# Dielectrics and capacitors at cryogenic temperature revealed by synchrotron cryo-X-ray microtomography

Jaianth Vijayakumar, Yves Watier, Paul Thompson, Sofiane Guessasma, Paul Tafforeau

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Jaianth Vijayakumar, Yves Watier, Paul Thompson, Sofiane Guessasma, Paul Tafforeau. Dielectrics and capacitors at cryogenic temperature revealed by synchrotron cryo-X-ray microtomography. Journal of the European Ceramic Society, 2026, 4 (6), pp.117966. 10.1016/j.jeurceramsoc.2025.117966. hal-05528384

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# Dielectrics and capacitors at cryogenic temperature revealed by synchrotron cryo-X-ray microtomography

Jaianth Vijayakumar a,*, Yves Watier a, Paul Thompson b, Sofiane Guessasma c, Paul Tafforeau a,†

## ARTICLE INFO

Dataset link: https://data.esrf.fr/, https://doi.org/10.15151/ESRF-ES-2002456918

**Keywords:**

Cryo-Synchrotron X-ray microtomography

Capacitors

Dielectrics

Ferroelectrics

## ABSTRACT

The functionality/reliability of electronic devices in extreme low temperatures are limited. Therefore, understanding their characteristics at low temperature is important for optimizing the performance/design of individual electronic components. Capacitors are one such electronic components sensitive to temperature. Conventional low temperature electrical characterization lack spatial information. Here we combine synchrotron-cryo-microtomography, finite element modeling, and electrical characterization, to correlate the electrical and microstructural properties within capacitors down to -197 °C. Our experiments reveal that a change in capacitance at low temperature is due to micro-structural changes in the dielectrics, seen as opening/closing of cracks. We find that the macroscopic/microscopic structural changes are induced by local thermal contraction, and these are stronger with multiple interfacing materials, affecting their electrical characteristics. Our results show new insights towards the functionality of commercial capacitors at low temperatures and provide an important benchmark for developing and designing future capacitors for extreme environmental conditions.

## 1. Introduction

The use of electronics and electronic devices at low temperature conditions is a necessity, and is on a constant rise, particularly with the increase in space explorations, [1] or even polar expeditions on earth [2]. While low/cryogenic temperature is suitable for quantum devices and circuits, low temperatures can affect the functionality and reliability of the standard electronics and their individual components (e.g. capacitors). [3] The lower operational temperature of electronic components such as a capacitor is restricted down to around -55 °C (218 K) [4]. To be able to use these electronics at even lower temperatures, they are encapsulated in a climatic controlled chamber to obtain their optimal functionality. For miniaturization and effective use of resources, it would be essential to develop electronic materials and components suitable for low temperature applications without the need for climatic controlled chambers. To achieve this, a detailed testing of the individual components can be crucial to improve the design and manufacturing process. Testing of an electrical component, involves direct current (DC) based measurements such as current-voltage characteristics or alternating current (AC) based measurements such as impedance characterization [5,6]. Similar measurements have also

been employed to characterize capacitors at cryogenic temperatures down to 4 K, see Ref. [5-14]. These characterizations, are standard, robust and well suited for large-scale testing, however, they lack spatial and micro/macro structural information which can be critical to the functionality of the devices, particularly at low temperatures and it still remain unexplored. Some of the electrical characterizations can indeed be used to determine the structural properties such as internal defects [15]. However, they can be prone for misinterpretation without applying a non-destructive imaging technique such as X-ray microtomography; where one acquires X-ray transmission images at different sample rotation with respect to X-rays and computationally reconstruct the cross sections of the sample to obtain 3D information [16]. While room temperature X-ray microtomography of electrical components is well known, [17-19] performing low temperature X-ray microtomography of electrical components is unexplored. Key challenge is to achieve both high resolution imaging with lowest temperature possible to complement electrical characterization; on a standard cryostat this can be down to 4 K. One can consider using such cryostat for X-ray microtomography, however, one of many possible issues in these cryostats is that they are prone to vibrations due to the presence of vacuum

<footnote>a European Synchrotron Radiation Facility, 71 avenue des Martyrs, Grenoble, 38000, France</footnote>

<footnote>b University of Liverpool, Dept. of Physics, Oliver Lodge, Liverpool, L69 7ZX, United Kingdom</footnote>

<footnote>c INRAE, Research Unit BIA UR1268, Rue Geraudiere, Nantes, F-44316, France</footnote>

<footnote>* Corresponding author.
E-mail address: Jaianth.Vijayakumar@esrf.fr (J. Vijayakumar).</footnote>
or cryogenic pumps. Such mechanical vibrations are not suitable to perform X-ray microtomography especially at high resolution (e.g. pixel size of 2–3 µm).

Low temperature microtomography has indeed been carried out using thermal insulation containers, [20] dry ice, [21] air blower, [22] or Peltier cooling systems [23,24] with temperature capable of reaching down to 200–160 K. Although surface characterizations, and when samples can be made thin, scanning electron microscopy (SEM), tomography, transmission electron microscopy (TEM), or scanning probe microscopy can be performed at low temperature, and in some cases even at 1.8 K [25–27]. Nevertheless, with microtomography as in Ref. [28], a customized chamber is used, that is capable of reaching temperature down to 85 K, these samples (~5 cm length) are characterized by lab-based microtomography setup with an acquisition time of 50 min, with a voxel size of 11.6 µm. Such long acquisition time is often due to low X-ray flux from lab-based X-ray source, and can also be due to the thick climatic chamber necessary for better insulation. The pixel size or the sample size is also determined by the size of sample environment chamber. Nevertheless, long acquisition time is not favored due to the possible movements as a result of sudden mechanical or thermal movements with time, which is more detectable at smaller pixel sizes. The lowest possible temperature one can reach, and combine microtomography is still unexplored. Key requirements to overcome these issue and push the limit of low-temperature microtomography is to use a high energy and high brilliant X-ray sources. Here we present a cryo-synchrotron microtomography measurement using a simple low temperature setup to characterize samples at –197 °C (77 K) and at around 2 µm pixel size. The experiments were made possible thanks to the high energy and high brilliant X-ray photons available at the newly developed BM18 beamline at European synchrotron radiation facility - Extreme bright source (ESRF - EBS) [29].

Using the developed cryo-microtomography setup, we study the effect of microstructural changes on capacitors at low temperature and correlate with the electrical characterization down to 20 K. Capacitors are one of the basic and an important electronic component. Different types of capacitors exist and can be classified based on the type of materials present such as ceramic, electrolytic or film capacitors to name a few. Here we study the low temperature effects of multilayer ceramic capacitors, solid electrolytic $Ta_2O_5$ capacitor and liquid electrolytic $Al_2O_3$ capacitors. The same capacitors are then characterized in a cryostat available at BM28 beamline at the ESRF. The electrical characterizations are performed to correlate the electrical and structural properties of the capacitors. Our phase-contrast microtomography results show clear microstructural changes occurring in the capacitor materials such as in dielectrics, metallic parts and also the resin insulation of the capacitors. The physical changes are significant and can potentially explain the changes in the capacitance values in the selected capacitors measured at low temperatures.

## 2. Cryo-X-ray microtomography

In synchrotron X-ray microtomography or in most of the lab-based X-ray microtomography, the sample is generally positioned on a rotating stage, which is rotated in an axis perpendicular to the X-ray propagation to collect projection images at different rotation angles. The projection images are then reconstructed to obtain the cross-section slices of the sample across its length. Such microtomography measurements can be fairly straight forward, however, setting up a sample environment system with a temperature close to liquid nitrogen on a rotation stage is challenging (for example, proper anchoring of the sample, or the liquid nitrogen level can change with time during the measurement). For example, Ref. [30], carried out microtomography imaging by dripping liquid nitrogen on the sample from a Dewar from the top of the sample, and disconnected from the rotation stage. Motivated by this approach, we develop an alternative solution such that the sample is always submerged inside liquid nitrogen ensuring

<figure><img src="image_4.png" /><figcaption>**Fig. 1.** (a) Schematic of the cryo-microtomography setup. 1 — Microcontroller connected to the 2 — Liquid nitrogen pump. 3 — Transfer line. 4 — Sensor (Thermocouple) and wireless communication to monitor the liquid nitrogen level connected to a (7) micro-controller. 5 — Metal mesh to cancel non-liquid nitrogen phase. 6 — Sample submerged inside the liquid nitrogen. 7 — Microcontroller to monitor liquid nitrogen level. 8 — computer connected by WiFi to (1) and (7). (8) Control computer present outside the experimental hutch. (b) X-ray energy spectrum simulated without and with liquid nitrogen (LN2) of 3 cm absorption length. The peak energy remained the same at around 140 keV in both cases. Liquid nitrogen density is considered to be 0.807 g/cm³.</figcaption></figure>

that the surrounding temperature is maintained at 77 K. Fig. 1(a) shows a schematic of the cryo-setup developed for the experiment at BM18. While a cryostat with a controlled temperature is ideal, we consider here measuring the sample within a liquid nitrogen environment, and only at 77 K. This makes the setup fairly simple and adaptable for different tomography stages, the only challenge here is to ensure that the liquid nitrogen level is maintained inside the container during the measurements. The cryo-setup here requires a standard liquid nitrogen Dewar, transfer line, liquid nitrogen pump, liquid nitrogen sensor and two microcontrollers with built-in WiFi.

