Currently, in the era of big data and 5G communication technology, electromigration has become a serious reliability issue for the miniaturized solder joints used in microelectronic devices. Since the effective charge number (Z*) is considered as the driving force for electromigration, the lack of accurate experimental values for Z* poses severe challenges for the simulation-aided design of electronic materials. In this work, a data-driven framework is developed to predict the Z* values of Cu and Sn species at the anode based LIQUID, Cu₆Sn₅ intermetallic compound (IMC) and FCC phases for the binary Cu-Sn system undergoing electromigration at 523.15 K. The growth rate constants (k_em) of the anode IMC at several magnitudes of applied low current density (j = 1 × 10⁶ to 10 × 10⁶ A/m²) are extracted from simulations based on a 1D multi-phase field model. A neural network employing Z* and j as input features, whereas utilizing these computed k_em data as the expected output is trained. The results of the neural network analysis are optimized with experimental growth rate constants to estimate the effective charge numbers. For a negligible increase in temperature at low j values, effective charge numbers of all phases are found to increase with current density and the increase is much more pronounced for the IMC phase. The predicted values of effective charge numbers Z* are then utilized in a 2D simulation to observe the anode IMC grain growth and electrical resistance changes in the multi-phase system. As the work consists of the aspects of experiments, theory, computation, and machine learning, it can be called the four paradigms approach for the study of electromigration in Pb-free solder. Such a combination of multiple paradigms of materials design can be problem-solving for any future research scenario that is marked by uncertainties regarding the determination of material properties.

当前，在大数据和5G通信技术时代，电迁移已成为微电子设备中使用的微型焊点的严重可靠性问题。由于有效电荷数（Z *）被认为是电迁移的驱动力，因此缺乏准确的Z *实验值给电子材料的仿真辅助设计提出了严峻的挑战。在这项工作中，开发了一个数据驱动的框架来预测在二元Cu-Sn系统在_{60 ℃下}电迁移的阳极基LIQUID，Cu ₆ Sn ₅金属间化合物（IMC）和FCC相在阳极处的Cu和Sn物种的Z *值。523.15 K.增长率常数（k _em从基于一维多相场模型的模拟中提取了几种施加的低电流密度（j = 1×10 ⁶至10×10 ⁶ A / m ²）的阳极IMC的）。使用Z *和j作为输入特征的神经网络，而利用这些计算出的k _em数据作为预期输出进行训练。用实验增长率常数对神经网络分析的结果进行优化，以估算有效电荷数。在低j值下，温度的升高可以忽略不计，发现所有相的有效电荷数均随电流密度的增加而增加，而对于IMC相，这种增加更为明显。有效电荷数Z的预测值然后在2D模拟中使用*来观察阳极IMC晶粒生长和多相系统中的电阻变化。由于这项工作包括实验，理论，计算和机器学习等方面，因此可以称为研究无铅焊料中电迁移的四个范例方法。材料设计的多种范例的这种组合可以解决任何未来研究方案的问题，这些方案的特征是确定材料特性方面的不确定性。