Residual Stresses in Multilayer Ceramic Capacitors: Measurement and Computation

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1 Jaap M. J. den Toonder Mem. ASME Philips Research Laboratories, Eindhoven, The Netherlands Christian W. Rademaker Philips Center for Industrial Technology, Eindhoven, The Netherlands Ching-Li Hu Phycomp Research and Development Department, Kaohsiung, Taiwan Residual Stresses in Multilayer Ceramic Capacitors: Measurement and Computation In this paper, we present a combined experimental and computational study of the thermomechanical reliability of multilayer ceramic capacitors (MLCC s). We focus on residual stresses introduced into the components during the cooling down step of the sintering process. The technique of microindentation turned out to be a useful method to measure the stresses locally. The computations were done with three-dimensional finite element simulations. We find that the cooling step introduces compressive in-plane stresses in the ceramic layers. There is reasonably good overall agreement between the residual stresses obtained from the indentation experiments and the numerical simulations. Some discrepancies do exist, though, for measurements on cross-sectioned MLCC s. Possible reasons for the differences are discussed. DOI: / Introduction Contributed by the Electronic and Photonic Packaging Division for publication in the JOURNAL OF ELECTRONIC PACKAGING. Manuscript received November Associate Editor: L. Ernst. The basic structure of a multilayer ceramic capacitor MLCC consists of alternating thin layers of dielectric ceramic material and metal electrodes, as shown schematically in Fig. 1. Two metal end terminations function as electrical contacts and are used to solder the MLCC on a printed circuit board. The trend for these components is a reduction in overall size and in layer thickness, accompanied by an increase in the number of layers. The reliability of multilayer ceramic capacitors is related directly to their thermomechanical integrity; for a review see Ref. 1. Therefore each MLCC must meet certain standard requirements with respect to its thermomechanical integrity, and these requirements become more and more stringent. Tests such as the flex test, the temperature cycling test, the temperature shock test or resistance to solder heat RSH test are used to assess the thermomechanical reliability of the components. The behavior of the components during these tests is determined by many factors. First, material parameters such as the elastic modulus, the fracture toughness, and the thermal expansion coefficient play a role. Second, residual stresses present in the components due to processing are important. Finally, it is obvious that the stress distribution generated in the components during testing is a key factor. The present study focuses on residual stresses introduced into the MLCC during the cooling traject after sintering of the component. The manufacturing of MLCC s consists of many process steps, see, e.g., Ref. 2. One important step is sintering. At this stage, the component consists only of a stack of ceramic and metal layers, so the end terminations visible in Fig. 1 have not been applied yet this happens at a later stage in manufacturing. This geometry is called a brick. The brick is sintered at a temperature of about 1300 C, during which the ceramic material densifies and obtains properties critical for a proper functioning of the final MLCC. After sintering the component is cooled down to room temperature. During the cooling down, the metal electrodes solidify. Moreover, both the metal and the ceramic layers decrease in volume. However, due to the differences in thermal expansion between metal and ceramic, residual stresses are introduced after the metal has solidified. These resididual stress may play a crucial role in the mechanical integrity of the final components; see, e.g., Ref. 1. We have carried out full three-dimensional finite element simulations of this process step to compute these stresses. The material properties needed as input parameters have been measured with various experimental techniques. At the same time, we have carried out dedicated experiments to measure the residual stresses to be able to validate the simulation results. The technique we have used is microindentation. 