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精确计算和模拟压力膜片上位移和应力分布是为设计高性能压力传感器的重要环节。实际压力传感器具有异性腐蚀形成硅杯的三维结构,存在不同介质层的热应力与弹性体本身的各向异性问题等。过去计算应力分布的数值方法通常采用有限差分法和有限元法,80年代发展起来的边界元法(BEM)有其独特的优点,此法使求解问题的维数降低一维,它只需将表面离散化,大大减少了方程个数和输入数据。并且引入了方程算子的基本解,具有离散和解析相结合的特点,数值精度一般优于各有限元法。本研究利用边界元法计算了具有腐蚀硅杯的三维矩形膜片的位移和应力分布,和有限元法模拟程序SAP与的计算结果吻合。在此基础上,计算压敏电阻的平均应力,结合版图设计规则优化了压力传感器的设计,提高了器件性能。
Accurately calculate and simulate the pressure diaphragm displacement and stress distribution is an important part of the design of high-performance pressure sensor. The actual pressure sensor has the three-dimensional structure formed by the anisotropic etching of the silicon cup, and there are problems of the thermal stress of different dielectric layers and the anisotropy of the elastomer itself. In the past, the finite element method and the finite element method were used to calculate the stress distribution. The Boundary Element Method (BEM) developed in the 1980s has its unique advantages. This method reduces the dimensionality of the problem by one dimension, Surface discretization greatly reduces the number of equations and input data. And the basic solution of the equation operator is introduced, which has the characteristics of the combination of discretization and analysis. The numerical accuracy is generally better than the finite element method. In this study, the displacement and stress distribution of three-dimensional rectangular diaphragm with corroded silicon cup were calculated by using the boundary element method, which is in good agreement with the finite element simulation program SAP. Based on this, the average stress of piezoresistor is calculated, and the design of pressure sensor is optimized in combination with the layout design rules to improve the device performance.