積層陶瓷電容器經過繁複的製程，可能導致結構內部產生變形及內部缺陷，進而造成其應用功能異常。本研究主要針對由近百層的鈦酸鋇與鎳電極薄膜經交錯堆疊後所製成的積層板，於高壓及高溫的層壓(Lamination)製程後所產生的變形及應力變化加以分析討論。首先利用奈米壓痕實驗來得到薄膜（陶瓷與電極）的機械性質，並提供給後續的理論與數值模擬分析使用。接著觀察鈦酸鋇陶瓷與鎳電極薄膜，於4種不同溫度及持溫時間的條件作用下，其表面微結構的變化情形，結果顯示薄膜表面並無明顯的相變化情形產生。
理論分析採用古典積層板理論配合線彈性假設與平衡方程式，依據實際的製程狀況使用三種邊界條件，分別為四邊簡支撐、兩對邊簡支撐，其他邊自由及四邊自由，另外再加上四邊角固定及底部為一彈性支撐等條件，依照上述的假設及邊界條件來進行理論分析。接著利用以有限元素法為基礎所發展的模擬軟體ANSYS來進行數值模擬分析，進而得到積層陶瓷電容器的變形與應力場來驗證理論預測的結果。經由理論分析與模擬分析的結果比較，以邊界條件為四邊自由及角點固定的誤差0.1~6.2％為最佳，而邊界條件為兩對邊簡支撐，其他邊自由時其誤差0.13~6.15％尚可接受，而邊界條件為四邊簡支撐時其誤差太大。藉由所採用的理論分析方法在不採用商用數值模擬分析軟體時，可提供另一種選擇來分析近百層的積層陶瓷電容器。
積層陶瓷電容器是由多層介電與內電極薄膜經交錯堆疊後所壓製而成，基於上述的理由，探討薄膜承受拉力作用時的變形是迫切需要的。而陶瓷多層結構製程中薄帶成型(Tape Casting)製程是另一個重要的步驟。於薄帶成型製程中，薄膜受拉力作用時所產生的皺摺可能導致積層陶瓷電容器的陶瓷積層板表面形成厚度不均的現象進而產生缺陷，故針對薄膜受拉力作用時所產生的皺摺現象來加以探討。採用微拉力實驗分別對4種厚度(25、38、50及75 μm)的薄膜進行一系列幾何尺寸(例如：長寬比)與皺摺有關的結構穩定測試，並藉由類靜態拉伸的過程，來測量拉伸過程中薄膜所對應的皺摺臨界拉力值，藉此瞭解薄膜承受拉力作用時，因不同物理參數的總合影響所造成的薄膜皺摺現象。

The manufacturing process may cause the deformation and internal defects in multi-layered ceramic capacitors (MLCCs) that results in the malfunction for applications. This work aims to investigate the deformation of MLCCs that composed of nearly a hundred of BaTiO3 and Ni electrode films interleaved and stacked due to high pressure at elevated temperature. Nanoindentation tests were performed to measure the moduli of both ceramic and electrode films for theoretical analysis and numerical simulation. Then, the thin films of BaTiO3 ceramic and Ni electrode were tested under four conditions combined with temperature and duration time first to assure that almost no phase changes were found according to the evaluation of microstructure by SEM.
On theoretical analysis, classical laminated plate theory, linear elastic assumptions and equilibrium equations were adopted. Associated with the practical process three types of boundary conditions (BCs) were used, such as all edges simply-supported, two edges simply-supported and the other two free, and four edges free. Also, two more conditions need be added, including four fixed points at corners and the elastic foundation at bottom. As for the numerical simulation the finite element method (FEM) incorporated with software ANSYS was used to obtain the displacement field of MLCCs to validate the analytical prediction. Compared with the numerical results the analytical solutions were found satisfactorily acceptable, i.e., the errors were about 0.1%- 6.2% for the BCs of four edges free and four corners fixed. The errors about 0.13%- 6.15% were also acceptable for the BCs of two edges simply-supported and the others free. However, the analytical solution for the case of all the edges simple-supported did not agree well with the numerical results. Finally, the achieved analytical methodology offers another choice of handling MLCCs theoretically without using the numerical simulation methods incorporated with commercial softwares, such as FEM and ANSYS, to analyze a nearly and over hundred layered MLCCs.