2 Description of the Experiments 2.1 Indentation Method. The indentation method was used to estimate the residual stresses in MLCCs after the sintering process step 3. This method was chosen since it offers the possibility to measure stresses in brittle materials locally, with a spatial resolution of microns to tens of microns, unlike methods like x-ray diffraction that requires a much larger area to get practical results. The review paper by Malzbender et al. 4 gives an overview of indentation as a technique to measure mechanical properties. The principle of indentation is to press a sharp indenter into the material with a certain load P. The indenter is usually made of diamond. The geometry of the indenter is usually pyramidal, either with four faces Vickers indenter or with three faces cube corner or Berkovich indenter. When indenting a brittle material, like our MLCC ceramic, cracks will form in the indented material due to the large stresses caused by the indentation. Figure 2 shows so-called radial cracks that could occur during indentation with a Vickers indenter, along with a photograph of an actual indent in the MLCC ceramic material. Also, so-called lateral cracks may occur during indentation in a brittle material; these initiate under the tip and grow underneath and parallel to the surface of the material see Cook and Pharr 5. Here, we focus on the radial cracks. The length of the radial cracks indicated by the symbol c in Fig. 2 depends on both the material properties of the material, in particular, the fracture toughness K lc, and the internal stresses that are present in the surface. In particular, the following relation links the applied indentation load P to the length c of the cracks 3 : H E 1/2 P c 3/2 K lc r Yc 1/2. (1) E and H are Young s modulus and the hardness of the indented material, and r is the residual prestress in the surface. and Y are constants that depend on the indenter geometry. To calibrate these factors for our particular Vickers indenter, we carried out indentations on reference glass specimens with known fracture toughness. The residual stress in the glass was controlled by load- 506 Õ Vol. 125, DECEMBER 2003 Copyright 2003 by ASME Transactions of the ASME

2 Table 1 Geometry of the Y5VÕ1206Õ22 F MLCC Length mm 3.01 Width mm 1.60 Height mm 1.52 Thickness of nickel layer m 2 Thickness of barium titanate layer m 4 Cover layer thickness m 72 Number of layers 230 Width creepage path m 100 Length creepage path m 206 Fig. 1 Schematic drawing of a cross-sectioned MLCC ing the specimens in four-point bending during indentation. The parameters and Y were calibrated to be and This agrees quite well with the values and 1.26 quoted in the literature 3. The relation shows, that by carrying out indentations at various loads, measuring the crack lengths, and finally plotting (E/H) 1/2 Pc 3/2 against Yc 1/2, the fracture toughness and the stresses can be obtained by fitting to a straight line. The intercept with the vertical axis gives the fracture toughness, and the slope of the line corresponds to the stress. Under the assumption that the stress component parallel to a crack does not affect the growth of the crack, the stresses can be estimated in two perpendicular directions x and y, as indicated in the figure, because they are related to the two perpendicular directions of the cracks in case of the Vickers indenter. 2.2 Specimens and Measurement Procedure. The specimens were so-called Y5V/1206/22 F MLCCs taken out of the production process after the sintering process step. The end terminations see Fig. 1 are applied at a later process step, so we do not consider these, and the geometry is called a brick. The dielectric material is doped barium titanate, and the metal electrodes are of nickel. The thickness of the dielectric layers is 4 m, whereas the electrode thickness is 2 m. The component has a total number of 230 electrode layers. The outer layers, so-called cover layers, are thicker, i.e., 72 m. The overall length, thickness, and width are 3.01 mm, 1.52 mm, and 1.60 mm, respectively. These figures are summarized in Table 1. In this table, the length creepage path is the lengthwise distance from the ends of the electrodes to the side of the component indicated by the horizontal arrow in Fig. 1, and the width creepage path is equal to the distance between the ends of the electrodes and the side of the component in the width direction indicated by the vertical arrow in Fig. 1. The MLCC s were cross-sectioned, carefully polished, and glued onto sample plates to prevent them from sliding during indentation. The cross sections were made perpendicular to the electrodes, in the length direction, and halfway through the width. On these cross sections, ten Vickers indentations were set in the barium titanate cover layers at the points indicated in Fig. 3. Due to symmetry, it can be noted that there are only three different independent positions, indicated by 1,2,3. It was not possible to carry out any meaningful measurements in the middle part of the cross section, since there the metal electrodes interfered with the measurements. The indentation loads used were mn, mn, and mn. For each load and for each position, at least ten measurements were done to get a good statistical result. That means that we used at least ten different components per load all taken from the same batch and post-treated identically. The indentations were set with a Leitz-Miniload microhardness apparatus. The lengths of the cracks were measured with another Leitz microscope and attached image processing system. Next to the measurements on the cross sections, indentations were also set on the outer top side of the components, i.e., the