Compressively strained Si0.7Ge0.3 layers were grown on Si(001) by gas-source molecular beam epitaxy from Ge2H6/Si2H6 mixtures at 450 °C. The combination of the relatively low growth temperature and high steady-state hydrogen surface coverage, θH=0.52 monolayer, completely suppresses strain-induced roughening and provides extremely flat surfaces with root mean square widths w≪1.5 Å for fully coherent layers. These samples were used as the starting point to probe mechanisms that control misfit-dislocation-induced surface roughening (i.e., crosshatch) along 90°-rotated <110> directions. For film thicknesses t just larger than the critical value for misfit dislocation formation, tc≃1000 Å, surface roughness is dominated by single- and multiple-atomic-height steps generated by the motion of threading dislocations associated with interfacial misfits. The surface steps are preferential H desorption sites and the increase in total step length results in a decrease in θH on terraces as well as at step edges. The latter effect allows a higher adatom crossing probability at ascending steps, leading to the formation of periodic ridges in response to local strain fields associated with misfit dislocation clusters; w increases from 3.1 Å at t=1350 Å (corresponding to strain relaxation R of 1%) to 27 Å at t=4400 Å (R=78%). Simultaneously, the decrease in θH on terraces strongly affects film growth kinetics as the de- position rates increase from 10 Å min-1 with t≪tc to ≃60 Å min-1 with t≃1400–4400 Å. Overall, in films with t>~1440 Å (R>~5%), crosshatch is due to surface steps that result from multiple misfit dislocations on single glide planes. At higher film thicknesses (R=22–78%), crosshatch becomes dominated by local strain-induced roughening and leads to periodic ridge formation. © 2003 American Institute of Physics.