On the electrochemical applications of the bending beam method

Measuring the bending of a plate to determine the stress in thin films coated on one side of a substrate is a common technique. The surface stress changes can be estimated by using an appropriate form of Stoneyʹs equation, if the thickness of the film is sufficiently less than that of the substrate. The changes in the bending of the substrate are usually calculated from the displacement of the reflected laser beam measured, e.g., with a position sensitive photo detector (PSD). Since the displacement of the light spot on the PSD is measured in air outside the liquid phase (where the mirroring surface is located), the measured values should be corrected according to Snellʹs law of refraction. A relation between the reciprocal of curvature radius of the substrate and the displacement of the laser beam on PSD was derived by taking into account the bending of the laser beam due to refraction at the optical window. It is shown that the neglect of the refraction at the optical window may cause an error of 25–30% in the estimation of the stress changes.