The Monte Carlo study of the surface structure under MBE growth condit
ions is carried out. Characteristic surface diffusion field is obtaine
d with respect to each growth mode. Two-dimensional nucleation on the
terrace is investigated in atomic level using the time evolution of th
e density of clusters. Concerning the anisotropy of surface structure,
the main reason for this is not the surface diffusion anisotropy but
the anisotropic bond energy. The stoichiometric A-B crystal with the l
ayer-by-layer mode is obtained in a range phi(AA) = phi(BB) = phi(AB)/
r, r greater than or equal to 1, J(A) = J(B), where phi(AA), phi(BB),
and phi(AB) are the bond energies of A-A, B-B and A-B bonds, J(A) and
J(B) are the flux of A and B atoms, respectively. It is found that the
orderliness S of A-B crystal is a function of (2 phi(AB)/kT - Delta m
u/kT), where Delta mu/kT is the parameter representing the intensity o
f the flux.