Surface mount technology feedthrough ceramic capacitors are gaining popularity in Hi-Rel systems due to small size and great filtering characteristics. In this work, BME feedthrough capacitors compliant with AEC-Q200 requirements have been evaluated, screened and qualified for a space project. Evaluation included analysis of the effect of post-soldering thermal shocks, temperature dependencies of leakage currents, distribution of breakdown voltages, assessments of high-current capability, and thermal resistance of the parts. The parts have been screened and qualified at conditions close to the military requirements for ceramic capacitors. No failures were detected during screening including burning-in, but two samples failed during monitored 2000 hour life testing at 125C and two times rated voltage. Failure analysis revealed manufacturing defects that required additional analysis of screening and qualification test conditions. Highly accelerated life testing (HALT) has been carried out to assess reliability acceleration factors and the probability of failure at the use conditions. An approach to selection of adequate burning-in and life test conditions is discussed.

The paper was presented by Alexander Teverovsky, Jacobs Engineering, Inc./NASA GSFC, USA at the 3^{rd} PCNS 7-10^{th} September 2021, Milano, Italy as paper No.3.2.

**HALT and Discussion**

Leakage currents in three groups of the feedthrough capacitors with 40 samples each were monitored during HALT at 125 °C and voltages of 200, 300, and 400V. Results of these measurements are shown in Fig. 10. Failures of the parts were easily identified by increasing leakage currents above 1 mA that followed a period of a relatively smooth increasing of currents that lasted a few hundred hours at 200V, dozens of hours at 300V, and hours at 400V.

Parts that did not fail during HALT had also currents increasing with time. The intrinsic increase of leakage currents occurs exponentially with time and the rate of increase was consistent between different samples in the group. Variations of intrinsic currents with time can be described using a characteristic time of degradation *t**: I ~ exp(t/**t**)*. The characteristic time decreases substantially with voltage as shown in Fig. 11a, and following the Prokopowicz-Vaskas model, can be described with a power function, *t** ~ (V/VR) ^{-m}*, where in our case

*m*= 3.84.

Fig. 11b shows distributions of times-to-failure (TTF) in Weibull coordinates during HALT at different voltages. The median times to failure (TTF_{50}) are also plotted against the normalized test voltages in Fig.11.a. Similar to *t*, variations of TTF_{50} were approximated with a power function, *TTF _{50} ~ (V/VR)^{-n}*, where

*n*= 3.43. Close values of the exponents indicate that similar mechanisms might cause degradation and failures of the parts. Extrapolation to

*V/VR*= 1 in both cases indicate times exceeding 20 years at 125 °C. Conservative estimations (

*E*=0.7eV) show that reduction of temperature to 85 °C increases these times by a factor of 10.

_{a}The shape of distributions suggests the presence of infant mortality (IM) and wear-out (WO) failures. By treating these two groups of samples separately (competing failure modes), we can analyze distributions of IM and WO failures independently. The slopes of distributions (*b*) for WO failures (solid lines in Fig.11b) at all stress conditions was close and varied from 6.5 to 7.5, which is well within the criteria for WO failures, *b* > 1. Due to a wide spread of data, the accuracy of estimations of *b * for IM failures is poor, but assuming similar slopes for IM distributions at different stress voltages, these slopes were assessed as 0.7 as shown by dashed lines in Fig. 11b.

The interception point of the lines approximating WO and IM distributions (Fig. 11b) gives an assessment of the proportion of IM failures in the group, *P(V)*, that depends on the stress voltage. This proportion increases from ~10% at 200V to 20% at 300V and 27% at 400V. Assuming that the failures observed during the standard life test condition (125 °C 100V) were also IM failures. *P(100)* = 3.3%. The value of *P* decreases linearly with voltage (see Fig. 11a) and might be well below 1% at the rated voltage. Considering that temperature has also a strong effect on the probability of IM failures, the risk of having these failures at operating conditions might be negligibly small. Apparently, the higher the level of stress, the larger proportion of IM parts can be revealed.

Analysis of the mechanisms of failures in BME ceramic capacitors shows that defect-related IM failures and WO failures are due to the same mechanism, migration of oxygen vacancies that is significantly accelerated at the defect areas such as local thinning of the dielectric [7]. In the first approximation, the same acceleration factors can be used for IM and WO failures and the probability of failures can be modeled using a general log-linear model that allows for presenting the characteristic time to failure, *TTF _{char}* in a form compliant with the Prokopowicz-Vaskas equation:

*TTF*. Results of this modeling are shown in Fig.12 where the lines were calculated using maximum likelihood estimation (MLE) method as

_{char }= A×V^{-n }*A*= 1.4E13 hr,

*b*= 1.14, and

*n*= 4.12. The voltage acceleration constant,

*n*, is in the range of values (from 3.9 to 8.7) determined for various X7R BME capacitors in [8]. Note, that the slopes of distributions in Fig.12 are substantially less than for WO failures shown in Fig.11b due to the inclusion of IM failures.

Based on this model, the probability of failures at the use conditions can be estimated (see Fig.12). For wear-out degradation, the most important parameter is the time to the failures’ inception, which can be defined as a time when 1% of failure occurs. For the life test conditions (125 °C, 100V), this time is ~ 400 hours, but for operating voltages (5V) it is 1.7E8 hours or 19,000 years. At 5V and 125 °C the inception of failures at 90% confidence, exceeds 1000 years. This indicates that failures detected at the military-level life test conditions will practically never happen at the use conditions. Conservative estimations show that the risk of failure for a 20 year mission at 5V is negligibly small, below 1E-7.

Modeling shows that the probability of failures at the BI conditions (160hr, 125 °C, 100V) is ~ 0.08%. This is in agreement with our experimental data showing no failures in 300 samples. Assessments based on the analysis of WO failures only, show that the time for the failure inception at 125 °C 100V exceeds 10,000 hours, which is far greater than the duration of the BI testing (160 hr). This means that the used BI conditions practically do not consume the life resource of the part and can be safely used for screening of the feedthrough capacitors.

A gradual increase of leakage currents before catastrophic failures as evident from Fig.8 and Fig.10 is consistent with the failure model suggested in [7]. According to this model, degradation of leakage currents occurs more rapidly in defect areas with thin dielectric due to increased electric field that intensifies migration of the positively charged oxygen vacancies, V_{O}^{++}, in the ceramic. Accumulation of the vacancies at the cathode reduces the barrier at the cathode-dielectric interface and increased current density exponentially. As a result, the temperature of the defect increases, which increases the current and creates a risk of the thermal run-away. A catastrophic failure happens when the hot spot temperature approaches melting points of ceramic or nickel (above 1000 °C). The probability of the run-away depends on the thermal resistance of the local area that decreases substantially with the size of defects, and on the availability of sufficient concentration of oxygen vacancies to reduce the barrier height.

Increasing temperature and voltage during HALT increases the probability of catastrophic failures caused by a defect substantially. However, this failure might never happen at normal operating conditions and the temperature of the defect can stabilize at a relatively low level. Results of HALT, where the larger proportion of IM failures indicating larger portion of defects in the parts that can be revealed at higher test voltages is in agreement with the model.

Results show that the existing system of qualifying parts for a space project by requiring that a certain number of samples pass life testing at 125 °C and two times rated voltage is not adequate not only for the automotive grade feedthrough capacitors, but in general, for advanced thin dielectric BME capacitors. The applicability of a given lot of capacitors for a specific space mission conditions should be based on adequate burning-in screening and assessments of the probability of failure during the mission. The latter can be done using a physics of failure approach, reliability modeling, and assessments of the acceleration factors using HALT.