Residual stresses are caused by nonuniform thermal expansion and chemical shrinkage taking place during processing. For thin-film high-temperature superconductors, residual stresses result because of the thermal expansion mismatch between the film and substrate, and the introduction of oxygen into the film after in-situ deposition, which makes the unit cell dimensions change (chemical shrinkage) as the oxygen stoichiometry changes. Since both the reliability of the film—especially the bond between the film and substrate—and the film critical temperature are functions of the state of stress, it is important to understand how the residual stresses vary with processing conditions. Here, a three-dimensional residual stress analysis is carried out based on laminate theory, which assumes the lateral dimensions of the entire system to be much larger than its thickness. The normal residual stress components in the film, and the peeling stress at the film/substrate interface, are calculated. The results demonstrate the crucial role that chemical shrinkage plays in the formulation of residual stresses. A large portion of the stresses arises from the initial change of the unit cell dimensions due to changes in the film oxygen stoichiometry. Therefore, the processing temperature, and especially the initial oxygen pressure in the deposition chamber, are the key variables that impact the residual stresses.
Residual Stresses for In-Situ Deposition of Thin-Film High-Temperature Superconductors
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Phelan, P. E., and Ghasemi Nejhad, M. N. (December 1, 1994). "Residual Stresses for In-Situ Deposition of Thin-Film High-Temperature Superconductors." ASME. J. Electron. Packag. December 1994; 116(4): 249–257. https://doi.org/10.1115/1.2905695
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