The MLCCs is composed of a multi-layered ceramic capacitors stacked alternately by dielectric layers and internal electrode layers due to compression. As above mentioned works, it was importantly urgent to realize the deflections of thin films due to in-plane tension for commonly used membrane. Tape casting is another important processing step in the manufacturing of ceramic multilayer devices. The tape casting manufacturing process may cause the defects on non-uniform surface of green sheets for MLCCs by wrinkling thin film due to extension. The important phenomenon of wrinkling in rectangular thin films cause by extension is presented. A series of micro-tensile tests was carried out on thin films in 4 different thickness (25, 38, 50 and 75 μm) in order to investigate the effect of film dimension (i.e., length/width ratio) on the structural instability in terms of the wrinkling onset; and a series of measurements of the quasi-static tensile process were performed on each film at several desired load levels. Our primary interest has been in understanding how various combinations of physical parameters influence the wrinkled response of the thin film to tensile loads.

中文摘要 i
ABSTRACT ii
CONTENTS iv
LIST OF FIGURES vi
LIST OF TABLES ix
NOMENCLATURE xi
Chapter 1 Introduction 1
1.1 Background 1
1.1.1 Current Trends in Multi-Layered Ceramic Capacitors 1
1.1.2 Wrinkling of Thin Film 5
1.2 Motivation and Achievement 7
1.3 Scope and Layout 9
Chapter 2 Experiments 13
2.1 Microstructure and Mechanical Properties of MLCCs 13
2.1.1 Introduction 13
2.1.2 Basic formulation 14
2.1.3 Sample preparation 17
2.1.4 Sample microstructure 18
2.1.5 Nanoindentation test 18
2.1.6 Results 19
2.2 Wrinkling test 20
2.2.1 Film Material 20
2.2.2 Equipment Setup and Holder Frame Design 20
2.2.3 Experimental Procedure 22
2.2.4 Results 23
Chapter 3 Theoretical Formulation 54
3.1 Classical Lamination Theory 54
3.2 Rectangular Plate on Elastic Foundation 62
3.2.1 All edges simply-supported 63
3.2.2 Two opposite edges simply-supported and the other two free 64
3.2.3 Four edges free and four corners fixed 66
3.3 Results 69
Chapter 4 Numerical Simulation 75
4.1 Introduction 75
4.2 Simulation Procedure 76
4.3 Results 78
Chapter 5 Discussion 99
5.1 Deformation and Stress of MLCCs 99
5.2 Wrinkling of Thin Film 101
Chapter 6 Conclusion 107
6.1 Multi-Layered Ceramic Capacitors 107
6.2 Wrinkling of Thin Film 108
REFERENCES 110

[1] Y. Sakabe, Multilayer ceramic capacitors, Current Opinion in Solid State and Materials Science, vol. 2, pp. 584-587, 1997.
[2] W. G. Jiang, X. Q. Feng, C. Nan, A three-dimensional theoretical model for estimating the thermal residual stresses in micro multilayer ceramic capacitors, Composites Science and Technology, vol. 68, pp. 692-698, 2008.
[3] P. Ren, H. Fan, X. Wang, J. Shi, Effects of silver addition on microstructure and electrical properties of barium titanate ceramics, Journal of Alloys and Compounds, vol. 509, pp. 6423-6426, 2011.
[4] V. P. Pavlović, J. Krstić, M. J. Šćepanović, J. Dojčilović, D. M. Minić, J. Blanuša, S. Stevanović, V. Mitić, V. B. Pavlović, Structural investigation of mechanically activated nanocrystalline BaTiO3 powders, Ceramics International, vol. 37, pp. 2513-2518, 2011.
[5] R. Z. Zuo, L. T. Li, N. X. Zhang, Z. L. Gui, Interfacial reaction of Ag/Pd metals with Pb-based relaxor ferroelectrics including additives, Ceramics International, vol. 27, pp. 85-89, 2001.
[6] R. Z. Zuo, L. T. Li, Z. L. Gui, Relationships between interfacial interaction, electrode formulation and cofiring mismatch of relaxor-based multilayer ceramic devices, Journal Materials Science: Materials in Electronics, vol. 12, pp. 117-121, 2001.
[7] R. Z. Zuo, L. T. Li, Z. L. Gui, Interfacial development and microstructural imperfection of multilayer ceramic chips with Ag/Pd electrodes, Ceramics International, vol. 27, pp. 889-893, 2001.
[8] J. Wang, S. Jiang, D. Jiang, J. Tian, Y. Li, Y. Wang, Microstructural design of BaTiO3-based ceramics for temperature-stable multilayer ceramic capacitors, Ceramics International, vol. 38, pp. 5853-5857, 2012.
