A.1 Reducing Dislocation DensityDislocations contribute to strengthening in metallic materials while they deteriorate performance of semiconductors. For reducing the dislocation density in crystals thermal cyclic annealing, developed by Dr. Kitajima of Kyushu University, is very effective [1]. In this method, crystals are annealed in a temperature range changing periodically. This method was first applied to FCC and HCP metals where the P-N force is low, but later successfully applied to BCC metals and Si where the P-N force is high [2,3]. (010) and (001) surfaces were chosen as typical examples, however, needless to say, any two surfaces will work. However, the error is minimized when the two surfaces make an angle 90• .To improve the preciseness many (more than two) surfaces are to be analyzed. For this purpose a cylindrical specimen is suitable. Figure A A.7(a) shows an example. Here, at SF the slip lines appear only weakly, while at TF they appear strongly. At SF (i.e., side face) b is parallel to the surface, so that steps associated with slip do not appear, while at TF (i.e., top-face) the steps become a maximum. In other words, information on the slip direction is also obtained by this method. A.8 Inverse transformation of stress (Eq. 3.21)