Modelling and numerical simulation of the electrical, mechanical, and thermal coupled behaviour of Multilayer capacitors (MLCs)

Prume, K.; Franken, Klaus; Böttger, U.; Waser, Rainer; Maier, Henning

doi:10.1016/s0955-2219(01)00439-3

Cited by 30 publications

(51 citation statements)

References 11 publications

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“…Therefore, the reason why the measured values ͑−30 to −60 MPa͒ in Ref. 10 was far lower than the predicted values in the current work may result from the fact that the thicker dielectric layer in Ref. 10 received less thermal contraction stress from nickel electrode during cooling.…”

Section: Comparison With Experimentscontrasting

confidence: 52%

“…Thus, FEM has been widely used to analyze the stress state in many nano- 9 and microstructures including MLCCs. [10][11][12][13] It has thus been adopted herein to elucidate the physical origin of the evolution of residual stresses in a MLCC and the numerical result has been compared with some experimental data in the literature. Figure 1 shows the considered geometry of a MLCC as well as a one-eighth space of the three-dimensional ͑3D͒ geometry that was modeled with appropriate boundary conditions to reduce computational load.…”

Section: Physical Origin Of Residual Thermal Stresses In a Multilayermentioning

confidence: 99%

“…10,11 of a number of specimens were measured by x-ray and the values were in the range of −30 to −60 MPa depending on the type of specimens. Although the thicknesses of nickel electrode and dielectric layer were not specified explicitly, based on Ref.…”

Section: Comparison With Experimentsmentioning

confidence: 99%

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Physical origin of residual thermal stresses in a multilayer ceramic capacitor

Shin

Park

Hong

et al. 2007

Journal of Applied Physics

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Residual stress evolution in multilayer ceramic capacitors corresponding to layer increase and its correlation to the dielectric constant J. Appl. Phys. 97, 094504 (2005) The physical origin of the residual stresses developed in the ceramic layer of the active region in a multilayer ceramic capacitor was numerically investigated. The compressive in-plane stress components 11 and 22 originate without regard to the presence of the margins but rather from the difference in in-plane thermal shrinkage between ceramic and metal electrode. The out-of-plane stress component 33 physically originates mainly through the presence of the housing margin; the presence of the lateral margin is a minor source: the more ceramic-rich margins hinder the apparent vertical shrinkage of the active region to yield tensile 33 .

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Section: Comparison With Experimentscontrasting

confidence: 52%

Section: Physical Origin Of Residual Thermal Stresses In a Multilayermentioning

confidence: 99%

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Physical origin of residual thermal stresses in a multilayer ceramic capacitor

Shin

Park

Hong

et al. 2007

Journal of Applied Physics

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“…Franken et al [5] and Prume et al [7] presented a 2D plane-stress finite element (FE) model to simulate the behavior of MLCCs and predict their reliability during soldering and bending. Shin et al [8] calculated the residual stresses in the active region of a MLCC based on 2D plane-strain assumption.…”

Section: Fig 1 Schematic Structure Of a Mlcc And (B) Its Unit Cell mentioning

confidence: 99%

Size Dependence of Residual Thermal Stresses in Micro Multilayer Ceramic Capacitors by Using Finite Element Unit Cell Model Including Strain Gradient Effect

2013

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Abstract. The residual thermal stresses induced by the high-temperature sintering process in multilayer ceramic capacitors (MLCCs) are investigated by using a finite element unit cell model, in which the strain gradient effect is considered. The numerical results show that the residual thermal stresses depend on the lateral margin length, the thickness ratio of the dielectrics layer to the electrode layer, and the MLCC size. At a given thickness ratio, as the MLCC size is scaled down, the peak shear stress reduces significantly and the normal stresses along the length and thickness directions change slightly with the decrease in the ceramic layer thickness t d as t d >1 μm, but as t d <1 μm, the normal stress components increase sharply with the increase in t d . Thus, the residual thermal stresses induced by the sintering process exhibit strong size effects and, therefore, the strain gradient effect should be taken into account in the design and evaluation of MLCC devices.

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“…Some recent work has been directed towards investigation on the residual stress states in MLCCs [6][7][8][9][10][11][12][13]. For example, Nakano et al [6] measured the residual stress in MLCCs by X-ray diffraction (XRD) analysis and found that the stress increases as the number of the dielectric ceramic layers increases.…”

Section: Introductionmentioning

confidence: 99%