[9] F. He, W. Ren, G. Liang, P. Shi, X. Wu, X. Chen, Structure and dielectric properties of barium titanate thin films for capacitor applications, Ceramics International, vol. 39, pp. S481-S485, 2013.
[10] F. Wang, Y. Wang, Development and Utilization of Integral Thin Film Capacitors, Procedia Environmental Sciences, vol. 18, pp. 871-874, 2013.
[11] Y. Nakano, T. Nomura, T. Takenaka, Residual stress of multilayer ceramic capacitors with Ni-electrodes (Ni-MLCCs), Japanese Journal of Applied Physics, vol. 42, pp. 6041-6044, 2003.
[12] K. Saito, H. Chazono, Stress and electric field responses of X5R type multilayer ceramic capacitor with Ni internal electrode, Japanese Journal of Applied Physics, vol. 42, pp. 6045-6049, 2003.
[13] K. Franken, H. R. Maier, K. Prume, R. Waser, Finite-element analysis of ceramic multilayer capacitors: failure probability caused by wave soldering and bending loads, Journal American Ceramic Society, vol. 83, pp. 1433-1440, 2000.
[14] K. Prume, K. Franken, U. Bottger, R. Waser, Modeling and numerical simulation of the electrical, mechanical, and thermal coupled behavior of multilayer capacitors (MLCs), Journal European Ceramic Society, vol. 22, pp. 1285-1296, 2002.
[15] H. Shin, J. S. Jung, K. S. Hong, Investigation of useful or deleterious residual thermal stress component to the capacitance of a multilayer ceramic capacitor, Microelectronic engineering, vol. 77, pp. 270-276, 2005.
[16] J. S. Park, S. Kim, H. Shin, H. S. Jung, K. S. Hong, Residual stress evolution in multilayer ceramic capacitors corresponding to layer increase and its correlation to the dielectric constant, Journal Applied Physics, vol. 97, 094504, 2005.
[17] H. Shin, J. S. Park, K. S. Hong, H. S. Jung, J. K. Lee, K. Y. Rhee, Physical origin of residual thermal stresses in a multilayer ceramic capacitor, Journal Applied Physics. vol. 101, 063527, 2007.
[18] Y. I. Shin, K. M. Kang, Y. G. Jung, J. G. Yeo, S. G. Lee, U. Paik, Internal Stresses in BaTiO3/Ni MLCCs, Journal European Ceramic Society, vol. 23, pp. 1427-1434, 2003.
[19] S. G. Lee, U. Paik, Y. I. Shin, J. W. Kim, Y. G. Jung, Control of residual stresses with post process in BaTiO3-based Ni-MLCCs, Materials & Design, vol. 24, pp. 69-176, 2003.
[20] D. Zhou, L.-X. Pang, J. Guo, G.-Q. Zhang, Y. Wu, H. Wang, X. Yao, Low temperature firing microwave dielectric ceramics (K0.5Ln0.5)MoO4 (Ln = Nd and Sm) with low dielectric loss, Journal of the European Ceramic Society, vol. 31, pp. 2749-2752, 2011.
[21] R. Schmidt, M. C. Stennett, N. C. Hyatt, J. Pokorny, P.-G. Jesús, M. Li, D. C. Sinclair, Effects of sintering temperature on the internal barrier layer capacitor (IBLC) structure in CaCu3Ti4O12 (CCTO) ceramics, Journal of the European Ceramic Society, vol. 32, pp. 3313-3323, 2012.
[22] Y.-C. Lee, Y.-Y. Yeh, P.-R. Tsai, Effect of microwave sintering on the microstructure and electric properties of (Zn,Mg)TiO3-based multilayer ceramic capacitors, Journal of the European Ceramic Society, vol. 32, pp. 1725-1732, 2012.
[23] Y.-R. Zhang, T. Motohashi, Y. Masubuchi, S. Kikkawa, Sintering and dielectric properties of perovskite SrTaO2N ceramics, Journal of the European Ceramic Society, vol. 32, pp. 1269-1274, 2012.
[24] L. Li, R. Fu, Q. Liao, L. Ji, Doping behaviors of NiO and Nb2O5 in BaTiO3 and dielectric properties of BaTiO3-based X7R ceramics, Ceramics International, vol. 38, pp. 1915-1920, 2012.
