The easy-to-use point-load on elastic foundation (PoEF) test, similar (or alternative) to a typical biaxial bending ball-on-ring test, is studied for determining the bending strength of thin silicon dies. The feasibility of this test method with a linear theory is also evaluated using a nonlinear finite element method (NFEM) by taking into account geometric and contact nonlinearities. The mechanics of the PoEF test is discussed in terms of geometric linearity and nonlinearity. The results show that the geometric nonlinearity would cause significant errors of bending strength data, due to the maximum applied stress moving away from the loading pin center, if the linear theory is applied for thin die specimens in this test. The comprehensive fitting equations based on the NFEM results, with better accuracy than the linear theory, are proposed for calculating the thin die strength. Some key parameters, including the head radius of the loading pin (r), elastic modulus of the foundation (E EF ), elastic modulus of the test specimen (E), and test specimen thickness (t), are also discussed individually by studying their effects on the fitting equations. In an experimental implementation, the thin silicon die specimens with various thicknesses are actually performed in the PoEF test. It is found that the thinner specimen suffers from more severe geometric nonlinearity effect. The statistical strength data converted by the fitting equations are demonstrated and show that the geometric nonlinearity has to be taken into account in the PoEF test when the thin specimens are tested. The ready-to-use fitting equations proposed in this study are proved to be viable solutions for the conversion of those nonlinear test data.

中文翻译：

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PoEF 测试中薄硅芯片双轴弯曲强度的几何非线性效应


研究了易于使用的弹性基础点载荷 (PoEF) 测试，类似于（或替代）典型的双轴弯曲球环测试，用于确定薄硅芯片的弯曲强度。该测试方法采用线性理论的可行性也通过考虑几何和接触非线性的非线性有限元方法（NFEM）进行了评估。从几何线性和非线性角度讨论了 PoEF 测试的力学原理。结果表明，如果在该测试中将线性理论应用于薄模具样本，由于最大施加应力远离加载销中心，几何非线性会导致弯曲强度数据出现显着误差。提出了基于NFEM结果的综合拟合方程来计算薄模强度，该方程比线性理论具有更好的精度。通过研究，还分别讨论了一些关键参数，包括加载销头部半径（r）、基础弹性模量（E EF ）、试件弹性模量（E）和试件厚度（t）它们对拟合方程的影响。在实验实施中，实际执行了不同厚度的薄硅芯片样本的 PoE 测试。研究发现，试件越薄，几何非线性效应越严重。论证了拟合方程转换的统计强度数据，表明在薄试件测试时，PoEF测试必须考虑几何非线性。本研究中提出的现成拟合方程被证明是这些非线性测试数据转换的可行解决方案。