Investigation of useful or deleterious residual thermal stress component to the capacitance of a multilayer ceramic capacitor

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Abstract

The state of residual thermal stress in the active region of a multilayer ceramic capacitor (MLCC) was analysed through finite element method in order to uncover useful or deleterious stress component to the capacitance of an MLCC. A Ni-electrode layer of an as-fabricated MLCC is in tension in the in-plane direction, while a BaTiO3 layer is in compression. The change in stress state due to the external loading either in in-plane direction or in out-of-plane direction was analysed and compared with the change in the apparent capacitance in each case reported elsewhere. It was shown that the compressive in-plane stress (out-of-plane tension) component in BaTiO3 layer is beneficial to the capacitance while vice versa for in-plane tension (out-of-plane compression). The results were in accordance with the observations in single-layered ferroelectric thin film capacitors, which may be explained by the alignment of ferroelectric domains by stress field.

Introduction

Multi-layer ceramic capacitor (MLCC) is an essential component in mobile electronic circuitry products such as cellular phones and personal computers that are required to be miniaturized with higher performance and lower electric power consumption [1]. MLCCs prevail nowadays over their conventional single-layer counterparts because of their superior capacitance with smaller size, higher reliability, and better high-frequency characteristics. In MLCCs, two different materials, a dielectric ceramic material and a metal electrode, are laminated alternately with each other and co-fired at high temperatures of 1200–1300 °C, in case of Ni-based MLCCs. Because of the introduction of two dissimilar materials with different coefficients of thermal expansion (CTE), and the high temperature processing, the presence of residual stress in the hetero-structure is unavoidable; its influence increases as the number of layers in the structure increases.

The residual stress inside MLCCs is responsible for not only the generation of structural defects such as cracks, delamination, and crooked shapes during fabrication processes [2], but also the modification of capacitance of the overall structure [3], [4]. The estimation and understanding of residual stress induced in the MLCC structure are essential for improvements in performance and lifetime of MLCCs. Therefore, there has been much interest in the characterization of residual stress in MLCCs [2], [3], [4], [5], [6]. In order to exploit residual stress for designing MLCCs with better performance and longer lifetime, it is important to understand first how the residual stress develops in the active region of the as-fabricated structure. It is also of the utmost importance to find out which stress component is beneficial or deleterious to overall dielectric properties of the structure. In this aspect, the recent works by Nakano et al. [3] and by Saito and Chazono [4] provide very informative clues to the problems, which initiated the present study. According to them, the dielectric constant of MLCCs is lowered when a compressive load is externally applied in perpendicular to the plane of layers, while it is raised if the external compressive load is in plane with the layers (Fig. 1). However, no direct information about the stress state especially in the active region is available in their works. If we find out accurately how the external loads imposed on the as-fabricated structure change the stress state in the active region of the MLCCs, we can unambiguously relate the increase or decrease of the dielectric constant to a certain stress component.

For this purpose, the determination of the stress state in the active region is essential, while the previously used experimental characterization methods including X-ray diffraction [7], indentation method [5], [6], and beam bending technique [8], give only the information about surface stresses [5], [6], [7] or about averaged apparent values [8]. It is practically difficult to get the experimental data about the detailed stress state directly from the active region of MLCCs, as the thickness of the layers is very small (only a few μm). However, the reliability of the stress calculations based on the continuum mechanics in this scale of dimension has been well documented [9]. Thus, the present work employs the finite element method (FEM) to characterize the detailed stress state developed in the active region of the MLCCs with the application of external loads. This work will correct some previous qualitative description of the residual stress in the as-fabricated MLCCs by other authors. Then, it will clarify which stress component is beneficial or deleterious to the overall capacitance of MLCCs through the analysis of the stress state in the externally loaded MLCC structure.

Section snippets

Numerical analysis

To describe fully the stress state in an MLCC structure, a 3D model is required. Yet a 2D model is sufficient when the stress state in the active region of an MLCC is concerned, because the edge portion of the MLCC structure is fairly remote from the central (active) region. In this work, the 2D plane strain geometry was used for the residual stress calculation in the active region of the structure as shown in Fig. 2. The length of the model is 3 mm [3], [5], [6] with 11 ceramic layers inside.

Residual thermal stress in an as-fabricated MLCC

The results for the residual thermal stress components σxx and σyy along the path a–b that corresponds to the central axis of model MLCC (as illustrated in Fig. 2) under the condition of no external load are plotted in Fig. 3. The value of σxx shows a periodical pattern reflecting layered structure, while σyy is almost zero independently of y distance. The calculated value of σxx in the BaTiO3 layers is −218 MPa (compressive) and for the Ni electrode layers it is 600 MPa (tensile). The

Conclusions

The state of residual thermal stress in the active region of an MLCC was analysed through finite element method and the effect of each stress component on the apparent capacitance was determined. A Ni-electrode layer of an as-fabricated MLCC is in tension in the in-plane direction, while a BaTiO3 layer is in compression. It was investigated how the external compressive load imposed in the direction perpendicular to the plane of layers changed the stress state, in which condition a significant

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