Introduction

With thinner dielectric layers and more repeated metal/dielectric/metal structures stacked together, multilayer ceramic capacitors (MLCCs) provide higher capacitance in smaller case sizes to reduce space usage and weight. They serve critical functions such as filtering, coupling, decoupling, bypassing, tuning and oscillation capabilities, with applications spanning consumer electronics, telecommunications, aerospace, and defense systems1,2,3. Among these, barium titanate (BaTiO3)-based MLCCs are extensively utilized in fields such as aerospace, nuclear energy, and military equipment because of their relatively stable electrical properties4,5,6. Electronic devices used in these environments are continuously exposed to extreme conditions, including high-energy radiation fields. Gamma rays, a pervasive form of high-energy radiation, can alter the microstructure and electrical properties of materials, thereby affecting the reliability of electronic systems7,8,9,10,11,12. Thus, understanding the effects of gamma radiation on BaTiO3-based MLCCs is critical for designing more stable and reliable electrical systems6.

BaTiO3-based MLCCs with capacitances ranging from 300 pF to 3.3 µF (1.0 ± 0.2 V at 1 kHz) are classified as Class II ceramic dielectrics (X7R) 1,5. These capacitors have complex chemical compositions, with variations in formulations and manufacturing processes across different manufacturers. However, BaTiO3 remains the primary component and is modified with elements such as Nb, Ta, Co, Mg, Mn, and other trace elements, to achieve advantageous properties, including a high dielectric constant, excellent temperature stability and insulating performance2,3,10,13,14,15. The key to investigating the effects of gamma radiation on the performance of MLCCs lies in examining how such radiation affects the microstructure of BaTiO3-based dielectric layers9,11.

In recent years, increasing attention has been given to the structural and performance evolution of BaTiO3-based materials under irradiation. In 2003, E. G. Fesenko et al.16 reported that gamma radiation induced instability in head-to-head domain walls with negative spontaneous polarization in BaTiO3 single crystals, revealing a strong correlation between the domain configuration and defect structure. In addition, the ability of gamma radiation to reduce the ferroelectricity of BaTiO3 ceramics can be attributed to changes in surface grain morphology and/or tetragonality reduction9. In 2018, B. S. Ahmed et al.17 conducted transmission electron microscopy (TEM) analysis on gamma-ray-irradiated BaTiO3 nanoparticles, and observed a gradual decrease in grain size with increasing dose and an anomaly in AC conductivity. In 2022, H. A. Ghamdi et al.8 reported that gamma radiation decrease the dielectric constant and impedance of Ba0.95Bi0.05TiO3 ceramics and analyzed these effects in terms of lattice distortion, oxygen vacancy, charge compensation, and band gap. A comprehensive review of the literatures indicates that with increasing gamma radiation dose, BaTiO3-based materials experience lattice distortion, increased defect concentrations, and grain size reduction or stabilization, leading to decreased resistivity and weakened dielectric and ferroelectric properties8,18.

Owing to the harsh experimental conditions, the aforementioned conclusions are primarily derived from ex-situ characterizations conducted after irradiation, which may not fully capture real-time property changes during irradiation. J. Bock et al.19 at Sandia National Laboratories (SNL) in the U.S. introduced an experimental method for real-time testing of BaTiO3-based MLCCs and concluded that gamma ray irradiation increased the conductivity and decreased the capacitance. Unfortunately, this work focused mainly on changes in electrical properties but lack of structural evidence. Furthermore, most studies have focused on high-dose-rate radiation, with limited investigations into the effects of varying dose rates, particularly at lower levels, which is a more realistic aerospace environment. Therefore, this study aimed to investigate the in-situ property evolution of BaTiO3-based MLCCs under different radiation conditions.

In this work, three dose rates (1E-1, 1E-3, and 3.35E-6 Gy/s) were selected and marked as high, medium and low, respectively. For in situ capacitance monitoring, the irradiation times were 320, 4400, and 4400 min, and the total doses reached 1920, 264, and 0.8844 Gy, respectively. Additionally, for high-dose-rate (1E-1 Gy/s), different total doses (0, 100, 300, 500, 1000, 2000 Gy) were achieved by changing the irradiation time. Structural characterization techniques, including electron paramagnetic resonance (EPR) and scanning transmission electron microscopy (STEM), were employed to analyze the effects of radiation, with the goal of elucidating the physical relationships among radiation conditions, microstructural changes, and macroscopic properties.

