  A model that describes self diffusion, island nucleation and film growth on
FCC(001) metal substrates is presented. The parameters of the model are
optimized to describe Cu diffusion on Cu(001), by comparing activation energy
barriers to a full set of barriers obtained from semi-empirical potentials via
the embedded atom method. It is found that this model (model I), with only
three parameters, provides a very good description of the full landscape of
hopping energy barriers. These energy barriers are grouped in four main peaks.
A reduced model (model II) with only two parameters, is also presented, in
which each peak is collapsed into a single energy value. From the results of
our simulations, we find that this model still maintains the essential features
of diffusion and growth on this model surface. We find that hopping rates along
island edges are much higher than for isolated atoms (giving rise to compact
island shapes) and that vacancy mobility is higher than adatom mobility. We
observe substantial dimer mobility (comparable to the single atom mobility) as
well as some mobility of trimers. Mobility of small islands affects the scaling
of island density $N$ vs. deposition rate $F$, $N ~ F^\gamma$, as well as the
island size distribution. In the asymptotic limit of slow deposition, scaling
arguments and rate equations show that $\gamma = i*/(2 i* + 1)$ where $i*$ is
the size of the largest mobile island. Our Monte Carlo results, obtained for a
range of experimentally relevant conditions, show $\gamma = 0.32$ for the EAM,
0.33 for model I and 0.31 for model II barriers. These results are lower than
the anticipated $\gamma >= 0.4$ due to dimer (and trimer) mobility.
