In-Situ Electric Field Observation of Small Precipitates in BaTiO₃ Multilayer Ceramic Capacitors

Abstract

The electric potential distribution within a commercial multilayer ceramic capacitor under an applied voltage was determined by electron holography. We demonstrated that equipotential contour lines present essential information about the electrical conductivity of submicrometer-scale precipitates formed in commercial BaTiO₃ multilayer ceramic capacitors. Considerable changes observed in the equipotential contour map of precipitates could be explained by simulations taking into account the electrical conductivities of the precipitates and BaTiO₃ matrix. This method can lead to a deeper understanding of the relationship between the complex microstructure and the material functionalities in capacitors widely used in industry.

Fig. 1 (a) Schematic illustration of a thin-foil specimen of a multilayer ceramic capacitor. Refer to the text for details. (b) ADF-STEM image of a thin-foil specimen. The yellow patches indicate deposited Pt electrodes to forming part of the anode. The black arrows in the middle indicate the position of precipitate. (c) Nonlinear I–V curve obtained from local resistivity measurement of the thin-foil specimen.

1. Introduction

Multilayer ceramic capacitors (MLCCs), which employ BaTiO₃ as a dielectric substance, are among the most important electronic components used in modern industrial products. As in the case of other metallic systems (e.g., hard magnets, steels, actuators, and other such functional materials), control of the microstructure of MLCCs is crucial for improving their electrical properties as well as for allowing further miniaturization. In the engineering of the microstructure of MLCCs, the use of elemental additives is a key technology. An electrode in an MLCC, which is conventionally made of Ni, is an example of a component subject to microstructural engineering through the use of elemental additives.¹⁾ Although the use of pure Ni may cause physical disconnections in several portions of the electrode, the addition of Cr dramatically improves the continuity of electrodes due to the effective formation of an additional metallic phase in the vicinity of the interface.^2,3) Researchers have reported a significant role for added Mg and rare-earth elements in controlling the temperature dependence of the dielectric constant.^4,5) However, the addition of such elements induces complex precipitation within the dielectric substance (e.g., Cr-rich phase,²⁾ Si-rich phase,⁶⁾ and others). Since these precipitates have totally different dielectric constants from that of the BaTiO₃ matrix, they are likely to degrade the performance of the capacitor. For example, some of precipitates may cause a significant change in the local electric field, leading to a harmful electrical breakdown. Furthermore, physical contact between the BaTiO₃ matrix and the precipitates may lead to the formation of a Schottky barrier,^3,7,8) which is undesirable in capacitor applications. Thus, it is important to study the local electrical properties in the neighborhood of submicrometer-scale precipitates. Kuramae et al. reported an electron holographic study on model capacitor samples under an applied voltage using a probing technique in transmission electron microscopy (TEM).⁹⁾ This technique can be applied for point-by-point measurements of the electric properties of small precipitates in MLCCs. In this study we characterize submicrometer-scale precipitates formed in MLCCs and identify the objects that cause harmful electric breakdowns using electron holography^10–12) with the handling microprobes in TEM.^13–16)

2. Experimental Procedure

A commercial X7R-type MLCC was polished using a focused ion beam (FIB) system, to prepare thin-foil specimens for TEM studies. Figure 1(a) shows a schematic diagram of a thin-foil specimen (20 µm × 6 µm × 100 nm) with a stacked Ni cathode, dielectric substance (BaTiO₃), and Ni anode. Note that the cathode and anode are physically connected to Pt prongs, to which metallic Pt–Ir probes are brought into contact with when applying an electrical voltage to the specimen. Electron holography studies were carried out using a 300-kV JEM-3000F TEM. The electric potential distributions can be reconstructed from the phase information in the electron holograms. In the experiments of electron holography, the phase shift of the object electron wave ϕ(x, y), as defined in the x–y plane, which is perpendicular to the incident electrons in the z axis, can be expressed by¹¹⁾   

\begin{equation} \phi(x,y) = \alpha\int\varphi(x,y,z)\,dz, \end{equation} (1)

