A promising route for growing atomically flat Si on Ge(100) is described. The key to this achievement is the control of growth kinetics on an atomic level. We have identified the cause for the development of rough growth fronts: the descent of atoms across steps, a prerequisite fur prolonged layer-by-layer growth, is strongly suppressed at double steps. The developedprocedure for smooth growth avoids the formation of these double steps. The approach can be applied at low temperature (<550 K) and thus inherently avoids ill chemical definition of the interface due to intermixing. It is expected to be generally applicable for epitaxy of pure Si and Ge on both Ge(100) and Si(100) substrates. [S0163-1829(98)03148-8].