Measurement of the Dependence of Stress and Strain on Crystallographic Orientation in Cu and Al thin Films
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Sanchez and Artz make the critical assumption that the flow stress in a grain with a particular orientation can be described by the sum of the above equation and a grain size strengthening term. This is justified by two assumptions. First, the grain is assumed to be columnar and rigidly attached to the substrate, limiting the forces that adjacent grains can impose upon each other. Second, the dislocation flow processes described by the above model are assumed to occur solely in an individual grain and therefore will not induce flow in neighboring grains. This model has several implications for microstructural evolution in thin films. If grains with different orientations support different stresses, a local stress gradient will be established. Sanchez and Artz postulate that hillocking may arise from a mechano-diffusional mass flux from (111) grains to (100) grains, inducing out-of-plane growth and reducing the biaxial film stress in the local region. Since lattice and interface diffusion are normally much slower than grain boundary diffusion at typical temperatures for hillocking, stress relief will principally occur within the network of surrounding grain boundaries and will not fully relieve the stresses in grain interiors. The authors point out that this model also has implications for abnormal grain growth in thin films. Thompson has described the rate of growth of a particular grain as the product of grain boundary mobility and a sum of relevant driving forces [4]. Normal grain growth is due to energy minimization from reduction of grain boundaries and is not dependent on grain orientation. Abnormal grain growth, however, has been shown to be orientationally dependent with a driving force that depends on the difference in surface and interface energies between the growing grain and the average of the surrounding matrix. Sanchez and Arzt point out that differences in the strain states between grains of different orientations can result in a driving force of comparable magnitude to that of surface energy minimization due to differences in the strain energy density. 429 Mat. Res. Soc. Symp. Proc. Vol. 356 0 1995 Materials Research Society
Although the Sanchez model is specific to plasticity in isotropic materials, Thompson [5] has pointed out that a similar driving force can develop during elastic response in elastically anisotropic materials. Assuming that the strain applied to the film due to differences in the thermal expansion coefficients between the substrate and the film is supported equally in each orientation, in fcc metals the differences in stress that result in each grain lead to an energetic advantage for the film to convert to a (001) texture, rather than the (111) orientation favored by surface energy minimization. This texture has been observed in abnormally growing grains upon annealing Cu films deposited at room temperature [6], but not in films deposited at elevated temperatures. Zielinski, et. al. have explained the suppression of abnormal grain growth as the result of the increased initial gr
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