Linking strain anisotropy and plasticity in copper metallization

The elastic anisotropy of copper leads to significant variation in the x-ray elastic constants (XEC), which link diffraction-based strain measurements to stress. An accurate depiction of the mechanical response in copper thin films requires a determination of an appropriate grain interaction model that lies between Voigt and Reuss limits. It is shown that the associated XEC weighting fraction, x*, between these limits provides a metric by which strain anisotropy can be quantified. Experimental values of x*, as determined by a linear regression scheme of diffraction data collected from multiple reflections, reveal the degree of strain anisotropy and its dependence on plastic deformation induced during in-situ and ex-situ thermal treatments