where φ(x, y, z) represents the electrical potential at position x, y, z. α is the interaction constant which depends on the accelerating voltage. Hence, the observed phase information is represented in terms of cos ϕ(x, y) as the electric potential distribution projected in the x–y plane. In this study, the phase information was amplified to twice the input. The current vs. voltage (I–V) curves for the thin-foil specimen were acquired using a picoammeter Keithley 6487, current source meter Keithley 6220, and nanovoltmeter Keithley 2182A. We detected a small electric current from the I–V measurements, as shown in Fig. 1(c), which may be due to a leakage current in the specimen because of polishing damage. Note that the acquired electric potential distributions by electron holography contain essential information on the dielectric crystal layer between the electrodes because it was confirmed that the spacing of the observed equipotential contour lines is reduced by increasing the applied voltage. Therefore, the leakage current in the specimen surface does not hamper the acquisition and/or analysis of electron holograms for various applied voltages, as detailed later. A composition analysis was carried out by energy dispersive X-ray spectroscopy (EDS) using a 200-kV JEM-2200FS TEM. We also employed annular dark-field scanning transmission electron microscopy (ADF-STEM) for the compositional analysis. A two-dimensional simulation of the electric field was performed using the finite element method (FEM). The model in the simulation was based on the configuration of the specimen observed in the ADF-STEM image. To investigate the electric field distribution change due to the electric resistance of the precipitates, the simulation model consists of a BaTiO₃ matrix layer containing a precipitate inserted between a metallic anode and cathode. In the equilibrium state, we used the equivalent circuit model considering only the electric resistances of the matrix layer and precipitate as insulators under flowing the leakage current.

Fig. 1

(a) Schematic illustration of a thin-foil specimen of a multilayer ceramic capacitor. Refer to the text for details. (b) ADF-STEM image of a thin-foil specimen. The yellow patches indicate deposited Pt electrodes to forming part of the anode. The black arrows in the middle indicate the position of precipitate. (c) Nonlinear I–V curve obtained from local resistivity measurement of the thin-foil specimen.

3. Results and Discussion

Figure 1(b) shows a ADF-STEM image of a thin-foil specimen prepared by the method detailed above. Due to the relationship between the brightness and the atomic number of the constituent elements in the ADF-STEM image, certain portions of the Ni electrodes are clearly distinguished from the layers of the dielectric substance. The disconnections of Ni anode, were filled with Pt (highlighted in yellow), using a spot evaporation technique. This assures satisfactory electrical conduction over the long electrodes. More importantly, the image shows the presence of small precipitates (indicated by black arrows) produced in the dielectric substance. Figures 2(a) and 2(c) show magnified ADF-STEM images of two specimens. Precipitates, appearing as dark contrast, are labeled as A, and B. One specimen includes the precipitate A, shown in Fig. 2(a). The other specimen, shown in Fig. 2(c), includes the precipitates B. The presence of these precipitates does not cause meaningful change in the brightness in the interior regions, implying that the composition is approximately uniform within these precipitates.

Fig. 2

(a) ADF-STEM and (b) reconstructed phase images in the area around precipitate A. (c) ADF-STEM and (d) reconstructed phase images around precipitate B. The phase information was amplified by a factor of two in the reconstructed phase images of (b) and (d).

To gain further information on the precipitates, we made EDS observations. Figure 3 shows the results of elemental mapping, collected from the same viewing fields as those in Fig. 2(a) (for the upper panels in Fig. 3) and Fig. 2(c) (for the lower panels in Fig. 3). The observations indicate that precipitate A is rich in Si and poor in Cr, with reference to the signals from the BaTiO₃ matrix. Conversely, precipitate B is rich in Cr and poor in Si. The oxygen content appears to be enhanced in all these precipitates. Again, the intensity is almost uniform within each precipitate area, which is consistent with the prediction made based on the ADF-STEM observations. Table 1 provides the detailed compositional analysis results for the precipitates A, and B, with the major detected elements presented in units of mass%.

