Background and Principles of Piezoresponse Force Microscopy

Electromechanical coupling is one of the fundamental mechanisms underlying the functionality of many materials. These include inorganic macro-molecular materials, such as piezo- and ferroelectrics, as well as many biological systems. This application note discusses the background and principles of piezoresponse force microscopy (PFM) measurements using the MFP-3D™ AFM and Cypher™ AFM from Asylum Research.

Background

The functionality of systems ranging from non-volatile computer memories and micro electromechanical systems to electromotor proteins and cellular membranes are ultimately based on the intricate coupling between electrical and mechanical phenomena. The applications of electromechanically active materials include sonar, ultrasonic and medical imaging, sensors, actuators, and energy harvesting technologies. In the realm of electronic devices, piezoelectrics are used as components of RF filters and surface-acoustic wave (SAW) devices. The ability of ferroelectric materials to switch polarization orientation - and maintain polarization state in a zero electric field - has lead to emergence of concepts of non-volatile ferroelectric memories and data storage devices. Electromechanical coupling is the basis of many biological systems, from hearing to cardiac activity. The future will undoubtedly see the emergence, first in research labs and later in industrial settings, of the broad arrays of piezoelectric, biological and molecular-based electromechanical systems. Progress along this path requires the ability to image and quantify electromechanical functionalities on the nanometer and molecular scale (Figures 1 and 2). Areas such as nanomechanics and single-molecule imaging and force measurements have been enabled by the emergence of microscopic tools such as nanoindentation and protein unfolding spectroscopy.

Figure 1. PFM amplitude channel overlaid on AFM height (top) and phase image overlaid on height (bottom) of lead zirconium titanate (PZT), 20µm scan.

Figure 2. PFM amplitude overlaid on AFM topography (left) and PFM phase overlaid on topography (right) on (100) oriented BaTiO3 single crystal (from Castech Crystals). The amplitude and phase image show 90° and 180° domain walls in BaTiO₃. 10µm scan courtesy of V. R. Aravind, K. Seal, S. Kalinin, ORNL, and V. Gopalan, Pennsylvania State University.

Similarly, the necessity for probing electromechanical functionalities has led to the development of PFM as a tool for local nanoscale imaging, spectroscopy, and manipulation of piezoelectric and ferroelectric materials.

Principles of Piezoresponse Force Microscopy

Basics

PFM measures the mechanical response when an electrical voltage is applied to the sample surface with a conductive tip of an AFM. In response to the electrical stimulus, the sample then locally expands or contracts as shown in Figure 3.

Figure 3. Depiction of PFM operation. The sample deforms in response to the applied voltage. This, in turn, causes the cantilever to deflect, which can then be measured and interpreted in terms of the piezoelectric properties of the sample. Image courtesy S. Jesse, ORNL.

When the tip is in contact with the surface and the local piezoelectric response is detected as the first harmonic component of the tip deflection, the phase φ, of the electromechanical response of the surface yields information on the polarization direction below the tip. For c^- domains (polarization vector oriented normal to the surface and pointing downward), the application of a positive tip bias results in the expansion of the sample, and surface oscillations are in phase with the tip voltage, φ = 0. For c⁺ domains, the response is opposite and φ = 180°.

Detection of the lateral components of tip vibrations provides information on the in-plane surface displacement, known as lateral PFM. A third component of the displacement vector can be determined by imaging the same region of the sample after rotation by 90°. Provided that the vertical and lateral PFM signals are properly calibrated, the complete electromechanical response vector can be determined, an approach referred to as vector PFM. Finally, electromechanical response can be probed as a function of dc bias of the tip, providing information on polarization switching in ferroelectrics, as well as more complex electrochemical and electrocapillary processes.

PFM requires detection of small tip displacements induced by relatively high amplitude, high frequency voltages measured at the same frequency as the drive. Any instrumental crosstalk between the drive and the response will result in a virtual PFM background that can easily be larger than the PFM response itself, especially for weak piezo materials. Minimizing crosstalk between the driving voltage and the response imposes a number of serious engineering limitations on the microscope mechanics and electronics. In the past, significant post-factory modifications were required to decouple the drive and response signals. Asylum's PFM uses a unique proprietary design of the head and the high voltage sample holder to eliminate drive crosstalk.

Piezo Effect

The relationship between the strain and the applied electric field (often referred to as the "inverse piezo effect") in piezoelectric materials is described by a rank-3 tensor. The most important component of this tensor for typical "vertical" PFM is the d₃₃ component, since it couples directly into the vertical motion of the cantilever. The voltage applied to the tip is

resulting in piezoelectric strain in the material that causes cantilever displacement

due to piezoelectric effect. When the voltage is driven at a frequency well below that of the contact resonance of the cantilever, this expression becomes

where we have implicitly assumed d₃₃ depends on the polarization state of the material. From this last equation and from Figure 3, the magnitude of the oscillating response is a measure of the magnitude of d₃₃ and the phase is sensitive to the polarization direction of the sample.

