Thermomigration in Sn‐Pb solder bumps: Modelling and simulation
Thermomigration in Sn‐Pb solder bumps: Modelling and simulation
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SnâPb 焊料凸块中的热迁移：建模和仿真
DOI：
10.1002/pamm.201610230
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发表时间：
2016
期刊：
影响因子：
--
通讯作者：
K. Weinberg
中科院分区：
文献类型：
--
作者：
S. Schuß;C. Hesch;K. Weinberg
众所周知，均相二元合金在温度梯度作用下会变得不均匀。这种分解现象被称为热迁移或热输运或索雷特效应，它是热传导和原子扩散之间不可逆过程中的交叉效应。为了描述焦耳加热引起的热迁移效应，我们重点研究了受温度梯度影响的分离过程的扩散界面模型，并结合了热扩散方程。具体地说，我们关注锡和铅组成的焊料凸起中的相分离。因此，我们讨论了吉布斯构型自由能密度的建模，以及化学迁移率、热输运迁移率和Dufour系数作为粒子浓度和绝对温度的充分光滑函数的建模。得到的偏微分方程组包含四阶空间导数。因此，问题的变分形式要求近似函数至少是连续的。为了满足这一要求，提出了一种基于B样条的有限元方案。B样条的主要优点之一是可以精确地表示复杂的几何形状。然而，在有限元分析中，特别是弯曲的B样条几何不能用直接的方式来处理。为此，我们演示了边界条件的实现，以避免产生数值扰动。（©2016 Wiley‐VCH Verlag GmbH & Co. KGaA, Weinheim）
It is well known a homogeneous binary alloy subjected to a temperature gradient will become inhomogeneous. This decomposition phenomenon is called thermomigration or thermotransport or Soret effect, which is a cross‐effect in irreversible processes between heat conduction and atomic diffusion. In the present contribution we focus on a diffuse interface model for separation processes affected by temperature gradients coupled with a heat diffusion equation in order to describe thermomigration effects caused by joule‐heating. To be specific, we focus on phase separation in solder bumps consisting of tin and lead. Therefore we discuss the modelling of a Gibbs' configurational free energy density as well as the modelling of the chemical mobility, mobility of thermotransport and Dufour coefficient as sufficiently smooth functions in particle concentration and absolute temperature. The resulting set of partial differential equations involves spatial derivatives of fourth order. Consequently, the variational formulation of the problem mandates approximation functions which are at leastC1‐continuous. In order to fulfill this requirement a B‐Spline based finite element scheme is provided. One of the main advantages of B‐Splines is the possibility to represent complex geometries exactly. However, it has been shown that especially curved B‐Spline geometries can not be treated in a straight forward manner in finite element analysis. For this reason we demonstrate the implementation of boundary conditions to avoid the arising numerical perturbations. (© 2016 Wiley‐VCH Verlag GmbH & Co. KGaA, Weinheim)
SnPb 焊料中的热迁移：材料模型
影响因子：
3.9
作者：
S. Schuß;K. Weinberg;C. Hesch
通讯作者：
C. Hesch