Measurement technique for the evaluation of residual stress in epitaxial thin film by asymmetric X-ray diffraction

An analytical technique to determine residual stress in eqitaxial thin film by asymmetric X-ray diffraction (XRD) was studied. The residual stresses of PbTiO₃ films were determied by XRD technique and displace measurement technique. Measurement results by these techniques were compared with each other to consider the respective advantages of each technique. The stresses measured by XRD technique were not consistent with those by displacement measurement technique, because the latter technique involves errors which origined from the shape and the size of the substrate. The stress in a polycrystalline film measured by modified sin²Ψ method was in good agreement with that measured by normal sin²Ψ method. This result suggests that modified sin²Ψ method can be applied to stress measurement not only in epitaxial thin films, but also in polycrystalline thin films. We further discuss the precision of the stress determination technique. Residual stress of epitaxial PbTiO₃ film on (100)SrTiO₃ substrate measured by modified sin²Ψ method was comparable to the theoretical stress estimated from the difference in thermal expansion coefficients between the film and the substrate. Stress values measured by modified sin²Ψ method may thus have the precision re-quired for actual application.