Nature of Atomic Bonding and Atomic Structure in the Phase-Change ${\mathrm{Ge}}_2{\mathrm{Sb}}_2{\mathrm{Te}}_5$ Glass

Using electronic structure calculations, we demonstrate a global valence alternation in the amorphous ${\mathrm{Ge}}_2{\mathrm{Sb}}_2{\mathrm{Te}}_5$, a prototype phase-change alloy for data storage. The resulting $p$ bonding profoundly influences the local atomic structure, leading to right-angle components similar to those in the crystalline counterpart of this chalcogenide glass. The dominance of $p$ bonding is revealed by (i) distributions of the coordination number (CN) and the bond angle, for truly bonded atoms determined based on the electron localization function, and (ii) a direct evaluation of the $p$ (and $s$) orbital occupation probability for the $\mathrm{CN}=3$ Ge atoms that form 90° bonds with neighbors.

Figure 1

Calculated (a) total and partial pair-correlation functions and (b) bond-angle distributions of $a$-GST. Inset in (a) displays a ball-stick model (189 atoms) of the $a$-GST, quenched from liquid to 300 K. The density is $6.11\mathrm{g}/{\mathrm{cm}}^3$. The green (medium gray), purple (dark gray), and yellow (light gray) balls represent Ge, Sb, and Te atoms, respectively.

Figure 2

Schematic of (a) the electronic structure and the bonding geometry of Ge, Sb, and Te in an ideal glass model, and (b) the valence alternation process between Ge and Te. In 3D space, the $s{p}^3$ bonds have the tetrahedral shape with bond angles of 109°, while the $p$ bonds are perpendicular to each other. The valence alternation changes not only the CN of the Ge and Te, but also the bond angle around Ge.

Figure 3

(a) Representative ELF profiles for a Ge atom and its neighbors (the neighboring atom at 3.03 Å appears to be not covalently bonded). (b) The ELF distribution between all atom pairs within a distance cutoff of 3.5 Å. The threshold ELF value (0.58 for actual bonding) is labeled by the arrow, which cuts across the valley separating the peak and tail. (c) The CN around each element, for chemically bonded neighbors. (d) Bond-angle distributions for Ge atoms with $\mathrm{CN}=3$ and $\mathrm{CN}=4$, respectively. The 90° and 109° angles are marked with dashed lines.

Figure 4

The total and projected DOS for (a) Ge in $a$-GST, (b) Sb in $a$-GST, and (c) Ge in diamond Ge. (d) Occupation probability of $4s$ and $4p$ orbitals (within the core region) for Ge atoms in $a$-GST, showing that the $\mathrm{CN}=3$ and $\mathrm{CN}=4$ Ge atoms belong to two bifurcated groups. Average values for Ge in crystalline Ge ($s{p}^3$) and Ge in $c$-GST ($p$-type bonding in rocksalt structure) are also given as references.