The coupling between an electrical and mechanical response is an essential property that makes a number of applications, ranging from sensor and actuators to energy harvesting and biology, more functionally effective. Most materials exhibit electromechanical coupling in nanometer-sized domains. For this reason, characterization at the nanoscale is a crucial tool for understanding the relationship between structure and functions of different materials.
Piezoelectric force microscopy (PFM), which is a mode that all atomic force microscopes (AFMs) from Park Systems possess, can measure the aforementioned property directly and in a non-destructive manner. It also has the ability to evaluate the switching of piezoelectric domains, which makes it useful as a spectroscopic tool.
The following paper examines how PFM is used in a failure analysis of a multilayered ceramic capacitor. Correlative imaging of topography and electrical signals revealed discontinuous structures in the device that likely had a direct effect the performance of the device.
Spectroscopy was also performed at a specific piezoelectric region to measure domain properties, including the electric field required to flip the polarization direction (coercive voltage).
Introduction
Coupling (or ‘piezoelectric effect’) of electrical and mechanical behavior is something that multiple materials exhibit. Such materials range from those used in renewable energy, to electronics and biology. This essential property creates a mechanical response that is induced by applying an electrical field. Coupling is implemented in a multitude of applications, ranging from ultrasonic imaging to actuators and sensors.1
The most commonly encountered man-made piezoelectric materials are ceramics, such as barium titanate and lead zirconate titanate. Other polymers, such as polyvinylidene fluoride can also exhibit piezoelectric properties. Naturally-occurring piezoelectric materials include bone, quartz, and DNA.
Piezoelectric force microscopy, which is also known as ‘piezoresponse force microscopy’is a common non-destructive technique that enables observation of electromechanical responses at the nanometer length scale.
Piezoelectric force microscopy by Park Systems is also termed ‘dynamic-contact electrostatic force microscopy’ (DC-EFM). The microscopy is conveyed in an atomic force microscope (AFM), which is set in contact mode and possesses an electrically-biased conductive tip that responds to electronic stimuli by probing nanoscale displacements. These sample displacements are often very small with a low signal-to-noise ratio. Therefore, a lock-in amplifier is connected to the deflection signal to selectively drive the desired frequency and bypass unwanted signals.
The photodiode of the microscope is position-sensitive, so the piezoelectric force microscopy is capable of identifying the direction of electrical polarization in active piezoelectric or ferroelectric domains. To capture this directionality, there are two distinct imaging modes: vertical piezoelectric force microscopy and lateral piezoelectric force microscopy (VPFM, LPFM), both of which are sensitive to domains polarized out-of-plane and in-plane, respectively.2 (Fig. 1).
Vector piezoelectric force microscopy can help to define the direction of the polarization by identifying the components of a local polarization. Both vertical and lateral components should also be considered.
Vertical Piezoelectric Force Microscopy
In VPFM, the cantilever responses to the applied bias by deflecting normally in relation to the sample surface. This indicates a presence of piezoelectric domains that point out-of-plane or normal to the sample surface (Fig. 1a-b). This results in a bright appearance for domains that point upward and dark for domains that point downward in the EFM signal in the AFM.
Lateral Piezoelectric Force Microscopy
To detect the piezoelectric domains that are pointed in-plane during LPFM, the sample must exhibit displacement shearing on the surface. A possible result of this would be torsional displacement of the cantilever, which would be detected by the position sensitive photodiode as a lateral deflection indicating a polarization direction parallel to the sample surface (Fig. 1c-d).
Vector Piezoelectric Force Microscopy
In piezoelectric samples with arbitrary crystallographic orientations, applying a tip bias will result in both in-plane and out-of-plane displacement. This is also possible using piezoelectric samples with arbitrary crystallographic orientations. By simultaneously collecting both VPFM and LPFM signals, vector PFM can be used to determine the final direction of the polarization vector in nanometer-sized grains. This makes it possible to acquire piezoelectric constants of the material or a local orientation map. At the same time, most researchers assume that the local polarization orientation correlates with crystal orientation on the macro scale.3
Figure 1. A schematic representation of (a-b) vertical and (c-d) lateral PFM. Vertical deflections are observed via the AFM laser. The deflections correspond with (a) downward or (b) upward out-of-plane electrical polarization. Lateral PFM allows the cantilever to exhibit torsion in response to (c-d) lateral in-plane polarization directions. The direction of the polarization vector is indicated by the black arrows, in each case assuming that the relationship between polarization and crystal orientation is conserved.
