Figure 1. A schematic representation of (a-b) vertical and (c-d) lateral PFM. Vertical deflections are obvious through 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 arrowheads, in each case assuming that the relationship between polarization and crystal orientation is conserved.
Many diverse applications, ranging from sensors and actuators to energy harvesting and biology, make use of the coupling between electrical and mechanical response in a material property. Piezoresponse force microscopy (PFM) in Park Systems’s atomic force microscopes (AFMs) measures this property directly. It also directly probes the response of a material to an electrical bias.
Here we demonstrate the utility of PFM for failure analysis of a multilayered ceramic capacitor. The response to switching of the electric field was evaluated to analyze the piezoresponse of the dielectric. Discontinuous structures in the device were subsequently identified that potentially effected the performance of the device directly.
There are numerous materials that exhibit a coupling of electrical and mechanical behavior, ranging from renewable energy to electronics and biology. This coupling is known as piezoelectric effect, and it is an intrinsic property of materials. Through it, the mechanical response is produced via the application of an electrical field. The material property is implemented in a large number of applications, ranging from ultrasonic imaging to actuators and sensors.
Common man-made piezoelectric materials include ceramics, such as barium titanate and lead zirconate titanate. Polymers, such as polyvinylidene fluoride, also exhibit piezoelectric properties. Naturally occurring piezoelectric materials include bone, quartz, and DNA.
Observing local electromechanical response at the nanometer length scale is possible with the piezoresponse force microscopy (PFM). It is an established, non-destructive technique used by Park Systems, which is also known as dynamic-contact electrostatic force microscopy (DC-EFM). It is performed in an atomic force microscope (AFM), which operates in contact mode with an electrically-biased conductive tip to probe local nanoscale displacements in response to electronic stimuli.
A lock-in amplifier is connected to the deflection signal in order to drive the desired frequency and by-pass unwanted signals. This is needed because the sample displacements and often both very small and have a low signal-to-noise ratio. Since the AFM photodiode is position-sensitive, PFM can also identify the direction of electrical polarization in active piezoelectric or ferroelectric domains.
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 show in panels b – d 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.
There are two different imaging modes - vertical PFM and lateral PFM (VPFM, LPFM). They capture the directionality and sensitive to domains polarized out-of-plane and in-plane, respectively.2 (Fig. 1). Taking both vertical and lateral PFM components into account, one can identify the components of a local polarization vector. This helps to define the direction of the polarization vector using vector PFM.
In VPFM, the cantilever will deflect normal to the sample surface in response to the applied bias. This suggests the presence of piezoelectric domains that point out-of-plane or normal to the sample surface (Fig. 1a-b). Consequently, the EFM phase signal in the AFM will appear bright for domains that point upward and dark for domains that point downward.
In LPFM, displacement shearing the surface is observed in the sample to detect the piezoelectric domains pointed in-plane. This is a lateral movement and will affect the cantilever by displacing the torsion. This would be detected by the position sensitive photodiode as a lateral deflection indicating a polarization direction parallel to the sample surface (Fig. 1c-d).
Both in-plane and out-of-plane displacements are evident through the application of tip bias. This is also possible in piezoelectric samples with arbitrary crystallographic orientations. By simultaneously collecting both VPFM and LPFM signals, vector PFM can be performed to determine the final direction of the polarization vector in nanometer-sized grains. It is possible to acquire piezoelectric constants of the material or a local orientation map. All the same, most researchers assume that the local polarization orientation correlates with crystal orientation on the macro scale.3
In a practical setting, there are some limitations that cannot be ignored when combining vertical and lateral PFM signals. It is important to bear those limitations in mind because a ‘crosstalk’ can arise from geometrical constraints of the cantilever. Furthermore, effects such as friction can lead to sample displacement, due to underestimation of the tip displacement in a lateral direction compared to surface displacement of the sample.4
Multilayer Ceramic Capacitors
Piezoelectric materials have both sensing and actuating properties, and this makes it possible for them to be used in countless applications in the electronics industry.5 Ceramics, such as barium titanate, are a good example of a material that exhibits piezoelectric behavior and has proven to act as a robust dielectric material in capacitors. These are also resistant to humidity and temperature while also being cost effective and exhibiting high intrinsic dielectric constants.
