Highly Accelerated Life Stress Testing (HALST) of Base-Metal Electrode Multilayer Ceramic Capacitors

An improved highly accelerated life stress test (HALST) procedure and modeling method was developed to evaluate the reliability of multilayer ceramic capacitors with base-metal electrodes (BMEs). Reliabilities of ceramic capacitors with precious-metal electrodes (PMEs) and BMEs are discussed. A combination of leakage current and mean-time-to-failure (MTTF) measurements under accelerated life stress conditions have been used to distinguish and separate the MTTF data into two failure groups: slow degradation and catastrophic. The slow degradation failures, characterized by a near-linear leakage increase against stress time, fit well to an exponential model over an applied field. A characteristic exponential growth time, τSD, is defined to describe the reliability life of this failure mode. The two separated MTTF data groups have been fitted to the 2-parameter Weibull model. When data points in the catastrophic subset are used for reliability modeling, the data points of the slow degradation subset are treated as suspensions, and vice versa. MTTF of most BME capacitors reveals an exponential dependence on an applied electric field due to the mixed failure modes. The initial MTTF data for slow degradation failures appears to follow the exponential law, and that for catastrophic failures follows the conventional power law. The reliability model developed with respect to mixed failure modes and acceleration factors agrees well with the HALST results -not only with the MTTF data, but also with the failure modes (catastrophic or slow degradation). BX life has been used to replace MTTF for evaluating the reliability life of BME capacitors at 125C and 2x rated voltage (Vr), the condition that all MLCCs are subject to pass at at least 1,000 hours life test for consideration for high-reliability space applications. This B0.8 approach can be used to select BME capacitors that exhibit the potential for passing the life test when evaluated using the quick turnaround HALST method developed in this work. Introduction Highly accelerated life testing has been commonly used for the reliability evaluation of MLCCs [1-7]. The testing involves the determination of time-to-failure (TTF) of capacitors at elevated life stress conditions (usually external applied voltage and temperature) that are higher than regular use-level conditions (room temperature and rated voltage, typically). However, highly accelerated life testing results for many BME MLCCs, particularly those with thin dielectric layers, have been found to not always give rise to correct predictions of use-level lifetimes [6,7]. In many cases, the calculated MTTF is longer than that actually achieved through life testing. Several factors may account for this problem: (1) higher accelerated life stresses are often required to generate failures, which results in the introduction of new failure modes. This is especially common for BME capacitors, since the improved microstructure of BME MLCCs will need much higher life stresses to cause a failure in a reasonable period of time, as compared to the conventional PME ceramic capacitors. (2) The failure modes characterized by the Weibull slope parameter β are very likely to change when extrapolating the TTF data at high life stress levels down to the use-level that is normally more than 100C lower in temperature and several times less in voltage. (3) A statistical method that can handle the multiple failure modes and handle specific acceleration factors needs to be developed. Some studies have indicated that the acceleration factors of BME MLCCs do not always follow the conventional powerlaw relationship over applied voltage; rather, they likely follow an exponential relationship (E-model) [1,8]. March 26-29, 2013 CARTS International Houston, TX 236 Reliability of BME and PME MLCCs The reliability of an MLCC is the ability of the dielectric material to retain its insulating properties under stated environmental and operational conditions for a specified period of time t. The reliability of a capacitor device can be expressed when a 2-parameter Weibull model is used: R(t) = e t η) β (1) where e is the base for natural logarithms, β is the dimensionless slope parameter whose value is often characteristic of the particular failure mode under study, and η is the scale parameter that represents a characteristic time at which 63.2% of the population has failed and that is related to all other characteristic times, such as mean time to failure (MTTF): MTTF = ηΓ(1 + 1 β) ⁄ , (2) where Γ(x) is the gamma function of x (Note: Γ (1+1/ β) ≈ 0.9 when β >3.0). Eq. (1) provides a simple and clear understanding of reliability: (1) Reliability is a function of time and always decreases with time, which indicates that the loss of reliability is a common behavior for all devices. (2) Since η and β always exceed zero, the value of R(t) is always between 0 and 1, indicating that reliability can also be viewed as the probability of a failure occurring. (3) Reliability typically defines the durability of a system that can function normally. When β >3 and t < η, R(t) ~1, suggesting a reliable life span before η. When t > η, R(t) decreases rapidly to 0. The lifetime of a device to sustain its function can be characterized by η, as shown in Eq. (2). It is widely known that the failure rate for MLCCs that is caused by a single failure mode when both V and T are changed from V1 to V2 and T1 to T2 is the product of the separate acceleration factors: AVT = t1 t2 = �2 V1 � n exp �a k � 1 T1 − 1 T2 ��. (3) where n is an empirical parameter that represents the voltage acceleration factors, Ea is an activation energy that represents the temperature acceleration factor, and k is the Boltzmann constant. This so-called Prokopowicz and Vaskas equation (P-V equation) [9] has proven to be useful in the capacitor industry for testing PME MLCCs at various highly accelerated testing conditions. An average of n ~3 has been found for the voltage acceleration factor, and an average value of 1 < Ea < 2 eV is typical for the temperature acceleration factor [10-12]. Since only a single failure mode is assumed, the value of β in Eq. (1) should not change over applied stresses. Only the Weibull distribution scale parameter η will change with external stresses. It can be expressed, according to Eq. (3), as η(V,T) = C Vn ∙ e B T, (4) where C and B = Ea/k are constants. Therefore, when the external stresses V and T are both taken into account, the Weibull reliability from Eq. (1) can be expressed again as: R(t,V,T) = e −� ne−� Ea kT� C � β