Introduction

Multilayer ceramic capacitors (MLCCs) have been an important passive component in the expanding market for electronic products such as laptops, tablets, and smartphones. Recently, the demand for components with high lifetime reliability used in harsh environments has increased dramatically due to the development of autonomous driving and electric vehicles1. In the case of MLCCs used in automobile applications, warranty conditions have significantly higher temperature and voltage levels than those used in general electronics. The life expectancy calculated under accelerated conditions calls for a lifespan that is approximately 50 times higher than the average lifespan of an IT application2.

To meet these demands and improve the lifetime of MLCC, a typical method have been approached from dispersing and mixing barium titanate (BaTiO3) with various additives of rare earth oxides. (i.e., Dy, Y, Ho, Yb, Er, etc.) Among them, Dy has long been known to play the most important role as a donor to improve insulation resistance and lifetime reliability3,4,5,6. Furthermore, when the rare earth elements are added to the BaTiO3 ceramic used as the base material for MLCCs, the role of rare earth elements is well known to inhibit the formation and the migration of oxygen vacancies leading to a major cause of failure2,7.

$$\text{Ba site} : {{\text{R}}}_{2}{{\text{O}}}_{3} \to 2{{\text{R}}}_{{\text{Ba}}}^{*}+ {{\text{V}}}_{{\text{Ba}}}^{"}+3{{\text{O}}}_{{\text{O}}}$$
(1)

Equation (1) is a defect equation using the Kroger-Vink diagram to substitute the rare earth element Dy for the element Ba at the A-site. It can be explained that Dy can act as a donor and significantly improve lifetime reliability by suppressing oxygen vacancies leading to a major cause of defects due to + 1 valence of Dy than Ba. This approach has been shown to cause MLCCs to fail in experiments by a number of researchers since the 1990s4.

However, recent studies have a different opinion in comparison to the conventional hypothesis that oxygen vacancies are a major factor for the conduction mechanism in BaTiO3 in spite of suppression of oxygen vacancies by the effect of rare earth oxide additives. Even though higher activation energies have been reported in recent studies of MLCCs, it has been referred that band shifts or electron polaron hopping associated with oxygen vacancies are a major factor. The previous concept of mobile oxygen vacancies was issued for understanding the electrical behavior of perovskite oxide ferroelectrics, because it mimics the phenomenon of oxygen vacancy migration8,9. Therefore, we propose that the failure mechanisms explained solely by the oxygen vacancy migration in BaTiO3 based MLCCs should be reconsidered from an electronic perspective.

Here, we evaluate the lifetime of the prototype MLCCs using high-acceleration life testing (HALT) to obtain the mean time to failure (MTTF). The MTTF is used as a key factor to calculate the thermal activation energy of the MLCC with Arrhenius based Prokopowicz–Vaskas (P–V) equation by comparing it with values reported in previous papers. The activation energy values in the thermal activation process of the prototype MLCCs were investigated and compared to previous values based on the mobile oxygen vacancy concept. From these results, we discuss the failure mechanism of MLCCs with temperature acceleration in relation to the electronic process rather than the similar motion of oxygen vacancies.

Experimental

Three prototypes of rare-earth-doped BaTiO3-based MLCCs (4.7 μF, 0.22 μF, and 10 μF) with the highest rated voltage (global standard) for automotive applications were used in this paper. Table 1 summarizes the specifications of capacitance, temperature characteristics, rated voltage, and dielectric thickness. The microstructures of the three MLCCs were examined using a scanning electron microscope to obtain average dielectric layer thickness. The cross-sectional SEM images of the 4.7 μF, 0.22 μF, and 10 μF MLCCs used in this study are shown in Fig. 1.

Table 1 Specifications of the prototype MLCCs for automotive applications used in this work.
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Figure 1
figure 1

Cross-sectional SEM images of the (a) 4.7 μF, (b) 0.22 μF, and (c) 10 μF MLCCs used in this study.

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In order to calculate MTTF of the MLCCs, all electrical measurements were conducted in a custom-made apparatus with a power supply system, a chamber with temperature controller, and a digital multi meter (DMM 7510, Keithley). The time-dependent insulation resistance (IR) degradation of MLCCs was evaluated under a constant dielectric current (DC) bias (70 V, 80 V and 95 V) for HALT as function of temperature ranges from 140 to 160 °C up to ~ 1500 h. To show successful introduction of Dy (rare-earth metal) into grains of dielectric layer, the high-resolution transmission electron microscopy (HR-TEM) is used (Tecnai Osiris 200 kV, FEI, USA).

