Surface of glassy $\mathrm{GeS}{}_2$: A model based on a first-principles approach

First-principles calculations within the framework of the density functional theory are used to construct realistic models for the surface of glassy $\mathrm{GeS}{}_2\left(g\text{−}\mathrm{GeS}{}_2\right)$. Both calculations at $T=0$ K and at finite temperature ($T=300$ K) are considered. This allows for a comparison between the structural and electronic properties of surface and bulk $g\text{−}\mathrm{GeS}{}_2$. Although the $g\text{−}\mathrm{GeS}{}_2$ surface recovers the main tetrahedral structural motif of bulk $g\text{−}\mathrm{GeS}{}_2$, the number of fourfold coordinated Ge atoms and twofold coordinated S atoms is smaller than in the bulk. On the contrary, the surface system features a larger content of overcoordinated S atoms and threefold coordinated Ge atoms. This effect is more important for the $g\text{−}\mathrm{GeS}{}_2$ surface relaxed at 0 K. Maximally localized Wannier functions (WF) are used to inspect the nature of the chemical bonds of the structural units present at the $g\text{−}\mathrm{GeS}{}_2$ surface. We compare the ability of several charge derivation methods to capture the atomic charge variations induced by a coordination change. Our estimate for the charges allows exploiting the first-principles results as a data base to construct a reliable interatomic force field.

Figure 1

Typical molecular configuration of the 480 atoms forming the $g\text{−}\mathrm{GeS}{}_2$ surface models refined at (a) 300 K [$g\text{−}\mathrm{GeS}{}_2\left(s\right)$] and (b) 0 K [$g\text{−}\mathrm{GeS}{}_2\left(s\right)@0$K]. For each system, the blue lines show the simulation box. Colors: S atoms in yellow and Ge atoms in ochre. Red tetrahedra show tetrahedrally coordinated Ge atoms. Cyan spheres are the bottom atoms kept frozen during the simulations (104 atoms).

Figure 2

Ge-S (top), Ge-Ge (middle), and S-S (bottom) pair correlation functions: $g_{\alpha \beta }\left(r\right)$ for $g\text{−}\mathrm{GeS}{}_2\left(b\right)$ (black line) and ${\tilde{g}}_{\alpha \beta }\left(r\right)$ for $g\text{−}\mathrm{GeS}{}_2\left(s\right)$ (red line) at 300 K; the data for $g\text{−}\mathrm{GeS}{}_2\left(s\right)$ were corrected for the finite size of the sample (see text). (Inset) Detailed view of the first peak for the $g_{\mathrm{GeS}}\left(r\right)$. Dashed lines: position of the first peak of the Ge-S $g_{\alpha \beta }\left(r\right)$ for $g\text{−}\mathrm{GeS}{}_2\left(b\right)$.

Figure 3

S-Ge-S (top) and Ge-S-Ge (bottom) bond-angle distributions (BAD). The black and red lines correspond to the data for $g\text{−}\mathrm{GeS}{}_2\left(b\right)$ and $g\text{−}\mathrm{GeS}{}_2\left(s\right)$, respectively. The inset shows the BAD for $g\text{−}\mathrm{GeS}{}_2\left(s\right)$ which is decomposed in corner-sharing (CS, dashed line) and edge-sharing (ES, solid line) contributions.

Figure 4

Total structure factors for $g\text{−}\mathrm{GeS}{}_2\left(b\right)$ (black line) and the $g\text{−}\mathrm{GeS}{}_2\left(s\right)$ model (red line).

Figure 5

The Faber-Ziman partial structure factors $\mathrm{S}{}_{\mathrm{SS}}^{\mathrm{FZ}}\left(k\right)$ (top), $\mathrm{S}{}_{\mathrm{GeGe}}^{\mathrm{FZ}}\left(k\right)$ (middle), and $\mathrm{S}{}_{\mathrm{GeS}}^{\mathrm{FZ}}\left(k\right)$ (bottom). The black and red lines correspond to the data for $g\text{−}\mathrm{GeS}{}_2\left(b\right)$ and for $g\text{−}\mathrm{GeS}{}_2\left(s\right)$, respectively.

Figure 6

Electronic density of states (EDOS) extracted from the Kohn-Sham eigenvalues $\left(\Delta E=E-E_{\mathrm{Fermi}}\right)$ The black and red lines correspond to the data for $g\text{−}\mathrm{GeS}{}_2\left(b\right)$ and for $g\text{−}\mathrm{GeS}{}_2\left(s\right)$, respectively.

Figure 7

Zoom in a configuration of $g\text{−}\mathrm{GeS}{}_2\left(s\right)$ showing both heteropolar and homopolar bonds. Details are given in the text. Ge and S atoms appear as ochre and yellow spheres, respectively. The purple spheres are the WF centers, which correspond to both lone $\left(\mathrm{WF}{}_{lp}\right)$ and bond pairs $\left(\mathrm{WF}{}_b\right)$ of electrons.

Figure 8

Correlation functions of S-WF pair, $g_{\mathrm{SWF}}$(r) for $g\text{−}\mathrm{GeS}{}_2\left(s\right)$ (red line). The dashed lines show the position of the peaks for the $g\text{−}\mathrm{GeS}{}_2\left(b\right)$. $\mathrm{WF}{}_{lp}$ and $\mathrm{WF}{}_b$ indicate the peaks due to the correlation between S atoms and the WF lone pairs and WF bonds, respectively (see text).

Figure 9

Ge (top) and S (bottom) partial atomic charges as a function of the coordination number, i.e., the total number of atoms (Ge or S) around a given atom. The different sets of data correspond to charges derived from the following methods: Qeq (red), EQeq (orange), Mulliken (purple), Löwdin (pink), ESP (green), and Bader (blue) (see text).