Abstract: A compositionally-graded, strain relaxed Si1-xGex (0<x<1) material having a surface roughness of less than 1 nm. In a preferred aspect, the compositionally-graded material is Si1-xGex (0<x<0.3) material having a threading dislocation density <1×105 defects/cm2 of surface area. The compositionally-graded material is readily formed by vapor deposition or other suitable technique, in which the temperature is selectively modulated during the growth process, optionally with modulation of germanium precursor flow rate, to produce a low surface roughness, low threading dislocation defect density graded silicon-germanium film suitable for forming strained heterostructures such as Si1-xGex/Si.