It is important to note that there are several practical limitations in the way vertical and lateral signals are combined, which is due to the fact that crosstalk often arises from the geometrical constraints of the cantilever. Additionally, tip displacement in the lateral direction can be underestimated compared to surface displacement of the sample due to effects such as friction.4
Multilayer Ceramic Capacitors
Piezoelectric materials have both sensing and actuating properties, which makes it possible for them to be used in many different applications in the electronics industry.5 Ceramics like barium titanate, are an example of a material that exhibits piezoelectric behavior and have proven to be robust dielectric materials in capacitors. These materials are also resistant to humidity and temperature, as well as being cost effective and having high intrinsic dielectric constants.
Each year, more a trillion (1012) barium titanate-based MLCCs are fabricated, which means that multilayer ceramic capacitors (MLCCs) are produced in very large quantities.6 They can have different applications, varying from cars (where they are applied to control anti-lock brake systems), or in hospitals (where they are used in heart monitors).
Despite society’s reliance on MLCCs, they are somewhat susceptible to failure. Thermal stress, for example, can be caused by the high temperatures that result from soldering. Storage, cracking, increased currents, or shorts could also occur.
Another serious problem are high-energy surges, which can cause leakage currents or even rupture of the device itself. There are several ways in which a device can fail, either during use, storage or assembly. To understand where the failure occurs and to analyze how functional the devices are, the PFM technique, including MLLCs, has proven to be a useful technique.
Featured below is an analysis report of an MLCC cross section using LPFM. The discrete metal-dielectric domains within the device are identified. Regions within the dielectric material that exhibit unique polarization directions can be resolved. Both topography and electrical signals present discontinuities in the individual materials, which could potentially affect the performance of the device.
Experimental
A cross-section of an MLCC was analyzed using a Park NX20 AFM, and the LPFM signal was acquired using a scan rate of 0.2 Hz. A conductive NANOSENSORSTM PointProbe® Plus-Electrostatic Force Microscopy (PPP-EFM) cantilever was used, with a nominal spring constant of k = 2.8 N/m and a resonant frequency f = 25 kHz. It was also coated with PtIr5 on both the front and back sides and had a nominal curvature radius of 25 nm. The AFM tip was biased with 2 V AC, with no additional external bias applied to the sample during imaging.
Results and Discussion
AMLCC is typically monolithic, featuring alternating dielectric (ceramic) and metal (electrode) layers which extend to corresponding connecting terminals at either end of the device (Fig. 2a). In the present work, the cross-section of an MLCC (which is illustrated in the “slice” of blue in Fig. 2a) is thus characterized. Alternating vertical structures are shown through the topography signal from this sample (Fig. 2b). These also correlate to both dielectric and electrode layers.
The continuity of the alternative structures is lost from the top to the bottom of the image, (indicated with red arrows). These discontinuities could be indications of a defect in the device. Striations can also be observed, which are possibly a result of the sample preparation in which mechanical polishing was performed.
Figure 2. The architecture and PFM results of the cross-section of an MLCC. (a) A schematic of an MLCC device showing individual layers of the dielectric and electrode. The plane that was cut to produce a cross-section image can be observed in panels b – d, which is marked by the blue feature. (Image source: http://www.tonar.com/posts/kemet-news_3) The (b) topography (c) PFM amplitude and (d) PFM phase images of the cross-section of an MLCC. Scalebars: 2 µm. Red arrowheads depict regions where the morphologies are discontinuous, which suggests device failure.
Representative LPFM amplitude and phase images were useful in investigating the piezoelectric response of the device. The PFM amplitude signal (Fig. 2c) defines the local electromechanical activity of the sample surface. The amplitude signal also follows the sample displacement, which is a result of the piezoelectric effect.
External contributions, such as capacitive cantilever-surface interactions or electrostatic contributions, can result in artifacts in the electromechanical signal. Efforts to minimize this effect provide better quality data.
The PFM phase signal (Fig. 2d) provides information on the polarization vector of the individual domains. Specifically, the piezo-response will oscillate in-phase or out-of-phase when the polarization direction is parallel or antiparallel to the field, respectively.
Figure 3. A 3D representation of MLCC (a) PFM amplitude and (b) PFM phase overlaid with height images showing discontinuities in the electrode and dielectric material traversing the electrodes at these defect sites.
The images obtained from the MLCC show regions that are taller in the topography image, but lack amplitude or phase signals. This indicates that those regions do not exhibit piezoelectric behavior.
As mentioned, the ceramic dielectric tends to be piezoelectric, which allows researchers to identify the non-responsive areas as regions that contain the metal electrode. The red arrowheads in Figure 2 and Figure 3 show that dielectric has the ability to traverse the gaps in the electrode. This would result in reduced device performance, and could potentially lead to a failure to meet specifications.
In addition, the amplitude and phase images of the MLCC show multiple domains within the piezoelectric material. The appearance of bright or dark regions is an indication of a difference in the direction of the polarization vector. Variations in the absolute direction of the vector and bright and dark regions in the phase image results from the user setting, such as the polarity of the applied bias.