On the stage we place a stainless steel container which is magnetic (in this case an espresso coffee cup). Some capacitor materials were also magnetic, therefore we first attach the sample on a magnet which is then placed inside the cup, anchoring all the parts by magnetic field. For non-magnetic materials, we considered attaching the sample by a cyanoacrylate glue on the magnet, which is then fixed inside the cup. The glue eventually comes off after multiple room and liquid nitrogen temperature measurements, and caused some minor movements at low temperature, which did not significantly affect the measurements. To reach low temperatures, liquid nitrogen is poured from the Dewar connected by a transfer line using a liquid nitrogen pump controlled by a microcontroller. To monitor the level of liquid nitrogen in the container, a sensor (in this case thermocouple) connected to a microcontroller is attached closed to the rim of the sample container. Both the microcontrollers are connected using WiFi and is monitored by a computer outside the hutch also connected by WiFi. If the level of liquid nitrogen goes below the sensor, it is detected by the two microcontrollers, then the pump pours in liquid nitrogen till the level reaches the sensor. The dimension of the container used for this experiment is approximately 5 cm × 3 cm × 3 cm, and the time to fill the container can take about ~ 1 min. During the first 15–20 s one can observe cold liquid nitrogen vapor on the sample.

Sample container filled with liquid nitrogen can reduce the X-ray transmission compared to the same with air. Fig. 1(b), shows the simulated energy spectrum of the beamline configuration, with the average energy of detected photons ~140 keV. From the spectrum one can find a large change in the transmission > 40% with liquid nitrogen
in the container, resulting in an average energy shift of 1.1 keV, and peak energy is shifted by 0.2 keV. The spectrum practically remain unchanged, therefore to offset the change in X-ray transmission, one can consider increasing the exposure time of the detector such that the pixel values at room temperature with air is same/or comparable with the pixel values at liquid nitrogen temperature. To increase the transmission, the attenuators configuration can be changed, however, this will result in a change in the beam spectrum, and in turn in the gray scale values in the object [31].

The liquid nitrogen will boil in the container, and this is causing an inhomogeneity in the images inducing noise in the final reconstruction. To remove this effect on the images, we acquire the flat field image with the container and liquid nitrogen, just few cm above the sample. This flat field is subtracted during reconstruction and can be very crucial to have a noise free reconstruction on the sample at 77 K. We typically acquired 50–100 flat field images. Measuring the flat field image with air as reference reduces the signal-to-noise ratio (SNR) of the reconstructed image by 10%, this can be significant when identifying small features sizes ranging from 5–10 pixels. Finally, during the reconstruction, despite the flat field correction, the presence of inhomogeneities in the flat field image and projection images, produce additional noise and ring artifact. To reduce this, we perform a double flat field correction on the projection images, i.e. average all the projection images and apply a small Gaussian filter (kernel size of 3 × 3 or 5 × 5), then subtract this from each projection images in addition to the flat field correction.

### 3. Capacitors and temperature

Capacitors are electronic devices which can store charges by applying an electric field, they have a metal-insulator-metal structure, and the insulator/dielectric is the main component of a capacitor. The unit of a capacitor is capacitance, and it varies directly by the surface area, dielectric constant/permittivity, and inversely by the thickness of the dielectric [C = $εA/d$]. Different types of capacitors exist based on the dielectric. Sometimes to increase the capacitance, the surface area of the device is increased, either by making the capacitor into multilayers or by using a liquid conductive electrolyte to have better contact on the rough dielectric as in $Al_2O_3$ capacitors. Therefore, the effect of temperature can vary depending on the type of capacitors. For instance, ceramic and thin film capacitors are classified based on the capacitor tolerance and the temperature coefficient (i.e. sensitivity of capacitance with temperature, smaller this value, greater the stability with temperature). For example, class 1 ceramic capacitor are typically made of para-electric dielectric, and have the least temperature coefficient, and the capacitance value do not change even at 4 K [6,32]. However, the disadvantage of such capacitors is that they have low permittivity and only exist for low capacitance values, restricting broader usage. As previously shown (e.g. Ref. [6,32]), film capacitors such as PET (Polyethylene Terephthalate), polyester capacitors, showed the least change at low temperatures. Multilayer ceramic capacitors, such as X7R, Z5U, show the largest change (>50%), and $Ta_2O_5$ capacitors showed, a change of about 10%–20%. The liquid electrolyte capacitor showed even more drastic changes at low temperatures. Therefore, we consider the latter three capacitors, multilayer ceramic, solid electrolyte $Ta_2O_5$ and $Al_2O_3$ liquid electrolytic capacitors and investigate the microstructural changes in the materials using the cryo-X-ray microtomography setup. We selected lead type-capacitor for better anchoring, and did not use surface mount capacitor due to its small size and limited available resolution (~2 µm pixel size). Following is a brief description of these capacitors;

1. Tantalum capacitors. It is a solid electrolytic capacitor and widely used in electronic devices. The dielectric is $Ta_2O_5$, and has a permittivity of about 25. The final capacitor is highly porous as the starting material is powdered Ta sintered on a Ta rod as an electrode. The powdered Ta surface is later converted

to $Ta_2O_5$ (~100–200 nm in thickness depending on the capacitance) by electrochemical process. The complete manufacturing procedure can be found in Ref. [33]. Typically, the capacitive structure consists of $Ta/Ta_2O_5/MnO_2$/Ag, Fig. 2(a) shows a schematic description of the different layers. The formation of these capacitive structure depends on the penetration ability of the $Mn(NO_3)_2$, which is later heated to form a conductive solid electrolyte $MnO_2$. Therefore the net capacitance is the sum of all the capacitive structure formed on the Ta powder surface present inside the dark contrast cylindrical structure shown in Fig. 2(d) radiography image. These capacitors are polarized and hence not suitable for AC signals. The capacitor used here is embedded inside a molded epoxy resin casing. Here we use commercially available Ta capacitors with capacitance value of 47 µF.

2. Multilayer ceramic capacitors. These capacitors typically have high stability and low dielectric loss, hence are used in high frequency applications. The dielectric constant of the ceramic used can be in the order of 200–500 or more. The capacitive structure consists of metal-insulator-metal, and to obtain the necessary surface area, the capacitors are produced with multiple layers of metal-insulator-metal similar to an interdigitated electrodes [see the schematic in Fig. 2(b)]. The final structure is covered by a protective layer of epoxy resin (an epoxy-dipped style) [see radiography image in Fig. 2(e)]. Here we use commercially available multilayer ceramic capacitors (104 M5E) with 100 nF capacitance. The dielectric in this capacitor is typically $BaTiO_3$ with some additives which are unknown, for simplicity, we consider the dielectric as $BaTiO_3$ and the electrodes are typically made of Ni [34]. $BaTiO_3$ is also a ferroelectric material, i.e. they have spontaneous electric polarization and can be switched with applied electric field.

3. Aluminum electrolytic capacitor. It is a liquid electrolytic capacitor, where the different layers are synthesized as thin sheets and are rolled into a cylindrical structure [see radiography image in Fig. 2(f)]. They are frequently used for their wide voltage, capacitance ranges and are cost effective. The aluminum electrolytic capacitor have layers of $Al/Al_2O_3$/liquid electrolyte/$Al$ [see schematic in Fig. 2(c)]. The liquid electrolyte (typically ethylene glycol) is impregnated in a porous membrane or paper. The $Al_2O_3$ is synthesized on the surface of Al metal. The $Al_2O_3$ thickness can be around 100 nm with dielectric constant around 8–10. We use aluminum electrolytic capacitors (manufactured by Philips) with capacitance value of 9.5 µF.