Results

Property damage induced by gamma ray irradiation

In situ gamma ray irradiation experiments were conducted with a removable sample holder to control the gamma-ray dose rate by varying the distance from the source (Supplementary Fig. 1). According to the frequency dependence of the capacitance at three different dose rates (Fig. 1a and Supplementary Fig. 2), the in situ variation in the capacitance as a function of the total dose under f = 1 kHz is summarized in Fig. 1b. As the radiation dose increases, the capacitance begins to decrease gradually. Interestingly, an enhanced low dose rate sensitivity (ELDRS) effect was observed, which is often reported in active devices, especially in silicon based bipolar transistors20,21. Until now, no published work has shown ELDRS in passive devices, let alone MLCCs. These passive components are usually considered insensitive to radiation. The ELDRS indicates that for the same total ionizing dose, the sample irradiated at a lower dose rate experiences a greater reduction. To further analyze and understand the mechanism of radiation-induced damage, a power function from the literature22,23 (Eq. 1) was used to fit the capacitance data (Supplementary Fig. 3a–c).

$$y={{{\rm{a}}}_{1}} ^{*} {{x}}^{\wedge} {{{\rm{b}}}_{1}}+{{{\rm{c}}}_{1}}$$
(1)

y represents the percentage of capacitance loss. x represents the total radiation dose in Gy, and c1 corresponds to the initial value (100%). The parameter a₁, expressed in units of %/Gy, represents the radiation-induced damage coefficient. The fitting parameter b₁, a dimensionless quantity, is associated with the intrinsic properties of the material.

Fig. 1: Property damage of MLCCs under gamma ray irradiation.
figure 1

a Frequency-dependent capacitance of MLCC under 1E-1 Gy/s with different total doses; b In situ capacitance degradation curves for irradiation dose rates of 1E-1 Gy/s, 1E-3 Gy/s and 3.35E-6 Gy/s, measured at f = 1 kHz; c Bar chart illustrating the percentage of capacitance degradation, alongside fitting parameters a1 and b1; d In situ irradiation and aging process of the capacitance (data are the average values in Fig. 1b); e In situ self-recovery process of capacitance with longer aging time. The irradiation times for 1E-1 and 1E-3 Gy/s were the same (4400 min) to rule out the influence of the irradiation time on the aging behavior. In addition, the difference between Fig. 1e and Fig. 1d is that the sample was immediately taken out after irradiation and subjected to continuous aging testing outside the source. C0 represents the capacitance value before radiation; f Pr values of the MLCCs for 1E-1 Gy/s, 1E-3 Gy/s and 3.35E-6 Gy/s extracted from ex situ P-E loops before and after irradiation.

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Importantly, a negative value of a₁ indicates that the damage increases with increasing radiation dose, and the absolute value of |a₁| is strongly correlated with the rate of change in the capacitance. The fitted values of |a1| and b1 obtained at different irradiation dose rates, along with the y values, are presented in Fig. 1c and Supplementary Fig. 3d–f. For 1E-1 Gy/s, 1E-3 Gy/s and 3.35E-6 Gy/s, |a1| ranges from 0.017 to 0.044, 0.55 to 2.45, and 1.69 to 2.91, respectively. The values of |a1| are notably greater under lower dose rates, confirming the existence of ELDRS. The values of b1 range from 0.57 to 0.68, 0.11 to 0.19 and 0.13 to 0.23 for the high, middle, and low dose rates, respectively. These results suggest distinct differences in the microstructural evolution mechanisms of BaTiO3-based MLCCs under high and low radiation dose rates.

Several parameters that characterize radiation-induced damage have been summarized to better understand ELDRS (Supplementary Table 1-3). Under high-dose-rate, the rate of damage per unit time is greater because the sample receives more gamma photons per unit time, leading to a higher generation rate of electron‒hole pairs and, consequently, a higher concentration of charged point defects, resulting in greater capacitance degradation per unit time. In contrast, at low dose rates, the damage per unit dose and the radiation-induced damage coefficient |a1| are significantly greater, reflecting the ELDRS. In other words, when an equivalent number of gamma photons irradiate the sample at a “slower” rate over a longer period, the damage becomes more pronounced, and the efficiency of radiation-induced damage is greater.

After terminating radiation, further in situ electrical property measurements revealed different capacitance aging behaviors within 3 hours (Fig. 1d). First, a discontinuity is present at t = 0 for 1E-1 and 1E-3 Gy/s, indicating an immediate recovery step in capacitance, closely related to the space charge effects. Furthermore, for high-dose-rate, irradiation-induced capacitance damage undergoes partial self-recovery. In contrast, for the middle and lower dose rates, the capacitance gradually decreases with aging time. Therefore, high- and low-dose-rates-irradiated MLCCs exhibit completely different aging behaviors. To verify this conclusion, we retested the aging behavior of samples irradiated at 1E-1 and 1E-3 Gy/s over longer periods (Fig. 1e). Self-recovery was observed at 1E-1 Gy/s; that is, the capacitance increased gradually with aging time. Fitting these data suggests that it would take approximately one year to achieve complete capacitance recovery. However, for 1E-3 Gy/s, the capacitance gradually decreased during the first 8 hours of continuous testing, similar to that shown in Fig. 1d. With further extension of the aging time, partial recovery behavior became detectable. Consequently, high- and low-dose-rate-treated MLCCs exhibit distinctly different aging behaviors: high-dose-rate MLCCs show a gradually increasing capacitance during aging, whereas the capacitance of low-dose-rate-irradiated MLCCs decrease initially but then begin to recover. This means that the damage to MLCCs in circuits in real continous-irradiation environments is much greater than that simulated using ex situ testing; ex situ testing is the method adopted by most of the literature, many results in the literature thus deviate substantially from reality. The mechanism of aging behavior will be discussed later. Ex situ ferroelectricity measurements were also conducted (Fig. 1f and Supplementary Fig. 4). A direct comparison of the same MLCC is shown in Fig. 1f, with no changes in Pr before and after irradiation, which may be caused by the self-recovery effect and/or masking of irradiation-induced differences due to the application of a high electric field during P-E testing. In brief, BaTiO3-based MLCCs exhibit three kinds of gamma radiation effects: (1) total ionizing dose (TID), (2) enhanced low dose rate sensitivity (ELDRS), (3) self-recovery effects.