Every year, more than a trillion (1012) barium titanate-based MLCCs are manufactured, which means that multilayer ceramic capacitors (MLCC) are produced in large quantities.6 MLCCs have many 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).
Society currently relies heavily on MLCCs, despite the fact they are somewhat susceptible to failure. An example of this is how thermal stress can be created by high temperatures produced from soldering or storage, hence, cracking, increased current or shorts. A high-energy surge could also prove to be catastrophic and cause high leakage currents (or even rupture) within the device.
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, PFM (which includes the use of MLLCs), proves to be a useful technique.
Below is an analysis 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. Moreover, both topography and electrical signals present discontinuities in the individual materials, which could possibly affect the performance of the device.
A cross-section of an MLCC was analyzed using a Park NX20 AFM. The LPFM signal was obtained using a scan rate of 0.2 Hz. A conductive NANOSENSORSTM PointProbe® Plus-Electrostatic Force Microscopy (PPP-EFM) cantilever, with nominal spring constant k = 2.8 N/m and resonant frequency f = 25 kHz was used. The cantilever was also coated with PtIr5 on both the front and back sides, and the nominal radius of the curvature was 25 nm. The AFM tip was biased with 2 V AC, and no further bias was applied to the sample during imaging.
Figure 3. 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.
Results and Discussion
AMLCC is typically monolithic, with alternating dielectric (ceramic) and metal (electrode) layers that 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 characterized. Alternating vertical structures are shown in the topography signal from this sample (Fig. 2b). These structures also correlate to dielectric and electrode layers.
The continuity of the alternative structures is lost from the top to the bottom of the image (indicated with red arrowheads). These discontinuities could be indications of a defect in the device. Striations can also be observed that are possibly a result of the sample preparation in which mechanical polishing was performed.
Representative LPFM amplitude and phase images helped in the investigation of 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 that is the result of the piezoelectric effect.
External contributions, such as capacitive cantilever-surface interactions or electrostatic contributions can result in artifacts to the electromechanical signal. To combat this, better quality data is available when this effect is minimized.
The PFM phase signal (Fig. 2d) provides information about 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 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 difference between light and dark regions is presented with green arrowheads and shows a 180º phase shift. The shift proves that the domains polarize in both parallel and antiparallel directions.
The images obtained from the MLCC show regions that are taller in the topography image, but lack amplitude or phase signals. This is an indication that these regions do not exhibit piezoelectric behavior.
As mentioned, the ceramic dielectric tends to be piezoelectric, which allows for the identification of non-responsive areas as regions that contain a 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 a reduction in the performance of the device 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 will occur depending on user-specific settings, such as the polarity of the applied bias.
However, the domains that show a reversed phase signal (180º), have opposite in-plane polarization directions. This is shown in Figure 4. LPFM is implemented here, and the regions that show less than a 180º phase shift exhibit polarization directions that have both in-plane and out-of-plane components.
Figure 5. PFM switching spectroscopy on the dielectric material of an MLCC. (a) The theoretical strain-bias response from a ferroelectric material. 1-5 shows the behavior with increasing bias and 6-10 indicates what the response is 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 shows 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.
PFM also has the ability to perform spectroscopy at defined 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 directly measures the displacement of the sample, which means that the response - which could be a function of the sample - can be measured in the dielectric of the MLCC. This is shown 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 between sweeping from a negative to positive voltage and back demonstrates retention performance of the material. Repeated polarization reversal could also provide information about ferroelectric fatigue.
This paper has detailed how LPFM can be used to characterize the cross-section of an 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 a function of applied bias to evaluate material characteristics, including hysteresis and coercive voltage.
To conclude, the ability to characterize the piezoresponse of materials at the nanoscale and quantify the polarization vector of a material with 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.
This information has been sourced, reviewed and adapted from materials provided by Park Systems Inc.
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