Result and discussion

Weibull plots for the time to failure at each temperature are shown in Fig. 2, showing MTTFs of the three prototype MLCCs (4.7 μF, 0.22 μF, and 10 μF) after HALT evaluation. Overall, it is clearly seen that time to failure decreases with increase of temperature from 140 to 160 °C and electric field from 17.1 to 29.7 V/μm, regardless of capacitance. It is found that the temperature and electric field applied to the dielectric are critical for lifetime of MLCCs. To calculate MTTF of the MLCCs from the time to failure, the two-parameter statistical Weibull distribution model was used. MTTF can be obtained from the following equation:

$$MTTF = \eta \Gamma \left( {1 + \beta^{ - 1} } \right)$$
(2)

where β is the dimensionless slope parameter for characteristic of the particular failure mode, η is the scale parameter, which represents the characteristic time at the population of the failed specimens reaching 63.2%, and Γ is the gamma function (Note: Γ(1 + β-1)  ≈ 0.9, when β > 3.0)10.

Figure 2
figure 2

Weibull distribution for HALT results as a function of temperature from 140 to 160 °C at the constant electric field of 17.1 V/μm for (a) 4.7μF MLCC, 21.1 V/μm for (b) 0.22μF MLCC and 29.7 V/μm for (c) 10μF MLCC for ~ 1500 h.

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The calculated MTTFs of the three MLCCs (4.7 μF, 0.22 μF, and 10 μF) are shown in Fig. 3a. It is obvious that the MTTF of the MLCCs increases exponentially with decreasing temperature from 160 to 140 °C. It is clearly shown that the higher the test temperature, the smaller the MTTF of MLCC. The empirical equation suggested by Prokopowicz and Vaskas (P–V) is commonly employed in order to predict the use-level lifetime of MLCCs as follows11,12:

$$A = \frac{{t_{1} }}{{t_{2} }} = \left( {\frac{{V_{2} }}{{V_{1} }}} \right)^{n} exp\left[ {\frac{{E_{a} }}{{k_{B} }}\left( {\frac{1}{{T_{1} }} - \frac{1}{{T_{2} }}} \right)} \right],$$
(3)
Figure 3
figure 3

(a) The calculated MTTFs of the MLCCs (4.7μF, 0.22μF, and 10μF) and (b) Arrhenius plot for the MTTFs under temperature-accelerated lifetime test as a function of temperature from 140 to 160 °C at the constant electric field of 17.1 V/μm for 4.7μF MLCC, 21.1 V/μm for 0.22μF MLCC and 29.7 V/μm for 10μF MLCC for ~ 1500 h. Fit lines can be calculated by Arrhenius equation to obtain the activation energy.

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where A is the ratio of two times-to-failure or the acceleration factor in relation to time-to-failure t1 (h) under the first condition in voltage V1 (V) and temperature T1 (K) to time-to-failure t2 under the second condition in V2 and T2. Ea is the activation energy (eV), n is voltage acceleration constant, and kB is the Boltzmann constant (eV/K) for HALT. When the voltage is constant, Eq. (3) can be expressed as the following:

$$\frac{1}{MTTF} = K_{0} exp\left[ { - \frac{{E_{a} }}{{k_{B} T}}} \right],$$
(4)

where K0 is the degradation rate constant. Equation (4) means thermal activation process related to dielectric breakdown for HALT of MLCC2,13,14. Figure 3b shows Arrhenius plot for the MTTF data with a fit line using Arrhenius-type Eq. (4). As depicted in Fig. 3b, the activation energy estimated from the Arrhenius-type equation fitting can exhibit an average value of 1.52 eV for all MLCCs, higher than the activation energy values of ~ 0.9 eV first reported by paper to use the P–V equation15. The 1.52 eV value in this study is especially distinguished from the activation energy value of 1.0 eV proposed by Waser et al. due to a phenomenon caused by oxygen vacancy migration7. The agreement of these experimental values led to the interpretation that the main cause of failure in MLCCs is related to oxygen vacancy migration. However, recent products developed for high lifetime reliability exhibit a relatively high activation energy, which converges to ~ 1.6 eV as in this paper. Due to an obvious difference in activation energy values, it difficult to explain the conduction for failure by only oxygen vacancy migration.

Figure 4 shows the activation energy calculated from the reference2,11,12,13,15,16,17,18,19,20,21 and this work as functions of electric field during HALT, dielectric thickness of MLCC, and published year since 1969. As the electric field during HALT increases, the activation energies in references and this work are close to a constant value of ~ 1.6 eV, which is close to a half the energy band gap22 (Eg/2 ≈ 1.6 eV) of BaTiO3 as shown in Fig. 4a. In case of the prototype MLCCs, the high electric field means that higher manufacturing skills for materials, equipment, etc. are required in comparison to conventional MLCCs of the past. It is also seen that the thinner the dielectric thickness, the more values close to 1.6 eV as shown in Fig. 4b. Since 1969, activation energy in chronological order is shown in Fig. 4c. The detailed reference data corresponding to Fig. 4 is summarized in Table S1 in Supplementary information.

