In Situ High-Temperature Scanning Tunneling Microscopy Studies of
Two-Dimensional TiN Island Dynamics on Epitaxial (001) and (111) TiN
Terraces

S. Kodambaka, V. Petrova, S.V. Khare, David L. Chopp, I. Petrov, and J.E.
Greene
Department of Materials Science and the Frederick Seitz Materials Research
Laboratory, University of Illinois, Urbana, IL 61801


Abstract
Using in situ high-temperature (1000-1250 K) scanning tunneling microscopy
measurements of two-dimensional (2D) TiN island coarsening/decay, temporal
shape-fluctuations about the equilibrium island shape, and coalescence
kinetics on highly anisotropic TiN(001) and TiN(111) surfaces, we present
recent progress toward developing generalized theoretical approaches,
applicable for describing 2D island dynamics on both isotropic and highly
anisotropic surfaces.
We derived an analytical expression for the Legendre transformation of the
2D equilibrium island shapes, which relates orientation-dependent step
energies to the equilibrium shape function through an
orientation-independent scale factor, the equilibrium chemical potential
of the island per unit area. Two approaches have been developed to
determine absolute step energies. In the first method, coarsening/decay
kinetics of 2D islands are modeled based upon steady-state diffusion
equations solved by adaptive finite-element methods with the modified
Gibbs-Thomson equation describing anisotropic islands serving as the
boundary condition. Calculated island decay results are then compared with
the experimental measurements to extract step energies. The second method
is based upon an exact theoretical formulation relating the temporal
change in island free energy to thermal fluctuations about the anisotropic
equilibrium shape. Orientation-dependent step energies are then used as
input to quantitatively describe 2D island-island coalescence kinetics on
both TiN(001) and TiN(111) surfaces.