Theory of large-scale electronic structure calculation and nanoscale mechanical property in fracture behavior of silicon

Several theories and program codes were developed for large-scale atomistic simulations with fully quantum mechanical description of electron systems. The fundamental concepts are generalized Wannier state and Krylov subspace. Test calculations were carried out with upto 106 atoms using a standard workstation. How electronic state is described in large-scale calculation was demonstrated on Si(001)-(2×1) surface. As a practical application, cleavage fracture of silicon was simulated with 10-nm-scale samples for investigating its nanoscale mechanical behavior. Discussions are focused on the unstable (001) cleavage mode and the stable (experimentally observed) (111)-(2×1) cleavage mode. As well as elementary surface reconstruction, step formation and bending in cleavage path were observed. These results were compared with experiments, such as scanning tunneling microscope (STM).