Determination of Stresses in Incrementally Deposited Films From Wafer-Curvature Measurements
Determination of Stresses in Incrementally Deposited Films From Wafer-Curvature Measurements
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DOI：
10.1115/1.4047572
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发表时间：
2020-10
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影响因子：
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通讯作者：
Z. Rao;Hanxun Jin;A. Engwall;E. Chason;Kyung-Suk Kim
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文献类型：
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作者：
Z. Rao;Hanxun Jin;A. Engwall;E. Chason;Kyung-Suk Kim
我们报告封闭形式的公式来计算的增量沉积应力，弹性松弛应力，和残余应力在一个有限厚度的薄膜从晶片曲率测量。计算显示了新的应力层到膜的增量沉积如何影响膜/晶片曲率的量和先前沉积的层的应力状态。该公式允许的增量沉积应力和弹性弛豫，以正确地计算从所测量的曲率与厚度的任意厚度和双轴模量的膜和基板的斜率。从增量沉积应力历史中减去累积弹性松弛，就会产生整个沉积过程后留在薄膜中的残余应力。通过对不同厚度的镍膜的曲率测量，验证了公式的正确性。
We report closed-form formulas to calculate the incremental-deposition stress, the elastic relaxation stress, and the residual stress in a finite-thickness film from a wafer-curvature measurement. The calculation shows how the incremental deposition of a new stressed layer to the film affects the amount of the film/wafer curvature and the stress state of the previously deposited layers. The formulas allow the incremental-deposition stress and the elastic relaxation to be correctly calculated from the slope of the measured curvature versus thickness for arbitrary thicknesses and biaxial moduli of the film and the substrate. Subtraction of the cumulative elastic relaxation from the incremental-deposition stress history results in the residual stress left in the film after the whole deposition process. The validities of the formulas are confirmed by curvature measurements of electrodeposited Ni films on substrates with different thicknesses.