The defect structure in relaxed gradedGe/GexSi1−x/Sistructures grown on (001) exact and (001) off-cut substrates using ultra-high vacuum chemical vapor deposition was characterized using transmission electron microscopy (TEM), atomic force microscopy, and electron beam induced current. The samples grown on off-cut (001) substrates showed a remarkable improvement in surface roughness and dislocation pile-up densities. By applying both a dislocation blocking criterion and surface roughness to graded Si-Ge/Si(001) structures, we can predict the formation of dislocation pile-ups in graded structures. Nonparallel misfit dislocation networks in off-cut wafer samples are not as efficient at blocking perpendicular dislocation motion, leading to a large reduction in dislocation pile-up density. The lower pile-up density on layers grown on off-cut wafers results in less stress-induced surface instability during growth, leading to surfaces with much lower roughness. TEM studies revealed that the array of 60° dislocations, that usually forms to relieve the misfit stress, transforms into a lower energy hexagonal dislocation network consisting of edge dislocations with Burgers vectors of the type 1/2⟨110⟩, 1/2⟨1¯10⟩, and ⟨100⟩. Such reactions were found to be more prevalent in the samples grown on off-cut substrates. Favorable intersections of {111} type planes on the off-cut substrates were found to aid such reactions. ©1997 American Institute of Physics.