### 4. Methods

**Microtomography:** The experiments were carried out at BM18 during 4-bunch filling mode with 40 mA current in the storage ring. We measure projection images over 360 degrees. The imaging was carried out using 2x Otus 100 mm/Nikkor 200 mm tandem optics with IRIS 15 sCMOS camera coupled to a 50 µm thick LuAG:ce scintillator with a reflective layer on its front side. The sample-detector distance was 1 m, leading to an effective object isotropic voxel size of 2.207 µm. The measurement parameters of all the capacitors are shown in Table 1. Here we also highlight the effect of the stainless steel cup which can potentially attenuate the energy spectrum. For instance, setting the beamline with 1.3 mm thick Mo attenuator can result in average detected energy of 116 keV, with the stainless cup of ~4 mm, this can change to 163 keV. Hence with a stainless steel cup one can expect an increase in average detected energy by 10%–15%. The capacitance was measured at 300 K and 77 K without the X-rays, with hand held LCR (inductance-capacitance-resistance) meter - BK-precision model 879B. The instrument accuracy is 0.5% at 100 Hz measuring frequency. The capacitors were exposed to the beam about 3–4 times and we find no significant changes in the capacitance values for all the capacitors
<table><caption>**Table 1**
Beamline configuration and measurement parameters used for all the capacitors. MLCC refers to multilayer ceramic capacitor. We take 50 flat field and dark images. *Corresponds to average detected energy. Propagation distance is kept at 1 m for all cases.</caption><thead><tr><th>Sample</th><th>Energy*<br>(keV)</th><th>Attenuators</th><th>Exp.-time<br>(300 K/77 K)</th><th>No.<br>proj.<br>images</th><th>Image<br>dimension</th></tr></thead><tbody><tr><td>Ta<sub>2</sub>O<sub>5</sub></td><td>151</td><td>Mo - 3.75 mm</td><td>0.2/0.35 s</td><td>5000</td><td>1800 × 1800</td></tr><tr><td>MLCC</td><td>116</td><td>Mo - 1.3 mm</td><td>0.15/0.22 s</td><td>4000</td><td>1200 × 2400</td></tr><tr><td>Al<sub>2</sub>O<sub>3</sub></td><td>116</td><td>Mo - 1.3 mm</td><td>0.1/0.18 s</td><td>3600</td><td>2960 × 2500</td></tr></tbody></table>

<figure><img src="image_5.png" /><figcaption>**Fig. 2.** Schematic and radiography image of (a,d) tantalum oxide capacitor, (b,e) multilayer ceramic capacitor, and (c,f) aluminum oxide capacitor, respectively. The scale bar in radiography images corresponds to 500 µm and in each image the gray scale is adjusted for a better contrast.</figcaption></figure>

suggesting no beam induced damages. The images were constructed using Tomwer/Nabu reconstruction software [35].

For cryo-microtomography, the capacitors were attached to a Nb-magnet, when needed by an cyanoacrylate glue, and fixed to the metallic container. The capacitor terminals are connected by insulated copped wire protruding out from the container and fixed on the stage to avoid possible movements. The room temperature and low temperature X-ray microtomography measurements were carried out on the same setup. The wires are connected to the hand-held LCR meter by crocodile clips. The capacitance is measured before and after pouring the liquid nitrogen in the absence of X-rays. Once the capacitors are in liquid nitrogen the capacitance value is monitored till it is stable to start the microtomography measurements (typical time is ~ 10–15 min). Fig. 2(d–f) shows the radiography image of the different capacitors inside the container. Before analyzing the data the image slices/volume are corrected for the drift in 3D, to correlate the changes between 300 K and 77 K.

**Image processing** — For segmentation and data analysis, we used gray value thresholding. When needed we normalize the image by a bandpass filter. Then, the gray scale value was adjusted visually to segment the pores. To obtain the error associated with the thresholding, we vary the range of pixel intensities and measure the number of connected pores. The median of the number of pores and the corresponding threshold value range was considered for the analysis. The error associated will be presented as the standard deviation of the number of segmented pores and is given as percentage.

**Electrical Characterization** — We performed electrical characterization on the same samples without the X-rays at BM28 beamline at ESRF [36]. The sample is mounted in a closed cycle DE202 ARS cryogenic cryostat. The sample is fixed on a copper plate by silver paint, and is cooled by a compressor. The surface temperature is controlled by a cernox sensor and a resistive heater using a Lakeshore temperature controller model 340. The cooling rate is around 2–5 K/min and we wait for about 5 min for the temperature to stabilize before the measurements. From the cryostat, the sample is connected by high voltage coaxial cable. We perform I–V characteristics, to understand the transport mechanism across the capacitors as a function of temperature. The sample is connected to a function generator where we apply a triangular wave with voltage range from ± 10 V. For multilayer ceramic capacitor we use an additional voltage amplifier. The current is measured from the same terminal (as a 4-point probe measurement) using a Stanford research current amplifier (SR570) connected to an analogue to digital converter read by the computer. The frequency and voltage range are adjusted for each sample, and when required we apply a bandpass filter (6 db, filtering frequency is adjusted from 0.1 Hz–10 Hz) to remove some electrical noise. The sensitivity (current/voltage) of the amplifier is also varied, depending on the ramp voltage frequency and amplitude. The oscillating voltage frequency is kept between 1 mHz to 10 Hz, and the range is adjusted with the sample. With faster ramping of voltages, one can expect a square hysteresis like I–V plot for a pure capacitive device due to $C = I dV/dt$ relationship. However, this curve also depends on the rise time of the capacitor and if the frequency is close to the self-resonant frequency of the capacitor. At low frequency however, we let the system to relax, i.e. we wait longer than the capacitor rise time, these measurements are useful to understand the electron transport mechanism across the insulator. At low frequency, the capacitor acts as a pure insulator, and the measured current will be less when compared to high frequency voltage ramp, where the capacitive impedance reduces $(1/j\omega C)$, resulting in a higher measured current. In addition, during the cooling we measure the change in capacitance as a function of temperature using Metrix (MX23) multimeter.

**Finite element modeling** — The simulation was carried out by ANSYS mechanical simulation software. We simulate a two-step coupled thermal-structural analysis for 3D solid model. The 3D model of Ta/Ta<sub>2</sub>O<sub>5</sub>/MnO<sub>2</sub> layers is shown in Fig. 8(a–b), a part of the multilayers shown in Fig. 2(a). The solid phase is uniformly meshed, with each structural element defined as a cubic cell consisting of eight nodes, each possessing three translational degrees of freedom (x, y, and z) for structural mechanics analysis and temperature (T) for thermal analysis [Fig. 8(b)]. The model size does not exceed 30 000 degrees of freedom. An isotropic linear elastic material model is employed for all phases with the physical constants detailed in Table 2. The coupling problem is solved iteratively, where the steady-state thermal problem is solved to derive the temperature distribution within the material. As for loading conditions, at Ta layer, temperature is fixed to 77 K, and at the MnO<sub>2</sub> layer, the temperature is varied. The temperature assignment in Ta layer at 77 K, MnO<sub>2</sub> layer at 300 K is shown in Fig. 8(b). The temperature field is retrieved from the thermal analysis to include the thermal expansion effects in the structural analysis. Together was used to evaluate thermal stresses and deformations due to temperature gradients.
<table><caption>**Table 2**
Simulation parameters. For Ta see Ref. [37–41], Ta₂O₅ see Ref. [42–44], MnO₂ see Ref. [45–47]. \* taken at 77 K, rest of the values were taken from room temperature data.</caption><thead><tr><th>Parameters</th><th>Ta</th><th>Ta<sub>2</sub>O<sub>5</sub></th><th>MnO<sub>2</sub></th></tr></thead><tbody><tr><td>Thermal conductivity W/mK</td><td>57.7</td><td>1</td><td>4</td></tr><tr><td>Thermal expansion coefficient</td><td>6.1 × 10<sup>-6</sup>(*)</td><td>6.72 × 10<sup>-6</sup></td><td>3.3 × 10<sup>-6</sup></td></tr><tr><td>Young's Modulus (GPa)</td><td>185</td><td>138</td><td>25</td></tr><tr><td>Poisson coefficient</td><td>0.34</td><td>0.33</td><td>0.2</td></tr></tbody></table>

# 5. Results

## 5.1. Cryo-X-ray microtomography

### 5.1.1. Tantalum oxide solid electrolytic capacitor

Fig. 3(a) shows the vertical cross-section of a tomography volume of Ta₂O₅ capacitor at 300 K, the bright center rod and the outer curved shaped structure are the electrodes for external contacts. The capacitive structures are present inside the central cylindrical structure. Fig. 3(b-c) shows the horizontal cross-section at 300 K and 77 K, respectively, here one can clearly see the changes in the pore structures, two regions are highlighted by white dotted circles and the magnified images are shown in Fig. 3(d). The structural changes in the pores are random throughout the volume, we typically find contraction or expansion across the region, which results in opening and closing of pores. Pores which opens up, is identified as a new pore during segmentation. Similarly, when a pore closes, it suggests that the size is smaller than the resolution to be detected. Fig. 3(e) shows the change in the number of individual detected pores and their sizes at 300 K and 77 K across the full capacitor volume in the cylindrical region. Here one can find the number of pores to reduce at 77 K, a decrease of 3700 ± 700 (~ -5%) pores and this corresponds to a change in pore fraction of 15%–17%. In addition, the sizes of the remaining pores slightly increased at 77 K. Fig. 3(f) shows a 3D rendered image of the local changes in the pores across the volume. This image is obtained by taking the difference between the two volumes, and analyzing their local thickness. Here one can find that a large displacement is occurring on the top and bottom region of the capacitor, possibly due to stronger strain on these regions [see the supplementary information S.I on image processing]. Furthermore, we also find clear displacement of the metal electrode surrounding the capacitor, Fig. 3(g) shows the line profile showing the change in the position of the electrode by 5–6 µm inwards compressing the structure, between 300 K and 77 K. We find this displacement to vary across different regions. For better visualization please see raw image sequence provided in the supplement. The line profile is taken from the outer corner of the electrode marked in white dotted line in Fig. 3(c-d). We find similar displacement in the vertical direction, showing a compressive effect of the overall structure at 77 K. With these morphological changes, the capacitance changed from 47.4 µF at 300 K to 37.2 µF at 77 K, a change of 21% ± 5% (averaged with 3 similar capacitors).