Structural evolution under gamma ray irradiation

To elucidate the structural origin of the gamma radiation phenomenon in MLCCs, we firstly investigated the microstructure of the MLCCs without radiation treatment. Cross-arranged electrodes and dielectric layers without obvious cracks can be seen via scanning electron microscopy (SEM) (Supplementary Fig. 5a). Low-magnification TEM images of both the dielectric and electrode layers are shown in Fig. 2a. The interface between the dielectric and electrode layers was clear. The dielectric layer had a dense microstructure with obvious grain boundaries and nanosized grains of approximately 200 nm. The magnified TEM images measured along the [100] and [110] planes were measured to obtain the diffraction spots (Fig. 2b and Supplementary Fig. 5b). The selected area electron diffraction (SAED) results conform to the typical characteristics of the ABO3 perovskite structure (Fig. 2c and Supplementary Fig. 5c). The presence of a core-shell structure is shown in Fig. 2d. The ceramic powder used for preparing MLCCs is typically doped with multiple elements in BaTiO3, leading to the formation of a core-shell grain structure with a diffuse phase transition to improve the temperature stability of the dielectric constant24,25. Ferroelectric domains could be seen in the core region (denoted by the white dashed circle), whereas no visible domain were observed in the shell region. To determine the chemical composition of the MLCCs, energy dispersive spectrometry (EDS) was applied, and the results are displayed in Supplementary Fig. 5d, e. The white dashed box represents mainly Ni, which serves as the inner electrode. Ba, Ti, and O were detected in the dielectric layer, indicating that the dielectric layer is mainly a BaTiO3 ceramic. High-magnification EDS revealed obvious element diffusion. To further elucidate the chemical diffusion, electron energy loss spectra (EELS) at the electrode‒dielectric interface were obtained (Fig. 2e). The mutual diffusion of elements was observed, making accurate definition of an interface solely based on EELS difficult. However, the diffusion depths of Ba, Ti and O differed and the diffusion of Ba was more significant than that of O and Ti. After the basic information of the MLCCs was examined, SEM, EDS, and TEM images were obtained to determine the microstructural evolution of the MLCCs after gamma ray irradiation (Supplementary Fig. 6, 7). No radiation-induced destructive damage was observed, and the grain integrity was unaffected by irradiation, excluding the effect of the microstructure.

Fig. 2: Microstructure of the MLCC and gamma irradiation-induced average structure evolution.
figure 2

Microstructure of the MLCC without gamma itradiation: a Overall morphology of the sample used for TEM testing; b TEM image and c corresponding SAED along [100]; d High-resolution TEM image showing the core-shell structure; e EELS spectra of the dielectric-electrode layers. Average structure of BT-Ce ceramics before irradiation (0 Gy/s) and after irradiation with various dose rates (1E-1 Gy/s with 100 Gy, 1E-3 Gy/s with 264 Gy, 3.35E-6 Gy/s with 0.8844 Gy): f Magnified XRD patterns, g FWHM of (110) XRD peaks and h Raman spectra.

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Owing to the multilayer structure of MLCCs and the presence of Ni electrodes, it is difficult to perform X-ray diffraction (XRD), X-ray photoelectron spectrometry (XPS), EPR etc., directly on the dielectric layers to extract effective crystal and defect information, which may be important factors affecting the reliability of MLCCs. For example, in the EPR patterns of MLCCs with different total doses and dose rates (Supplementary Fig. 8), an obvious characteristic signal appears at 3000–4000 Gauss, much broader than common EPR signals. This finding indicates that the electron spin energy level of the MLCCs is almost continuous without obvious splitting, a characteristic that mainly comes from the spin of free electrons in the conductor (Ni) in the magnetic field. Therefore, we synthesized Ce-doped BaTiO3 ceramics (BT-Ce) and studied their ex situ electrical properties and structural evolution before and after gamma ray irradiation (Fig. 2f–h and Supplementary Fig. 9). BT-Ce ceramics were selected because the dielectric layer of commercial MLCCs typically comprises BT ceramics doped with various trace rare earth elements, and Ce doping is believed to reduce radiation-induced conductivity19. SEM images before and after radiation revealed no significant changes, similar to those in MLCCs (Supplementary Fig. 10).

