The volumes of the phase defects were measured using an SPM (L-Trace II, Hitachi High-Tech Science Corp., Tokyo, Japan). The cantilevers used in this study employed a triangular pyramid shaped tip (SI-DF40P2, Hitachi High-Tech Science Corp., Tokyo, Japan). A probe material made of Si with a spring constant of was incorporated into the cantilever. The typical values of the resonant frequency and tip radius of curvature were 300 kHz and 7 nm. The scan area and speed were set to and 1.7 Hz. The numbers of the image pixels were 512 or 1024 points for the direction, and 128, 256, 512, and 1024 points for the direction. After capturing the SPM image, the defect volume was calculated as illustrated in Fig. 2. Figure 2(a) shows the SPM image of the multilayer surface that includes the phase defect. To eliminate the volume of the reference area that is caused by the multilayer surface roughness from the phase defect volume, a setting of an adequate datum plane was made. As the first step, a masking area, in other words an area that includes the phase defect, was set to calculate the datum plane as shown in Fig. 2(b). Figure 2(c) shows the SPM image of the multilayer surface with the masking area. Figure 2(d) represents a histogram of the pixel heights of Fig. 2(c). The datum plane was set to the total volumes of the above and below the datum plane that corresponded to the areas A and B in Fig. 2(d) so that they were equal. The removed phase defect shown in Fig. 2(b) was put back in place while taking into account the datum plane adjustment. A histogram of the pixel heights of Fig. 2(e) is shown in Fig. 2(f). The histogram curve greater than 0 nm in height was changed from red to blue [Fig. 2(g)]. An area C in Fig. 2(g), bounded by the horizontal axis, vertical axis, and the blue curve greater than 0 nm in height, corresponds to the total volume of the surface roughness above the datum plane, whereas the area A in Fig. 2(d) excludes the masking area from the calculation of the volume of the surface roughness. An area D represents an axisymmetric domain of the area C. As prescribed, after setting an adequate datum plane, the total volume of the surface roughness below the datum plane, expressed in the area D, is equal to the volume expressed in the area C. The volume below the datum plane includes the volume of the phase defect and the reference area. Therefore, the area E in Fig. 2(g), subtracted the area D from the volume below the datum plane, corresponds to the volume of the phase defect.