In situ high-temperature (1165–1248 K) scanning-tunneling microscopy was used to measure temporal fluctuations about the anisotropic equilibrium shape of two-dimensional TiN(111) adatom and vacancy islands on atomically smooth TiN(111) terraces. The equilibrium island shape was found to be a truncated hexagon bounded by alternating 〈110〉 steps, which form [100] and [110] nanofacets with the terrace. Relative step energies β as a function of step orientation φ were obtained from the inverse Legendre transformation of the equilibrium island shape to within an orientation-independent scale factor λ, the equilibrium chemical potential of the island per unit TiN area. We find that for alternating $S_1$ and $S_2$ 〈110〉 steps, the ratio ${\beta }_1/{\beta }_2=0.72\mathrm{}\pm \mathrm{0.02.}$ The parameter λ and, hence, absolute orientation-dependent values of β(φ) and step stiffnesses $\tilde{\beta }\left(\phi \right)$ were extracted from quantitative shape fluctuation data using an exact theoretical approach valid for anisotropic islands. For the two 〈110〉 steps, we obtain ${\beta }_1=0.23\mathrm{}\pm 0.05$ and ${\tilde{\beta }}_1=1.9\mathrm{}\pm 1.1\mathrm{eV}/\AA$ with ${\beta }_2=0.33\mathrm{}\pm 0.07$ and ${\tilde{\beta }}_2=0.08\mathrm{}\pm 0.02\mathrm{eV}/\AA$ over the observed temperature range. Due to the correspondingly high kink energies, TiN(111) step energies exhibit only a very weak temperature dependence between 0 K and the maximum measurement temperature 1248 K.

• Received 15 August 2002

DOI:https://doi.org/10.1103/PhysRevB.67.035409