The XRD patterns on BT-Ce with different dose rate are shown in Fig. 2f, and the full width at half maximum (FWHM) of the (110) diffraction peaks is given in Fig. 2g. After gamma ray irradiation, the FWHM clearly increases because of collectively increased local strain and lattice disorder. However, the average phase composition can be still maintained according to the Rietveld refinement before and after gamma ray irradiation (Supplementary Fig. 11). This finding indicates that the overall crystal structure remains stable under gamma-ray exposure and that the total dose of gamma radiation is insufficient to induce common-method-detectable structural degradation or phase transformation in the material. Although the Raman intensity increases significantly after low-dose-rate irradiation, the peak positions and shapes remain essentially unchanged (Fig. 2h). The intensity enhancement after low-dose-rate radiation may be influenced by crystal anisotropy and molecular polarizability. On the one hand, vibrations involving large-scale electron cloud movement usually have significant polarization rate changes, resulting in higher intensity. Gamma radiation effect of BaTiO3 is dominant to Compton scattering, and the generation of electron–hole pairs inevitably affects the motion state of electrons outside the atomic nucleus. For a low-dose-rate, a longer irradiation time has a more significant effect on electron motion. On the other hand, the atomic polarizability, which reveals the atomic displacement polarization, may also contribute to the intensity variation; the evidence regarding atomic displacement will be discussed later.

According to the literature, defects are critical factors in radiation effect research26. Thus, the EPR of BT-Ce with different dose rates was measured (Fig. 3a). An apparent signal peak near 340 mT was observed, flanked by three weaker signal peaks on each side, and the spacing and intensity of these three signal peaks are essentially the same, indicating that the central peak originates from the spin motion of unpaired electrons, whereas the flanking peaks arise from hyperfine interactions associated with Ti3+ ions27. To further verify the results, the EasySpin program, which is based on the MATLAB package, was used to fit the EPR patterns. The fitting results for 0 Gy/s and 3.35E-6 Gy/s are given in Fig. 3b. The significant asymmetric EPR signal is due to the motion of defect carriers under the action of a magnetic field28. The samples are semiconducting, causing the signal to be Dyson-like and preventing direct fitting; hence, a quadratic correction was applied using Eq. 229,30:

$$y=\left(A+\sqrt{2\pi {g}^{2}}\right)*\exp \left(-0.5 \,*\, \left({\left.\left(x-\delta \right)/{g}^{2}\right)}^{2}\right)+B \,*\frac{Z}{\pi*\left({\left(x-\delta \right)}^{2}+{Z}^{2}\right)}\right)$$
(2)
Fig. 3: Defect structure evolution after gamma ray irradiation.
figure 3

a EPR spectra of BT-Ce ceramics before (0 Gy/s) and after gamma ray irradiation (1E-1 Gy/s with 100 Gy, 1E-3 Gy/s with 264 Gy, 3.35E-6 Gy/s with 0.8844 Gy); The reason for selecting 1E-1 Gy/s with 100 Gy instead of 2000 Gy is from the in-situ capacitance evolution in Fig. 1b, and to ensure that the total dose did not differ much. b Fitted EPR curves (Exp means experimental data; Sim represents the line fitted using EasySpin considering Vo and Ti3+; Dy is the line fitted considering the dysonian based on Sim); c Fitted XPS curves of BT-Ce ceramics with 0 Gy/s and 3.35E-6 Gy/s; d Oxygen vacancy (VO), Ti3+, and Ba vacancy (VBa) concentrations as a function of the radiation dose rate; e–i SSPFM mapping (Vc and Vi) and representative amplitude/phase curves of MLCCs: e–g before and h–j after gamma ray irradiation.

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The corrected fitted curves (Dy) closely match the experimental results. The flanking peaks resulting from orbital electron‒nuclear hyperfine interaction of Ti3+ ions are observed on both sides of the signal peaks, and the intensity of all the signal peaks increases with decreasing radiation dose rate, indicating an increase in the concentration of oxygen vacancies (VO) and Ti3+ ions31. The concentration of Ba vacancies (VBa) can be extracted from the fitted XPS data (Fig. 3c). The concentration variations of VO, VBa and Ti3+ as a function of dose rate are summarized (Fig. 3d). As the dose rate decreases, the concentration of all the defects increases. Changes in the defect type and concentration cause significant changes in the bias field of the samples; thus, the coercive field (VC), imprint field (Vi) and corresponding switching spectroscopy piezo force microscopy (SSPFM) amplitude and phase curves of the MLCCs before and after radiation were tested (Fig. 3e–j). Both VC and Vi clearly increased after radiation, which implies that the internal electric field caused by defective dipoles increases32, which is consistent with the EPR results.