### 5.1.2. Multilayer ceramic capacitor

Fig. 4(a) shows the reconstructed cross-section of the multilayer ceramic capacitor across the long axis. One can find, the resin (indicated by two black arrows) surrounding the structure with large pores, the two electrodes are on the sides and the center part consist of the multilayers of ceramic and metal. The dotted line represents the layer corresponding to the metal electrode, with pores size ranging from 10–40 µm diameter. Fig. 4(b) shows the horizontal and magnified cross-section of Fig. 4(a) where one can see the different layers of metal through the ceramic region. The beam hardening effect, where one can find a decrease in the contrast (or shadow effect) from outside of a highly absorption material towards the center of the image, can be seen here and it is indicated by black arrows [in Fig. 4(b)]. Due to the high aspect ratio one can also find streak artifact in the long axis of the structure [in Fig. 4(b)]. Fig. 4(c), shows the magnified image of the multilayers

taken from the region marked with white square in Fig. 4(b). At 300 K one can find a smooth metal layers with intermediate pores. At 77 K, one can find the opening of cracks, and deformation of some larger pores highlighted by white dotted square. Similarly, the difference of 300 K and 77 K images, highlighting the region with crack opening or closing with black and white contrast, respectively. These cracks are spread across most of the layers and are largely visible within the vicinity of the metal electrode. We find similar changes in the region only with the ceramic without the metal electrodes. In these regions we also find opening of cracks [See supplementary information-S.II]. Fig. 4(d) shows the number of detected individual pores/cracks within the multilayer region, and their sizes at 300 K and 77 K, respectively. Here, one can find an increase of 24000 ± 5000 pores (an increase of 17%), at low temperature. Furthermore, comparing the two horizontal cross section [as Fig. 4(b)] we find the large displacement in the resin part ~10 µm and very subtle changes in the capacitor region ≤ 2.2 - 6 µm (See supplementary image sequence for better visualization). Fig. 4(e-f), shows the 3D rendered image of the individual pores and their volume at 300 K and 77 K, respectively. With these morphological changes the capacitance changed from 101.8 nF at 300 K to 6.9 nF at 77 K a decrease of 95% ± 1% (averaged over 3 capacitors).

### 5.1.3. Aluminum oxide-liquid electrolytic capacitor

Fig. 5(a–b) shows the cross-section of the aluminum oxide liquid electrolytic capacitor. The bright spiral region corresponds to the anode and cathode, with the former consisting of a layer of Al₂O₃ as dielectric. The region separating the electrode corresponds to the paper/separator soaked in liquid electrolyte. One can notice some parts of the separator with openings, with new pores being opened. See for instance the region marked with white dotted lines in Fig. 5(a–b), whose magnified image is shown in Fig. 5(d–e). Here we find the capacitance to change from 9.5 µF to ~ 100 fF reaching the lower limit of the instrument at 100 Hz. This large change is due to the frozen electrolyte not being able to move the ions towards the interface. Typical electrolyte used in Al₂O₃ capacitor is ethylene glycol, that has a freezing point between 260–228 K [48,49]. Here we find clear contraction, and changes as displacement of different components, Fig. 5(c) shows the line profile for the distance between the electrodes, the two layers of the electrodes moved inward by 20–30 µm and the distance between them reduced by 10–15 µm.

## 5.2. Temperature dependent electrical characterization

### 5.2.1. Tantalum capacitor

Fig. 6(a) shows the I–V curves as a function of temperature of Ta₂O₅ capacitor whose images are shown in Fig. 3. The measurements were carried out with a voltage ramping frequency of 5 Hz. Here one can find a square hysteresis even at 20 K, with a slower rate of change in current at higher voltages and low temperatures. This is attributed to the slow mobility of the charge carrier across the solid electrolyte at low temperature. At +2.5 V we see an increase in current possibly due to reaching the break down voltage. From the I–V curve we find the capacitance changed from 48 µF to 42 µF. The I–V characteristics of a second 47 µF capacitor at 20 K is shown in supplementary information S.III, where the capacitance reduced to 41 µF. In both capacitors we find an I–V curve behavior similar to a real capacitor and the decrease in capacitance at 20 K is around of 12%. Here, we highlight that the
<figure><img src="image_6.png" /><figcaption>**Fig. 3.** (a) Vertical cross section of tantalum oxide capacitor at 300 K. (b-c) Horizontal cross section of the capacitor taken from dotted red line in (a), at 300 K and 77 K respectively. (a-c) The scale bar represents 500 µm. (d) Examples of magnified images taken from the dotted circles from (b) and (c), showing changes in the pore structure and size between 300 K and 77 K respectively. The scale bar corresponds to 100 µm. (e) Plot representing pore size distribution from the cylindrical part of the capacitor. The individual detected pores as a number is in x-axis, and the corresponding volume as number of voxels is in the y-axis. The small red circle and large black square indicates pores at 77 K, and 300 K, respectively. (f) 3D rendered image of the local structural difference between 300 K and 77 K datasets, the region showing large difference (> 2 pixels) are shown here (video is available in the supplement). The color bar represents the local changes of the pores in µm. (g) Intensity profile of the outer electrode edge at 300 K and 77 K, the profiles are obtained from the white dotted line shown in the bottom right of (b) and (c). The arrow inside the plot shows the direction of the shift towards the center of the capacitor.</figcaption></figure>

<figure><img src="image_7.png" /><figcaption>**Fig. 4.** (a) Cross-section of the multilayer ceramic capacitor across the long axis. The region indicated by the dotted line represents one of the metal layers, with many pores inside. (b) Cross-section of the multilayer ceramic capacitor across the horizontal direction showing the multilayer cross-section. The slice is near the horizontal line shown in Fig. 2(e). (a–b) The scale bar corresponds to 500 µm. (c) Magnified images of the multilayers at 300 K, 77 K and their differences, a region where the pore opened is identified by a black arrow. The two magnified regions are taken from the white squares in (b). The scale bar corresponds to 70 µm. The white dotted rectangles in (c) indicate the region where cracks are opened at 77 K. The maroon markings in between the images corresponds to the position of the metal electrode layers. (d) Plot representing the individual detected pore as a number in x-axis, and the corresponding volume as number of voxels in the y-axis. The small red circles and large black squares indicate detected pores at 77 K, and 300 K, respectively. 3D rendered image of the pores and their individual volumes as number of voxels at (e) 300 K and (f) 77 K. (Video is available in the supplement).</figcaption></figure>

change in capacitance is less compared to the cryo-microtomography measurement, this is possibly due to the slow rate of cooling of the capacitor, creating less stress. Also, the surface area in contact to the cold surface is less compared to immersing the sample fully in liquid nitrogen.

### 5.2.2. Multilayer ceramic capacitor

Fig. 6(b) shows the I-V curve of a multilayer ceramic capacitor (images are shown in Fig. 4) measured with 1 Hz voltage ramp. Here one can find a hysteresis loop like curve, however, do not represent the ideal I-V curve of a capacitor as observed in $Ta_2O_5$ capacitor [in Fig. 6(a)]. This can be attributed to the effect of ferroelectric switching and its frequency dependence on the overall capacitance of the device. Since the dielectric $BaTiO_3$ is also ferroelectric, at low frequency ramp voltage (at 0.05 Hz), we identify the characteristic switching curve, a typical ferroelectric I-V property. The I-V curve at low ramping voltage frequency can be found in the supplementary information S.III,

where we find a strong dependence on the switching voltage with temperature. The switching voltage changed from around 80 V at 20 K to 1.5 V at 300 K at 0.05 Hz. Similarly in 1 Hz ramping voltage, one can also find an increase in the saturation voltage (where the current do not change with increase in voltage) with temperature. At 300 K, we find a curve with a single opening, with current saturating from 10 V. At 70 K, one can find a multi-opening hysteresis with different rate of change of current saturating around ±40 V. At 20 K, we find again a single curve with large opening in the center with reduced current and not reaching saturation at 100 V. Here the measured capacitance changed from 100 nF to 4–5 nF. The complete evolution of these I-V curve at a step size of 10 K is shown in supplementary information S.III. Here the change in capacitance is similar to the cryo-microtomography experiment, it is possible that the cooling is more efficient due to smaller size sample anchored on curved surface covering larger surface area with the cold surface.
<figure><img src="image_8.png" /><figcaption>**Fig. 5.** (a–b) Cross-section of Al₂O₃ liquid electrolytic capacitor. The slice is near the horizontal line shown in Fig. 2(f). The region highlighted by white dotted line indicates the change in the pores within the separator at 300 K and 77 K respectively. The scale bar corresponds to 500 µm. (c) The line profile from the black line shown in (a) and (b), indicating a change in the position of the electrode and their spacing between them. (d–e) Magnified image of the white dotted lines in (a), (b) respectively. The scale bars in (d) and (e) corresponds to 200 µm.</figcaption></figure>

