High resolution spatial mapping of the electrocaloric effect in a multilayer ceramic capacitor using scanning thermal microscopy

Electrocaloric (EC) materials show a reversible change in temperature in response to the adiabatic application or removal of an external electric field. Interest in using EC materials as the basis for solid-state cooling applications has increased in recent years after the discovery of a giant EC effect [1, 2] with associated temperature changes of up to 12 K reported in ferroelectric systems close to their Curie temperatures. Although cooling devices based on EC elements are still restricted to the level of lab prototypes, technologies exploiting magnetocaloric and barocaloric effects have now matured to the point where commercial prototypes are being developed (www.magnotherm.com/, https://barocal.com/), suggesting significant potential for these as viable environmentally-friendly cooling technologies.

Temperature changes in caloric materials are typically evaluated by either 'direct' or 'indirect' measurements, with the latter approach making up around 85% of published works for EC materials [3]. In indirect measurements, Maxwell relations are used to infer the field-induced temperature change through measurement of pyroelectric currents or the temperature dependence of the electric displacement field. Although indirect measurements are often much easier to achieve experimentally than direct ones [4], the predicted temperature changes rely on several assumptions that do not necessarily reflect real world conditions. For example, in thin film samples, heat sinking by the substrate can significantly diminish measured temperature changes compared to indirect predictions which assume true adiabaticity [5]. Furthermore, hysteresis losses and Joule heating can act against cooling and in some cases even totally obscure the EC response [4]. Reports that EC measurements in notionally the same samples can result in different reported temperature predictions [3] can also obfuscate matters. Therefore, it is clear that direct temperature measurements, typically involving contact thermometry or infrared (IR) thermal imaging, are extremely important for establishing confidence in the stated performance of EC materials when considering using these materials for cooling applications.

In both direct and indirect studies, the EC response is typically characterised by a single temperature for the entire sample, with comparatively few studies focusing on how temperature distributions are expected to evolve spatially [4]. Experimentally, the IR thermal imaging camera has been an indispensable tool for exploring the spatial distribution of caloric heating and cooling. The IR camera provides an excellent non-contact thermal imaging platform that combines high spatial resolution, large field of view and high frame rate capture and has been leveraged for imaging EC temperature distributions in multi-layer ceramic capacitors (MLCCs) [6, 7], polymer ferroelectrics [8, 9] and antiferroelectric ceramics [10]. In the case of MLCCs, the dynamics of heat exchange with the surrounding inactive material and environment have been visualised, with complementary finite element modelling [11, 12] providing a means for optimising the thermal design of the EC elements for heat extraction. In antiferroelectric PbZrO₃ ceramics, use of a wedged sample geometry allowed visualisation of a temperature front propagating through the sample spatially coincident with the phase transition front [10]. Because of its versatility, the IR camera has also been applied to monitor temperature changes in the related families of magnetocaloric [13, 14] and elastocaloric materials [15–17]. The martensitic transition in elastocaloric TiNi alloys is noteworthy, since the development of the temperature distribution follows the nucleation and growth of the transformed phase, demonstrating a clear link between microstructural development and strain driven temperature changes [16, 17]. Taking this further, the potential for engineering site-specific heating and cooling has been strikingly demonstrated by IR thermal imaging in elastocaloric polymer samples fabricated into a diamond trellis geometry [15].

Despite their advantages, limitations of IR thermal imaging include the need for surface emissivity corrections [7] and a spatial resolution that is fundamentally diffraction limited to a few microns. In this respect, scanning thermal microscopy (SThM) might be considered a complementary tool that enables temperature mapping with the capability of sub-100 nm spatial resolution. The technique typically involves monitoring the temperature dependent resistance of a micropatterned thermal probe as it is rastered over a sample surface, allowing spatially resolved maps of temperature to be obtained. In a pioneering study by Kar-Narayan et al [7], the authors compare SThM based EC measurements taken proximate to the terminal of a biased MLCC with those taken by IR imaging and find that the measured temperatures compare well, therefore validating the SThM approach. In a follow up work, some of the authors demonstrated that EC temperature changes in thick films could be observed but were significantly reduced, compared to indirectly calculated values that assume true adiabaticity [5]. More recently, Shan et al took the SThM approach further, by spatially sampling the MLCC EC response at several points across the ceramic surface, allowing reconstruction of a spatial map of temperature with sub-millimetre spatial resolution [18]. However, these studies have not fully capitalised upon the potential for SThM to spatially map temperature profiles at microscopic length scales, despite the demonstrated possibility for resolving temperature features on the order of ∼10 nm in size in other SThM studies [19]. Here, we present spatially resolved measurements of the EC effect in a commercial MLCC on microscopic length scales using SThM. Our approach paves the way for imaging dynamic EC temperature fields on the length scales of key microstructural features in ferroelectrics, such as grain boundaries and domain walls, that would be otherwise be difficult to access using IR based thermal imaging.

