Faceting of stepped silicon (113) surfaces: Self assembly of nanoscale gratings

Synchrotron X-ray scattering studies of the phase behavior and phase transformations of stepped Si(113) surfaces tilted towards [001] are reviewed for temperatures between 300 and 1500 K. At the highest temperatures, these surfaces are uniformly stepped, and the intensity of near-specularly scattered X-rays increases with decreasing temperature. This is two-dimensional critical opalescence, which foreshadows a faceting transformation. At temperatures below the faceting transformation, (113) facets appear in coexistence with a stepped phase, leading to a mesoscopically grooved morphology. Both the misorientation angle at the phase boundary separating one- and two-phase regions and the intensity of the near-specular diffuse scattering may be described as power laws versus reduced temperature. This can be understood qualitatively on the basis of a mean-field theory, which incorporates an attractive interaction between steps. At lower temperatures, the surfaces are completely faceted, comprising (114) and (113) facets. The kinetics of faceting is also described. Following a quench from a one-phase region of the phase diagram into a two-phase region, the grooved superstructure forms and subsequently coarsens in time. For times between one and several hundred seconds, the surface morphology is self-similar at different times, with a characteristic groove size that evolves as a power law versus time. At later times, the groove size approaches a limiting value, as a result of elastic effects.