Lattice parameters and local atomic structure of silicon-rich Si-Ge/Si (100) films

The lattice parameters and Ge-to-Si nearest-neighbor and next-nearest-neighbor distances were measured using x-ray rocking curves and extended x-ray-absorption fine-structure spectroscopy for four different Si-rich ${\mathrm{Si}}_{1\mathrm{-}\mathit{x}}$ ${\mathrm{Ge}}_{\mathit{x}}$/Si(100) epitaxial films. The Si-Ge films, two prepared by molecular-beam epitaxy and two by chemical-vapor deposition, had thicknesses of 500-900 Å and Ge concentrations of ${\mathit{x}}_{\mathrm{Ge}}$=0.06–0.18. Lattice parameters of the films, corrected for coherency strain, agreed with values reported for bulk Si-Ge alloys. Ge-to-Si distances were 2.375±0.02 Å and 3.85±0.06 Å for nearest and next-nearest neighbors, respectively, and were independent of Ge concentration within these experimental uncertainties. A simple, random-solid-solution model using composition-independent values for nearest-neighbor distances ${\mathit{r}}_{\mathrm{Si}\mathrm{-}\mathrm{Si}}$,${\mathit{r}}_{\mathrm{Ge}\mathrm{-}\mathrm{Ge}}$, and ${\mathit{r}}_{\mathrm{Ge}\mathrm{-}\mathrm{Si}}$ reproduced the average nearest-neighbor distance 〈r〉(${\mathit{x}}_{\mathrm{Ge}}$) deduced from observed lattice parameters a(${\mathit{x}}_{\mathrm{Ge}}$) for our range of Ge concentrations. Composition variations of interatomic distances expected from various theoretical models [Martins and Zunger, Phys. Rev. B 30, 6217 (1984); Shih et al., B 31, 1139 (1985); Thorpe and Garboczi, Bull. Am. Phys. Soc. 35, 781 (1990)] all fell within our experimental uncertainty of ±0.02 Å.