sergei V. Kalinin,et al.  Piezoresponse force spectroscopy of ferroelectric-semiconductor materials , 2006, cond-mat/0610764.

[37]  A. Cleland.  Foundations of nanomechanics , 2002 .

[38]  A. Tagantsev,et al.  Piezoelectricity and flexoelectricity in crystalline dielectrics. , 1986, Physical review. B, Condensed matter.

[39]  T. Mura.  Micromechanics of Defects , 1992 .

[40]  Alexei Gruverman,et al.  Nanoscale ferroelectrics: processing, characterization and future trends , 2006 .

[41]  A. Petrov,et al.  Flexoelectricity of model and living membranes. , 2002, Biochimica et biophysica acta.

[42]  Toshio Mura,et al.  Micromechanics of defects in solids , 1982 .

[43]  A. Kholkin,et al.  Locally induced charged states in La0.89Sr0.11MnO3 single crystals , 2009 .

[44]  Yi Zhang,et al.  Spontaneous vortex nanodomain arrays at ferroelectric heterointerfaces. , 2011, Nano letters.

[45]  Jürgen Schubert,et al.  A strong ferroelectric ferromagnet created by means of spin–lattice coupling , 2010, Nature.

[46]  I. Krakovský,et al.  A few remarks on the electrostriction of elastomers , 1999 .

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

[48]  G. Catalan,et al.  Strain gradients in epitaxial ferroelectrics , 2004, cond-mat/0411471.

[49]  Larry L. Hench,et al.  Principles of electronic ceramics , 1990 .

[50]  Electromechanical detection in scanning probe microscopy: Tip models and materials contrast , 2006, cond-mat/0607543.

[51]  R. Blinc,et al.  Spontaneous flexoelectric/flexomagnetic effect in nanoferroics , 2009 .

[52]  S. M. Sze,et al.  Physics of semiconductor devices , 1969 .

[53]  Stephen Jesse,et al.  Real space mapping of Li-ion transport in amorphous Si anodes with nanometer resolution. , 2010, Nano letters.

[54]  Ute Rabe,et al.  Excitation of atomic force microscope cantilever vibrations by a Schottky barrier , 2008 .

[55]  E. Wachsman,et al.  Defect equilibria and chemical expansion in non-stoichiometric undoped and gadolinium-doped cerium oxide , 2009 .

[56]  M. Mogensen,et al.  Conductivity and expansion at high temperature in Sr0.7La0.3TiO3−α prepared under reducing atmosphere , 2006 .

[57]  Neha Sharma,et al.  Electromechanical coupling in nonpiezoelectric materials due to nanoscale nonlocal size effects: Green's function solutions and embedded inclusions , 2006 .

[58]  S. Kalinin,et al.  Extrinsic size effect in piezoresponse force microscopy of thin films , 2007, 0704.2829.

[59]  D. Tsvetkov,et al.  Oxygen nonstoichiometry, defect structure and defect-induced expansion of undoped perovskite LaMnO3±δ , 2010 .

[60]  A. Tagantsev,et al.  Room-temperature ferroelectricity in strained SrTiO3 , 2004, Nature.

[61]  The piezoresponse force microscopy of surface layers and thin films: Effective response and resolution function , 2007, 0705.3449.

[62]  P. Yang,et al.  Giant piezoresistance effect in silicon nanowires , 2006, Nature nanotechnology.

[63]  Sergei V. Kalinin,et al.  Local polarization dynamics in ferroelectric materials , 2010 .

[64]  Rainer Waser,et al.  Unit-cell scale mapping of ferroelectricity and tetragonality in epitaxial ultrathin ferroelectric films. , 2007, Nature materials.

[65]  E. Landahl,et al.  Nonlinear piezoelectricity in epitaxial ferroelectrics at high electric fields. , 2008, Physical review letters.

[66]  R. Moos,et al.  Hall mobility of undoped n-type conducting strontium titanate single crystals between 19 K and 1373 K , 1995 .

[67]  U. Böttger,et al.  Effects of ferroelectric switching on the piezoelectric small-signal response (d33) and electrostriction (M33) of lead zirconate titanate thin films , 2004 .

[68]  Marin Alexe,et al.  Atomic-scale study of electric dipoles near charged and uncharged domain walls in ferroelectric films. , 2008, Nature materials.

[69]  J. Kortus,et al.  Formation of Schottky-type metal/SrTiO3 junctions and their resistive properties , 2010 .

[70]  Wei Shyy,et al.  Intercalation-Induced Stress and Heat Generation within Single Lithium-Ion Battery Cathode Particles , 2008 .

[71]  A. Kovalevsky,et al.  Chemically Induced Expansion of La2NiO4+δ-Based Materials , 2007 .

[72]  Gustau Catalan,et al.  The effect of flexoelectricity on the dielectric properties of inhomogeneously strained ferroelectric thin films , 2004 .

[73]  A. Tagantsev,et al.  Novel Electromechanical Phenomena at the Nanoscale: Phenomenological Theory and Atomistic Modeling , 2009 .

[74]  Fuqian Yang.  Interaction between diffusion and chemical stresses , 2005 .

[75]  Eiichi Fukada,et al.  On the Piezoelectric Effect of Bone , 1957 .

[76]  B. Meyer,et al.  Schottky barriers at transition-metal/ SrTiO 3 ( 001 ) interfaces , 2009 .

[77]  J D Burton,et al.  Suppression of octahedral tilts and associated changes in electronic properties at epitaxial oxide heterostructure interfaces. , 2010, Physical review letters.

[78]  J. M. Worlock,et al.  Electric-Field-Induced Raman Scattering in SrTi O 3 and KTa O 3 , 1968 .

[79]  G. Pharr,et al.  Measurement of hardness and elastic modulus by instrumented indentation: Advances in understanding and refinements to methodology , 2004 .

[80]  Paul Muralt,et al.  Pb(Zr,Ti)O3 thin films on zirconium membranes for micromechanical applications , 1996 .

[81]  H. Takagi,et al.  Coupling between magnetism and dielectric properties in quantum paraelectric EuTiO 3 , 2001 .

[82]  S. Alpay,et al.  Influence of mechanical boundary conditions on the electrocaloric properties of ferroelectric thin films , 2008 .

[83]  A. Morozovska,et al.  General approach for the description of size effects in ferroelectric nanosystems , 2009, Journal of Materials Science.

[84]  N. Dimitrijević,et al.  Spatially Confined Corner Defects Induce Chemical Functionality of TiO2 Nanorods , 2006 .

[85]  Tahir Cagin,et al.  Enhanced size-dependent piezoelectricity and elasticity in nanostructures due to the flexoelectric effect , 2008 .

[86]  Mark W. Verbrugge,et al.  Evolution of stress within a spherical insertion electrode particle under potentiostatic and galvanostatic operation , 2009 .

[87]  A. M. Glass,et al.  Principles and Applications of Ferroelectrics and Related Materials , 1977 .

[88]  Strain propagation in nanolayered perovskites probed by ultrafast x-ray diffraction , 2006 .