Ferroelectrics are a subclass of piezoelectrics, namely, materials that experience mechanical deformation under applied voltage or charging under mechanical force. Ferroelectrics exhibit a wide range of functional properties, including high and switchable electric polarization, strong piezoelectricity, high non-linear optical activity, outstanding pyroelectricity, and notable non-linear dielectric behavior. These properties are indispensable for the applications in numerous electronic devices such as sensors, actuators, IR detectors, microwave filters and, recently, non-volatile memories, to name a few. Due to this unique combination of properties researchers and engineers have been focusing on visualization of ferroelectric domains (areas with unique polarization direction) at different scales.
Recent advances in synthesis and fabrication of micro-and nanoscale ferroelectrics brought to life new physical phenomena and devices that need to be studied and understood at this scale. As structure dimensions are getting smaller, ferroelectrics exhibit a pronounced size effect manifesting itself in a significant deviation of the properties of low-dimensional structures from their bulk analogs. In this sense, ferroelectrics are similar to magnetic materials since surface energy cannot be neglected in small volumes and long-range dipole interaction is significantly modified in reduced geometries. It also depends on whether a ferroelectric is confined in one-, two-, or all threedimensional structures.
Following the miniaturization challenge, novel techniques are required for the evaluation of ferroelectric and piezoelectric properties with the high, ultimately nanoscale resolution. Many fundamental issues have nowadays to be addressed such as effect of the geometry confinement on ferroelectric and piezoelectric properties, relationship between local piezoresponse and macroscopic properties, as well as microscopic mechanisms of polarization switching, domain stability and degradation, including polarization phenomena at the interface.
Beyond the novel nanoscale applications, functionality of ferroelectric films, polycrystalline ceramics, and even single crystals is often dominated by defects that act as nucleation and pinning centers for moving domain walls and thus determine the piezoresponse. In addition, the unique electromechanical properties of relaxor ferroelectrics (materials with giant strain and dielectric constant) originate from the interplay of polarization with chemical and charge disorder on the nanometer scale. Finally, there is a novel class of multiferroics where polarization is coupled to the magnetization at the local scale.
To address the fundamental mechanisms underpinning the functionality of ferroelectric materials and devices, domain structures and their evolution under bias have to be studied at the micro and nanometer scales. The rapid development of scanning probe microscopy and, especially, Piezoresponse Force Microscopy (PFM) has resulted in a fabulous advancement in this area as will be highlighted below after the short description of the method.
Principles and Instrumental Aspects of Piezoresponse Force Microscopy (PFM)
Basic Principles of PFM
The PFM approach for probing piezo-and ferroelectric properties at the nanoscale is based on the strong coupling between polarization and mechanical dispacement. Apparently, coupling can be addressed by applying a highly localized electric field to the material and probing the resultant minute surface displacements with a picometer precision (Fig. 1).
Figure 1. Schematic of the Piezoresponse Force Microscopy arrangement where both ac and dc voltages are applied to the metallized tip and mechanical displacement is measured via conventional AFM method.
Common AFM provides an ideal platform for local piezoeffect study due to high vertical resolution and high localization of electric field at the junction between the metalized tip and the surface. Hence, PFM is a contact-mode AFM in which an electrically biased conductive AFM tip is used as a probe of local electromechanical coupling via the converse piezoelectric effect. Remarkably, the basic image formation mechanism in PFM is complementary to force-based AFM methods (force is applied and the tip deflection is measured) and scanning tunneling microscopy (STM) (bias is applied and a current is measured).
History of PFM
Following the invention of STM and AFM, the first examples of measuring a bias-induced deformation due to piezoelectricity with a scanning probe were in 1991 where piezoresponse was studied using scanning acoustic microscopy and STM . Later on, the first papers on piezoelectric measurements and ferroelectric domain visualization by AFM have appeared. Following this a series of pioneer results have been obtained by Takata et al (using strain imaging via tunneling acoustic microscopy), Franke et al , Kolosov et al and Gruverman et al. The work by Gruverman with coauthors is particularly important because it demonstrated imaging and switching in common ferroelectrics and coining the terms 'Piezoresponse' and 'PFM' which have now become standard. In the past 15 years, PFM has become the premier tool for studying static and dynamic properties of ferroelectric materials, as evidenced by a number of recent books and reviews.
