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Prediction of microelectronic substrate warpage using homogenized finite element models

机译:均质化有限元模型预测微电子基板的翘曲

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The focus of this study was to numerically predict effective thermo-mechanical properties and substrate warpage of high-density microelectronic substrates used in organic CPU packages. Microelectronic substrates are typically composed of several polymer, fiber-weave, and copier layers and are filled with a variety of complex features, such as electric traces, plated-through-holes, micro-vias, and adhesion holes. When subjected to temperature changes, these substrates may warp, driven by the mismatch in coefficients of thermal expansion (CTE) of the constituent materials. This study focused on predicting substrate warpage in an isothermal condition. The numerical approach consisted of three major tasks: estimating homogenized (effective) thermo-mechanical properties of the features; calculating effective properties of discretized layers using the effective properties of the features; and assembling the layers to create two-dimensional (2D) finite element (FE) plate models and to calculate warpage of the substrates. The effective properties of the features were extracted from three-dimensional (3D) unit cell FE models, and closed-form approximate expressions were developed using the numerical results, curve fitting, and some simple bounds. The numerical approach was applied to predict warpage of production substrates, analyzed, and validated against experimentally measured stiffness and CTEs. In this paper, the homogenization approach, numerical predictions, and experimental validation are discussed.
机译:这项研究的重点是在数值上预测有机​​CPU封装中使用的高密度微电子基板的有效热机械性能和基板翘曲。微电子基板通常由几个聚合物,纤维编织层和复印机层组成,并填充有各种复杂的特征,例如电迹线,镀通孔,微通孔和粘合孔。当经受温度变化时,这些基板可能会由于构成材料的热膨胀系数(CTE)不匹配而翘曲。这项研究专注于预测等温条件下的基板翘曲。数值方法包括三个主要任务:估计特征的均质(有效)热机械特性;使用特征的有效属性计算离散层的有效属性;组装这些层以创建二维(2D)有限元(FE)板模型并计算基板的翘曲。从三维(3D)晶胞有限元模型中提取了特征的有效属性,并使用数值结果,曲线拟合和一些简单的边界开发了闭合形式的近似表达式。数值方法被用于预测生产基板的翘曲,进行了分析,并针对实验测量的刚度和CTE进行了验证。本文讨论了均质化方法,数值预测和实验验证。

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