NOTE: In reality, the d₃₃ component in Equation 3 is an "effective" d₃₃ that depends on the contribution from other tensor elements and on the crystallographic and real space orientation of the piezo material, as well as details of the tip-sample contact.

Typical values for d₃₃ range from 0.1pm/V for weak piezo materials to 500pm/V for the strongest. Table 1 shows a listing of representative values.

Table 1

*1. The PFM signal is given by Equation 6, A=d₃₃V_acQ where d₃₃ is material property, V_ac is driving voltage, and Q is the quality factor. Q = 1 for low frequency PFM, and Q = 20-100 if resonance enhancement (DRFT or BE) method is used. V_ac is limited by material stability and polarization switching. The microscope photodetector sensitivity, thermal noise and shot noise impose the limit A > 30pm. The ultimate limit is A = thermal noise.
*2. Quantitative spectroscopic measurements require probing bias to be one to two orders of magnitude smaller than coercive bias, limiting the voltage amplitude.
*3. Measurements are not possible above this limit due to sample and tip degradation.

As mentioned above, the direction of sample polarization determines the sign of the response. Figure 4 demonstrates this idea. If the polarization is parallel and aligned with the applied electric field, the piezo effect will be positive, and the sample will locally expand. If the local sample polarization is anti-parallel with the applied electric field, the sample will locally shrink. This sign-dependent behavior means that the phase of the cantilever provides an indication of the polarization orientation of the sample when an oscillating voltage is applied to the sample.

Figure 4. Sign dependence of the sample strain. When the domains have a vertical polarization that is pointed downwards and a positive voltage is applied to the tip, the sample will locally expand. If the polarization is pointed up, the sample will locally contract. The phase of the measured response is thus proportional to the direction of the domain polarization. Figure courtesy of S. Jesse, ORNL.

The relationship in Equation 1 and the values for d₃₃ in Table 1 suggest that typical deflections for a PFM cantilever are on the order of picometers. While the sensitivity of AFM cantilevers is quite impressive - of the order of a fraction of an angstrom (or tens of pm) in a 1kHz bandwidth - it also implies a very small signal-to-noise ratio (SNR) for all but the strongest piezo materials.

Because of this small SNR, piezoelectricity is most frequently detected by a lock-in amplifier connected to the deflection of the AFM cantilever. By employing an oscillating electric field, low-frequency noise and drift can be eliminated from the measurement. Until recently, PFM was usually accomplished by researchers who modified a commercial SPM system with an external function generator/lock in setup. As a result, in most cases, the operation frequency was limited to <100kHz. This and the lack of sophisticated control options precluded the use of resonance enhancement (see sections below on DART and BE) in PFM since typical contact resonance frequencies are >300kHz.

Piezoresponse Force Microscopy Imaging Modes

The three typical PFM imaging modes and piezoelectric lithography are briefly described below.

Vertical PFM

In vertical PFM imaging, out-of-plane polarization is measured by recording the tip-deflection signal at the frequency of modulation. Figure 5 shows an example image of vertical PFM for a lead titanate film. Antiparallel domains with out-of-plane polarization can be seen in the PFM phase image, while in-plane domains are seen in the PFM amplitude image as yellow stripes due to the weak vertical piezoresponse signal

Figure 5. Vertical PFM amplitude overlaid on AFM topography (left) and PFM phase overlaid on AFM topography (right) images of lead titanate film, 5µm scan. Images courtesy of A. Gruverman and D. Wu, UNL. Sample courtesy H. Funakubo.

Lateral PFM

Lateral PFM is a technique where the in-plane component of polarization is detected as lateral motion of the cantilever due to bias-induced surface shearing.

Vector PFM

In vector PFM the real space reconstruction of polarization orientation comes from three components of piezoresponse: vertical PFM plus at least two orthogonal lateral PFM. Figure 6 shows an example of a vector PFM image of a barium strontium titanate film (BST), permitting qualitative inspection of the correlation of grain size, shape and location with local polarization orientation and domain wall character. Here, the color wheel permits identification of the local orientation of the polarization. Regions colored as cyan (darker blue/green) possess polarizations which are oriented predominantly normal to the plane of the film, whereas regions that appear magenta-blue or light green possess polarizations which are oriented predominantly within the plane of the film. The intensity of the color map denotes the magnitude of the response.

Figure 6. BST film with vector PFM overlaid on AFM topography, 1µm scan. Image courtesy of C. Weiss and P. Alpay, Univ. of Conn., and O. Leaffer, J. Spanier, and S. Nonnenmann, Drexel University. Color wheel indicates PFM vector orientation.

Lithography

For ferroelectric applications, PFM can be used to modify the ferroelectric polarization of the sample through the application of a bias. When the applied field is large enough (e.g. greater than the local coercive field) it can induce ferroelectric polarization reversal. This technique can be used to 'write' single domains, domain arrays, and complex patterns without changing the surface topography. Figure 7 shows an example of PFM bit-mapped lithography where the color scale of a black and white photo was used to control the bias voltage of the tip as it rastered over the surface and then re-imaged in PFM mode.

