Effects of strain energy on the recrystallization within narrow metallization
Elastic strain energy within materials due to recrystallization of grains with a specific orientation, or texture, can be calculated through the use of Eshelby inclusions, where a recrystallized grain can be treated as an elastically anisotropic inclusion in an elastically isotropic matrix. The evolution of texture that minimizes elastic strain energy is shown to be dependent on the specific strain state. The interaction strains generated by this elastic incompatibility and corresponding strain energy have been derived for grains with cubic symmetry for general forms of the applied strain tensor. For uniaxial and isotropic, biaxial strain tensors, the interaction strain tensor and corresponding elastic strain energy density are proportional to the orientation parameter, Γ, which relates the Miller indices of the recrystallized grain to the loading direction: either parallel to the uniaxial strain direction or perpendicular to the plane in which isotropic biaxial strain is applied. It is rigorously proven that for elastically isotropic inclusions, corresponding to Γ = 1/5, the interaction strain is zero. Although blanket films often possess an isotropic, biaxial stress state, metallization trenches can exhibit a combination of normal and shear strain components, particularly near the trench corners. It is shown that in cases where shear is present, the resulting elastic strain energy can be lowered by the development of (110) texture despite its higher surface energy, as has been observed in thin films and interconnect trenches. These results suggest that shear strain can play an important role in the evolution of texture in narrow, metallization structures.