ATTRACTIVE STEP-STEP INTERACTIONS, TRICRITICALITY, AND FACETING IN THE ORIENTATIONAL PHASE-DIAGRAM OF SILICON SURFACES BETWEEN [113] AND [114]

A synchrotron x-ray scattering study is presented of the orientational phase diagram of Si surfaces misoriented by up to 6°from the cubic [113] direction towards [001] and for temperatures between 300 and 1500 K. At the highest temperatures (above 1223 K), the surface is uniformly stepped. In this region, the intensity of near-specularly scattered x rays increases with decreasing temperature, suggesting a corresponding increase in the surface roughness. Specifically, the temperature dependence of the intensity of the near-specular diffuse scattering may be described as a power law versus reduced temperature: ID∼ts-λ, with λ=0.76±0.2 (ts(θ)=[T-Ts(θ)]/Ts(θ), where Ts(θ) is spinodal temperature for surface misorientation θ). Below Tt=1223±40 K, there is a two-phase region in which (113) facets appear in coexistence with the stepped phase. We identify Tt as a tricritical point. The misorientation angle at the phase boundary separating one- and two-phase regions may be also described as a power law versus reduced temperature: θ=θ0tβ, with β=0.42±0.10 [t=(Tt-T)/Tt]. The behavior of the intensity of the diffuse scattering above Tt and of the phase boundary below Tt can be understood qualitatively on the basis of a mean-field theory incorporating a direct attractive interaction between steps. However, the observed tricritical exponents are not given correctly. For temperatures between a triple point at T3=1134±40 and 300 K, coexistence between the (113) facet and the (114) facet is found. © 1995 The American Physical Society.