Thin film/substrate systems featuring arbitrary film thickness and misfit strain distributions. Part I: Analysis for obtaining film stress from non-local curvature information
Thin film/substrate systems featuring arbitrary film thickness and misfit strain distributions. Part I: Analysis for obtaining film stress from non-local curvature information
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DOI：
10.1016/j.ijsolstr.2006.10.016
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发表时间：
2007-03
影响因子：
3.6
通讯作者：
D. Ngo;Xue Feng;Yonggang Huang;A. Rosakis;M. Brown
中科院分区：
文献类型：
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作者：
D. Ngo;Xue Feng;Yonggang Huang;A. Rosakis;M. Brown
目前用于通过曲率测量来推断薄膜应力的方法被严格地限制于应力和曲率状态，该应力和曲率状态被假设为在整个膜/衬底系统上保持均匀。最近，Huang，Rosakis和同事[Huang，Y.，Ngo，D.，Rosakis，A.J.，2005.非均匀轴对称错配应变：在板基片/基片系统上粘接的薄膜中：非均匀薄膜应力与系统曲率之间的关系。《机械学报》21，362-370; Huang，Y.，Rosakis A.J.，2005. Stoney公式在薄膜/基片系统非均匀温度分布中的推广。径向对称的情况。J. Mech. Phys. Solids 53，2483-2500; Ngo，D.，黄，Y.，Rosakis，A. J.，Feng，X. 2006.粘接在平板衬底上的薄膜的空间非均匀各向同性失配应变：非均匀薄膜应力与系统曲率之间的关系。薄膜固体薄膜（印刷中）]建立了薄膜/基板系统的方法，受到不均匀的失配应变和温度变化。发现膜应力非局部地依赖于系统曲率（即，取决于全场曲率）。然而，现有的方法都假定均匀的膜厚度，这在薄膜/基板系统中经常被违反。我们将这些方法扩展到任意非均匀膜厚的薄膜/基板系统的非均匀失配应变。值得注意的是，如果用应力计算点处的局部值代替膜厚，则均匀膜厚的应力曲率关系仍然成立。这一结果在本文的第二部分得到了实验验证。
Current methodologies used for the inference of thin film stress through curvature measurements are strictly restricted to stress and curvature states which are assumed to remain uniform over the entire film/substrate system. Recently Huang, Rosakis and co-workers [Huang, Y., Ngo, D., Rosakis, A.J., 2005. Non-uniform, axisymmetric misfit strain: in thin films bonded on plate substrates/substrate systems: the relation between non-uniform film stresses and system curvatures. Acta Mech. Sin. 21, 362–370; Huang, Y., Rosakis A.J., 2005. Extension of Stoney’s Formula to non-uniform temperature distributions in thin film/substrate systems. The case of radial symmetry. J. Mech. Phys. Solids 53, 2483–2500; Ngo, D., Huang, Y., Rosakis, A. J., Feng, X. 2006. Spatially non-uniform, isotropic misfit strain in thin films bonded on plate substrates: the relation between non-uniform film stresses and system curvatures. Thin Solid Films (in press)] established methods for film/substrate system subject to non-uniform misfit strain and temperature changes. The film stresses were found to depend non-locally on system curvatures (i.e., depend on the full-field curvatures). The existing methods, however, all assume uniform film thickness which is often violated in the thin film/substrate system. We extend these methods to arbitrarily non-uniform film thickness for the thin film/substrate system subject to non-uniform misfit strain. Remarkably the stress-curvature relation for uniform film thickness still holds if the film thickness is replaced by its local value at the point where the stress is evaluated. This result has been experimentally validated in Part II of this paper.