Shan Guangbao, Wu Xudong, Li Guoliang, Xing Chaoyang, Zhang Shengchang, Fu Yu
School of Microelectronics, Xidian University, Xi'an 710071, China.
Beijing Institute of Aerospace Control Devices, Beijing 100039, China.
Micromachines (Basel). 2023 Feb 9;14(2):411. doi: 10.3390/mi14020411.
An efficient multi-objective optimization method of temperature and stress for a microsystem based on particle swarm optimization (PSO) was established, which is used to map the relationship between through-silicon via (TSV) structural design parameters and performance objectives in the microsystem, and complete optimization temperature, stress and thermal expansion deformation efficiently. The relationship between the design and performance parameters is obtained by a finite element method (FEM) simulation model. The neural network is built and trained in order to understand the mapping relationship. Then, the design parameters are iteratively optimized using the PSO algorithm, and the FEM results are used to verify the efficiency and reliability of the optimization methods. When the optimization target of peak temperature, bump temperature, TSV temperature, maximum stress and maximum thermal deformation are set as 100 °C, 55 °C, 35 °C, 180 Mpa and 12 μm, the optimization results are as follows: the peak temperature is 97.90 °C, the bump temperature is 56.01 °C, the TSV temperature is 31.52 °C, the maximum stress is 247.4 Mpa and the maximum expansion deformation is 11.14 μm. The corresponding TSV structure design parameters are as follows: the radius of TSV is 10.28 μm, the pitch is 65 μm and the thickness of SiO is 0.83 μm. The error between the optimization result and the target temperature is 2.1%, 1.8%, 9.9%, 37.4% and 7.2% respectively. The PSO method has been verified by regression analysis, and the difference between the temperature and deformation optimization results of the FEM method is not more than 3%. The stress error has been analyzed, and the reliability of the developed method has been verified. While ensuring the accuracy of the results, the proposed optimization method reduces the time consumption of a single simulation from 2 h to 70 s, saves a lot of time and human resources, greatly improves the efficiency of the optimization design of microsystems, and has great significance for the development of microsystems.
建立了一种基于粒子群优化算法（PSO）的微系统温度和应力高效多目标优化方法，用于映射硅通孔（TSV）结构设计参数与微系统性能目标之间的关系，并有效地完成优化温度、应力和热膨胀变形。通过有限元方法（FEM）仿真模型获得设计参数与性能参数之间的关系。构建并训练神经网络以理解映射关系。然后，使用PSO算法对设计参数进行迭代优化，并利用FEM结果验证优化方法的效率和可靠性。当将峰值温度、凸点温度、TSV温度、最大应力和最大热变形的优化目标分别设置为100℃、55℃、35℃、180MPa和12μm时，优化结果如下：峰值温度为97.90℃，凸点温度为56.01℃，TSV温度为31.52℃，最大应力为247.4MPa，最大膨胀变形为11.14μm。相应的TSV结构设计参数如下：TSV半径为10.28μm，间距为65μm，SiO厚度为0.83μm。优化结果与目标温度之间的误差分别为2.1%、1.8%、9.9%、37.4%和7.2%。通过回归分析验证了PSO方法，FEM方法的温度和变形优化结果之间的差异不超过3%。分析了应力误差，验证了所开发方法的可靠性。在确保结果准确性的同时，所提出的优化方法将单次仿真的时间消耗从2小时减少到70秒，节省了大量的时间和人力资源，大大提高了微系统优化设计的效率，对微系统的发展具有重要意义。
