Grid reflection method

In other words, the orientation angle of the surface at point M for the curved substrate is proportional to the deviation of the grid point image from that reflected from a flat mirror. The substrate curvature is determined to be 

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Fig. 2.10. The grid reflection method, (a) Overall set-up. (6) Schematic and definition of key dimensions.

Fig. 2.25. Measured normalized curvature versus normalized mismatch strain for Si wafers with W films. The data points represent experiments conducted for different combinations of wafer diameter, wafer thickness and film thickness. The filled circles correspond to curvature measurements made by Finot et al. (1997) using the scanning laser method for the pre-bifurcation data points or the grid reflection method for the post-bifurcation data points. The other symbols denote experiments using the coherent gradient sensor method. Superimposed on the experimental data are the predicted trends for the stable symmetric and stable asymmetric cases replotted from Figure 2.24 with i = 0.26.

Fig. 2.26. Micrographs obtained using the grid reflection method which illustrate large deformation of Si wafers containing W Aims the wafer diameter is 150 mm. Nonlinear deformation with axially symmetric curvature, prior to bifurcation, is shown on the left. A post-bifurcation asymmetric shape is shown on the right. Note that the axially symmetric curvature of the wafer on the left causes the hole in the grid plane to be reflected as a dark circle in the center of the wafer, whereas the post-bifurcation shape of the wafer on the right causes the hole to be reflected with an elliptical shape. (After Finot et ai, 1997.)...

The data shown in Figure 2.25 were obtained by means of the wafer curvature scan, the grid reflection method, or the coherent gradient sensor method. The last of these will be discussed further in Section 2.6.2 in the context of a visualization of deformation via Mohr s circle for curvature. The grid reflection method was described in Section 2.3.3, and a typical set of images obtained with this method is shown in Figure 2.26. 

Bazant Z. R, Spurious Reflection of Elastic Waves in Nonuniform Finite Element Grids, Comp. Methods Appl. Mech. Eng., 16, 91 (1978). 

Depending on purposes, a plastic film under the vapor-deposited C is dissolved away with a solvent. By this method, a very thin C support-film of smaller than lOnm in thickness can be made easily. An aluminum (Al) support-film can be made similarly, by vapor-deposition of Al onto a plastic film put on a grid and then by dissolving away the plastic film. The reflection rings from the Al support-film can be used as an internal reference to calibrate the camera length of SAED pattern, and this support film does give no amorphous halo. When an ultra-thin C support-film (less than 5nm in thickness) is desired, a microgrid (MG see Section 3.1.2) should be used on which an ultra-thin film made by indirect vapor-deposition of C has been put in advance. 

In the present work, we monitor the laser-driven dynamics designed by the present formulation by numerically solving the time-dependent Schrodinger (5.2). It is solved by the split operator method [52] with the fast Fourier transform technique [53]. In order to prevent artificial reflections of the wavepacket at the edges, a negative imaginary absorption potential is placed at the ends of the grid [54]. The envelope of the pulses employed is taken as... 

In principle, any method which is able to produce a molecular interaction field (MIF) could be applied to the characterization of the targets. However, almost exclusively the GRID program [19] has been used. This is due to the size of the problem which excludes the use of standard ah initio or semiempirical methods to produce interaction maps. It also reflects the many successful applications of the GRID force field in the characterization of protein active sites and the interpreta-... 

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