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The Si single crystal has anisotropic elastic properties. The in-plane isotropy on the (111) plane, however, is maintained [W. A. Brantley, J. Appl. Phys. 44, 534 (1973)]. In the calculations the Young's modulus and Poisson ratio of the (111) oriented wafer were taken to be those along the (111) plane. The accuracy of this choice was evaluated by performing more involved calculations using the anisotropic elastic properties for a particular line geometry (Specimen 6), and it was found that the errors induced are negligible. The curvature values obtained in directions perpendicular and parallel to the lines are the same, and only very slight discrepancies in the stress field exist. The small differences are such that the contour plots of various stress components presented in this article are essentially unaffected.
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In these calculations, the etching process is equivalent to thermal straining of the film-substrate system from the initially stress-free state to room temperature, and then removing a part of the film material to form lines. It is also equivalent to the situation wherein etching is done at the initial state when no internal stresses are present, and then imposing thermal strains on the line-substrate structure so that the final state corresponds to room temperature. These two different procedures lead to identical results which establish the equivalence of the etching and thermal loading processes, when the material exhibits a linear elastic behavior.
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