Atomic structure of Si and Ge surfaces: Models for (113), (115), and stepped (001) vicinal surfaces

A new class of structure models for the (113) and (115) orientations of Si and Ge is proposed. They are based on dimer and adatom formation as the main building blocks for the reduction of dangling bonds (DB), on relaxation towards more ${\mathit{sp}}^2$- or ${\mathit{s}}^2$ ${\mathit{p}}^3$-like configurations, and on the minimization of strain. Four structural alternatives are discussed for (113) which are consistent with the observed 3×1 and 3×2 periodicities. They have either a low DB density and large strain or a higher DB density and low strain. For Si(113), a decision between them on the basis of the available experimental results is not unique. The analysis of the orientation-dependent adsorption of ${\mathrm{H}}_2$S and NO in terms of preferential adsorption by certain structural elements favors the models for Ge(113) which have not the minimum DB density but the minimum of strain. Steps on (001) vicinals induce strain due to bond stretching which is equilibrated over the terraces as long as they are wide enough. The switching of the twofold periodicity of the dimers along [1¯10] on (001) and its vicinals to the threefold periodicity at (115) is explained to occur because the 3×n models resolve bond stretching into bond bending by a meandering arrangement of microterraces which are separated by the energetically most favorable type-${\mathit{S}}_{\mathit{A}}$ single-layer steps.