A vicinal Si (001) surface may form stripes of terraces, separated by monatomic-layer-high steps of two kinds, ${S}_{\mathrm{A}}$ and ${S}_{\mathrm{B}}$. As adatoms diffuse on the terraces and attach to or detach from the steps, the steps move. In equilibrium, the steps are equally spaced due to elastic interaction. During deposition, however, ${S}_{\mathrm{A}}$ is less mobile than ${S}_{\mathrm{B}}$. We model the interplay between the elastic and kinetic effects that drives step motion, and show that during homoepitaxy all the steps may move in a steady state, such that alternating terraces have time-independent, but unequal, widths. The ratio between the widths of neighboring terraces is tunable by the deposition flux and substrate temperature. We study the stability of the steady-state mode of growth using both linear perturbation analysis and numerical simulations. We elucidate the delicate roles played by the standard Ehrlich-Schwoebel (ES) barriers and inverse ES barriers in influencing growth stability in the complex system containing $({S}_{\mathrm{A}}+{S}_{\mathrm{B}})$ step pairs.