  Several methods are constructed for large-scale electronic structure
calculations. Test calculations are carried out with up to 10^7 atoms. As an
application, cleavage process of silicon is investigated by molecular dynamics
simulation with 10-nm-scale systems. As well as the elementary formation
process of the (111)-(2 x 1) surface, we obtain nanoscale defects, that is,
step formation and bending of cleavage path into favorite (experimentally
observed) planes. These results are consistent to experiments. Moreover, the
simulation result predicts an explicit step structure on the cleaved surface,
which shows a bias-dependent STM image.
