Nucleus-driven crystallization of amorphous Ge${}_2$Sb${}_2$Te${}_5$: A density functional study

Early stages of nucleus-driven crystallization of the prototype phase change material Ge${}_2$Sb${}_2$Te${}_5$ have been studied by density functional/molecular dynamics simulations for amorphous samples (460 and 648 atoms) at 500, 600, and 700 K. All systems assumed a fixed cubic seed of 58 atoms and 6 vacancies. Crystallization occurs within 600 ps for the 460-atom system at 600 and 700 K, and signs of crystallization (nucleus growth, percolation) are present in the others. Crystallization is accompanied by an increase in the number of “$ABAB$ squares” ($A$: Ge, Sb, $B$: Te), and atoms of all elements move significantly. There is no evidence of cavity movement to the crystal-glass interface, as suggested recently, and the existence of Te-Te, Ge-Ge, Ge-Sb, and Sb-Sb (“wrong”) bonds is an inevitable consequence of rapid crystallization.

Figure 1

Visualization of (a–d) the 460-atom and (e, f) 648-atom system at different stages of crystallization at 600 K. The atoms with crystalline local environment are highlighted (ball- and stick), and the fixed cubic seed is visible in the center of (a) and (e). Green: Ge, purple: Sb, and orange: Te.

Figure 2

PDF of atom pairs in 460-atom simulation at 600 K. Each plot is the average over 20 ps of a trajectory. Red: $80–100$ ps, green: $180–200$ ps, blue: $280–300$ ps; magenta: $380–400$ ps, black: $480–500$ ps, orange: $580–600$ ps. Successive plots are shifted by 0.5. The vertical lines correspond to the fixed crystalline seed with lattice constant 3.0 Å.

Figure 3

(a) Total energy (normalized for box size), (b) fraction of crystalline atoms, and (c) number of $ABAB$ rings/atom in each simulation. The discontinuities in slope (steps) in (c) are due to changes in supercell size.

Figure 4

Number of crystalline atoms by element in (a) 500, (b) 600, and (c) 700 K simulations. The vertical dashed lines mark reductions in the supercell size until the crystalline density is reached.

Figure 5

Number of crystalline atoms (460-atom simulations) in the first (0–6 Å from nearest fixed atom) and second (over 6 Å from nearest fixed atom) shell around the fixed seed. The vertical dashed lines mark changes in the supercell size.

Figure 6

(a) Average number of wrong bonds per atom (all simulations). (b) Number of wrong bonds by type at 600 and (c) 700 K. In (a) 460 atoms, red: 500 K, blue: 600 K, magenta: 700 K. 648 atoms, 600 K: black. In (b) and (c): red: Ge-Ge, black: Ge-Sb, blue: Sb-Sb, magenta: Te-Te.

Figure 7

Local environment of Ge atoms 65 and 78 (Ge-Ge bond in center) after 600 ps. Green: Ge, purple: Sb, orange: Te. Two cavities (red) are shown.

Figure 8

Size of percolating crystalline cluster as a function of time. Left, middle, and right columns are 500, 600, and 700 K simulations, respectively. Top, middle, and bottom rows are percolation along $x$, $y$, and $z$ axes, respectively.

Figure 9

MSD for all atoms and for each element at (a) 500, (b) 600, and (c) 700 K. Vertical dashed lines denote changes in box size. Insets show $\sigma \left(\text{MSD}\right)/\text{MSD}$. Fixed atoms were excluded.

Figure 10

Variation of total cavity volume in 460-atom simulations. (a) 600 and (b) 700 K. Vertical dashed lines show changes in box size, shaded areas correspond to the periods of fastest crystallization [$325–450$ ps in (a) and $150–200$ ps in (b)].

Figure 11

Radial distribution of cavity centers from center of seed. (a) 600 and (b) 700 K simulation. Dashed vertical lines show the distances to nearest and farthest edges of the seed.

Figure 12

Cavity size distribution weighted by the cavity volume in 600 K simulation. (a) Before ($0–50$ ps) and (b) after crystallization ($550–600$ ps), and at 700 K. (c) Before ($0–50$ ps) and (d) after crystallization ($320–350$ ps).

Figure 13

Partial PDF involving cavities (cav) in 460-atom simulation at 600 K. (a) Ge-cav, (b) Sb-cav, (c) Te-cav, and (d) cav-cav. Red: Average over $0–100$ ps, dashed blue: average over $500–600$ ps. Note the different scales.