(5) A common experimental method to characterize the mechanical behavior thin films is the Thin Film Bulge Test. With this method, a window is etched into a silicon wafer and a thin film is suspended over it. Then the specimen is mounted on a pressure chamber so that pressure, P, can be applied to one side of the film, which causes the film to bulge out into a circular shape. The applied stress in the film can be determined as a function of the pressure and the geometry of the bulged film and the induced strain can be determined as a function of the geometry of the bulged film. Figure 1 shows the cross-section of a rectangular window that has been etched into a wafer. The width of the opening is 2a, the film thickness is t and the film develops a radius of curvature R upon loading. Derive the stretch ratio of the deformed film as well as the stress in the film that is valid for the range 0 < a/R 1. FIGURE 1. R 2a