Fig. 3

STEM-EDS mappings of (a) silicon, (b) chromium, and (c) oxygen in the area around precipitate A. STEM-EDS mappings of (d) silicon, (e) chromium, and (f) oxygen in the area around precipitate B.

Table 1 Chemical compositions in mass% of the precipitates A, and B obtained by STEM-EDS.

The composition of precipitate A is clearly different from precipitate B. The compositions of these precipitates are similar to the complex precipitations typically observed within the dielectric substance in MLCCs.^2,6) However, the crystallographic phase identification is as yet incomplete because of the presence of many constituent elements and the inadequacy of the diffraction studies conducted on these small precipitates. This remains a challenge with regard to the MLCC components. Nevertheless, we are able to classify the precipitates into two groups: precipitates A (referred to as the “Si-rich phase”) and precipitate B (referred to as the “Cr-rich phase”). These two groups offer distinct observations of electron holography, as detailed in the next section.

Figures 2(b) and 2(d) show the results of electron holography, acquired from the same area as that from which the ADF-STEM images shown in Figs. 2(a) and 2(c), were obtained. The Ni cathode and Ni anode regions are indicated by blue and red, respectively, while the Pt inset is indicated by yellow. The area containing precipitates A is highlighted in orange, and that containing precipitate B is highlighted in green. The contour lines represent the x–y plane component of the electric potential projected in the z axis of the incident electrons.¹¹⁾ Here, we briefly describe the image processing method used for the holography results shown in Fig. 2. Since BaTiO₃ is an insulator, it produces an unwanted electric field as a result of charging (caused by electron exposure), which is superposed on the information of interest due to the applied voltage between Ni cathode and anode. Moreover, the holography results include unwanted phase information due to significant changes in the mean inner potential at the positions of the precipitates, thickness variations in the specimen, Bragg reflections, and the magnetic field from the Ni electrodes. To suppress this unwanted phase information, we subtracted the phase shift information acquired under an applied voltage of 3 V from that acquired under 10 V. Note that the charging effect, mean inner potential, Bragg reflections, and magnetic field are approximately independent of the applied voltage. After this subtraction, the information related to the applied voltage is mainly retained—in practice, the results represent the equipotential lines under an effective applied voltage of 7 V (i.e., 10 V–3 V), as displayed in Figs. 2(b) and 2(d). In this experimental setup, the plate of the Ni cathode (0 V) plays an important role in reducing the electric field in the reference wave outside the specimen. For details on this shielding effect, see Refs. 9, 17, and 18). In the case of turning off the objective lens, a spacing of the interference fringe in acquired electron holograms was 30 nm at a biprism voltage of 50 V. By considering the interference fringe and conditions of the Fourier transform, the spatial resolution after subtracting the phase shift information is estimated at 90 nm. This value satisfies the spatial resolution for the evaluation of even smaller precipitate B (130 nm × 350 nm). Besides, the observed phase shift between anode and cathode in Fig. 2(d) is about 43 rad for the BaTiO₃ area in which the effective voltage of 7 V was applied. This phase shift is well matched with the past result of Ref. 9). The phase resolution of 0.68 rad could be determined from the experimental conditions. This value is also high enough to evaluate the phase shift of 4.5 rad observed in the precipitate B. The equipotential lines appear to approximately trace the shape of the electrodes. The number of contour lines observed between anode and cathode in Fig. 2(b) are larger than that in Fig. 2(d), which can be explained by the differences in thicknesses of the two specimens and/or net voltages applied between the Ni anode and cathode in the observed areas. The net voltages may become small due to the potential drops of the contact resistances between the probes and Pt prongs. It is important to note that there is a change in both the spacing and directions of the contour lines in the neighborhood of precipitate B, which can be attributed to the difference in the electrical conductivity between precipitate B and the BaTiO₃ matrix. In contrast, the contour lines appear almost unchanged around precipitate A, implying that the conductivity of precipitate A may not be significantly different from that of the matrix. We hereafter focus on the precipitate B, which causes a considerable change in the contour map.

