Orientation-dependent mobilities from analyses of two-dimensional TiN(111) island decay kinetics

We present a method for the determination of orientation-dependent mobilities Γeff(φ) based upon analyses of the detachment-limited coarsening/decay kinetics of equilibrium-shaped two-dimensional islands. An exact analytical expression relating the orientation-dependence of Γeff(φ) to that of the anisotropic step energies β(φ) is derived. This provides relative values of Γeff(φ) to within an orientation-independent scale factor that is proportional to the decay rate of the island area. Using in situ high temperature (T = 1550–1700 K) low-energy electron microscopy measurements of two-dimensional TiN island coarsening/decay kinetics on TiN(111) terraces for which β(φ) values are known [Phys. Rev. B 67 (2003) 35409], we demonstrate the applicability of our analytic formulation for the determination of absolute Γeff(φ) values.