Although lattice models have been very successful in modelling many as
pects of epitaxial growth, the confinement of atoms to sites on a regu
lar lattice is a severe impediment to extending these simulation studi
es to the heteroepitaxial growth of materials with a lattice mismatch.
In principle molecular dynamics overcomes this limitation, but the di
sparity between simulational and laboratory timescales limits this met
hod to the submonolayer regime of growth. Following the early work of
Faux et al. [Phys. Rev. B 42 (1990) 2914], we have developed a Monte C
arlo simulation where a continuous range of atomic positions are allow
ed. By adopting hard sphere interactions and a simple form of site hop
ping, we have investigated the effects of mismatch on the growth mode
and made comparisons with Lennard-Jones molecular dynamics simulations
. We will discuss the strengths and limitations of this way of combini
ng the Monte Carlo and molecular dynamics methods for modelling epitax
ial growth.