outer sides parallel to the inner electrodes. It was necessary to first carefully polish the surface to get clearly visible cracks for small loads. It was checked that the polishing procedure had not influenced the results, which was confirmed for large loads. For low loads the cracks in the unpolished samples could not be made visible due to the effect of surface roughness. The positions at Fig. 2 Illustration of the plastic imprint and the radial cracks due to indentation with a Vickers indenter. Left: schematic view of the surface and of the cross section; right: micrograph of an actual Vickers indent in our MLCC ceramic. a is the half-diagonal of the plastic imprint, c is the radial crack length, and rx and ry are stresses in two orthogonal directions, perpendicular to the radial cracks. Journal of Electronic Packaging DECEMBER 2003, Vol. 125 Õ 507

3 Fig. 5 Quarter model of the MLCC, including definition of the coordinate axes Fig. 3 Fig. 4 Indentation positions on the cross-sectioned MLCC s MLCC s top face view, with nine indentations set which the top sides were indented are shown in Fig. 4. Here, loads of mn, 981 mn, and 1961 mn were used. Again, at least ten indentations on ten different, but identical specimens were made for each load and for each position. For indentations that are set close to the free edge of the components, the presence of the edge can influence the length of the radial cracks parallel to the edge and the inferred residual stress will be incorrect. We have attempted to correct for this effect by a method described in Ref. 6. However, due to uncertainties still present in the results after the correction procedure, we will not report these results here, and we will concentrate on data that are free from any errors due to a possible edge effect. The values that were used for Young s modulus E and the hardness H are GPa and 9 GPa, respectively. The first was found from nanoindentation see Ref. 7, and the second followed directly from the Vickers indentation results. 3 Description of the Numerical Model A three-dimensional 3D parametric model was made of the Y5V/1206/22 F MLCC brick in the finite element program AN- SYS 5.6. The exact geometry of the actual component has been described above in Sec To reduce the simulation effort it was assumed that the brick is symmetrical. Only a quarter of the entire component was therefore modeled see Fig. 5. The cooling down after sintering was simulated, so the end terminations see Fig. 1 were not part of the model. For the structural analysis the 20-node quadratic element SOLID95 was used 8. Implementing the model of the MLCC brought with it several problems. The main problem was that the number of nickel layers is so large 230 and the size of the layers is so thin 2 m that the required finite element model is too large in terms of elements over ) to be handled by the current computing infrastructure. Therefore several preliminary activities were undertaken to investigate the possibilities of using a simplified model that gives the same results. Thus several 2D simulations were carried out to investigate the influence of reducing the number of layers. Results from these preliminary simulations showed that it is indeed possible to get reasonable estimates of the residual stresses when simulating only 28 nickel layers, when both the nickel and the barium titanate layers are artificially thickened such that the volume fraction nickel/barium titanate is identical to the real case with 230 layers. Decreasing the number of layers below 28 turned out to give significant differences with the original 230-layer solution. Hence, the 28-layer model was considered to be a good compromise between accuracy of the results and the required computation time. The 28-layer model geometry is depicted in Fig. 5. We should note that we also attempted to use superelements, however this turned out to be unreliable mainly due to the fact that we had to deal with a combination of elastic barium titanate and elastoplastic nickel materials. As mentioned above, due to the differences in thermal expansion between nickel and barium titanate, residual stresses are introduced during the cooling down after sintering. In our simulations, we assume that this indeed is the main mechanism by which residual stresses come about. Also, we assume that during the cooling phase, the component will remain stress-free until a temperature of 700 C is reached. Above this temperature, plastic flow of the nickel layers is assumed to be responsible for relaxation of all stresses. Since in reality the cooling down is a relatively slow process, which takes hours, we use a steady state analysis. Symmetry boundary conditions are prescribed on the plane of symmetry x 0 no displacements along the x direction and on the plane of symmetry z 0 no displacements along the z direction. One node needs to be fixed in the y direction to constrain rigid body motion. The node in the middle of the component is chosen for this purpose. The