[25] S.-H. Kweon, M. Im, G. Han, J.-S. Kim, S. Nahm, J.-W. Choi, S.-J. Hwang, Sintering behavior and dielectric properties of KCa2Nb3O10 ceramics, Journal of the European Ceramic Society, vol. 33, pp. 907-911, 2013.
[26] B. Bhushan, G. B. Agrawal, Stress analysis of nanostructures using a finite element method, Nanotechnology, vol. 13, pp. 515-523, 2002.
[27] D. W. Kim, J. H. Kang, S. H. Park, H. C. Kim, Y. G. Jung, Crack formation in MLCCs depending on position with and without post-heat treatment, Journal Electroceramics., vol. 17, pp. 381-385, 2006.
[28] Z. Zhang, J. Kan, G. Cheng, Y. Jia, H. Wang, Influence of multiple piezoelectric effects on sensors and actuators, Mechanical Systems and Signal Processing, vol. 35, pp. 95-107, 2013.
[29] D. Jurków, L. Golonka, Low-pressure, thermo-compressive lamination, Journal of the European Ceramic Society, vol. 32, pp. 2431–2441, 2012.
[30] M. A. Piwonski, A. Roosen, Low Pressure Lamination of Ceramic Green, Journal of the European Ceramic Society, vol. 19, pp. 263-270, 1999.
[31] A. Roosen, Ceramic Substratest: Tends in Materials and Application, Ceramic Transactions, vol. 106, pp. 479-492, 2000.
[32] F. Li, C. M. Wang, K. A. Hu, Optimization of non-aqueous nickel slips for manufacture of MCFC electrodes by tape casting method, Materials Research Bulletin, vol. 37, pp. 1907-1921, 2002.
[33] R. E. Mistler, E. R. Twiname, Tape Casting, American Ceramic Society, Westerville, 2000.
[34] F. Naruse, N. Tada, Deformation Behavior of Multilayered Ceramic Sheets with Printed Electrodes under Compression, Journal of Solid Mechanics and Materials Engineering, vol. 6, pp. 760-770, 2012.
[35] S. Timoshenko, S. Woinowsky-Krieger, Theory of plates and shells, 2nd Edition, pp. 259-281, McGraw-Hill, Incorporation, New York, 1959.
[36] O. Adewale, Application of the singularity function method to semi-infinite orthotropic rectangular plates on an elastic foundation, Mechanical Sciences, vol. 43, pp. 2261-2279, 2001.
[37] J. S. Arul, C. V. Vaidyanathan, Post critical behaviour of biaxially compressed plates on elastic foundation, Computer & Structures, vol. 54, pp. 239-246, 1995.
[38] H. S. Shen, Postbuckling of shear deformable laminated plates under biaxial compression and lateral pressure and resting on elastic foundations, Mechanical Sciences, vol. 42, pp. 1171-1195, 2000.
[39] T. Horibe, N. Asano, Large Deflection Analysis of Rectangular Plates on Two-parameter Elastic Foundation by the Boundary Strip Method, JSME International Journal Series A, vol. 44, pp. 483-489, 2001.
[40] L. Lanzoni, Analysis of stress singularities in thin coatings bonded to a semi-infinite elastic substrate, International Journal of Solids and Structures, vol. 48, pp. 1915-1926, 2011.
[41] A. M. Zenkour, A. F. Radwan, On the simple and mixed first-order theories for functionally graded plates resting on elastic foundations, Meccanica, vol. 48, pp. 1501-1516, 2012.
[42] J. Bocko, V. Nohajová, T. Harčarik, Symmetries of Differential Equations Describing Beams and Plates on Elastic Foundations. Procedia Engineering, vol. 48, pp. 40-45, 2012.
[43] J. L. Bucaille, S. Stauss, Pa Schwaller, J. Michler, A new technique to determine the elastoplastic properties of thin metallic films using sharp indenters, Thin Solid Films, vol. 44, pp. 239-245, 2004.
[44] G. M. Pharr, W. C. Oliver, F. R. Brotzen, On the generality of the relationship among contact stiffness, contact area, and elastic modulus during indentation, Journal Materials Research, vol. 7, NO. 613, 1992.
[45] M. Zhao, Y. Xiang, J. Xu, N. Ogasawara, N. Chiba, X. Chen, Determining mechanical properties of thin films from the loading curve of nanoindentation testing, Thin Solid Films, vol. 516, pp. 7571-7580, 2008.
