Phase change memory materials: Rationalizing the dominance of Ge/Sb/Te alloys

Rewritable optical storage is dominated by alloys of a small number of elements, overwhelmingly Ge, Sb, and Te. For over 30 years, Ge/Sb/Te alloys in the composition range ${\left(\mathrm{GeTe}\right)}_{1-x}{\left({\mathrm{Sb}}_2{\mathrm{Te}}_3\right)}_x(0\le x\le 1)$ have been the materials of choice in commercial devices: all have metastable rock-salt structures that change little over decades at archival temperatures, and all contain vacancies (cavities). The special status of Ge/Sb/Te alloys arises from the close similarity of their valence orbitals as measured by the orbital radial moments, so that bonds are stronger than in other combinations of elements of groups 14–16 with appropriate valences. The orbital similarity arises from the irregular changes in atomic orbitals and properties as the atomic number increases (“secondary periodicity”). Jones showed [P. R. Soc. London, Ser. A 147, 396 (1934)] that the simple cubic structure of (metallic) Bi (valence configuration $6s^{2}6p^3$) is unstable to a distortion to a (semimetallic) rhombohedral structure. This picture can be adapted to Ge/Sb/Te alloys to explain the metastable structure of the above family of compounds where vacancies almost always occur next to Te atoms, which form one sublattice of the rock-salt structure. The disorder in the Ge/Sb/vacancy sublattice is not random.

Figure 1

Radial orbital functions $r{R}_{nl};(n=2–6)$ for $s$- (solid curves) and $p$- (dashed curves) valence electrons in group 14 elements. Secondary periodicity is particularly evident in the $p$ orbitals.

Figure 2

First radial moments [Eq. (1)] for $s$- (solid curves) and $p$- (dashed curves) valence electrons in elements of groups 13–16.

Figure 3

Radial orbital functions $r{R}_{nl}$ for $s$- (full curves) and $p$- (dashed curves) valence electrons in Ge (green), Sb (red), and Te (blue).

Figure 4

Nearly free-electron model of Peierls [64].

Figure 5

Free-electron bands for structures with the translational periodicity of fcc lattices. $X$: 100, $\mathrm{\Gamma }$: 000, $L$: $\frac{1}{2}\frac{1}{2}\frac{1}{2}$, and $W$: $1\frac{1}{2}0$ [in units of ($2\pi /a)$, where $a$ is the lattice constant]. Energies in units of (${2\pi /a)}^2$. Also shown are the band degeneracies and the Fermi energies corresponding to eight (blue, dashed) and ten (red, solid) valence electrons in the unit cell.

Figure 6

SC structure (green, dashed) represented as two fcc lattices (red, black) displaced by half of the body diagonal of the latter.

Figure 7

(a) Fourth Brillouin zone and (b) Jones zone of structures with the fcc translational structure. (c) Fifth Brillouin zone of the fcc structure and (d) Jones zone of the bismuth ($A7$) structure.

Figure 8

Calculated electronic density of states (DOS) of amorphous [(am), red], crystalline [(cr), blue], and liquid [(liq), green] GST at 900 K [84]. The vertical dashed line at $E=0$ marks the Fermi energy. Amorphous and crystalline calculations used a $2\times 2\times 2$ Monkhorst-Pack mesh, and the liquid DOS is based on five snapshots with one $k$ point ($k=0$).

Figure 9

Structure of (metastable) crystalline GST [28]. Orange: Te, gray: Ge, and purple: Sb. Ordering in the Te layers is almost complete. Segregation in the other layers is evident.