Figure 7. R&D 100 logo written on a sol-gel PZT thin film by PFM lithography. PFM phase is overlaid on top of the rendered topography, 25µm scan. Oak Ridge and Asylum Research were awarded an R&D100 award for Band Excitation in 2008.

Spectroscopy Modes

PFM spectroscopy refers to locally generating hysteresis loops in ferroelectric materials. From these hysteresis loops, information on local ferroelectric behavior such as imprint, local work of switching, and nucleation biases can be obtained.

Understanding the switching behavior in ferroelectrics on the nanometer scale is directly relevant to the development and optimization of applications such as ferro-electric non-volatile random access memory (FRAM), and high-density data storage. Multiple studies have addressed the role of defects and grain boundaries on domain nucleation and growth, domain wall pinning, illumination effects on the built-in potential, and domain behavior during fatigue.The origins of the field date back to the seminal work by Landauer, who demonstrated that the experimentally observed switching fields correspond to impossibly large (~10³ - 10⁵ kT) values for the nucleation activation energy in polarization switching. Resolving this 'Landauer paradox' requires the presence of discrete switching centers that initiate low-field nucleation and control macroscopic polarization switching. However, difficulties related to positioning of the tip at a specific location on the surface (due in part to microscope drift), as well as time constraints related to hysteresis loop acquisition, limit these studies to only a few points on the sample surface, thus precluding correlation between the material's microstructure and local switching characteristics.

Switching Spectroscopy Mapping

A new spectroscopy technique, Switching Spectroscopy PFM (SS-PFM), has demonstrated real-space imaging of the energy distribution of nucleation centres in ferroelectrics, thus resolving the structural origins of the Landauer paradox. These maps can be readily correlated with surface topography or other microscopic techniques to provide relationships between micro- and nanostructures and local switching behavior of ferroelectric materials and nanostructures. Figure 8 shows how it works. In SS-PFM, a sine wave is carried by a square wave that steps in magnitude with time. Between each ever-increasing voltage step, the offset is stepped back to zero with the AC bias still applied to determine the bias-induced change in polarization distribution (e.g. the size of the switched domain). It is then possible to see the hysteresis curve of the switching of the polarization of the surface (bottom diagram). If the measurements are performed over a rectangular grid, a map of the switching spectra of that surface can be obtained. Figure 9 shows an example image of a LiNbO₃ sample with the PFM signal overlaid on top. The image was taken after switching spectroscopy. The graph shows the hysteresis loops measured at one individual point.

Figure 8. Switching spectroscopy PFM diagram (see text for discussion). Reused with permission from Jesse, Baddorf, and Kalinin, Applied Physics Letters, 88, 062908 (2006). Copyright 2006, American Institute of Physics.

Figure 9. Rendered topography of a LiNbO₃ sample with the PFM signal overlaid on top, 4µm scan.

As additional examples, Figure 10 shows a sol gel PZT sample where the local switching fields were measured. After the switching spectroscopy, the area was re-imaged. The PFM signal clearly shows five dots in the phase signal denoting portions of the sample where the polarization was reversed during the hysteresis measurements. Figure 11 shows SSM-PFM of capacitor structures and Figure 12 shows an image of phase and amplitude hysteresis loops measured at five different locations on a lead zinc niobate - lead titanate (PZN-PTi) thin film.

Figure 10. Sol gel PZT sample where local hysteresis loops were measured and displayed (representative phase and amplitude loops shown at top). After the switching spectroscopy measurements, the area was imaged, the DART amplitude (middle) and phase (bottom) are shown, 3.5µm scan.

Figure 11. SS-PFM and hysteresis loops of capacitor structures. Data courtesy K. Seal and S.V. Kalinin, ORNL. Sample courtesy P. Bintacchit and S. Trolier-McKinstry, Penn State Univ.

Figure 12. Amplitude (left) and phase (right) hysteresis loops measured at five different locations on a PZN-PTi thin film.

Conclusion

Characterizing electromechanical responses in a variety of materials will be crucial for understanding and improving technologies ranging from bioscience to energy production. Scanning probe microscopy has emerged as a universal tool for probing such structures and functionality at the nanometer scale. Asylum's Piezoresponse Force Microscopy capabilities now allow characterization of an endless variety of materials and devices that previously could not be measured using conventional piezoresponse force microscopy. Research with this new tool will enable new advancements in many disciplines from biology to semiconductors, while yielding improvements for ongoing work in diverse areas from data storage devices and molecular machines to improved materials for renewable energy.

This information has been sourced, reviewed and adapted from materials provided by Asylum Research - An Oxford Instruments Company.

For more information on this source, please visit Asylum Research - An Oxford Instruments Company.