### 5.2.3. Al₂O₃ liquid electrolytic capacitor

Fig. 6(c) shows I–V characteristics of Al₂O₃ capacitors (images shown in Fig. 5) with voltage ramped at 0.1 Hz at 300 K and 160 K. Similar to Ta₂O₅ capacitor one can find a square loop at 300 K with an increase in current only at –7 V due to the polarity of the capacitor. At 160 K, the curve is smaller, and the current appears to linearly increase, with a drop of measured current by over 50%. After 160 K we find a sharp decrease in the current reaching few pA from 150 K. This change is due to the complete freezing of the electrolyte which appears to start from 220 K. Fig. 6(d) shows the frequency dependence on the measured current as a function of temperature. Here one can find the current to increases with frequency when the electrolyte is in a liquid state from 300 K–220 K, and from 150 K–20 K when it is frozen. Between 230 K and 150 K there is linear decrease in current, and at this state the frequency has no effect on the current. It is possible that there is a mixture of solid and liquid phase at these temperatures causing this effect. At 300 K, at higher frequencies, the current increased by three orders of magnitude (2.5 µA at 0.005 Hz to 0.1 mA at 10 Hz), while from 150 K, the current increased by two orders of magnitude (3.7 pA at 0.005 Hz to 1.7 nA at 10 Hz). Here it is interesting to note that the increase in current is occurring even in a frozen electrolyte, and we attribute this to the AC signal induced ionic movements in the electrolyte, with maximum current seen at 10 Hz.

## 6. Discussion

### 6.1. Change in capacitance — the origin

We have shown the results of the cryo-microtomography and the I–V characteristics carried out with no spatial resolution. For Al₂O₃ capacitors with liquid electrolyte, it is clear that the origin of the change in capacitance is due to the electrolyte freezing, however, for Ta₂O₅ and multilayer ceramic capacitor there are large changes in the microstructures. A correlation between the two results to understand the origin of the change in capacitance is elucidated as follows;

**Thermal stress:** Materials expand or contract with temperature, and they are quantified by their thermal expansion coefficient ($\alpha_T$). For metals and ceramics these values are typically obtained from a single crystal or as a bulk structure such as a rod/disc. For materials synthesized from a powder form, the thermal expansion coefficient would differ, and varies for example with porosity content or particle size [43].

While in a single crystal or solid structure, the expansion/contraction with temperature is anisotropic, for powdered materials it is isotropic due to polycrystalline/amorphous nature [50,51]. Furthermore, the capacitors are interfaced with different material, and each have a different expansion coefficient. Here with the cryo-microtomography setup, we are able to spatially visualize these changes. For Ta₂O₅ capacitors we find the displacement to be more localized with values ranging from 1–25 µm, with large displacement occurring in the long axis [see supplementary information S.I and Fig. 3(g)]. For ceramic capacitors, within the capacitor region excluding the external metal contact we find displacement in the form of crack opening and closing. Cracks with size of 5–10 µm are visible and these changes corresponds to an increase in the number of pores by 17%. In addition, we also find significant displacement in the metal contact region on the sides of the multilayers and it is around 10–15 µm [See supplementary information S.I]. For Al₂O₃ capacitor, the electrode is a rectangular sheet rolled into a cylinder, hence, we find no localized changes as seen in the former two capacitors. Nevertheless, we observe displacement (20–30 µm) on the electrodes, metal casing and paper separator [see Fig. 5(c)]. Furthermore, the Ta₂O₅ capacitor is encapsulated in a solid case resin, while multilayer ceramic capacitor is surrounded by dipping type resin, and it is possible that the resin part also contracted inducing some additional strain on the capacitor structure. However, previous studies have shown that for a surface mount multilayer capacitor without a resin protection can also have a change in capacitance of over 90% at low temperature (for example Ref. [11]). Therefore, the resin contraction might be independent to the contraction of the capacitor inside. A 5% change in the porosity with Ta₂O₅ capacitor resulted in a change of 21% in the capacitance, while a change in porosity of 17%, changed the capacitance by 95% in multilayer ceramic capacitor. The capacitance changes measured are in agreement with what was previously reported [5–14]. Despite these changes occurring at the low temperature, we find that the system is relaxing back at the room temperature coming back to its initial state. Fig. 7(a–b) shows of the capacitor cross section taken from two temperature cycle of 300 K–77 K. For the multilayer ceramic capacitor, one can find the opening of cracks at 77 K and is different between two 77 K images, however these openings are not present at both 300 K images. Same can be seen in Fig. 7(b) showing the sequence from Ta₂O₅ capacitor, where one can notice the pore structure to modify at 77 K (expanding at 77 K–2 and contracting at 77 K–4), and return back to its initial state at 300 K with few subtle differences. Similarly the measured capacitance also returns to the value measured at room temperature. The change in the porosity (as crack opening/closing) appears to vary at low temperatures, however, at 300 K the pores shape and size returns to its initial state with some subtle changes. These reproducible changes indicate that cooling does not result in permanent damages to these devices and might explain the reason for the capacitance to return to their initial values. [See supplementary information S.IV for a detailed discussion].

**Thermal stress–electrical properties:** For the Ta₂O₅ capacitor, from the I–V curve in Fig. 6(a), and based on previous studies, the decrease in current flow is attributed to the change in energy barrier [52–55], or increase in resistivity as a result of change from MnO₂ or Mn₂O₄ [56]. Based on our observations, it is possible that these changes are a result of thermal stress inducing defects within the multilayers (Ta/Ta₂O₅/MnO₂). While we observe a global structural change, the thermal expansion coefficients or thermal conductivity are different, see Table 2, hence such differences in the expansion coefficient can be a source of change in the MnO₂, or the creation of intrinsic defects within these layers increasing the energy barrier. The presence of defects can also increase the resistivity, for instance, Si₃N₄ dielectric membranes with oxygen defects and vacancies have higher resistivity than stoichiometric Si₃N₄ [57]. To understand the possible strain effects at the interfaces of Ta/Ta₂O₅/MnO₂ layers we perform finite element simulation and determine the presence of strain at the
<figure><img src="image_9.png" /><figcaption>Fig. 6. (a) I–V characteristics of Ta₂O₅ capacitor with voltage ramping frequency of 5 Hz at 300 K, 70 K and 20 K. (b) I–V characteristics of multilayer ceramic capacitors with voltage ramping frequency of 1 Hz. (c) IV characteristics of Al₂O₃ liquid electrolyte capacitor at 160 K and 300 K at 0.1 Hz. (d) Maximum current at +7 V, as a function of temperature and voltage ramp frequency in Al₂O₃ capacitor.</figcaption></figure>

<figure><img src="image_10.png" /><figcaption>Fig. 7. Magnified images of (a) cross section of multilayer ceramic capacitor, and (b) a pore from Ta₂O₅ capacitor taken at two continuous temperature cycle of 300 K–77 K. The number followed by the temperature (1-2-3-4) corresponds to the order of measurement. The small arrow indicates a region where the cracks are opened and closed in multilayer ceramic capacitor. For Ta₂O₅ capacitor in (b), one can find that the pores in 300 K images have similar shape, but in 77 K images they are different. The scale bar corresponds to 70 µm.</figcaption></figure>

interface as a result of varying thermal conductivity and expansion coefficients across the multilayers. The Ta layer in contact with the center electrode of the capacitive structure will have a faster rate of change of temperature due to higher thermal conductivity. Hence, one can expect a temperature gradient across the multilayer for short period of time before the system reaches a thermal equilibrium. This is one of many probable scenario which can occur during the cooling process. Fig. 8(a) shows the multilayer model, the overall volume is 2 × 2 × 7.1 µm, with Ta layer kept at 5 µm, Ta₂O₅ at 0.1 µm and MnO₂ at 2 µm. The Ta layer is fixed at 77 K, and MnO₂ layer is varied by fixing the temperature at 300 K, 200 K and 100 K. See **Method section** for details of the simulation. Fig. 8(d) shows the strain field along the long axis of the multilayer, where one can find a total strain (both thermal and elastic) at the Ta₂O₅ ~0.1% at 77 K–300 K gradient [Fig. 8(d)-III], ~0.09% at 77 K–200 K gradient [Fig. 8(d)-II], to ~0.003% at 77 K–100 K gradient [Fig. 8(d)-I]. The equivalent displacement at the interface is about 40 nm with 300 K–77 K gradient [Fig. 8(c)] and ~0.4 nm at 100 K–77 K gradient. The MnO₂ typically have higher strain (~80% higher) compared to Ta₂O₅ or Ta, in all the cases. Similarly, the interface between MnO₂/Ta₂O₅ have higher strain compared to the

Ta/Ta₂O₅ interface. These strain can potentially explain the change in stoichiometry or possibly even the dielectric constant [see for instance Ref. [58], the effect of strain on dielectric constant]. Despite these large structural changes in the Ta₂O₅ capacitor, we find a capacitive behavior with a square I–V curve even at 20 K [Fig. 6(a)], indicating its robustness at low temperature. This also indicates the benefits of using solid electrolytes for low temperature applications, making a key component not only in electronic devices but possibly for batteries to function at low temperatures.