temperature-dependent material properties of the nickel and the barium titanate are necessary input for the numerical simulations. For nickel we used a bilinear elastoplastic model; the barium titanate was modeled as a perfectly elastic material. We used temperature-dependent properties. The properties were either measured or looked up in the standard handbooks of Gmelin 9 or Landolt and Bornstein 10. Some selected properties at room temperature are listed in Table 2; the temperature dependence of the properties is not reported in the present paper in view of space limitations. We should note that we used bulk properties; it is known that thin-film properties may deviate from bulk values see, for example, Ref. 11 ; therefore this approximation may lead to deviations in the numerical results. 4 Results and Discussion 4.1 Experiments. A typical plot obtained from the indentation experiments is shown in Fig. 6, in which the data are plotted according to the scaling suggested by Eq. 1. The data points are averages over ten measurements. The two straight lines are fits to 508 Õ Vol. 125, DECEMBER 2003 Transactions of the ASME

4 Table 2 Selected material properties: Young s modulus E, thermal expansion coefficient, thermal conductivity, specific heat C p, density, and yield stress Y. All values are valid at room temperature, except for, which is an average over the simulated temperature range. In the computations, temperature-dependent properties were used. Barium titanate Nickel Property Source Property Source E GPa Nanoindentation/ E 200 GPa Pulse excitation pulse excitation /K Dilatometer /K Refs. 9 and W/mK Ref W/mK Ref. 9 C p 0.43 J/gK Differential C p 0.46 J/gK Ref. 9 scanning calorimetry 5800 kg/m 3 Weighing 8700 kg/m 3 Weighing Y 230 MPa Microindentation the measurement data, and they correspond to the two orthogonal directions of the radial cracks and hence the residual stresses. The fracture toughness of the barium titanate and the residual stress in the barium titanate layers can be deduced from the figure as explained in Sec A closer look at Fig. 6 shows that the error in estimating the slope is rather large, which leads to a significant error in the estimated residual stress. From a statistical analysis, we found that the measurement uncertainty can be as large as 50%. From an average over all the experiments, a fracture toughness of 0.91 MPa m was found. As an aside, we should note that the fracture toughness was also determined independently on a monolithic sample of the same barium titanate, processed in the same way as the components, and led to the same value. The measured residual stress in the components for the positions indicated in Figs. 3 and 4 are given in Table 3. Note, that the x direction is horizontal in both Figs. 3 and 4, whereas the z direction is vertical in Fig. 4. Hence, all stress values shown in the table refer to directions parallel to the electrode layers see also Fig. 5. From these results, we note that the in-plane stresses in the barium titanate layers are negative, hence compressive, in general. This was to be expected: due to the higher thermal expansion coefficient of nickel as compared to barium titanate, the nickel electrodes will attempt to contract to a larger extent than the barium titanate layers, leading to a tensile stress in the nickel layers and a compressive stress in the barium titanate layers. A small tensile value for x is found at position cross section 3. The results will be discussed further in the next section. 4.2 Simulations. The computed stress x in the symmetry plane z 0 after the cooling down simulation is shown in Fig. 7. A compressive stress appears in the ceramic parts, whereas the Fig. 6 A typical indentation plot obtained from the experiments Table 3 Measured residual stresses in MLCC s at positions given in Figs. 3 and 4 Position x MPa z MPa Cross section Fig Outer top surface Fig Journal of Electronic Packaging DECEMBER 2003, Vol. 125 Õ 509

5 Fig. 7 Left: Computed stress x after cooling down; only a quarter of the brick is shown see Fig. 5. Right: path plot of the computed stress component x along the path indicated in the left figure; the path traces the measurement points on the cross section. metal electrodes are in tension. This is the expected behavior, as discussed in the preceding section. The results show furthermore that the stresses become so high that the nickel electrodes deform plastically. To be able to compare with the experiments, we selected in the numerical model those positions corresponding to the measurement positions in Figs. 3 and 4. The computed residual stresses are compared to the measured ones in Table 4. The results for the outer top surface show reasonable agreement between experiment and simulation. All measured and computed stresses are compressive; they have the same order of magnitude, and they show the same trend. The measurements carried out on the cross section show larger deviations. In particular, the measured compressive stress at cross-section