  Non-linear transport properties of single-layer metal-on-metal islands driven
with strong static and time-dependent forces are studied. We apply a
semi-empirical lattice model and use master equation and kinetic Monte Carlo
simulation methods to compute observables such as the velocity and the
diffusion coefficient. Two types of time-dependent driving are considered: a
pulsed rotated field and an alternating field with a zero net force
(electrophoretic ratchet). Small islands up to 12 atoms were studied in detail
with the master equation method and larger ones with simulations. Results are
presented mainly for a parametrization of Cu on Cu(001) surface, which has been
the main system of interest in several previous studies. The main results are
that the pulsed field can increase the current in both diagonal and axis
direction when compared to static field, and there exists a current inversion
in the electrophoretic ratchet. Both of these phenomena are a consequence of
the coupling of the internal dynamics of the island with its transport. In
addition to the previously discovered "magic size" effect for islands in
equilibrium, a strong odd-even effect was found for islands driven far out of
equilibrium. Master equation computations revealed non-monotonous behavior for
the leading relaxation constant and effective Arrhenius parameters. Using cycle
optimization methods, typical island transport mechanisms are identified for
small islands.
