Morphology of monatomic step edges on vicinal Si(001)

Abstract

The roughness of monatomic A- and B-type step edges on 0.5\ifmmode^\circ\else\textdegree\fi{} misoriented Si(001) has been analyzed on an atomic scale with scanning tunneling microscopy. On small length scales, measured along the step edge (200 \AA{}), one-dimensional random-walk behavior is observed for both types of step edges. For the rough B-type step edge we also found evidence for waviness of the edge. The period of this wave is about 100 dimer-row spacings (\ensuremath{\approxeq}750--800 \AA{}). The energetic step-step interaction and entropic repulsion, which both scale as 1/${\mathit{L}}^{2}$ (L is the average terrace length), are estimated to be about 0.03--0.06 and 0.2 meV per dimer-row spacing, respectively, for a 0.5\ifmmode^\circ\else\textdegree\fi{} misoriented surface. These interactions are approximately three orders of magnitude smaller compared to the kink formation energies which are 0.1--0.2 eV. Despite the weak strength of energetic and entropic step-step interactions, these long-range interactions have a profound effect on the step-edge morphology, e.g., the distribution of terrace lengths and the long-range waving of the rough B-step edge.