To obtain information on the evolution of defects in the dielectric layer of MLCCs, aberration-corrected STEM (AC-STEM) high-angle angular dark field (HAADF) images were measured before and after irradiation (Supplementary Fig. 12a1–a3), where the measured region was far from the inner electrode (matrix region). The analysis focused primarily on structural insights through atomic intensity and bond length33,34,35,36,37. The occupation of Ba/Ti/O atoms under varying radiation conditions is illustrated in Fig. 4 and S12 to analyze structural information such as the intensity of the atomic column and bond length. From the Ba/O atom column intensity analysis, some Ba/O vacancies are present in the unirradiated MLCC matrix (Fig. 4a and Supplementary Fig. 12d), whereas Ti vacancies are essentially absent (Supplementary Fig. 12g)36. After gamma ray irradiation, the regions with decreased Ba/O intensity increase, especially for high-dose-rate. Therefore, the increase in vacancy defects after radiation illustrates the TID effect. In addition, the formation of vacancy defects is closely related to variations in the lattice and ion-displacement, reflected by the bond lengths (Fig. 4d–f) and polar vector maps (Supplementary Fig. 13). After gamma ray irradiation, greater fluctuations occur in the Ti–Ti bond lengths (white dashed boxes), which intensify with increasing radiation dose. Radiation also induced changes in the polarization state, specifically ion displacement. More significant changes in lattice or ion displacement correspond to increased defect content. Additionally, local stress fluctuations resulting from bond length changes were also observed via generalized plane strain (GPA) (Supplementary Fig. 12j–l)37. In summary, irradiation leads to an increase in the defect content and a change in the bond length within the ceramic layers of MLCCs. These structural changes likely underlie the observed degradation in the dielectric properties. One might argue that the STEM results explain only the TID rather than the ELDRS. (1) Stronger radiation causes more obvious local structural changes, so a high dose of 2000 Gy was selected for STEM analysis. (2) The total doses for EPR in Fig. 3a and STEM in Fig. 4 at 1E-1 Gy/s are different—100 Gy and 2000 Gy, respectively. It is understandable that a 20-fold increase in the total dose causes more defects. (3) The ELDRS effect is a complex process involving Compton scattering, defect formation, and charge trapping, which are explained in detail in the following section.

Fig. 4: Gamma radiation-induced local structure evolution of MLCCs along [100] for both the matrix and interface region.
figure 4

a–c Intensity distribution maps of O atom columns (IO) and d–f bond length distribution plots of Ti‒Ti bonds (dTi-Ti) for MLCCs without radiation (0 Gy/s), after low-dose-rate radiation (3.35E-6 Gy/s, 0.8844 Gy), and after high-dose-rate radiation (1E-1 Gy/s, 2000 Gy), measured from the matrix region; g–i Intensity distribution maps of Ba atom columns (IBa) for MLCCs with different radiation treatments, measured from the interface region.

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In addition to changes in the concentration of radiation-induced defects, the distribution of these defects is critical. Therefore, the microstructure of the dielectric layer near the Ni electrode in the MLCCs was characterized (interface region). On the basis of the HAADF image and GPA analysis of the unirradiated sample (Supplementary Fig. 14a, b), the ceramic‒electrode interface can be identified, as marked by the white dashed line. The intensity distribution maps of Ba/Ti atomic columns based on STEM-HAADF images under various radiation conditions are shown in Fig. 4g–i and Supplementary Fig. 14b–d. Similar to the matrix region, the Ti intensity distribution is also homogeneous in interface region, with no obvious Ti vacancies detected. Interestingly, the Ba vacancy at the interface region decreases (as indicated by the reduction in blue regions) after radiation, especially at high dose. This phenomenon indicates that irradiation can reduce the number of defects at the interface, contrary to the changes observed in the matrix region. Generally, vacancy defects in unirradiated samples are concentrated mainly near the electrodes, which is consistent with the understanding that defects migrate towards electrodes during the aging process. However, irradiation can induce the generation and movement of defects; that is, irradiation increases the defect content away from the electrode area, while causing vacancies at the interface to migrate away from the electrode region. Similar results were obtained in different regions (Supplementary Fig. 15), ruling out sample preparation artifacts or local measurement variability in HAADF analyses. This defect redistribution induced by gamma radiation is a new phenomenon, which can be explained as follows: (1) Discrepancy of formation energy. In the unirradiated sample after the generation and enrichment of defects near the interface, the energy required to generate new defects increases. Thus, the formation energy of defects at the interface becomes greater than that inside the matrix region, and the defects begin to move toward the matrix region under irradiation, eventually leading to the redistribution of defects38,39. (2) Defect concentration gradient. Before irradiation, the defect concentration near the interface is greater than that inside the matrix. This defect concentration drives migration from high- to low- concentration regions (interface to matrix) under irradiation40,41.