Elementary theory of PFM
In PFM, a voltage is applied to the conductive tip as
Vtip = VDC+ VAC cos(ωt)
Here VDC is the dc bias (switching bias), VAC is the ac bias (probing bias) and ω is the AC bias frequency (driving frequency). As the sample expands and contracts due to the converse piezoelectric effect, the tip deflection is monitored using a lock-in amplifier so that the tip oscillation
A = A0 + A1ω cos(ωt + φ)
where A0 is the static surface displacement and φ is the phase shift between the driving voltage VAC and the voltage induced deformation A1ω = d33eff VAC + (∂C/∂z) (VDC - V5)VAC. The first term is the true piezoresponse due local piezoelectric deformation described by the effective piezocoefficient d33eff and the second term is a local electrostatic deformation caused by both local and non-local Maxwell stress.20 Vs stands for the surface potential and C is the total capaciatance of the cantilever-sample system.
The PFM amplitude provides information on the magnitude of the local electromechanical coupling, while the PFM phase image gives local polarization orientation. Typically the imaging resolution of PFM is less than ~ 10-30 nm as determined from half of the width of a domain wall in the mixed PFM signal, PR = A1ω cos (φ) that is mostly used for the characterization (φ is ether close to 0º or to 180º). The resolution is limited by the tip-sample contact area (nominally determined by the radius of the tip apex), though additional mechanisms for broadening such as electrostatic interactions and the formation of a liquid neck in the tip-surface junction are possible.
Contrast Mechanism in Piezoresponse Force Microscopy
The contrast mechanism and detection of ferroelectric domain patterns with PFM is based on the fact that ferroelectric materials are necessarily piezoelectric. Basically, the cantilever performs three kinds of displacements: (i) vertical deflection as a result of the out-of plane force due to d33eff coefficient, (ii) torsion (caused by shear piezocoefficient d15eff ), and (iii) buckling from the interaction with the surface when an in-plane force acts along the cantilever axis. The first type of deformations are referred to as out-of-plane (or vertical PFM, or VPFM) measurements.
If the polarization and applied electric field are parallel (Fig. 2a), the deformation is positive (expansion) and piezoresponse signal is in phase with VAC. On the contrary, if the applied electric field is antiparallel to the spontaneous polarization, this will cause piezoelectric to contract with the consequent lowering of the cantilever (Fig. 2b). The electric field and the piezoresponse signal are shifted in phase by 180°. Similarly, the direction of the polarization for the in-plane polarized ferroelectric grain can be deduced via a relevant (shear) piezoelectric coefficient d15eff (Fig. 2c,d). In this case, the applied electric field causes a shear deformation of the grain, which is transferred via the friction forces to the torsional movement of the cantilever. These measurements will be further denoted as in-plane (or lateral PFM, or LPFM) measurements.
Due to the cantilever asymmetry, polarization in the direction of cantilever axis can only be recorded by physically rotating the sample by 90° along the z-axis and repeating the in-plane measurement. By acquiring all three components of the piezoresponse signal, it is possible to perform at least semiquantitative reconstruction of polarization orientation. However, precise orientation of polarization can be calculated only if all the components of the piezoelectric tensor are known. The first attempt to relate the amplitude of the piezoresponse signal to the orientation of the ferroelectric polarization has been undertaken by Harnagea and Pignolet and detailed formalism has been later developed by Kalinin et al. A careful analysis of the movement of the cantilever must be done with respect to its orientation relative to the crystallographic axes of the sample, allowing a clear attribution of the observed domain contrast to the driving forces. In the case of composite materials as ferroelectric polymer blended with particles or ferroelectric hybrid (organic-inorganic) materials this problem is approached by knowing the electromechanical behavior of each component.
Figure 2. Piezoelectric effect in a tetragonal ferroelectric investigated by PFM. (a) Electric field aligned parallel to the spontaneous polarization leads to a lifting of the cantilever due to the d33 effect (out-of-plane signal). (b) The antiparallel alignment of the electric field and the spontaneous polarization leads to a vertical contraction and a horizontal expansion of the ferroelectric. (c), (d) Electric field applied orthogonal to the polarization results in a shear movement due to the d15 coefficient. This movement causes a torsional deformation of the cantilever forcing the laser spot to move horizontally (in-plane signal).
