Selectively deposited GaInAs/InP quantum wells show extended monolayer terraces which are significantly larger than corresponding monolayer islands observed in the case of conventional non-selective epitaxy. We investigated the relation between the growth conditions and the formation of the monolayer step structure in lateral direction by cathodoluminescence. The influence of the arsine supply during GaInAs growth appeared to be the crucial parameter. A reduced V/III ratio during GaInAs growth results in a disappearance of the monolayer step structure. It is possible to control separately the vertical interface abruptness, limited by an As/P exchange at the interface, and the lateral interface configuration (terraces).