For the multilayer ceramic capacitor, the I–V curve [Fig. 6(b)] shows a low saturation voltage (also switching voltage in S.III) and a single open hysteresis at 300 K, however at 70 K, we see an increase in the saturation voltage and also three openings in the hysteresis. This indicates a variation in the capacitance until it saturates at ±50 V. This effect can be attributed to the presence of multiple regions with different switching voltages in the capacitors, caused by the strain and the crack openings observed in the micro-tomography data. The opening of cracks can possibly affect different grain boundaries, with some part of the dielectric switching with smaller voltages due to less concentration of pores, and region with high concentration of pores
<figure><img src="image_11.png" /><figcaption>**Fig. 8.** (a) 3D model used for finite element modeling. (b) The temperature assignment of the layers in the 3D model. (c) Local displacement of the structure with 77 K and 300 K gradient. (d) Local strain at (I) 77 K–100 K, (II) 77 K–200 K and (III) 77 K–300 K. (e) Capacitance vs temperature plot of multilayer ceramic capacitor: variation in change in measured capacitance (in red), capacitance extracted from high voltage region (in black) and low voltage region from the I–V curve (in magenta). The shaded region corresponds to the temperatures with 3-opening hysteresis.</figcaption></figure>

requiring higher voltages. See for instance Ref. [59] showing the effect of porosity on the switching field, and Ref. [60] showing the effects of grain boundaries and textures on the applied electric field in ferroelectric materials. In addition, the strain effect can also be attributed to the porous nature of the multilayer capacitor, and thin multilayers with different thermal expansion coefficients for $BaTiO_3$, [51,61] and the interfacing metal such as Ni, [62]. From our results we clearly see the opening of cracks and pores, potentially altering the morphology of the multilayer structure, influencing the surface area, or connection within the electrodes, or the thickness between two metal layers. The change in number of pores is 17% for ceramic-metal region, and 9% for ceramic only region [See supplementary information-S.III]. Furthermore, from the I–V curves, it is interesting that the saturating current at 300 K, starts from 1–2 V. At 77 K we have multiple hysteresis, for the central opening the rate of change of current with voltage decreases around 1–2 V range, but the current is reduced by 65%. At this stage, the capacitance is 6–7 nF (from $C = I$ dV/dt). However, as we increase the voltage, we find the current to saturate starting at around 40–45 V [Fig. 6(b)], here the capacitance value is close to the room temperature value at 111 nF. Similarly for 20 K, within the applied voltage range, we find that the current cannot be saturated at maximum voltage, and the capacitance is ~5 nF. All these information points to the crack openings observed from the cryo-microtomography images and can possibly be the source of the change in capacitance. Two more such capacitors were characterized and their I–V characteristics can be found in the supplementary information S.IV.

**Permittivity change or phase changes:** Capacitance varies directly with permittivity of the dielectric. Permittivity is a complex and a tensor quantity, hence it is directional and changes with crystal structure for example, and is common in phase transition materials such as $BaTiO_3$. Powdered/sintered materials are usually polycrystalline or amorphous, hence the permittivity value varies locally. Furthermore, the permittivity is also dependent on the macroscopic structural properties such as porosity or particle size [63]. For multilayer ceramic capacitor it has been shown that even a strain within the layers can cause a change of permittivity [64]. Typically a change in capacitance

is attributed to a change in permittivity [11,56]. While this can be true, it is still ambiguous, particularly, when permittivity is sensitive to different variables especially on structural properties. For crystalline $Ta_2O_5$ the permittivity can be 40–60 and in the amorphous state is around 22–28. For a polycrystalline phase an averaged permittivity is considered [54]. The $Ta_2O_5$ in the capacitor is amorphous, and transition to crystal from an amorphous state could occur and has only been reported at high temperatures [65]. Hence, from our experiment, taking into account large structural changes, it is likely that the thermal stress could play a dominant role in the capacitance change, which in turn may influence the permittivity.

For ferroelectric material, the permittivity value has a strong dependence on the local crystal orientation (and their phase transition with temperature), for example the dielectric constant of $BaTiO_3$ is different for the a- and c-axis [66]. However, the powdered and sintered form tend to vary with particle size, porosity or even sintering temperature [63,67–70]. Indeed the permittivity of single crystal can change by more than 50%, and would explain the change in capacitance that we see in the capacitors. However, it is unclear if this will be the same for sintered and device level capacitors, and electrical characterization may not be conclusive. Fig. 8(e) shows the capacitance as a function of temperature, the plot shows the measured capacitance, capacitance value extracted from high voltage range (~100 V) and low voltage range close to the formation of the central hysteresis opening (~7 V) in the I–V curve [Fig. 6(b)]. Here from 300 K–230 K, there is mismatch in the capacitance value for high voltage, this can be due to the accumulation of traps or additional charge carriers contributing to the capacitance. Similarly, there is a mismatch in the capacitance when measured with lower voltage from 300 K–220 K, this can be due to the fact that the accumulated charge is less, and hence the capacitance is calculated from 5 V–9 V to get a standard deviation. Nevertheless, from the onset of the three opening hysteresis at 220 K, one can find that the capacitance measured at low voltage is similar to the one measured using the multimeter. The capacitance measured using the higher voltage value is still in the 100 nF range. Hence, it is clear from our results that the measurement voltage plays a role.
Hand held LCR meters/multimeter typically have a test/probing voltage of ~1–5 V, depending on the device. Particularly, the measurement frequency can be similar to the I–V measurement performed (1 Hz). Despite a continuous change in capacitance measured by the instrument as a function of temperature, with high enough probe voltage, the capacitance value did not make significant change from 210 K–40 K. Therefore, the possibility that the permittivity/phase change playing a role is inconclusive, as one need to know the change in local crystal structure, which can be challenging to characterize on a fully fabricated commercial devices. Indeed a change in permittivity will have a direct effect in capacitance, however, with a direct observation of strain on the sample supported by the I–V curves, it is likely that the effect of strain can be a major contributor to the change in capacitance at low temperature, potentially affecting permittivity and/or the physical dimension of the capacitor. In the supplementary information S.V, we present two more capacitors showing similar effect. In addition, we also present an example from Ta₂O₅ and Al₂O₃ capacitor where the measured capacitance using multimeter matches with the value obtained from the I–V curve at all temperatures.

## 7. Conclusions

In conclusion, we have demonstrated a novel method by which one can characterize materials at a 77 K environment, and was made possible with the availability of a high flux, high energy X-ray source at BM18 beamline at the ESRF-EBS. As a proof of concept, we were able to address the microscopic origin of the change in capacitance in commercial Ta₂O₅ and multilayer ceramic capacitors at low temperatures, which was previously addressed only by using electrical characterization with no spatial resolution. Our results clearly indicate structural changes occurring in all capacitors, and when correlated with I–V characteristics showed clear evidence on the impact of structural changes on electrical characteristics. For Ta₂O₅ capacitor, the local structural changes can be a possible source of inducing defects and interfacial states, which as a result also show an increase in the resistivity and a decrease in measured current of the capacitor. For the multilayer ceramic capacitor, opening of cracks are clearly visible at low temperature. These crack openings resulted in significant changes as in the ferroelectric switching field, and displaying a 3-opening hysteresis curve resulting in significant decrease in the capacitance. Despite these changes, the microstructures return to its initial state also bringing back the capacitance value to the room temperature value before the cooling process. In both cases, our experiments show the importance of correlating electrical characterization with no spatial resolution and cryo-microtomography to understand the origin of the changes in the electrical properties. Our results will provide deeper understanding of capacitors at low temperature, enabling a better design for the low temperature environment by taking into account the thermal expansion coefficients of the materials. Our results also demonstrate the benefits of synchrotron cryo-X-ray microtomography for design and development of materials beyond electronic components for low temperature applications.

### CRediT authorship contribution statement

**Jaianth Vijayakumar:** Writing – review & editing, Writing – original draft, Visualization, Validation, Software, Project administration, Methodology, Investigation, Formal analysis, Data curation, Conceptualization. **Yves Watier:** Writing – review & editing, Validation, Software, Methodology, Investigation, Conceptualization. **Paul Thompson:** Writing – review & editing, Validation, Software, Methodology, Investigation, Formal analysis, Data curation, Conceptualization. **Sofiane Guessasma:** Writing – review & editing, Visualization, Validation, Software, Methodology, Formal analysis, Data curation. **Paul Tafforeau:** Writing – review & editing, Visualization, Supervision, Software, Methodology, Investigation, Formal analysis, Data curation, Conceptualization.

### Statement

During the preparation of this work the author(s) did not use any AI related tools or services. The author(s) reviewed and edited the content as needed and take(s) full responsibility for the content of the publication.

### Declaration of competing interest

The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.

### Acknowledgment

The beamtime was carried out part of an in-house proposal of European Synchrotron Radiation facility - ihmä595. XMaS beamline is a UK national research facility supported by EPSRC. We are grateful to all the beamline team staff for their support

## Appendix A. Supplementary data

Supplementary material related to this article can be found online at https://doi.org/10.1016/j.jeurceramsoc.2025.117966.

