On the basis of a kinetic growth model we discuss new methods to grow
atomically flat homoepitaxial layers in a controlled way. The underlyi
ng principle of these methods is to change the growth parameters durin
g growth of an atomic layer in such a way that nucleation on top of a
growing layer is suppressed, and thus, layer-by-layer growth is achiev
ed. Experimentally, this can be realized by changing the substrate tem
perature or deposition rate during monolayer growth in a well-defined
way. The same can be achieved at constant temperature and deposition r
ate by simultaneous ion bombardment during the early stages of growth
of a monolayer, or by adding suitable surfactants to the system. Model
experiments on Ag(lll) and on Cu(lll) using thermal energy atom scatt
ering and scanning tunneling microscopy demonstrate the success of the
se methods.