Some Aspects of the Failure Mechanisms in BaTiO3-Based Multilayer Ceramic Capacitors

The objective of this presentation is to gain insight into possible failure mechanisms in BaTiO3-based ceramic capacitors that may be associated with the reliability degradation that accompanies a reduction in dielectric thickness, as reported by Intel Corporation in 2010. The volumetric efficiency (μF/cm) of a multilayer ceramic capacitor (MLCC) has been shown to not increase limitlessly due to the grain size effect on the dielectric constant of ferroelectric ceramic BaTiO3 material. The reliability of an MLCC has been discussed with respect to its structure. The MLCCs with higher numbers of dielectric layers will pose more challenges for the reliability of dielectric material, which is the case for most base-metal-electrode (BME) capacitors. A number of MLCCs manufactured using both precious-metal-electrode (PME) and BME technology, with 25 V rating and various chip sizes and capacitances, were tested at accelerated stress levels. Most of these MLCCs had a failure behavior with two mixed failure modes: the well-known rapid dielectric wearout, and so-called “early failures.” The two failure modes can be distinguished when the testing data were presented and normalized at uselevel using a 2-parameter Weibull plot. The early failures had a slope parameter of β >1, indicating that the early failures are not infant mortalities. Early failures are triggered due to external electrical overstress and become dominant as dielectric layer thickness decreases, accompanied by a dramatic reduction in reliability. This indicates that early failures are the main cause of the reliability degradation in MLCCs as dielectric layer thickness decreases. All of the early failures are characterized by an avalanche-like breakdown leakage current. The failures have been attributed to the extrinsic minor construction defects introduced during fabrication of the capacitors. A reliability model including dielectric thickness and extrinsic defect feature size is proposed in this presentation. The model can be used to explain the Intel-reported reliability degradation in MLCCs with respect to the reduction of dielectric thickness. It can also be used to estimate the reliability of a MLCC based on its construction and microstructure parameters such as dielectric thickness, average grain size, and number of dielectric layers. Measures for preventing early failures are also discussed in this document. Introduction An inevitable trend in the miniaturization of MLCCs is an attempt to increase the capacitance volumetric efficiency (μF/cm). A typical monolithic MLCC structure is shown in Figure 1. A number of dielectric layers and internal electrodes are alternately stacked up together, and the internal electrodes are connected in parallel to form end terminations for the electrical contacts. The capacitance Ct of an MLCC can be represented by Ct = ε0 ∙ εr ∙ N ∙ S d , (1) March 26-29, 2012 CARTS International Las Vegas, NV 60 where S is the overlap area of internal electrodes, N is the number of the individual dielectric layers, εr is the relative dielectric constant of the ceramic BaTiO3 dielectric, d is the thickness of the dielectric layer, and ε0 is the dielectric constant of free space. Figure 1. A typical structure of an MLCC device. Volumetric efficiency can be defined and expressed as Ct V = ε0∙εr∙N∙ S d S∙h , (2) where h ≈ N ∙ d is the approximate height of an MLCC . Equation 2 can be simplified as Ct V ≈ ε0 εr d2 ≈ 8.854 × 10−8 εr d2 � μF cm3 �. (3) The approximate relationship shown in Equation 3 clearly reveals that in order to increase the volumetric efficiency (Ct/V), one needs to increase the dielectric constant εr , decrease the dielectric layer thickness d, or make both of these changes. For a wide range of dielectric thicknesses the grain size is almost unchanged at a given processing condition, so that it is more effective to increase the Ct/V by reducing the dielectric thickness d. However, several reports [1-3] have shown that once the grain size is below a certain point, εr will decrease dramatically with a further decrease in grain size. This is due to the fact that ceramic BaTiO3 begins to lose its ferroelectricity as the grain size of BaTiO3 decreases beyond a certain point. Therefore, there exists a limit of d below which the value of Ct/V will not increase with further reduction of d because of the grain size reduction in such thin dielectric layers. Furthermore, one should not expect to increase Ct/V simply by increasing the capacitor area S or the number of dielectric layers N of an MLCC. Figure 2 shows the results of a calculation of Ct/V as a function of dielectric thickness d for a number of ceramic BaTiO3 MLCCs. The dielectric thickness and grain size data are based on the measured data from our previous reports [11-12], and the dielectric constant data were taken from Figure 2 in reference 2. The Reliability of a Multilayer Ceramic Capacitor A monolithic MLCC can be converted both constructively and electrically to a number of single layer ceramic capacitors connected in parallel. Such an idea is shown in Figure 3. Assuming Ci is the i-th layer capacitor, the MLCC can be viewed as a parallel connection among C1, C2, C3,... Ci,..., and CN, where N is the number of dielectric layers inside an MLCC device. Since every single-layer capacitor Ci shares the same electrode area S, the same dielectric thickness d, and the same processing history, it is reasonable to assume that C1 = C2 = C3 = ⋯ = Ci ... = CN. So the sum of the capacitance Ct of an MLCC can be expressed as Ct = C1 + C2 + C3 ... + Ci ... + CN = N ∙ Ci (4) March 26-29, 2012 CARTS International Las Vegas, NV 61 Figure 2. Calculated capacitance volumetric efficiency as a function of dielectric thickness d. Similarly, the reliability of an MLCC with N layers of dielectric material Rt can be expressed as Rt = R1 × R2 × R3 ... × Ri ... × RN = Ri (5) where Ri is the reliability of an i-th single-layer capacitor. When a 2-parameter Weibull distribution is used, the reliability Ri of capacitor Ci can be written as Ri(t) = e −� η� β (6) where e is the base for natural logarithms, t is the failure time, slope β is the dimensionless shape parameter whose value is often characteristic of the particular failure mode under study, and η is the scale parameter that represents the point at which 63.2% of the population has failed. The reliability relationship shown in Equation 5 indicates that the overall reliability Rt of an MLCC device is dependent highly on the reliability Ri of a single-layer capacitor inside a monolithic MLCC. Since dielectric Figure 3. A cross-section view of a monolithic MLCC shows a stack of N layers of single-layer capacitors (a); this construction can be equivalently converted to the same number of single-layer capacitors connected in parallel.