Artifacts in PFM Acquisition
Unfortunately an unambiguous separation of the out-of-plane and in-plane acquisition channels is not always possible. This results in the cross-talk between both channels and misinterpreatation of the results irrespectively whether the cross-talk is of the mechanical or electrical reason. Although most commercially available AFMs are supplied with the programs capable to compensate the images during processing, PFM cross-talk correction is not included. NT-MDT (in cooperation with the University of Bonn) has developed a simple electronic circuit where the cross-talk compensation is done by simple signal processing of the in-plane and out-plane signals in the situation where either of them is present. The results shown below illustrate the situation where only in-plane signal is present. The out-of-plane PFM signal is fully compensated by the compensating circuit.
Figure 3. Topogaphy (a), out-of-plane PFM (b) and in-plane PFM (c) signals without (right image) and with (left image) cross-talk compensator in FF peptide nanotubes where only in-plane signal should be observed (Images courtesy of I. Bdikin and A. Kholkin, University of Aveiro, Portugal).
Polarization Patterning and Self-Assembly via PFM
Currently, the research is conducted to discover new types of materials that may assemble into uniquely functioning devices. The cornerstone of such studies is a vigorous synthetic effort that allows freedom to design, so that new structural types can be created. An unanswered question is how to devise general methods to assemble and to interconnect organic and biological structures into functioning molecular scale devices. To attain these critical interconnections, a new type of assembly must be developed allowing to attach different molecular species on the surface in the predetermined locations. Novel approach that was recently suggested is based on the assembly of nanostructures directed by atomic (ferroelectric) polarization on the surface. This is often referred to as ferroelectric lithography. Ferroelectric polarization can be indeed used to assemble various organic and inorganic species and to create nanostructures with controlled properties. As an example, we show here that P(VDF-TrFE), ultrathin films deposited by the Langmuir-Blodgett technique can be used as templates for the assembly of various phospholipids, which are the essential components of cell membranes. Both imaging and patterning could be done by PFM, so that the nanoscale patterns can be created. These were revealed by the formation of homogeneous and stable rounded blobs with diameters in the range 0.5-3µm.
In this way, ferroelectric polymer films were polarized by the application of various voltages via a conducting PFM tip and PFM images were then obtained showing controlled polarization distribution. After this, the phospholipid (1,2-di-O-hexadecyl- sn-glycero-3-phosphocholine) molecules were deposited from the solution. Conventional atomic force microscopy experiments were then performed to assess the selectivity of the deposition process. It was observed that the deposition process is very sensitive to the concentration of the solution. The selective deposition was observed mainly at the polarization boundaries where the selectivity reached a maximum value of about 20-40% (Fig. 4a). The pospholipid lines could be also directly deposited by the PFM tip as a nanoscale pen (Fig. 4b) and polarization can be also reversed in a phospholipid layer
Figure 4. (a) Polarization-driven assembly of the pospholipids on the surface of P(VDF-TrFE) films via PFM, (b) Pospholipid lines written and visualized by PFM and (c) ferroelectric domains writeen on the surface of phospholipid/ P(VDF-TrFE) bilayer films. Courtesy Alejandro Heredia, Igor Bdikin and Andrei Kholkin (University of Aveiro, Portugal).
Piezoresponse and Pseudoferroelectricity in ZnO
Zinc oxide (ZnO) is a well-known n-type semiconductor material having remarkable electronic and optical properties with great potential for micro-and optoelectronics. Highly resistive c-axis-oriented ZnO films are also of interest for various piezoelectric applications (e.g. as sensors, actuators, high-frequency acoustic transducers, etc) due to their notable and stable piezoelectric properties. Recently, ZnO has become a material of choice for piezoelectric harvesting devices because of the ease of growth in the nanorod and nanobelt geometries. However, the piezoelectric properties of ZnO are not well understood and characterized, especially in the case of polycrystalline films having mixed orientation of the grains and weak (if any) unipolarity. The example of the detailed investigation of piezoelectric properties of ZnO films is given in Fig. 5. Each grain is characterized by the contrast related to relevant piezoelectric coefficient, grain orientation, and clamping effect of other grains. Using PFM it was possible to obtain piezoelectric maps of the surface by measuring the response in vertical and 2 orthogonal lateral directions (Fig. 5a-c) and, based on the piezoelectric contrast, to deconvolute the orientation and polarity of each individual grain (Fig. 5c). For the first time, ferroelectric-like hysteresis was discovered in nominally pure ZnO (Fig. 5e) thus proving its pseudoferroelectric properties as predicted recently by Tagantsev.
