Structure of amorphous ${\mathrm{Cu}}_2{\mathrm{GeTe}}_3$ and the implications for its phase-change properties

The structure of amorphous ${\mathrm{Cu}}_2{\mathrm{GeTe}}_3$ is investigated by a combination of anomalous x-ray scattering and extended x-ray absorption fine-structure experiments. The experimental data are analyzed with reverse Monte Carlo modeling, and they are interpreted in terms of short-range-order parameters as well as by using ring statistics and persistent homology to study the intermediate-range order. Based on this information, the structural relationship of the amorphous phase to the corresponding crystal is discussed. It is found that the amorphous network can be rationalized by small atomic displacements of the crystal structure, directed toward the intrinsic void regions. This structural similarity establishes the possibility of a fast phase-change process. On the other hand, the atomic rearrangements also lead to the formation of new chemical bonds and to distortions on the intermediate-range-order level. These are realized by a collapse and contraction of the strict hexagonal ring arrangements of the crystal and by the formation of small, triangular rings as well as Cu cluster configurations. These structural features allow for a new understanding of the phase-change property contrast of this material, especially concerning the density change and the optical contrast.

Figure 1

Experimental data: (a) AXS and (b) XAFS. Black symbols are experimental data. RMC fits are displayed as colored lines, with data acquired near the absorption edges of Te (purple), Ge (blue), and Cu (red); the total $S\left(Q\right)$ is shown in gray.

Figure 2

RMC results for the partial structure factors $S_{ij}\left(Q\right)$ in the present model. The lines represent the average over the set of RMC calculations, which have standard deviations as indicated by the error bars.

Figure 3

RMC results for the partial pair correlations functions $g_{ij}\left(r\right)$ in the present model. The lines represent the average over the set of RMC calculations, which have standard deviations as indicated by the error bars.

Figure 4

Bond-angle distribution in amorphous CGT, around Cu (red), Ge (blue), and Te atoms (purple). The lines represent the average over the set of RMC calculations, which have standard deviations as indicated by the error bars. For reference, the angular distribution in the crystal is schematically shown as the dashed area.

Figure 5

Ring statistics in amorphous CGT (a) and the composition of the rings (b). The inset in (a) visualizes the sixfold rings in the crystal structure. The colors in (b) denote Cu (red), Ge (blue), and Te atoms (purple). The ring statistics and ring compositions were averaged over the set of RMC calculations, which have standard deviations as indicated by the error bars.

Figure 6

Persistence diagrams for the crystalline phase (a)–(d), which are Ge-centric (a), Cu-centric (b), Ge- and Cu-centric (c), and Te-centric (d), and in the same order for the amorphous phase (e)–(h). Average bond distances in the amorphous phase are indicated with dashed lines. Intensities are plotted in a logarithmic scale. The insets in (a)–(d) visualize the ring structures in crystalline CGT related to the signals in the PDs.

Figure 7

Atomic configurations extracted from one of the RMC configurations of the same slice with a size of about $32\text{Å}\times 32\text{Å}\times 13\text{Å}$. Atomic environments are highlighted around Cu (a), showing only the Cu clusters and chains (b), and around Ge (c) and Te (d). The colors denote Cu (red), Ge (blue), and Te (gold) atoms.

Figure 8

Relationship between the amorphous and crystalline phase of CGT. The crystal structure is shown in (a) and a schematic representation of the ring structure is shown in (b). The amorphous phase can be rationalized as a deformation of the crystal, with a displacement of the atoms toward the six-ring centers, resulting in new ring structures and the formation of wrong bonds (red) in the amorphous phase, illustrated in (c) and (d). Colors denote Cu (red), Ge (blue), and Te (gold) atoms. Images of the structures were produced using vesta [49]. In (b) and (d), filled circles denote Te and empty circles are Cu/Ge atoms. The numbers indicate the size of the ring.