Physical mechanism of the gamma radiation effect

One might argue that heating during radiation will also cause capacitor damage. To exclude this factor, we measured the temperature dependence of the capacitance of the MLCCs before and after irradiation, and excellent temperature stability of the capacitance was observed. Achieving approximately 3% capacitance degradation would require a temperature increase from room temperature by 65 °C. However, such a significant temperature increase is evidently not possible because of radiation, thus ruling out capacitance degradation caused by temperature elevation (Supplementary Fig. 16). Consequently, the defect variation and space charge effect induced by gamma ray irradiation comprise the primary contributors to property damage. To reflect the gamma radiation process, an in situ high-energy electron beam within the TEM was utilized. High-energy electrons can pass through the sample, while the remaining electrons collide with atoms and transfer energy. Upon absorbing energy, the sample experiences phenomena such as atomic displacement, phase transformation, and defect migration42,43. The oxygen atom intensity in annular bright field (ABF) STEM images of nonirradiated MLCCs after 3 min of electron beam bombardment were used to analyze changes in oxygen vacancies (Fig. 5a). After electron beam bombardment, more missing atomic columns appeared throughout the imaged area (compared with the magnified image showing a normal A site and a deficiency B site). Therefore, this experiment simulated the gamma radiation process, where gamma rays or electron beams interact with atoms, causing vacancy emergence.

Fig. 5: Physical mechanism of the effects of gamma radiation.
figure 5

a O atom intensity maps of ABF-STEM for the MLCC ceramic layers before and after electron beam bombardment; b Schematic diagram of Compton scattering; c Atoms removed to create vacancies; d Calculated average dielectric constants for different defects; Schematic illustration of the radiation dose rate effect at the e initial state, f high-dose-rate, g low-dose-rate, and h self-recovery.

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Herein, we elaborate on the physical mechanisms of the three types of radiation effects in MLCCs: (1) The total ionizing dose effect (TID), (2) the enhanced low dose rate sensitivity effect (ELDRS), and (3) the self-recovery effect.

Total ionizing dose (TID) effect

This effect refers to the phenomenon in which as the total dose of radiation increases, property damage increases. Gamma radiation is actually a Compton scattering process, including collision, defect formation, and microstructure structural evolution.

Collision processes

Gamma rays interact with the outer electrons of atoms through Compton scattering, exciting electron transitions and generating electron‒hole pairs (Fig. 5b)44. Ferroelectric materials, with their spontaneous polarization (P), create strong local electric fields (local field = P/3ε0). In the absence of external stimuli, the macroscopic average electric field inside the material is caused by the depolarization field (Ed) from polarized charges45. The electron‒hole pairs generated by gamma rays are swept toward the dielectric/electrode interface, effectively shielding Ed (Ed drives charge capture)46 (Fig. 5e). Electrons, being lighter and more mobile, easily migrate toward the electrode under Ed47. In contrast, owing to their greater mass and lower mobility, holes are more likely to be captured by defect sites at grain boundaries, domain walls, and electrode‒dielectric interfaces as they move toward the electrode, forming positively charged traps48. As the radiation dose increases, more electron‒hole pairs are generated, leading to increased charged traps. Uneven distribution of these charged traps results in an internal bias field (opposite to Ed). This internal bias field counteracts the applied external voltage, causing an asymmetric hysteresis loop (Fig. 3e–j). As trapped charges accumulate, more ferroelectric domains are locked in by the internal bias field, making it more difficult to respond to external fields49. This results in a decrease in the domain switching ability, with a reduction in the dielectric constant.

Defect formation process and microscopic structural evolution

While electron‒hole pairs generated by Compton scattering quickly recombine or form trapped charges, Compton electrons can also interact with atomic nuclei, inducing electric fields that displace atoms, forming vacancies, interstitial atoms, and anti-site defects. With respect to dielectric materials, increasing the total gamma ray dose significantly increases the oxygen and barium vacancy concentrations (as evidenced by the EPR, XPS, and STEM results). If gamma ray radiation energy is further increased, it can induce microstructural changes, such as changes in grain morphology and crystal structure evolution. Although XRD and Raman spectroscopy reveal no macroscopic changes in the crystal structure, the STEM results reveal that gamma ray irradiation indeed affects the local lattice structure of the MLCCs.

To reveal the intrinsic relationship between defects and the dielectric constant, first-principles calculations were adopted to perform plane-wave density functional theory calculations (Supplementary Fig. 17). Figure 5c, d shows the calculated average dielectric constants for different Vo and VBa values. The impact on the dielectric constant varies for different charge states/types of vacancies (Ba/O), and the different charge states can be attributed to the interaction between electron‒hole pairs and vacancy defects. With the exception of neutral oxygen vacancies (VO0), all the other defects decrease the dielectric constant, corresponding to the performance degradation caused by radiation damage (Fig. 5c, d). The increase in the dielectric constant for Vo⁰ stems from enhanced electron polarization, as Vo⁰ has the greatest number of localized electrons and contributes most strongly. The Vo-Ti3+ defect dipole is actually a free electron injected into an oxygen vacancy that hybridizes or localizes with one of the Ti atoms, making it equivalent to a Vo1⁺. According to formation energy calculations, divalent oxygen vacancies (Vo²⁺) have the lowest formation energy50, and their presence corresponds to the smallest dielectric constant. In addition, γ-ray radiation increases the defect content and trapped charges, enhances the domain wall pinning, and ultimately leads to radiation damage (Fig. 1b).