### Data availability

The raw data will be available in the ESRF public repository https://data.esrf.fr/ with DOI: https://doi.org/10.15151/ESRF-ES-2002456918 or it can be obtained from the corresponding author.

The image slices of all the data shown here is provided as a supplement. The 3D rendered images are also provided as a video file.

### References

[1] M. Elbuluk, A. Hammoud, R. Patterson, Power electronic components, circuits and systems for deep space missions, in: 2005 IEEE 36th Power Electronics Specialists Conference, 2005, pp. 1156–1162, http://dx.doi.org/10.1109/PESC.2005.1581775.

[2] X. Li, X. Cheng, R. Yang, H. Zhang, J. Zhang, F. Hui, F. Wang, A multi-interface ice and snow remote monitoring platform in the polar region, IEEE Sensors J. 14 (11) (2014) 3738–3744.

[3] F.A. Zwanenburg, A.S. Dzurak, A. Morello, M.Y. Simmons, L.C. Hollenberg, G. Klimeck, S. Rogge, S.N. Coppersmith, M.A. Eriksson, Silicon quantum electronics, Rev. Modern Phys. 85 (3) (2013) 961–1019.

[4] F. Balestra, G. Ghibaudo, Device and Circuit Cryogenic Operation for Low Temperature Electronics, Springer, 2001.

[5] R. Patterson, A. Hammoud, M. Elbuluk, Assessment of electronics for cryogenic space exploration missions, Cryogenics 46 (2–3) (2006) 231–236.

[6] M.-J. Pan, Performance of capacitors under DC bias at liquid nitrogen temperature, Cryogenics 45 (6) (2005) 463–467.

[7] M. Trainer, Measurement of the low temperature electrical properties of solid tantalum capacitors, Cryogenics 41 (4) (2001) 285–288.

[8] I. Valiente-Blanco, E. Diez-Jimenez, J. Cervantes-Montoro, J. Perez-Diaz, Characterization of commercial-off-the-shelf electronic components at cryogenic temperatures, Instrum. Exp. Tech. 56 (2013) 665–671.

[9] M. Song, J.Y. Yang-Scharlotta, M. Ashtijou, M. Mojarradi, Evaluation of commercial-off-the-shelf (COTS) electronics for extreme cold environments, in: 2018 IEEE Aerospace Conference, IEEE, 2018, pp. 1–12.

[10] L. Faria, A. Passaro, L. Nohra, R. d'Amore, Influence of the cryogenic temperature and the bias voltage on the spontaneous polarization effect of X5R dielectric capacitors, Proc. Int. Ref. J. Eng. Sci 1 (1) (2012) 14–21.

[11] F. Teyssandier, D. Prèle, Commercially available capacitors at cryogenic temperatures, in: Ninth International Workshop on Low Temperature Electronics-WOLTE9, 2010.

[12] A. Hammoud, S. Gerber, R.L. Patterson, T.L. MacDonald, Performance of surface-mount ceramic and solid tantalum capacitors for cryogenic applications, in: 1998 Annual Report Conference on Electrical Insulation and Dielectric Phenomena (Cat. No. 98CH36257), vol. 2, IEEE, 1998, pp. 572–576.

[13] A. Hammoud, E. Overton, Low temperature characterization of ceramic and film power capacitors, in: Proceedings of Conference on Electrical Insulation and Dielectric Phenomena-CEIDP'96, vol. 2, IEEE, 1996, pp. 701–704.
[14] R.L. Patterson, A. Hammond, S.S. Gerber, Evaluation of capacitors at cryogenic temperatures for space applications, in: Conference Record of the 1998 IEEE International Symposium on Electrical Insulation (Cat. No. 98CH36239), vol. 2, IEEE, 1998, pp. 468–471.

[15] Y. Ousten, S. Mejdi, A. Fenech, J.-Y. Deletage, L. Bechou, M.-G. Perichaud, Y. Danto, The use of impedance spectroscopy, SEM and SAM imaging for early detection of failure in SMT assemblies, Microelectron. Reliab. 38 (10) (1998) 1539–1545.

[16] L. Salvo, P. Cloetens, E. Maire, S. Zabler, J.J. Blandin, J.-Y. Buffiere, W. Ludwig, E. Boller, D. Bellet, C. Josserond, X-ray micro-tomography an attractive characterisation technique in materials science, Nucl. Instrum. Methods Phys. Res. Sect. B: Beam Interact Mater. Atoms 200 (2003) 273–286.

[17] Y. Sylvester, B. Johnson, R. Estrada, L. Hunter, K. Fahey, T. Chou, Y. Kuo, 3D X-ray microscopy: A non destructive high resolution imaging technology that replaces physical cross-sectioning for 3DIC packaging, in: ASMC 2013 SEMI Advanced Semiconductor Manufacturing Conference, IEEE, 2013, pp. 249–255.

[18] D.-P. Tran, T.-W. Lin, K.-C. Shie, C. Chen, Non-destructive micro analysis of electromigration failures in solder microbumps using 3D X-ray computed tomography, Mater. Charact. 194 (2022) 112404.

[19] S. Bord, A. Clement, J. Lecomte, J. Marmeggi, Investigation of IC samples using X-ray computer tomography, in: Journal de Physique IV (Proceedings), vol. 118, EDP sciences, 2004, pp. 413–417.

[20] T. Koutecký, T. Zikmund, D. Glittová, D. Paloušek, J. Živčák, J. Kaiser, X-ray micro-CT measurement of large parts at very low temperature, Rev. Sci. Instrum. 88 (3) (2017).

[21] F. Enzmann, M. Miedaner, M. Kersten, N. von Blohn, K. Diehl, S. Bormann, M. Stampanoni, M. Ammann, T. Huthwelker, 3-D imaging and quantification of graupel porosity by synchrotron-based micro-tomography, Atmos. Meas. Tech. 4 (10) (2011) 2225–2234.

[22] A. Zennoune, P. Latil, F. Flin, J. Perrin, T. Weitkamp, M. Scheel, C. Geindreau, H. Benkhelifa, F.-T. Ndoye, Investigating the influence of freezing rate and frozen storage conditions on a model sponge cake using synchrotron X-rays micro-computed tomography, Food Res. Int. 162 (2022) 112116.

[23] R. Granger, F. Flin, W. Ludwig, I. Hammad, C. Geindreau, Orientation selective grain sublimation–deposition in snow under temperature gradient metamorphism observed with diffraction contrast tomography, Cryosphere 15 (9) (2021) 4381–4398.

[24] N. Calonne, F. Flin, B. Lesaffre, A. Dufour, J. Roulle, P. Pugliese, A. Philip, F. Lahoucine, C. Geindreau, J.-M. Panel, et al., Celldym: A room temperature operating cryogenic cell for the dynamic monitoring of snow metamorphism by time-lapse X-ray microtomography, Geophys. Res. Lett. 42 (10) (2015) 3911–3918.

[25] Y. Li, W. Huang, Y. Li, W. Chiu, Y. Cui, Opportunities for cryogenic electron microscopy in materials science and nanoscience, ACS Nano 14 (8) (2020) 9263–9276.

[26] J. Schultheiß, L. Puntigam, M. Winkler, S. Krohns, D. Meier, H. Das, D.M. Evans, I. Kézmárkéri, Magnetoelectric coupling at the domain level in polycrystalline hexagonal ErMnO₃, Appl. Phys. Lett. 124 (25) (2024).

[27] E. Rennich, S.H. Sung, N. Agarwal, M. Gates, R. Kerns, R. Hovden, I.E. Baggari, Ultracold cryogenic TEM with liquid helium and high stability, Proc. Natl. Acad. Sci. 122 (36) (2025) e2509736122.

[28] Y. Li, Y. Wei, J. Meng, L. Zhang, P. Wang, H. Zheng, H. Lei, Damage evolution characterization of glass fabric composites at cryogenic temperatures via in-situ tensile X-ray computed tomography tests, Compos. Commun. 35 (2022) 101326.

[29] J. Vijayakumar, H. Dejea, A. Mirone, C. Muzelle, J. Meyer, C. Jarnias, K. Dollman, S. Zabler, L. Paolasini, A. Bellier, et al., Multiresolution phase-contrast tomography on BM18, a new beamline at the European Synchrotron Radiation Facility, Synchrotron Radiat. News (2024) 1–10.

[30] J. Bischof, B. Mahr, J. Choi, M. Behling, D. Mewes, Use of X-ray tomography to map crystalline and amorphous phases in frozen biomaterials, Ann. Biomed. Eng. 35 (2007) 292–304.

[31] S. Sanchez, V. Fernandez, S.E. Pierce, P. Tafforeau, Homogenization of sample absorption for the imaging of large and dense fossils with synchrotron microtomography, Nat. Protoc. 8 (9) (2013) 1708–1717.

[32] G. Bank, W. Virginia, Cryogenic Measurements of Surface Mount Multi-Layer Ceramic Chip Capacitors, Tech. Rep 214, Nat. Radio Astron. Observatory, Green Bank, WV, USA, 2009.

