Bond-length relaxation in crystalline Si1−xGex alloys: An extended x-ray-absorption fine-structure study

Abstract

Extended x-ray-absorption fine-structure spectra for crystalline ${\mathrm{Si}}_{1\mathrm{-}\mathit{x}}$ ${\mathrm{Ge}}_{\mathit{x}}$ alloys, measured at the K edge of Ge at room temperature, are analyzed with a curve-fitting method based on the spherical-wave approximation. The Ge-Ge and Ge-Si bond lengths, coordination numbers of Ge and Si atoms around a Ge atom, and Debye-Waller factors of Ge and Si atoms are obtained. It is shown that Ge-Ge and Ge-Si bonds relax completely, for all Ge concentrations of their study, while the lattice constant varies monotonically, following Vegard’s law. As noted by Bragg and later by Pauling and Huggins, the Ge-Ge and Ge-Si bond lengths are close to the sum of their constituent-element atomic radii: nearly 2.45 Å for Ge-Ge bonds and 2.40 Å for Ge-Si bonds. A study on the coordination around a Ge atom in the alloys revealed that Ge and Si atoms mix randomly throughout the compositional range studied.