SThM measurements were performed in ambient conditions using an Oxford Instruments MFP 3D Asylum atomic force microscope (AFM), equipped with Apex Probes KNT-SThM-2an probes. The sensor consists of a Si₃N₄ cantilever with a micropatterned NiCr/Pd tip coating and exhibits a resistance trend that depends linearly on temperature. Changes in tip resistance are monitored by a Wheatstone bridge and tip temperature calibration measurements were carried out on a controlled heating stage prior to the EC measurements. The EC measurements were carried out on commercially obtained, BaTiO₃ based, MLCCs (KYOCERA AVX, Northern Ireland, Model 1210ZG226ZAT2A). These samples were chosen as they are readily available, inexpensive and offer a good compromise of material properties for EC measurements. MLCCs were cut at a slight angle to the ceramic layers (see supplementary figure S1 for details of cut section), and mechanically polished using Al₂O₃ polishing papers to improve the surface quality for scanning. Silver paste served as an electrical contact between the end electrodes and 0.2 mm diameter copper wire (thin wire was used to minimise heat sinking effects). Poling voltages of up to 100 V were applied to the end terminals, using a Kepco 100-2M bipolar operational amplifier, driven by voltage pulses generated using the internal AFM electronics.

One of the main challenges for mapping temperature changes in EC samples by SThM is that image capture rates are slow (typically sub-Hz), which makes it impractical to spatially resolve the rapid temperature changes that occur across the sample surface during a single electric field cycle. To address this, we have employed an approach inspired by switching spectroscopy piezoresponse force microscopy [20] where a complete cycle of the field is applied, and the temperature response measured, at regularly spaced discrete locations within the microscopic area to be scanned. At each location, the tip was brought into contact until it reached the desired deflection set point. The temperature was recorded as a function of time at this fixed location while a square-pulse voltage waveform was delivered to the sample via the end terminal electrodes, typically over a duration on the order of 10 s. After the waveform had been applied, the tip then came out of contact and moved to the next site, where the process was repeated. A schematic of this measurement process is shown in figure 1(a), illustrating how a spatial pixel map of EC temperature changes can be constructed using this approach. A plan view of the sectioned and polished MLCC sample is shown in figure 1(b) and detailed further in supplementary figure S1. Figures 1(c) and (d) show an example of the typical voltage pulse sequence applied to the end terminals and the resulting EC temperature changes (ΔT) measured at a single location on the sample surface. The applied waveform consisted of an initial 1 s dwell time where no voltage was applied (to allow the system to stabilise after the tip had re-engaged), followed by 5 s voltage on, and finally a 5 s dwell with no voltage applied (figure 1(c)). Voltage rise times were on the order of a millisecond, to induce EC temperature changes under quasi-adiabatic conditions. The thermal decay time of the sample was such that ∼5 s was sufficiently long for the temperature to decay back to room temperature after electrocaloric heating or cooling. Following this method, the temperature change was recorded as a function of time (figure 1(d)) at each specific location in the pixel grid. As shown in figures 1(e) and (f), multiple cycles of the field can also be applied at each location allowing for multiple readings of the temperature change and the possibility for local averaging. To reconstruct spatial maps of the EC response, the magnitude of the EC heating/cooling was extracted relative to the temperature value measured immediately before turning on/off the voltage at each pixel. This approach for extracting EC temperature changes was adopted since it obviated any issues associated with background temperature drift and minimised the possible influence of any spurious temperature offsets, due to e.g. electrostatic interactions with the tip while the electric field was applied. All scans were taken in ambient conditions, approximately 20 °C.

