Deviations from Vegard's law in semiconductor thin films measured with X-ray diffraction and Rutherford backscattering: The Ge1-ySny and Ge1-xSix 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 < y < 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.

Raman shifts in MBE‐grown SixGe1 − x − ySny alloys with large Si content

“…Only slight deviations of up to 1.6 pm are found between the predictions of Vegard's law and the actual lattice constants (Table 1). Even better agreement could be found between our XRD results and an empirical nonlinear model discussed by Xu et al, [16] which includes bowing parameters for the lattice constant of Si x Ge 1 − x − y Sn y alloys. [16] This indicates the applicability of bowing parameters obtained from binary alloys to the ternary Si x Ge 1 − x − y Sn y system, even in the regime where both x Si and y Sn are high.…”

“…Quantitative information on composition for all samples was obtained from RBS measurements, as published elsewhere. [9,13] We note that the RUMP simulation software was used for fitting of the random RBS spectra with normalization with respect to the Ge buffer, as recommended by Xu et al [16] An example fit and detailed discussion is provided by Wendav et al [9] Table 1 shows the compositional information for the three different positions on the wafer, that is, at the center (I), at half the radius (II), and at the edge (III) of each wafer. For all samples, the Sn content as obtained from RBS measurements was found to increase from the center towards the edge of the wafer (Table 1).…”

“…In contrast, given its much shorter Raman penetration depth of 10 nm, [17] the T A B L E 1 Structural characterization results at the three positions on a 4-in. wafer for all samples: Si and Sn atomic fractions x Si and y Sn , in-plane and out-of-plane lattice constants a p and a s , theoretical unstrained lattice constant a 0 , prediction of Vegard's law a Veg , nonlinear prediction a nl , 16 Before we provide a quantitative treatment of our measurement results for the strongest modes (Ge-Ge, Si-Ge, and Si-Si), we briefly discuss the qualitative effects of compositional changes on all observable modes, starting from those with the largest Raman shift (Figure 1).…”

Strain engineering of transverse electric and transverse magnetic mode of material gain in GeSn/SiGeSn quantum wells

“…Remaining material parameters for (Si)GeSn alloys, which are needed for the electronic band structure and the material gain calculations, are obtained from the linear interpolation of material parameters for the parent materials (Si, Ge, and Sn) taken from refs 16,48,53–69 and are given in the Table 1. Currently it is experimentally documented that the lattice constant of GeSn is described by the linear interpolation 70 . This conclusion is also very consistent with the recent DFT calculations of the lattice constant for GeSn 16 .…”

Process for Growth of Group-IV Alloys Containing Tin by Remote Plasma Enhanced Chemical Vapor Deposition

“…Reciprocal space maps (RSM) of the (224) reflection and 2θ-ω scans of the (004) reflection were performed using a PANanalyical Empyrean X-ray diffractometer. Film composition and strain were determined (McSkimin, 1953;Xu et al, 2017) using these measured values of lattice parameters and the elastic constants for Ge and Sn. Crosssectional, bright field, transmission-electron-microscopy (TEM) along the <110> direction was used to evaluate the crystalline structure of the layer as well as to investigate the substrate/film interface.…”