Shape universality of equilibrated silicon crystals

Abstract

In order to check the Prokowski–Talapov (P–T) universality class behaviour, the profiles of equilibrated silicon crystals have been studied in the vicinity of a (111) facet at 900°C. The equilibrium shapes of three-dimensional (3D) or two-dimensional (2D) crystals have been produced by thermally equilibrating either an array of small silicon columns on a silicon substrate or a grating of silicon ridges. The samples have been observed either ex situ, by high-resolution SEM, or in situ by TEM and REM. The profiles have been measured along a (high symmetry) 〈110〉 zone, toward (110), within the angular domain 3–17°. For smaller angles (0–1.5° away from [111]) the profile has been reconstructed via the visualisation of steps by REM. The theoretical prediction of a 3/2 power law for the profile equation has been checked. The results are at variance with those obtained for metals. Within the angular domain 3–17°, the profile is compatible with a 3/2 power law. From the profile equation, the step interaction constant can be determined (0.36±0.09 J m −2 at 900°C), in good agreement with previous experiments on the terrace width distributions. No difference can be detected between 3D and 2D crystals. All this is the signature of a P–K behaviour, only involving repulsive 1/ x 2 step interactions, again in agreement with previous studies. However, at small angles (0–1.5°), no physically reasonable law can be assigned to the profile. This behaviour is not understood at present.