Enhanced low dose rate sensitivity (ELDRS) effect

Owing to the low-dose-rate of radiation corresponding to very low total doses, the STEM results reveal that the defect content in low-dose-rate samples (3.35E-6 Gy/s; total dose, 0.8844 Gy) was slightly lower than that in high-dose-rate samples (1E-1 Gy/s; total dose, 2000 Gy), and the changes in bond lengths and stress‒strain were smaller. However, even at such low total doses, STEM clearly revealed changes in the defect content, distribution, and bond lengths. Compared with the in situ capacitance results, the capacitance degradation for 2000 Gy (1E-1 Gy/s) is greater than that for 0.8844 Gy (3.35E-6 Gy/s), indicating that the performance aligns with the structural changes for TID. However, considering the same total dose (i.e., 0.8844 Gy), the in-situ capacitance curve clearly shows that the low-dose-rate sample experienced more damage, confirming ELDRS. Although there is a time discrepancy between 2000 Gy (1E-1 Gy/s) and 0.8844 Gy (3.35E-6 Gy/s), the results of the in situ capacitance test for samples with the same radiation time (1E-3 Gy/s and 3.35E-6 Gy/s) still reveal stronger radiation damage for the lower dose rate (3.35E-6 Gy/s).

The mechanism of ELDRS can be explained as follows: As noted above, radiation damage primarily arises from increased vacancy defect content and the redistribution of trapped charges, leading to enhanced domain wall pinning. For high-dose-rates, this process can be explained by the space-charge-limited current effect51. In a short period, radiation generates a large number of electron‒hole pairs. Electrons easily migrate to the electrode‒dielectric interface, but holes move much slower. As a result, numerous holes accumulate inside the material. Newly generated electrons migrate toward these accumulated holes, recombining quickly with them. This reduces the formation of trapped charges, leading to less performance degradation under the same total dose (Fig. 5f). At low dose rates, there is much fewer electrons generation but enough time for holes to migrate, and holes are likely captured by defects in more stable sites, resulting in the effective formation of positively charged trapped charges (Fig. 5g). Additionally, the increase in defect content verified by EPR/XPS and STEM further enhances domain wall pinning; thus, under the same total dose, the lower the dose rate is, the more defects and trapped charges are generated, resulting in more severe performance degradation. However, for high-dose-rates such as 1E-1 Gy/s, if the radiation time is long enough (e.g., 2000 Gy), it can achieve effects similar to or even exceeding those of low dose rates.

Self-recovery effect

Recovery step is determined by space charge effects: Although irradiation-induced defects are the primary factor contributing to the degradation of dielectric properties, the role of space charge effects should not be overlooked, as they exhibit distinct dynamic characteristics in the dielectric response. Unlike the cumulative impact of defects, space charge effects arise from the dynamic equilibrium of electron‒hole pairs during irradiation: charge carriers generated by the ionization of secondary electrons accumulate at grain boundaries or defects, forming a built-in electric field that screens the external field and reduces the dielectric constant. This effect is markedly different from that of defect mechanisms upon cessation of irradiation. When irradiation stops, the generation of electron‒hole pairs ceases immediately, while recombination continues, leading to the rapid dissipation of space charges and a step-like recovery of the dielectric constant (recovery step). The magnitude of this step is directly correlated with the irradiation dose rate—higher dose rates result in greater equilibrium carrier concentrations, more significant space charge accumulation, and consequently a more pronounced recovery step.

Aging behavior is determined by defect effects: In contrast, defect recovery relies on the thermal diffusion and annihilation of oxygen vacancies, resulting in a slow subsequent relaxation process. The in situ capacitance data show that MLCCs exhibit self-recovery behavior at high-dose-rate, where the capacitance gradually increases after irradiation. Low-dose-rate MLCCs present completely opposite aging behavior. That is, the capacitance decreases first with aging time but then starts to recover. This phenomenon can be explained as follows: During high-dose-rate irradiation, the number of shallow-level metastable trapped charges exceeds that of deep-level trapped charges52. These shallow-level trapped charges are gradually decaptured during the postradiation aging process at room temperature; i.e., the holes detached from their original defect sites, leading to partial self-recovery (Fig. 5h). Additionally, owing to the presence of deep-level trapped charges and radiation-induced defects such as oxygen vacancies, these deep-level trapped charges are difficult to recover quickly. The formation of oxygen vacancies and other defects is largely irreversible, which explains why the performance has not fully recovered after radiation. This is also why ex situ structural tests (EPR and TEM) can still detect significant defect evolution. In contrast, during low-dose-rate irradiation, lower generation rates of electron‒hole pairs promise that both electron and hole have enough time to migrate, after which more deep-level trapped charges can form. During the postradiation aging process, on the one hand, the electron‒hole pairs generated by irradiation still dynamically migrate, forming trapped charges and leading to capacitance degradation. On the other hand, with further extension of the aging time, partial recovery can be observed. This process is closely related to the decapture of shallow-level trapped charges.

