Atomic structure of high-index Ge surfaces consisting of periodic nanoscale facets

We have studied the clean and well-annealed Ge(103) surface with scanning tunnel microscopy (STM) and low-energy electron diffraction, whose morphology exhibits large 1 x 4 reconstructed (103) terraces along with tentlike protrusions consisting of (105), {216}, and {8116} facets. On the basis of the STM images, atomistic models have been proposed for the (103)1 x 4, the (216)1x1, and the (105)1x2 surfaces for further investigations. The former two surfaces consist of only nanoscale (113) terraces and hence belong to the (113) family while the latter consists of only nanoscale (001) terraces and thus belongs to the (001) family. The mini (001) terraces that the (105)1x2 reconstruction consists of, form a checkerboard pattern, thus implying a stress-relaxation driving force behind the reconstruction. These surface structures demonstrate that Herring's faceting theorem could be valid down to atomic scales, provided that the atomic-scaled facets could be connected into a large surface by-low-energy edges and/or corners.