[46] K. C. Tang, R. D. Arnell, Determination of coating mechanical properties using spherical indenters, Thin Solid Films, vol. 355-356, pp. 263-269, 1999.
[47] N. K. Chang, Y. S. Lin, C. Y. Chen, S. H. Chang, Size effect of indenter on determining modulus of nanowires using nanoindentation technique, Thin Solid Films, vol. 517, pp. 3695-3697, 2009.
[48] T. Y. Huang, Finite Element Analysis on MLCC BME Processes, Master Thesis, National Sun Yat-Sen University, Kaohsiung, Taiwan, 2009.
[49] P. L. Guo, Analysis on the Deflection of Multilayered Ceramic Capacitors under High Temperature and Uniform Pressure, Master Thesis, National Sun Yat-Sen University, Kaohsiung, Taiwan, 2011.
[50] H. L. Hu, Reliability of Evaluation and Failure Analysis for Multilayer Ceramic Capacitors (MLCCs). Master Thesis, National Cheng Kung University, Taiwan, 2006.
[51] E. Zahavi, The Finite Element Method in Machine Design, International Editions, pp. 47-51, Prentice Hall, Englewood Cliffs, 1992.
[52] Swanson Analysis System, Inc., ANSYS User’s Manual for Revision 5.0, vol. I Procedures, pp. 11-7-11-22, 1992.
[53] R. F. Gibson, Principles of Composite Material Mechanics, International Editions, McGraw-Hill, New York, 1994.
[54] H. Wagner, Flat sheet metal girder with very thin metal web. Part: I-III, Zeitschrift für Flugtechnik Motorluftschiffahrt, pp. 20, 200-207, 227-233, 256-262, 279-284, 1929.
[55] M. Stein, J. M. Hedgepeth, Analysis of partly wrinkled membranes, NASA Langley Research Center, NASA TN D-813, 1961.
[56] M. M. Mikulas, Behavior of a flat stretched membrane wrinkled by the rotation of an attached hub, NASA TN D-2456, 1964.
[57] E. H. Mansfield, Load transfer via a wrinkled membrane, Proceedings of the Royal Society of London Part A, vol. 316, pp. 269-289, 1970.
[58] C. H. Jenkins, F. Haugen, W. H. Spicher, Experimental measurement of wrinkling in membranes undergoing planar deformation, Experimental Mechanics, vol. 38, 147-152, 1998.
[59] J. R. Blandino, J. D. Johnston, J. J. Miles, J. S. Soplop, “Thin film membrane wrinkling due to mechanical and thermal loads, Proceedings of 42th AIAA/ASME/ASCE/AHS/ASC Structures, Structural Dynamics and Material Conference and Exhibit. AIAA-2001-1345, 2001.
[60] J. R. Blandino, J. D. Johnston, U. K. Dharamsi, Corner wrinkling of a square membrane due to symmetric mechanical loads, Journal of Spacecraft and Rockets, vol. 39, pp. 717-724, 2002.
[61] R. S. Pappa, J. T. Black, J. R. Blandino, T. W. Jones, P. M. Danehy, A. A. Dorrington, Dot-Projection Photogrammetry and Videogrammetry of Gossamer Space Structures, NASA/TM-2003-212146, 2003.
[62] T. W. Murphey, A nonlinear elastic constitutive model for wrinkled thin films, Doctoral Dissertation, Department of Mechanical Engineering, University of Colorado at Boulder, 2000.
[63] A. Papa, S. Pellegrino, Systematically Creased Thin-Film Membrane Structures, Journal of Spacecraft and Rockets, vol. 45, pp. 10-18, 2008.
[64] Y. W. Wong, S. Pellegrino, Wrinkled membranes I: experiments, Journal of Mechanics of Materials and Structures, vol. 1, pp. 2-23, 2006.
[65] C. G. Wang, X. W. Du, H. F. Tan, X. D. He, A new computational method for wrinkling analysis of gossamer space structures, International Journal of Solids and Structures, vol. 46(6), pp. 1516-1526, 2009.
[66] L. Zheng, Wrinkling of Dielectric Elastomer Membranes, Doctoral Dissertation, California Institute of Technology, 2009.
[67] Y. Lecieux, R. Bouzidi, Experimental analysis on membrane wrinkling under biaxial load-Comparison with bifurcation analysis, International Journal of Solids and Structures, vol. 47(18-19), pp. 2459-2475, 2010.
[68] ASTM D882-10, Annual book of ASTM standards. Philadelphia, PA: American Society for Testing & Materials, 2010.