Theory of large-scale electronic structure calculation and nanostructures formed in silicon cleavage simulation: surface reconstruction, step and bending

摘要

Several methodologies are developed for large-scale atomistic simulations with fully quantum mechanical description of electron systems. The important methodological concepts are (ⅰ) generalized Wannier state and (ⅱ) Krylov subspace. Test calculations are done with upto 10~6 atoms using a standard workstation. As a practical nanoscale calculation, the 10 nm scale structure in cleavage process of silicon is investigated. Discussions are focused mainly on the stable (experimentally observed) (111)-(2 x 1) cleavage process. Surface reconstruction and step formation are observed and compared with experiments. These processes are analyzed by the quantum mechanical freedoms of electron system, such as the local density of states (LDOS). We also observed the bending of cleavage plane into the (111) plane from other planes, which is a direct evidence of the stability of the (111) cleavage mode. Finally, several common aspects between cleavage and other phenomena are discussed from a. general viewpoint of 10 nm scale structure.