Deviations from Vegard's law in semiconductor thin films measured with X-ray diffraction and Rutherford backscattering: The Ge1-<i>y</i>Sn<i>y</i> and Ge1-<i>x</i>Si<i>x</i> cases

Abstract

The compositional dependence of the lattice parameter in Ge1-ySny alloys has been determined from combined X-ray diffraction and Rutherford Backscattering (RBS) measurements of a large set of epitaxial films with compositions in the 0 &amp;lt; y &amp;lt; 0.14 range. In view of contradictory prior results, a critical analysis of this method has been carried out, with emphasis on nonlinear elasticity corrections and systematic errors in popular RBS simulation codes. The approach followed is validated by showing that measurements of Ge1-xSix films yield a bowing parameter θGeSi =−0.0253(30) Å, in excellent agreement with the classic work by Dismukes. When the same methodology is applied to Ge1-ySny alloy films, it is found that the bowing parameter θGeSn is zero within experimental error, so that the system follows Vegard's law. This is in qualitative agreement with ab initio theory, but the value of the experimental bowing parameter is significantly smaller than the theoretical prediction. Possible reasons for this discrepancy are discussed in detail.