Structure, electronic properties, and energetics of oxygen vacancies in varying concentrations of ${\mathrm{Si}}_x{\mathrm{Ge}}_{1-x}{\mathrm{O}}_2$

SiGe alloys, widely used in various technological applications, are typically interfaced with a thermally grown oxide layer that is composed of ${\mathrm{Si}}_x{\mathrm{Ge}}_{1-x}{\mathrm{O}}_2$, a composite material which is also used for technological applications in its own right. Point defects in this oxide layer influence the electronic and structural properties, which can detrimentally affect the desired application. In this paper, we use ab initio calculations to investigate the canonical oxygen vacancy in systems of varying compositions of ${\mathrm{Si}}_x{\mathrm{Ge}}_{1-x}{\mathrm{O}}_2$. We find that the electronic structures and geometries of the vacancies remain qualitatively similar to their well-known analogs in ${\mathrm{SiO}}_2$ and ${\mathrm{GeO}}_2$ regardless of the composition and similar to previous results in the literature on Ge-doped ${\mathrm{SiO}}_2$. They show a wide distribution of formation energies and one-electron levels across the various concentrations of ${\mathrm{Si}}_x{\mathrm{Ge}}_{1-x}{\mathrm{O}}_2$. However, our results show that the factor defining their quantitative behavior is not the concentration, rather it is the chemistry of the atoms around the vacancy, each combination of which has its own distribution of properties. The resulting charge transition levels similarly cover a wide range of the band gap. These results aid the understanding of reliability issues in technological applications.

Figure 1

Total neutron structure factors of a-${\mathrm{SiO}}_2$ (top panel) and a-${\mathrm{GeO}}_2$ (middle panel) compared to experiment [37]. The black solid lines are the results from the calculated models, while the red markers with dashed lines are data points from experiment. The bottom panel shows the simulated structure factors for all concentrations of ${\mathrm{Si}}_x{\mathrm{Ge}}_{1-x}{\mathrm{O}}_2$ considered in this paper which show a smooth transition from the structure factor of a-${\mathrm{GeO}}_2$ to a-${\mathrm{SiO}}_2$.

Figure 2

Atomistic structure and highest occupied orbital of the neutral vacancy in ${\mathrm{Si}}_x{\mathrm{Ge}}_{1-x}{\mathrm{O}}_2$ where the Si content is 25%. The Si, Ge, and O atoms are represented by pink, yellow, and red spheres, respectively. The displayed vacancy is made of a Si and Ge atom. However, the vacancy had the same qualitative electronic and atomistic structure for all atom combinations. The orbital is occupied by two electrons and the isovalue of the orbital's surface is 0.05 eÅ${}^{-3}$.

Figure 3

Histograms of the neutral oxygen vacancy's formation energy in ${\mathrm{Si}}_x{\mathrm{Ge}}_{1-x}{\mathrm{O}}_2$ systems. The formation energies are decomposed by the atoms surrounding the vacancy, with green, yellow, and blue bars representing vacancies composed of Ge-Ge, Si-Si, or Si-Ge, respectively. From bottom to top, the rows represent 0%, 25%, 75%, and 100% Si concentration.

Figure 4

Scatter plot of the oxygen vacancy's formation energy in ${\mathrm{Si}}_x{\mathrm{Ge}}_{1-x}{\mathrm{O}}_2$ against the distance of the atoms surrounding the vacancy. The panels show results for the neutral, negative, and positive (dimer and puckered) charge states. Green, yellow, and blue circles are vacancies composed of Ge-Ge, Si-Si, and Si-Ge dimers, respectively.

Figure 5

The spin density and geometry of the negatively charged Ge-Ge vacancy in ${\mathrm{Si}}_x{\mathrm{Ge}}_{1-x}{\mathrm{O}}_2$ where the Si content is 50%. The atoms around the vacancy are both Ge, but the structure is qualitatively similar regardless of the atoms surrounding the vacancy. The color scheme is the same as that in Fig. 2. The orbital isosurface's isovalue was set to 0.05 eÅ${}^{-3}$.

Figure 6

Atomistic structure and spin density of the positively charged vacancy in ${\mathrm{Si}}_x{\mathrm{Ge}}_{1-x}{\mathrm{O}}_2$ where the Si content is 50%. The color scheme can be found in Fig. 2. The positive vacancy has two configurations: the dimer (top panel) and the puckered (bottom panel) configurations. For both configurations, an Si and a Ge atom was visualized. We note, however, that the atomistic and electronic structures are qualitatively similar regardless of the atoms around the vacancy. The interaction between the Si and a back oxygen in the puckered configuration is highlighted by a dashed ellipsis. Note that this is not a covalent bond, but rather an electrostatic interaction between the positively charged Si and the negatively charged O. The isovalue of both orbital's surface was set to 0.05 eÅ${}^{-3}$.

Figure 7

Histogram of the vacancy's charge transition levels in varying concentrations, indicated in the gray boxes, of Si in ${\mathrm{Si}}_x{\mathrm{Ge}}_{1-x}{\mathrm{O}}_2$. The levels are referenced to the top of the ${\mathrm{Si}}_x{\mathrm{Ge}}_{1-x}{\mathrm{O}}_2$ valence band for the relevant concentration. The green histograms correspond to Ge-Ge, yellow to Si-Si, and blue to Si-Ge vacancies. The ($+$/0) transition levels are the curves with a solid fill, while the curves with a hatched fill are the (0/$-$) transition levels. The shaded regions represent band edges: below 0 eV is the valence band edge, while the regions above 0 eV are the concentration-dependent conduction band edges as indicated.