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To demonstrate our SThM measurement method, an (80 × 20) µm² scan region on the polished surface of the MLCC was selected for investigation. The microstructure within the MLCC consisted of a dense network of individual grains, with an average grain size of between 2 and 3 µm. Two line profiles, shown in figure 2(a), were defined that spanned between two polish-exposed electrodes on the surface at the location identified by the red star in figure 1(b). Each line profile consisted of 128 equispaced sites, giving a pixel spacing of approximately 600 nm. Since the thermal decay time is of the order of seconds, each pixel in the final image requires on the order of 10 s to capture one complete heating and cooling cycle. Typical scan durations are therefore determined by the pixel density, with the area scanned in figure 2 taking ∼1 h in total. In principle, larger areas can be scanned but topographical drift over long scan durations can become an issue. Keeping total scan times to around 1 h in total was found to offer the best compromise between resolution (pixel density) in the final image and scanner drift. In figures 2(b) and (c), maps of the EC heating and cooling are presented for the case of 100 V applied across the end terminals (electric field of ∼150 kV cm⁻¹ between pairs of interdigital electrodes). Measurements across the same region were repeated for several different applied voltage values and the data for one of the line profiles is presented in figures 2(d)–(f). As expected, the magnitude of ΔT is seen to increase with the applied voltage. However, there are also finer scale temperature variations observed for each line section, which do not obviously mirror changes in local topography and appear to be largely stochastic in character. However, observation of a narrower distribution of EC temperature changes when repeated measurements are collected within a smaller area may indicate some real local variations in the EC response (supplementary note 1 and supplementary figure S2). In order to put this observation on firmer ground, the possible influence of varying tip/sample contact across the surface (which leads to differences between the probe temperature and true surface temperature) should also be taken into account and likely contributes to the observed variability in local temperature measurements when repeated scans of the same area are carried out (supplementary figure S3). In the study of Shan et al [18], the effect of an assumed tip-sample thermal contact resistance was considered for their doped Si probes through finite element modelling. They found that the experimentally obtained EC temperature changes could be reproduced when the heat transfer coefficient associated with the airborne cantilever was used as a fitting parameter. However, the influence of varying the tip-sample contact resistance on transient EC temperature signals was not investigated and is an avenue for future study which would help with interpretation of the small spatial temperature variations observed in our work. As a rough guide, we can also look to existing studies where spatial variations in tip-sample contact resistance have been mapped experimentally in actively heated samples [21–23]. Edge effects associated with nanostructured heater lines have been reported to cause fictitious temperature variations of order 10% [22, 23] which would be suggestive of temperature fluctuations on the order of 10 mK for our samples. This is comparable to the standard deviations of up to 40 mK associated with the temperature distributions measured in figure 2 (supplementary figure S2) and emphasises the need for careful determination of the tip-sample thermal resistance using established protocols [24] before spatially resolved temperature profiles can be confidently attributed to variations in local EC response.

