Methods for depositing epitaxial films such as epitaxial Ge and SiGe films. During cooling from high temperature processing to lower deposition temperatures for Ge-containing layers, Si or Ge compounds are provided to the substrate. Smooth, thin, relatively defect-free Ge or SiGe layers result. Retrograded relaxed SiGe is also provided between a relaxed, high Ge-content seed layer and an overlying strained layer.