球头压痕确定薄膜模量的等效膜厚法

Determination of the Elastic Modulus of Thin Film by Spherical Indentation Based on Equivalent Film Thickness Model

基于Hertz方程,修正了平头压痕薄膜系统的力学模型,建立了用于评估球头压痕确定薄膜弹性模量的等效膜厚法。采用有限元方法对模型进行计算分析,结果发现,当薄膜弹性模量大于基体时,计算误差小于Ranjana和William(RW)模型[1];当薄膜弹性模量小于基体时,对于较深的压痕计算得到的结果仍然和理论值相符,说明本模型可以用于比较深的压痕情况。另外,研究了薄膜屈服强度和球压头半径对计算结果的影响,结果显示,薄膜的压缩屈服强度越大,等效膜厚法得到的结果越准确;而在同一压痕深度下,较大的压头半径会带来较大的误差,当压痕深度较小时,薄膜的弹性模量受压头半径的影响较小。最后通过TiN/sapphire在球压头和三棱锥压头下的试验,验证了本方法。

Based on the Hertz equation, an equivalent film thickness method using spherical indentation was proposed to determine the modulus of thin films by means of modifying the mechanical model of flat cylindrical indentation. The FEM results verified by RW model show that the error of the proposed model is less than RW model when the elastic modulus of film is greater than that of the substrate; on the contrary, the results of the present method still agree well with the theoretic value while the indentation is much deeper. Therefore this model could be used to the instance that the indentation is more severe. In addition, the influences of yield strength of thin films and radius of the ball on the results were studied. It is found that the greater the yield strength of the thin films is, the smaller the error derived by proposed model is. At the same time, with the increase of the indenter radius, the error is greater under the same indentation depth. Furthermore, the influence of the radius on the modulus is smaller when the indentation is shallow. The proposed model is verified by indentation experiment on TiN/sapphire with Spherical indenter and Berkovich indenter.