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Although any spatial variations in EC temperature changes on the microscale in these samples seem to be minor, more substantial temperature differences are expected to occur over macroscopic length scales due to heat exchange between the sample exterior and its surroundings [6, 7]. Therefore, to further validate our SThM methodology, we compared temperature measurements performed on the exposed BaTiO₃ ceramic with those performed on the metallic end terminals (figure 3). In figure 3(a), histogram distributions of the EC heating and cooling temperature values are presented for three applied voltages for the (80 × 20) μm² ceramic region from figure 2. A representative average temperature change and standard deviation is then obtained for each distribution, and these are plotted in figure 3(b) (solid red circles) as a function of electric field. The same procedure is used to obtain averages for local areas measured on the surface of the end terminal (red triangles in figure 3(b)). For the range of applied fields studied, we find that the average EC temperature rise measured on the end terminal electrode is a factor 0.6 $\pm$ 0.1 of that measured on the ceramic layers. This compares well with the factor ∼0.7 reported in notionally the same commercial samples by Kar-Narayan et al [7, 25]. We also note that temperature variations across the surface of a different commercial MLCC were reported to be up to 51% of the average value [6]. In general, the observed temperature distributions in MLCCs can be expected to be affected by differences in sample geometry and material composition, as substantiated by studies in [11, 12, 26]. When considering the importance of efficient heat extraction for envisaged MLCC based EC coolers, thermal conductivity mapping of the electrocalorically active BaTiO₃ grains using the established 3ω SThM technique [27] would also be complementary to our SThM temperature mapping approach of EC heating. Previous studies have revealed that heterogeneity in thermal conductivity can be observed across different grains [28] as well as at grain boundaries [29], however such clear grain-related contrast is not evident in the BaTiO₃ MLCC studied by 3ω SThM by Du et al [30]. They do however identify locally enhanced thermal conductivity in pre-breakdown regions of degraded MLCC samples which may also be expected to give rise to a locally altered EC response. Local SThM temperature mapping could therefore be useful in the study of fatigue in EC response, where a decrease in the magnitude of the effect, or even reversal in sign, has previously been observed [31, 32].

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In order to explore the potential spatial resolution of our technique, a smaller (2 × 2) µm² region was mapped (figure 4), with local temperature measurements separated by 125 nm in a square grid. We were able to reconstruct the dynamic evolution of temperature in this region by plotting the temperature value at each pixel for the same time elapsed after delivery of the field pulse (figure 4(a)). By averaging the individual temperature vs time profiles obtained at each pixel we can obtain a well resolved EC heating/cooling temperature cycle that is representative of the whole 2 μm region (figure 4(b)). We note that the smallest resolvable feature by IR camera is diffraction limited to the order of a few microns, which is of comparable size to the entire area scanned by SThM in figure 4. This also represents a reduction in the pixel spacing of three orders of magnitude compared to the work of Shan et al [18] where they use SThM to explore the macroscopic variation in temperature across the surface of a commercial MLCC. In principle, our technique should allow for examination of the EC response at the scale of microstructural features, and additional small area scans spanning multiple grains are shown in supplementary information figures S4 and S5. However, despite the existence of several grains being imaged in the topography, we do not identify clear evidence of heterogeneity in the temperature maps that correlates with the microstructure. This could possibly be due to deliberate engineering of homogenous functional response in these commercial samples as well as transient features in the temperature maps being obscured by lateral heat flow on timescales shorter than the minimum measurement time of our system (∼0.5 ms). To improve the chances of resolving microstructural influences on the local EC properties, ceramic samples which exhibit clear core/shell structures could be investigated and inspiration taken from the lock-in techniques and fast thermal measurements demonstrated in the recent studies by the groups of Rudolph [33] and Defay [34].

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In conclusion, we have demonstrated a SThM based method that enables local imaging of the EC effect on microscopic length scales. Proof of principle measurements were performed on a sectioned and polished MLCC showing that entire heating and cooling cycles could be sensed point-by-point across the surface with pixel separation as small as 125 nm. The ultimate spatial resolution achievable with this technique remains to be determined but could be sub-100 nm if tip radius is the limiting factor. Differences in the magnitude of electrocaloric temperature change across macroscopically separated regions of the MLCC was found to be consistent with previous literature expectations based on heat exchange with the sample surroundings. Looking forward, it is hoped that the demonstrated thermal mapping capability will be a powerful tool for exploring the predicted effect of domain microstructure [35–37] or field heterogeneity on EC temperature changes.

This work was supported by a UKRI Future Leaders Fellowship (Grant Number MR/T043172/1). RGPMcQ and OEB acknowledge financial support from the Engineering and Physical Sciences Research Council (project reference 2442888, Grant Number EP/T518074/1). The authors would like to thank Dr Jonathan Moffat at Oxford Instruments Asylum Research for guidance on how to implement the SThM measurements on our AFM system and Dr Kristina Holsgrove at QUB for carrying out electron microscopy of the MLCC.

The data that support the findings of this study are openly available at the following URL/DOI: https://doi.org/10.17034/5f9008fd-3bc6-429c-b54e-f62b20ced5e5 [38]. Data will be available from 31 December 2023.