Figure 4
figure 4

Activation energy in references2,11,12,13,15,16,17,18,19,20,21 and this work as functions of (a) electric field from 1.4 to 29.7 V/μm during HALT, (b) dielectric thickness from 1.4 to 44.5 μm of MLCC and (c) published year from 1696 to present.

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From the difference in activation energy, we propose to explain the activation energy by the conduction mechanism of BaTiO3, based on the concept of the mobile charge carriers in BaTiO3 as electrons rather than oxygen vacancies in previously reported literature. Under thermal activation process, the effective mobile charge carriers can be considered as electrons, holes, and polarons localized in the oxygen vacancies or in the Ti element near the oxygen vacancies. Therefore, the conductivity (σBT) of BaTiO3 can be expressed as the sum of the conductivities of the three carriers as follows:

$${\sigma }_{BT} = {\sigma }_{e}+ {\sigma }_{h}+ {\sigma }_{p},$$
(5)

where σe, σh and σp are conductivities for electron, hole and polaron, respectively. Here, σh can be negligible because the hole mobility is very low compared to the electron mobility due to the nearly flat valence band23. σBT in Eq. (5) can be described as a single Arrhenius equation and employing the effective activation energy as follows:

$${\sigma }_{BT} \approx e{\mu }_{e}{N}_{CB}{exp}\left(-\frac{{E}_{C}-{E}_{F}}{{k}_{B}T}\right)+e{N}_{p}{\mu }_{p0}exp\left(-\frac{{E}_{p}}{{k}_{B}T}\right) \approx \left[e{\mu }^{*}{N}^{*}\right]exp\left(-\frac{{E}^{*}\left(T\right)}{{k}_{B}T}\right),$$
(6)

where e is the electron elementary charge, μe is the electron mobility, μp0 is the semi-empirical parameter, NCB is the density of states in the conduction band, Np is the polaron concentration, Ec, EF and Ep are the conduction band energy, Fermi energy and polaron binding energy, respectively. N*, μ* and E* are the effective parameters of concentration, mobility and activation energy, respectively23. The effective activation energy E*(T) can be taken on values between 0.3 eV corresponding to Ep24,25 and 1.6 eV corresponding to EC − EF of BaTiO3, which is approximately 1/2 Eg. It can be considered that the activation energy value will be a smaller value than 1.6 eV, if the electron polarons contribute more to conduction through a hopping mechanism. However, if oxygen vacancy formation is suppressed by using a donor-rich additive composition, the activation energy values that converge to 1.6 eV can be obtained, as shown in Fig. 5a. Thus, we can consider the band conduction in electronic process as the main conduction mechanism for failure, rather than the electron polaron hopping mechanism by oxygen vacancies. Based on the above the conduction mechanism for failure of typical MLCC, there are two main causes for the mechanism. First, vacancies produce shallow in-gap states below conduction band, e.g. oxygen vacancy related polaron hopping process, donor level, grain boundary, defect by processing error. The energy level for the vacancy is much smaller than Eg/2. The second is the excited electron based on band gap in electronic process. The values of activation energy under thermal activation process for state-of-the-art MLCC products are close to ~ 1.6 eV (~ Eg/2), much higher than these reported in the previous literature, because of recent sophisticated fabrication technologies and a significantly increased donor concentration to enhance lifetime reliability. Thus, the activation energy of MTTF under HALT can be caused by intrinsic behavior of dielectric material in MLCC and harsh evaluation conditions. In addition, the activation energy on the electrical conductivity can be represented as a slope in Arrhenius plot as shown in Fig. 5b. The main factors for conduction are the band gap of the material for intrinsic behavior at high temperature and the donor level for extrinsic behavior at low temperature. In addition, the conduction mechanism for degradation and failure of typical MLCC structure under DC bias is shown in Fig. S1 in Supplementary information.

Figure 5
figure 5

(a) Schematic images of simplified band diagrams for pure BaTiO3 showing oxygen vacancy related polaron hopping process and excited electron based on donor level/band gap in electronic process under thermal activation or electric field. (b) Arrhenius plot of electrical conductivity for an n-type semiconductor as a function of temperature26.