The modulation of the equipotential contour lines observed for precipitate B can be explained by the following mechanism. A voltage applied to a multi-phase system (namely, an MLCC containing precipitates) induces interface polarization due to the different dielectric constants of the constituent phases. In the presence of interface polarization, the matrix region (BaTiO₃) and precipitate B are subjected to different electric fields E_M and E_B, respectively. The electron holography observations indicate a reduction in the contour-line spacing for precipitate B. The currents σ_ME_M in the matrix and σ_BE_B in precipitate B are assumed to flow in a series circuit, where σ_M and σ_B are the electrical conductivities of the matrix and the precipitate, respectively. After reaching the equilibrium state, the displacement currents becomes zero, i.e., the flowing currents σ_ME_M = σ_BE_B = const. Accordingly, a nonuniform electric potential distribution due to the localized potential drop by the high electrical resistance of precipitate B is formed in the neighborhood of the precipitate, i.e., E_B > E_M. Based on the electron holography results and the equilibrium condition, we conclude that σ_B is smaller than σ_M.

Simulation of the electric field distribution enables us to obtain further information on the precipitate. Figure 4 shows the two-dimensional simulated electric field maps based on the FEM modelling. In the model specimen used in the simulation, the locations of precipitate B, the Ni electrodes, and the Pt deposition are similar to those observed in Fig. 2(d). The simulations of the electric field distributions in the equilibrium state after completely charging were calculated using those parameters: V_A = 1 V, and V_C = 0 V, where V_A, and V_C represent the electric potential of the anode (Ni and Pt) and cathode (Ni). σ_M was assumed to be 10⁻¹⁰ S/m, based on the information provided in Ref. 19). The applied voltage was tentatively fixed at 1 V, which makes the number of contour lines within the precipitate comparable with the observations. Note that the simulated contour lines simply shows equi-potential lines of the simulated electric field distribution within the model specimen. Here, the parameter σ_B is variable, and we assume that σ_B for the simulated precipitate (labeled as B′) is (a) 10⁻⁷ S/m, (b) 10⁻¹⁰ S/m, and (c) 10⁻¹³ S/m in Fig. 4. As shown in Fig. 4(a), the contour lines are significantly buckled near precipitate B′ when σ_B is sufficiently larger than σ_M. In this case, the area of the precipitate shows only a negligible change in electric potential. If σ_B is comparable with σ_M, there is no appreciable change in the contour lines near the precipitate, as shown in Fig. 4(b). In contrast, when σ_B is sufficiently smaller than σ_M, the contour lines are clearly observed inside the precipitate, as demonstrated in Fig. 4(c). In addition, the results in Fig. 4(c) explain several features of the observations (Fig. 2(d)), such as the reduced spacing of the contour lines within the precipitate and the gradual change in the spacing in the matrix area. Finally, we can conclude that the electrical conductivity of precipitate B is significantly smaller (presumably by two or three orders of magnitude, based on these preliminary calculations) than that of the BaTiO₃ matrix.

Fig. 4

Electric field distribution images obtained by simulations for the following relationships between the electrical conductivities of precipitate B′ and the BaTiO₃ matrix: (a) σ_B > σ_M, (b) σ_B = σ_M, and (c) σ_B < σ_M. Refer to the text for further details.

4. Conclusion

We have demonstrated a unique characterization method, based on electron holography, for determining the electrical properties of submicrometer precipitates produced in multilayer ceramic capacitors. A precise analysis of the equipotential contour lines provides essential information about the electrical conductivity of precipitates. Based on this technique and the electric field simulations, we have found that the conductivity of the Cr-rich phase (precipitate B) should be smaller than that of the matrix by two or three orders of magnitude. We anticipate that our method can be applied to microstructural investigations of various precipitates formed in electronic components.

Acknowledgements

This work was supported by the Global COE Program, “Materials Integration International Center of Education and Research, Tohoku University,” from MEXT; the program, “Post-Silicon Materials and Devices Research Alliance,” from MEXT; a Grant-in-Aid for Scientific Research (S) from the Japan Society for Promotion of Science; and CREST from the Japan Science and Technology Agency (JPMJCR 1664).

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