Absolute orientation-dependent TiN( [formula omitted]) step energies from two-dimensional equilibrium island shape and coarsening measurements on epitaxial TiN( [formula omitted]) layers

Abstract

In situ high-temperature (1030–1223 K) scanning tunneling microscopy was used to determine the equilibrium shapes of two-dimensional TiN vacancy islands on atomically smooth terraces of epitaxial TiN(0 0 1) layers. Inverse Legendre transformations of the equilibrium island shapes yield relative step energies as a function of step orientation within an orientation-independent scale factor λ, the equilibrium chemical potential of the island per unit TiN molecular area. We then use quantitative TiN(0 0 1) adatom island coarsening measurements to determine λ and, hence, absolute orientation-dependent step energies β and step stiffnesses β ̃ . For 〈1 1 0〉 and 〈1 0 0〉 steps on TiN(0 0 1), we obtain: β 1 1 0 =0.21±0.05 eV/Å, β 1 0 0 =0.25±0.05 eV/Å, β ̃ 1 1 0 =0.9±0.2 eV/Å, and β ̃ 1 0 0 =0.07±0.02 eV/Å. From the β ̃ values, we calculate kink formation energies ε 1 1 0 =0.40±0.2 eV and ε 1 0 0 =0.11±0.1 eV based on the unrestricted terrace-step-kink model.