However, the domains that have a reversed phase signal (180º) have opposite in-plane polarization directions. This is shown in Figure 4. In this case, LPFM is implemented, and the regions showing less than a 180º phase shift exhibit polarization directions that have both in-plane and out-of-plane components.
Figure 4. LPFM phase represents the polarization direction of in-plane ferroelectric domains. (a) The image with a vertical line and (b) the corresponding line trace. The green arrows show the difference between light and dark regions which show a 180º phase shift. This shift demonstrates that these domains have parallel and antiparallel polarization directions.
PFM also has the ability to perform spectroscopy at specific locations to measure the response to switching electric fields and sample hysteresis. This is also known as switching-spectroscopy PFM. The local ferroelectric behavior of the domains in the MLCC is characterized in Fig. 5. For reference, Figure 5a shows the theoretical curves of the relationship between strain and electric field, whereas Figure 5d shows the relationship between polarization and the electrical field.7,8
The amplitude has the ability to measure the displacement of the sample directly, which thus means that the response (which could be a function of the sample) can be measured in the dielectric of the MLCC. This is indicated with the asterisk in Figure 5b.
Figure 5c shows a characteristic “butterfly” shape that is similar to the ideal strain versus bias curve. The coercive voltage, which measures the ability to withstand an external electric field without depolarizing, is 0.7 V (See figure caption for details).
Figure 5d shows the theoretical hysteresis loop of the phase, or polarization response of a ferroelectric material.
Figure 5f presents the true response that the MLCC dielectric exhibits, with a sweeping electric field. It also shows a sharp transition at the bias voltage of ~0.7 V.
The offset of the value attained by sweeping from a negative to positive voltage and (vice versa), demonstrates retention performance of the material. Repeated polarization reversal could also provide information about ferroelectric fatigue.
Figure 5. PFM switching spectroscopy on the dielectric material of a MLCC. (a) The theoretical strain-bias response from a ferroelectric material. 1-5 shows the behavior with increasing bias and 6-10 indicates what is the response when bias is reduced. Points 3 and 8 on this curve provide the coercive voltage for the material. (b) The PFM amplitude image and the (c) corresponding “butterfly” shape of the amplitude as the electric field was swept from -9 V to +9 V (red) and back (blue). The red asterisk displays the region where the spectroscopy was performed (d) The theoretical polarization-bias response from a ferroelectric material. 1-5 shows the behavior when bias is increased and 6-10 points at the response when bias is reduced. The distance between points 3 and 8 reflects retention performance of the material. (e) PFM phase image and (f) the corresponding phase behavior as the electric field was swept forward (red) and back (blue). The red asterisk denotes the location at which the spectroscopy was performed.
Conclusions
This article has explored how LPFM can be used to characterize the cross section of a MLCC. The technique enables nanoscale characterization of piezoelectric domains within the dielectric of the capacitor. The electrode and the dielectric were differentiated, and the discontinuities in the device were identified as regions that could potentially compromise the performance of the device.
Both the response in strain (amplitude) and polarization (phase) were explored as functions of applied bias to evaluate material properties, including hysteresis and coercive voltage.
Overall, the ability to characterize the piezoresponse of materials at the nanoscale and quantify the polarization vector of a material using an applied electric field enables researchers to perform local electric measurements and establish structure-property relationships for multiple applications.
References and Further Reading
- Ikeda T. Piezoelectricity. Oxford university press; 1990.
- Soergel E. Piezoresponse force microscopy (PFM). J Phys D Appl Phys. 2011;44(46):464003.
- Kalinin S V., Rodriguez BJ, Jesse S, et al. Vector Piezoresponse Force Microscopy. Microsc Microanal. 2006;12(3):206. doi:10.1017/S1431927606060156.
- Peter F, Rüdiger A, Waser R. Mechanical crosstalk between vertical and lateral piezoresponse force microscopy. Rev Sci Instrum. 2006;77(3):36103.
- Vijaya MS. Piezoelectric Materials and Devices: Applications in Engineering and Medical Sciences. CRC Press; 2012.
- Ho J, Jow TR, Boggs S. Historical introduction to capacitor technology. IEEE Electr Insul Mag. 2010;26(1):20-25. doi:10.1109/MEI.2010.5383924.
- Bdikin IK, Kholkin AL, Morozovska AN, Svechnikov S V., Kim SH, Kalinin S V. Domain dynamics in piezoresponse force spectroscopy: Quantitative deconvolution and hysteresis loop fine structure. Appl Phys Lett. 2008;92(18). doi:10.1063/1.2919792.
- Koval V, Viola G, Tan Y. Biasing effects in ferroic materials. Ferroelectr Mater Charact. 2015.
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