Figure 5. Topography (a) and nanoscale piezoelectric maps in polycrystalline ZnO films (b-c) obtained by pulsed laser deposition. Polarity map (c) represents polarization (with sign) and orientation of individual grains while (g) demonstrates ferroelectric-like hysteresis in nominally undoped films. Courtesy Igor Bdikin and Andrei Kholkin (University of Aveiro, Portugal).
Electromechanics of Biological Systems
Piezoelectricity which stems from the non-centrosymmetric crystal structure is an intrinsic property of most biopolymers, including proteins and polysaccharides. Piezoelectric behaviour has been observed in a variety of biological systems, including calcified and connective tissues and plants, dentine, bones etc. Understanding the relationship between physiologically generated electric fields and mechanical properties on the molecular, cellular, and tissue levels has become the main motivation of studying piezoelectricity in biological systems. The interest is also due to the fact that pizoelectrically active biomaterials can be used as nanoscale sensors, actuators and transducers fully compatible with the biological environment. In addition, the strong orientation dependence of the piezoelectric effect is extremely important for the investigation of complex hierarchical structure in biological materials. It has been recently observed that short aromatic peptides self-assembled in the nanscale tubular geometries with a very high piezoeleffect (comparable to that in LiNbO3, one of the mostly used inorganic transducer materials). Figure 6 presents topography image of the nanotube (a), schematic of the polarization and measurement arrangement by PFM (b) and PFM contrast for oppositely oriented nanotubes where the d33eff (shear) piezoelectric coefficient is only responsible for the electromechanical coupling. The advantage of PFM is a high resolution and possibility to measure local piezoelectric effect in complex geometries. The strong and robust piezoelectric activity in bioinspired PNTs (never seen in the past) makes them promising candidates for future generations of "green" nanopiezoelectrics that might be extensively used in biomedical and medical applications. It is foreseen that these biocompatible and rigid nanotubes (as well as arrays of thereof) may serve as the key elements for future biosensors allowing direct contact with human tissue.
Figure 6. Topography (a), measurement arrangement (b), and piezoelectric contrast (c) in FF peptide nanotubes (courtesy Igor Bdikin and Andrei Kholkin, University of Aveiro, Portugal).
Nanoscale Studies of Multiferroic Materials
Multiferroics - materials which simultaneously have magnetic and ferroelectric ordering - attract now a considerable interest both because of fascinating physics and promising applications. One of the proposed driving mechanisms for ferroelectricity is the occurrence of charge ordering (CO) in mixed manganites combined with bond dimerization in order to break inversion symmetry. Considering that the polarization in these solids can exist in nanoscale volumes, Piezoresponse Force Microscopy can be used for studying bias-induced ferroelectric properties both below and above CO phase transition. Such bias-induced ferroelectricity studied via PFM may also be important for creating artificial multiferroic materials and memory cells. These experiments help to undertand the role of charge/orbital and magnetic ordering on the electrical polarization and assess the nature of the new source of multiferroicity. These exeriments were recently performed on the well-known (La,Sr)MnO3 mixed manganites and indeed a ferroelectric state was found at room temperatures, i.e., much higher than expected for CO phase transitions. Figure 7 exemplifies the bias field-induced ferroelectric island in the centrosymmetric manganite "sea". This confirms that high enough electric field could break a symmetry and induce polar state due to local "electric" doping of the material.
Figure 7. Nanoscale ferroelectric island induced by the PFM tim in La0.89Sr0.11MnO3 manganite (a) and piezoresponse hysteresis loops showing polarization reversibility. Courtesy Igor Bdikin and Andrei Kholkin (University of Aveiro, Portugal).
While the initial application of PFM was mainly to image ferroelectric domains significant in a few important but quite rare ferroelectric materials, the PFM can be currently applied to a large variety of materials including biomaterials and ionic conductors. Coupled electromechanical properties are inherent in hundreds of inorganic materials (even centrosymmetric at a macroscopic scale) and similarly in biological materials. The evolution of PFM provides a new window into the behavior of a wide range of materials. Equally important, the developments in PFM are part of a larger trend toward extreme high spatial resolution in quantification of electromagnetic properties. Several classes of functional properties are now probed at sub-nm resolution. In most cases the properties are represented by single scalar numbers like resistivity, conductivity, surface potential, charge density, etc. PFM is unique in that it carries this strategy into the realm of complex tensor properties. Significant advances of PFM (possible but unknown yet) are expected in the realm of new materials and devices based on them.
This information has been sourced, reviewed and adapted from materials provided by NT-MDT Spectrum Instruments.
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