[33] J. Gill, Basic Tantalum Capacitor Technology, AVX Limited, Paignton, England, 2012.

[34] G. Okuma, N. Saito, K. Mizuno, Y. Iwazaki, H. Kishi, A. Takeuchi, M. Uesugi, K. Uesugi, F. Wakai, Microstructural evolution of electrodes in sintering of multilayer ceramic capacitors (MLCC) observed by synchrotron X-ray nano-CT, Acta Mater. 206 (2021) 116605.

[35] H. Payno, P. Paleo, C. Nemoz, A. Mirone, P.-J. Gouttenoire, J. Lesaint, W. De Nolf, T. Vincent, P.-O. Autran, 2022, TOMWER - https://doi.org/10.5281/zenodo.8228891.

[36] O. Bikondoa, L. Bouchenoire, S.D. Brown, P.B. Thompson, D. Wermeille, C.A. Lucas, M.J. Cooper, T.P. Hase, XMaS@ the ESRF, Phil. Trans. R. Soc. A 377 (2147) (2019) 20180237.

[37] I. Savchenko, S. Stankus, Thermal conductivity and thermal diffusivity of tantalum in the temperature range from 293 to 1800 K, Thermophys. Aeromechanics 15 (4) (2008) 679–682.

[38] H.M. Rosenberg, The thermal conductivity of metals at low temperatures, Philos. Trans. R. Soc. Lond. Ser. A Math. Phys. Sci. 247 (933) (1955) 441–497.

[39] F. Nix, D. MacNair, The thermal expansion of pure metals, ii: molybdenum, palladium, silver, tantalum, tungsten, platinum, and lead, Phys. Rev. 61 (1–2) (1942) 74.

[40] G. Guisbiers, E. Herth, L. Buchaillot, T. Pardoen, Fracture toughness, hardness, and Young's modulus of tantalum nanocrystalline films, Appl. Phys. Lett. 97 (14) (2010).

[41] G. Abadias, J. Colin, D. Tingaud, P. Djemia, L. Belliard, C. Tromas, Elastic properties of α-and β-tantalum thin films, Thin Solid Films 688 (2019) 137403.

[42] C.D. Landon, R.H. Wilke, M.T. Brumbach, G.L. Brennecka, M. Blea-Kirby, J.F. Ihlefeld, M.J. Marinella, T.E. Beechem, Thermal transport in tantalum oxide films for memristive applications, Appl. Phys. Lett. 107 (2) (2015).

[43] S. Wu, H.M. Chan, M.P. Harmer, Compositional tailoring of the thermal expansion coefficient of tantalum (V) oxide, J. Mater. Sci. 41 (2006) 689–695.

[44] E. Çetinörgü, A new method to experimentally determine the thermal expansion coefficient, Poisson's ratio and Young's modulus of thin films, J. Mater. Sci. 44 (2009) 2167–2170.

[45] S. Walia, S. Balendhran, P. Yi, D. Yao, S. Zhuiykov, M. Pannirselvam, R. Weber, M.S. Strano, M. Bhaskaran, S. Sriram, et al., MnO₂-based thermopower wave sources with exceptionally large output voltages, J. Phys. Chem. C 117 (18) (2013) 9137–9142.

[46] I. Suzuki, S.-I. Okajima, K. Seya, Thermal expansion of single-crystal manganosite, J. Phys. Earth 27 (1) (1979) 63–69.

[47] J. Sermeus, R. Sinha, K. Vanstreels, P. Vereecken, C. Glorieux, Determination of elastic properties of a MnO₂ coating by surface acoustic wave velocity dispersion analysis, J. Appl. Phys. 116 (2) (2014).

[48] H. Yue, Y. Zhao, X. Ma, J. Gong, Ethylene glycol: properties, synthesis, and applications, Chem. Soc. Rev. 41 (11) (2012) 4218–4244.

[49] F.-J. Zhang, Y.-H. Niu, X.-Q. Zhou, J.-C. Li, X.-L. Fang, Q.-F. Hu, W.-C. Oh, Composition and performance of electrolyte for wide-temperature aluminum electrolytic capacitors, J. Korean Ceram. Soc. (2004) 1–11.

[50] L.P. Prisco, C.P. Romao, F. Rizzo, M.A. White, B.A. Marinkovic, The effect of microstructure on thermal expansion coefficients in powder-processed Al₂Mo₃O₁₂, J. Mater. Sci. 48 (2013) 2986–2996.

[51] Y. He, Heat. capacity, Thermal conductivity, and thermal expansion of barium titanate-based ceramics, Thermochim. Acta 419, 135–141.

[52] E. Deloffre, L. Montès, G. Ghibudo, S. Bruyère, S. Blonkowski, S. Bécu, M. Gros-Jean, S. Crémer, Electrical properties in low temperature range (5 K–300 K) of Tantalum Oxide dielectric MIM capacitors, Microelectron. Reliab. 45 (5–6) (2005) 925–928.

[53] T.-H. Chiang, J.F. Wager, Electronic conduction mechanisms in insulators, IEEE Trans. Electron Devices 65 (1) (2017) 223–230.

[54] C. Chaneliere, J. Autran, R. Devine, B. Balland, Tantalum pentoxide (Ta₂O₅) thin films for advanced dielectric applications, Mater. Sci. Eng.: R: Rep. 22 (6) (1998) 269–322.

[55] Y. Freeman, G. Alapatt, W. Harrell, P. Lessner, Electrical characterization of high voltage polymer tantalum capacitors, J. Electrochem. Soc. 159 (10) (2012) A1646.

[56] A. Teverovsky, Performance and reliability of solid tantalum capacitors at cryogenic conditions, 2006.

[57] J. Vijayakumar, M. Gaspar, L. Maurel, M. Horisberger, F. Nolting, C. Vaz, High frequency characterization of Si₃N₄ dielectrics for artificial magnetoelectric devices, J. Mater. Sci. 57 (42) (2022) 19872–19881.

[58] W. Chang, C.M. Gilmore, W.-J. Kim, J.M. Pond, S.W. Kirchofer, S.B. Qadri, D.B. Chirsey, J.S. Horwitz, Influence of strain on microwave dielectric properties of (Ba, Sr) TiO₃ thin films, J. Appl. Phys. 87 (6) (2000) 3044–3049.

[59] H. Amorín, M. Algueró, R. Del Campo, E. Vila, P. Ramos, M. Dollé, Y. Romaguera-Barcelay, J.P. De La Cruz, A. Castro, High-sensitivity piezoelectric perovskites for magnetoelectric composites, Sci. Technol. Adv. Mater. 16 (1) (2015) 016001.

[60] J. Wang, Z.-H. Shen, R.-L. Liu, Y. Shen, L.-Q. Chen, H.-X. Liu, C.-W. Nan, Texture engineering modulating electromechanical breakdown in multilayer ceramic capacitors, Adv. Sci. 10 (16) (2023) 2300320.

[61] M. Radhika Rao, A. Umarji, Thermal expansion studies on ferroelectric materials, Bull. Mater. Sci. 20 (1997) 1023–1028.

[62] F. Nix, D. MacNair, The thermal expansion of pure metals: copper, gold, aluminum, nickel, and iron, Phys. Rev. 60 (8) (1941) 597.

[63] L. Padurariu, F.F. Chamasemani, R. Brunner, L.P. Curecheriu, V.A. Lukacs, R.S. Stirbu, C.E. Ciomaga, L. Mitoseriu, Analysis of local vs. macroscopic properties of porous BaTiO₃ ceramics based on 3D reconstructed ceramic microstructures, Acta Mater. 255 (2023) 119084.

[64] J.-S. Park, S. Kim, H. Shin, H.S. Jung, K.S. Hong, Residual stress evolution in multilayer ceramic capacitors corresponding to layer increase and its correlation to the dielectric constant, J. Appl. Phys. 97 (9) (2005).

[65] C. Joseph, P. Bourson, M. Fontana, Amorphous to crystalline transformation in Ta₂O₅ studied by Raman spectroscopy, J. Raman Spectrosc. 43 (8) (2012) 1146–1150.
[66] W.J. Merz, The electric and optical behavior of BaTiO₃ single-domain crystals, Phys. Rev. 76 (8) (1949) 1221.

[67] L. Wu, M.-C. Chure, K.-K. Wu, W.-C. Chang, M.-J. Yang, W.-K. Liu, M.-J. Wu, Dielectric properties of barium titanate ceramics with different materials powder size, Ceram. Int. 35 (3) (2009) 957-960.

[68] H.-I. Hsiang, F.-S. Yen, Dielectric properties and ferroelectric domain of BaTiO₃ powders, Japan. J. Appl. Phys. 32 (11R) (1993) 5029.

[69] X.-H. Wang, R.-Z. Chen, Z.-L. Gui, L.-T. Li, The grain size effect on dielectric properties of BaTiO₃ based ceramics, Mater. Sci. Eng.: B 99 (1-3) (2003) 199-202.

[70] S.-F. Wang, G.O. Dayton, Dielectric properties of fine-grained barium titanate based X7R materials, J. Am. Ceram. Soc. 82 (10) (1999) 2677-2682.