As a result, the combined action of both mechanisms determines the dielectric behavior of BaTiO₃ under irradiation. This comparison highlights the transient nature of space charge effects: their influence responds rapidly to the initiation and termination of irradiation, whereas defect effects exhibit long-term accumulation and gradual recovery.

Discussion

In situ irradiation experiments were designed to explore the effects of gamma radiation on property degradation on commercial X7R-MLCCs. Three distinct gamma radiation effects were identified: (i) total ionizing dose (TID), (ii) enhanced low dose rate sensitivity (ELDRS), and (iii) self-recovery effects. Combined with multiscale structure analysis, the mechanisms behind irradiation effects were elucidated. With respect to the TID, an increased total dose induces property degradation, closely related to increased defect content and trapped charges, leading to domain wall pinning and property damage. With respect to the ELDRS, the dynamics of electron‒hole pairs and trapped charges contribute to this interesting phenomenon. Finally, the MLCCs also present completely different self-recovery effects after high- and low-dose-rate irradiation, attributed to both the space charge effect and the decapture of shallow-level trapped charges.

Methods

Radiation experiment

The MLCCs used in this study were X7R-25V-1.0μF, manufactured by Torch Electron Technology Co., Ltd. It is challenging to obtain precise macro electrical properties for such small-sized MLCCs. Therefore, a custom-designed printed circuit board (PCB) with 10 BNC connectors was employed. Four MLCCs were presoldered onto each PCB, sharing the same ground. A total of six identical PCBs, each containing the same type and batch of MLCCs, were prepared for various experimental conditions. To facilitate structural analysis, additional Ce-doped BaTiO3 ceramics (Ba0.96Ce0.04TiO3) were also fabricated for radiation.

Gamma ray irradiation experiments were conducted using a Co60 radiation source. The experimental protocol included the following:

1. A fixed radiation dose rate of 1E-1 Gy/s was used, with varying radiation times to expose the samples to different total doses. One PCB was used for in-situ capacitance measurements, while ex-situ data were collected from samples irradiated at 0 Gy, 100 Gy, 300 Gy, 500 Gy, 1000 Gy, and 2000 Gy.

2. Experiments with varying radiation dose rates: Samples were treated with radiation dose rates of 1E-1 Gy/s, 1E-3 Gy/s and 3.35 E-6 Gy/s, with radiation times of 320, 4400, and 4400 minutes, respectively.

3. Capacitor self-recovery measurements: Upon completion of in-situ radiation, the raised Co60 radiation source was lowered back, and the sample remained in place for 3 hours to continue detecting the capacitor.

A schematic diagram of the in-situ capacitance measurement under gamma ray irradiation is shown in Supplementary Fig. 1. Methodology Notes: 1) During the experiment, in situ capacitance testing was conducted while the radiation source is raised. Upon completion of the radiation, the radiation source was lowered, and a capacitance self-recovery test was performed. 2) The radiation dose rates at Sites 1 to 3 were 1E-1 Gy/s, 1E-3 Gy/s and 3.35E-6 Gy/s, respectively.

Characterization experiments

The capacitance properties of the MLCCs were tested in situ using an impedance analyzer, with a frequency range of 200 Hz to 2000 Hz and a test voltage of 50 mV AC. The ferroelectric properties of the MLCCs were tested ex situ using a ferroelectric tester at a frequency of 1 Hz several days after irradiation. The average crystal structure was characterized using a single-crystal X-ray diffractometer. Raman analysis was performed using an ultrahigh-resolution two-photon confocal laser scanning microscope. The bias field distribution was investigated by using piezoresponse force microscope (PFM). The fine structure of the defects was investigated using an X-band continuous-wave electron paramagnetic resonance (EPR) spectrometer equipped with a liquid helium cryostat at 9.54 GHz. As EPR cannot reflect cation vacancy defects, Ba vacancies were analyzed using X-ray photoelectron spectrometry (XPS). Ultrathin TEM samples of the MLCC were prepared using a focused ion beam (FIB) system, after which STEM images were captured with an aberration-corrected scanning transmission electron microscope.

First-principles calculations

To investigate the impact of defects, especially vacancy defects, on the dielectric constant of BaTiO3, we performed first-principles calculations based on density functional theory (DFT) using the Vienna Ab initio Simulation Package (VASP) software. The plane-wave cutoff energy was set to 400 eV (ENCUT = 400 eV), and a 1×1×1 K-point mesh centered at the gamma point is chosen for subsequent calculations. The interaction between electrons and atomic nuclei was described using the projected augmented wave (PAW) method, and generalized gradient approximation (GGA) with the PBE functional is used for the exchange-correlation functional. All the models underwent full structural relaxation calculations, where the positions of all the atoms in the supercell and the lattice parameters (size and shape) were allowed to change. The relaxation process was considered complete when the total force on any atom was smaller than 0.01 eV/Å, indicating convergence. The BaTiO3 unit cell was expanded to a 3×3×3 supercell (391 atoms), which was fully relaxed.