A hierarchical research by large-scale and ab initio electronic structure theories-Si and Ge cleavage and stepped (111)−2×1 surfaces

The ab initio calculation with the density functional theory and plane-wave bases is carried out for stepped Si(111)−2×1 surfaces that were predicted in a cleavage simulation by the large-scale (order-N) electronic structure theory (T. Hoshi, Y. Iguchi and T. Fujiwara, Phys. Rev. B 72 (2005) 075323). The present ab initio calculation confirms the predicted stepped structure and its bias-dependent STM image. Moreover, two (meta)stable step-edge structures are found and compared. The investigation is carried out also for Ge(111)−2×1 surfaces, so as to construct a common understanding among elements. The present study demonstrates the general importance of the hierarchical research between large-scale and ab initio electronic structure theories.