point 1 seems to be rather low, especially when this value is compared to that measured on the top surface at point 1. This discrepancy may be due to a partial relaxation of stresses caused by the process of crosssectioning the specimens. More worrisome, however, is the significant difference between experiment and simulation at points 2 and 3 of the cross section: whereas the simulation gives significant compressive stresses, in the measurements we find negligible or even slightly tensile stresses. The differences may be caused by several possible reasons. First, the numerical simulation results show that around position 2 of the cross section, a large stress gradient exists see Fig. 7. Hence, a small mismatch between the exact position in the experimental and the numerical analysis can lead to large differences. Second, in the simulation we assume that the geometry of the corner, i.e., the region close to point 3 of the cross section, is a perfectly rounded angle. In the real components, however, this corner often has a quite irregular shape. This difference in geometry could have led to the differences in stress values observed for point 3 of the cross section. Third, the differences could be due to the input parameters in the finite element model; for one thing, we assumed bulk properties to be valid for the thin nickel films, which may be incorrect. Finally, the cross-sectioning procedure could introduce or relax stresses in the components. In conclusion, the agreement between the residual stresses obtained from experiment and simulation is reasonable for the uncross-sectioned components. This gives some confidence in the validity of the finite element model. Some discrepancies do exist, though, for measurements on cross-sectioned MLCC s for several possible reasons, as explained above. 5 Conclusions In this paper, we have presented a combined experimental and computational study of the thermomechanical reliability of multilayer ceramic capacitors MLCC s. We focused on residual stresses introduced into the components during the sintering process step; these were measured with microindentation, as well as computed by three-dimensional finite element simulations. The main conclusions are as follows. Microindentation is a useful method to assess local stresses in microelectronic components. After the cooling down step, a compressive stress exists in the ceramic barium titanate layers in the plane of the layers, and a tensile stress exists in the metal nickel layers. There is reasonably good overall agreement between the residual stresses obtained from the indentation experiments and the numerical simulations for un-cross-sectioned components. Differences found between the results, particularly for cross-sectioned components, can be attributed to assumptions made in the numerical simulations, to the presence of large stress gradients that make the measurement less reliable, or a possible influence of the cross-sectioning procedure on the stress state. Acknowledgments We thank L.Y. Yi Phycomp, Taiwan and S. Oostra Phycomp, Netherlands for preparation of the specimens; A. van Leijsen Philips CIT, N. Fonteneau INSA, Lyon, G. Ebrard INSA, Lyon, and V. Leger INSA, Lyon are acknowledged for carrying out measurements and computations. Table 4 Measured and simulated stresses after cooling down, in MPa Point Stress MPa Measurement Simulation Cross section 1 x x x Outer top surface 1 x z z x x Õ Vol. 125, DECEMBER 2003 Transactions of the ASME

6 References 1 de With, G., 1993, Structural Integrity of Ceramic Multilayer Capacitor Materials and Ceramic Multilayer Capacitors, J. Eur. Ceram. Soc., 12, pp Buchanan, R. C., 1986, Ceramic Materials for Electronics. Processing, Properties and Applications, Marcel Dekker. 3 Marshall, D. B., and Lawn, B. R., 1977, J. Am. Ceram. Soc., 60, p Malzbender, J., den Toonder, J. M. J., Balkenende, A. R., and de With, G., 2002, Measuring Mechanical Properties of Coatings: A Methodology Applied to Nano-particle Filled Sol-Gel Coating on Glass, Mater. Sci. Eng., R., 36, pp Cook, R. F., and Pharr, G. M., 1990, J. Am. Ceram. Soc., 73, p Fonteneau, N., 2000, Determination of Stresses in Multilayer Ceramic Capacitors with Indentation, Philips Nat. Lab. Report No. 819/00 available from the present authors. 7 Oliver, W. C., and Pharr, G. M., 1992, J. Mater. Res., 7, p ANSYS user s manual. 9 Gmelin, 1990, Handbook of Inorganic and Organometallic Chemistry, Handbook Series, Volume VI AII, Springer, Berlin. 10 Landolt-Bornstein, 1990, Numerical Data and Functional Relationships in Science and Technology, Handbook Series, Volume III, Springer, Berlin. 11 Nix, W. D., 1989, Mechanical Properties of Thin Films, Metall. Trans. A, 20A, pp Kollie, T. G., 1977, Measurement of the Thermal-Expansion Coefficient of Nickel from 300 to 1000 K and Determination of the Power-Law Constant near the Curie Temperature, Phys. Rev., 16, pp Journal of Electronic Packaging DECEMBER 2003, Vol. 125 Õ 511

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