Evolution of strain energy during recrystallization of plated Cu films

Abstract

Microstructural evolution within thin films is dictated by energy minimization that can arise due to different mechanisms. Conventional treatments that estimate the driving force associated with elastic strain energy often employ a fibertextured microstructure to arrive at an analytical solution. By approximating the case of a recrystallized grain in a randomly oriented film as an elastically anisotropic inclusion in an elastically isotropic matrix, we can apply Eshelby's inclusion method to calculate both the interaction strains and the strain energy density generated by this elastic incompatibility. A comparison of these two approaches for grains with cubic symmetry reveals that a lower amount of elastic strain energy is generated in the case of an elastically anisotropic grain in an isotropic matrix, suggesting that it is less energetically favorable for Cu (111) grains to recrystallize in films possessing strong (111) texture than in randomly textured films. High-resolution X-ray diffraction measurements are used to extract the difference in the elastic response between recrystallized grains and the untransformed matrix, providing experimental quantification of the induced interaction strains. In addition, the corresponding elastic strain energy values are compared with the appearance of recrystallized (100) grains as a function of film thickness, allowing for a threshold energy density to be extracted. This threshold energy density can be correlated to the difference in surface energy values between (100)- and (111)-oriented grains.