Determination of absolute orientation-dependent TiN(001) and TiN(111) step energies

Abstract

We employ in situ high-temperature (1030–1250K) scanning tunneling microscopy to measure adatom island coarsening/decay kinetics and temporal fluctuations around the equilibrium shapes of two-dimensional TiN vacancy islands on atomically-smooth (0 0 1) and (1 1 1) TiN terraces. Using inverse Legendre transformations of the equilibrium island shapes, we obtain 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 either quantitative island coarsening measurements [in the case of TiN(0 0 1)] or an exact approach for the analysis of shape fluctuations, applicable to highly anisotropic TiN(1 1 1) islands, to determine λ and, hence, absolute orientation-dependent step energies and step stiffnesses.