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For a simple comparison, Fig. 6 shows the activation energy obtained by MTTF under HALT (destructive test) and conductivity by leakage current–voltage (I–V) curve (nondestructive test) under the same evaluation conditions for electric field and temperature. It is clearly seen that the activation energy on leakage current based conductivity is smaller than that on MTTF under HALT. It is attributed that the activation energy for leakage current based conductivity originates from polaron hopping process and excited electron from donor level, grain boundary, and defect. (extrinsic) Therefore, MTTF under HALT can exhibit more intrinsic behavior due to recent sophisticated fabrication technologies and a significantly increased donor concentration.

Figure 6
figure 6

A comparison of the activation energy obtained by (a) MTTF under HALT and (b) leakage current based conductivity by I–V curve at a constant electric field of 17.1 V/μm as a function of temperature range from 140 to 160 °C.

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Furthermore, in case of various additive elements with different valences added to BaTiO3, the activation energy for thermal activation process has long been considered in relation to the oxygen vacancies due to similar value to the activation energy (~ 1.0 eV) required for the diffusion of oxygen ions in BaTiO327,28,29,30,31,32. However, a value of 1.0 eV does not necessarily represent the activation energy for the oxygen vacancy, because higher oxygen vacancy migration energy than 1.0 eV for rare earth doped BaTiO3, as reported by Cheng et al.33, is possible. In terms of resistance degradation over time, the electronic process can also be fully described using the Lloyd model34,35 and injection/transport of carriers24, as approached by oxygen vacancies7,29,30. In addition, the electric field during HALT for an early model of MLCC in literature proposed by Waser et al.7 was 0.8 V/μm. It is relatively smaller than the electric field during HALT for the prototype MLCC products. Applying this small electric field to the prototype MLCC, it will almost certainly not fail. The MLCCs used in this study are state-of-the-art products, where the recent sophisticated fabrication technologies are accumulated for high rated voltage and high capacitance, which are composed of a significantly increased donor concentration to enhance lifetime reliability. As shown in Fig. 7, transmission electron microscopy (TEM) images show successful introduction of Dy (rare-earth metal) into grains of dielectric layer in 4.7 μF MLCC as a representative. Since the donor inhibits the formation of oxygen vacancies in BaTiO3, the concentration of electron polarons localized in the Ti element is also reduced. Thus, the band conduction behavior of the electrons needs to be considered for conduction mechanism for failure, because the electron polarons can be also excited up to the conduction band as applying high electric field or high temperature. Under the actual operating conditions of the application, it is reasonable to focus the analysis on the electronic processes, and oxygen vacancy migration can be neglected due to the mild conditions below HALT. Therefore, if the electronic process is dominant, a higher bandgap energy is required to enhance the lifetime reliability of MLCC. From the above evidences, we propose that the concepts of electronic processes and oxygen vacancies should be considered together to understand conduction mechanism for failure of BaTiO3-based MLCCs in thermal activation processes. It is preferable to utilize activation energy as an indicator for comparing physical properties between compositions and for designing robust MLCC product.

Figure 7
figure 7

(a) High-angle annular dark field (HAADF) and (b) energy dispersive spectroscopy (EDS) Dy mapping images of 4.7 μF MLCC.

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Conclusion

In summary, we estimated lifetime for three prototype MLCCs (4.7 μF, 0.22 μF, and 10 μF) to obtain the activation energy under thermal activation process. The MTTF of MLCCs was calculated by using the Arrhenius based P–V equation as a method. It was observed that the activation energy shows to be constant in the average value of 1.5 eV for three prototype MLCCs, higher than the activation energy values of ~ 1.0 eV related to the motion or diffusion of oxygen vacancies reported in the previous literature. The activation energy value of ~ 1.5 eV for three prototype MLCCs is close to a half the energy band gap (Eg/2 ≈ 1.6 eV) of BaTiO3 obtained from specific environment, where oxygen vacancies are stabilized by external containment such as the effect of rare earth oxide additives. Due to an obvious difference in activation energy values, it difficult to explain the conduction mechanism for failure by only oxygen vacancy migration. Herein, electron behavior based on the recently proposed semiconductor theory is employed as a new attempt to understand failure mechanism of MLCCs under thermal activation process. Additionally, under the actual operating conditions of the application, it is reasonable to focus the analysis on the electronic processes, and oxygen vacancy migration can be neglected due to the mild conditions below HALT. However, oxygen vacancy migration cannot be completely ignored, because it can occur during HALT at the significantly high temperature or electric field. Therefore, both electronic process and oxygen vacancy can be considered as major causes for failure of BaTiO3 based MLCC under thermal activation process. It is also preferable to utilize thermal activation energy as an indicator for comparing physical properties between compositions and for future MLCC development with high lifetime reliability.