Si(001)-c(4 X 4) surfaces are obtained by exposing Si(001)-2 x 1 surfaces at 600 degreesC to ethylene doses that determine C coverages in the submonolayer range. This reconstruction reveals a carbon enrichment of the topmost silicon layers. As the c(4 x 4) reflection high energy electron diffraction pattern can be maintained in spite of rather thick Si regrowth layers, we can conclude that this C derm is able to float at the surface during the Si capping. This segregation process is strongly dependent on the growth mode. As identified by RHEED intensity oscillations, a Si step flow growth is necessary to allow carbon to float in the first four silicon top-layers. An interplay is found between the kinetic growth conditions leading to this C-segregation and those of a self-organization process of C-rich clusters that we have observed in the course of Si1-yCy alloy growth obtained by codeposition of silicon and carbon.