We report measurements on the initial stages of relaxation of Si-doped In0.04Ga0.96As epitaxial layers on (001) GaAs using in situ high-resolution double-crystal x-ray topography during molecular beam epitaxial growth. For Si concentrations up to 5x10(18) cm(-3), the critical thickness for formation of the first B(g) misfit dislocations is modeled accurately by the Matthews-Blakeslee model, extended to include a lattice friction force varying linearly with the dopant concentration. Below a Si concentration of 2x10(18) cm(-3), the model can be used to predict the critical thickness for generation of the orthogonal A(g) dislocation set, with the x-ray topographs showing that the B(g) misfit multiplication occurs at damaged edges of the wafer. However, above 2x10(18) cm(-3) Si concentration, the critical thickness for A(g) nucleation becomes almost independent of concentration and the x-ray topographs show that cross slip becomes important in the multiplication process. For most of the Si concentrations examined, the critical thickness for nucleation of the slow A(g) misfit dislocations corresponded to that of multiplication of the fast B(g) set. (C) 2002 American Institute of Physics.