Ab initio investigation of amorphous Sb₂Te

Abstract

Chalcogenide phase-change alloys are an important class of materials for applications in data storage. In this work, we investigate the structural properties of the amorphous phase of the phase-change material Sb₂Te. We show that all the atoms in Sb₂Te are in a defective octahedral environment, that the majority of primitive rings are five- and four-membered, and that the voids are small and amount to about 2 % of the total volume of the system.

Graphical Abstract

Introduction

Phase-change materials (PCMs) are chalcogenide-based alloys that are capable of switching rapidly and reversibly between the amorphous and crystalline phases upon heating. The marked optical and electrical contrast between the two phases and the thermal stability of PCMs at room temperature has led to their application in data-storage devices, including rewritable optical media (CDs, DVDs, Blu-ray discs) and electronic nonvolatile memory (PC-RAM) [1, 2]. In these two classes of devices, heating is induced by laser irradiation and the Joule effect, respectively. Recent developments include the realization of PCM prototype devices displaying neuron-like processing capabilities [3], and the observation of magnetic contrast in PCMs doped with magnetic impurities [4–6]. Two classes of PCMs have proven to be the best candidates for practical applications: GeTe–Sb₂Te₃ pseudobinary alloys (group 1) and doped Sb–Te compounds near the eutectic composition Sb₇₀Te₃₀ (group 2). The structural and electronic properties of the crystalline and amorphous phases of these PCMs have been extensively studied experimentally [7–14]. There have also been numerous density functional theory (DFT) investigations of the crystalline phases of both groups of PCMs and the amorphous phases of group 1 materials [14–22]. However, only a few computational studies of amorphous group 2 PCMs have been performed [14].

The crystallization speeds of Sb₇₀Te₃₀ and other SbTe alloys, including Sb₂Te and Sb₄Te, are very high; however, their crystallization temperatures are relatively low (80–100 °C), which prevents their utilization in devices. The crystallization temperature can be significantly increased by doping with selected elements such as Ag, In, Ge, and Ga [23]. In [14], a Sb₄Te alloy doped with Ag and In, Ag_3.5In_3.8Sb_75.0Te_17.7 (AIST), was investigated using a combined experimental and DFT approach. It was shown that, just as it is in the crystalline phase, the local environment around Sb atoms in amorphous AIST is a 3 + 3 (distorted) octahedron. It was also suggested that fast crystallization occurs due to interchanges between short and long bonds. These results indicate that AIST behaves differently from most group 1 PCMs, in which the short-range order changes considerably upon amorphization [15–17, 19].

In the work described in the present paper, we performed ab initio molecular dynamics (AIMD) simulations to study the structural properties of clean amorphous Sb₂Te (a-Sb₂Te). Here, we compare the results of those simulations with the results of the previous work on AIST mentioned above [14], and discuss how the presence of Ag and In impurities and changes in the Sb concentration affect the short-range and medium-range order of the amorphous phase. In order to gain a better understanding, we also studied amorphous Sb₂Te₃ (a-Sb₂Te₃), an Sb–Te alloy that belongs to group 1 [24].

Results and discussion

We calculated the total g(r) and the partial pair-correlation functions (PPCFs) based on the MD trajectory at 300 K (see Fig. 1).

Fig. 1

Total and partial pair-correlation functions of amorphous Sb₂Te (red solid line) and Sb₂Te₃ (black dashed line) at 300 K. Vertical lines indicate the cutoff radius used to compute coordination numbers

In the case of a-Sb₂Te, the first peak in the Sb–Te and Sb–Sb PPCFs is around 2.95 Å, whereas the Te–Te PPCF shows no peak below 3.3 Å. This indicates that Te–Te bonds are absent, in agreement with the case of AIST [14]. The similar heights and widths of the first peaks in the Sb–Sb and Sb–Te PPCFs suggest that comparable amounts of heteropolar Sb–Te and homopolar Sb–Sb bonds are present. In the case of the Te-rich alloy Sb₂Te₃, on the other hand, the heteropolar Sb–Te bonds are prevalent, whereas the fraction of Te–Te bonds is relatively small. In a-Sb₂Te₃, there is also a significant fraction of Sb–Sb bonds, albeit much smaller than in a-Sb₂Te. In the total g(r) of a-Sb₂Te₃, a tiny shift of the first peak to smaller distances is observed as compared to the g(r) of a-Sb₂Te. For both compounds, the position of the first peak of the g(r) is slightly shifted (about 3 %) to shorter r with respect to the g(r) of the corresponding crystalline phases [25]. The g(r) of crystalline Sb₂Te and that of Sb₂Te₃ exhibit a second peak at 3.2–3.3 Å, which reflects the existence of longer bonds and 3 + 3 distorted octahedral structures due to Peierls distortion. Matsunaga et al. [14] observed a shoulder on the second peak in the total correlation function of amorphous AIST, which corresponded to the second peak of the crystal, suggesting the existence of 3 + 3 octahedral structures in the disordered phase as well. However, we did not see any such feature in the total g(r) and the PPCFs of our model of a-Sb₂Te. This might be due to the different stoichiometry (in particular, the lower concentration of Sb atoms in our model), or to the fact that their structure was refined using a reverse Monte Carlo method. It is interesting to note that, in the case of several group 1 PCMs such as GeTe and Ge₂Sb₂Te₅, much larger reductions in the average bond lengths occur upon amorphization [26].

Using the cutoff radius indicated in Fig. 1, we calculated the coordination numbers in both models. The distribution of the coordination numbers is shown in Fig. 2 and the average coordination numbers are presented in Table 1. In a-Sb₂Te, the majority of the Sb atoms are fourfold coordinated. The number of threefold- and fivefold-coordinated Sb atoms is quite large too. Te atoms have predominantly threefold or fourfold coordination, although a significant number of twofold-coordinated Te atoms are also present. While, in principle, there is no reason to expect a perfect agreement between our model and that for AIST provided in [14] given their different stoichiometries and the absence of impurities in our model, it turns out that the apparent discrepancies in the average coordination numbers of the Sb and Te atoms in the two models (see Table I in [14]) are mostly due to the larger cutoff radii used in our work. In a-Sb₂Te₃, the fraction of four-coordinated Sb atoms is larger than it is in a-Sb₂Te, and Te atoms are mostly two- and three-coordinated. In contrast to the case of a-Sb₂Te, the number of four-coordinated Te atoms is small. The latter results are in good agreement with those presented in [24].

Fig. 2

Distributions of coordination numbers in amorphous Sb₂Te and Sb₂Te₃

Table 1 Average coordination numbers of Sb and Te atoms in amorphous Sb₂Te and (in parentheses) in Sb₂Te₃

The local order parameter q [15] was computed for each atom in the two models, and the results indicated that no tetrahedral structure was present. To shed light on the local bonding environment, we also calculated angular distribution functions. In Fig. 3, we show the angular distribution functions averaged over all atoms (black curve), over all Sb atoms (red curve), and over all Te atoms (blue curve) for both a-Sb₂Te and a-Sb₂Te₃. The distributions exhibit a large peak at ~90° and a smaller peak at ~165°, indicating that most atoms are in a (defective) octahedral-like environment in both systems. In the case of a-Sb₂Te₃, there is no peak in the distribution function of Te near 180°, consistent with the fact that most Te atoms have a twofold or threefold coordination—without neighbors on opposite sides. In a-Sb₂Te, the number of Te atoms in a fourfold defective octahedral configuration is larger (see Fig. 2), hence a broad shoulder appears at large angles in the corresponding angular distribution function. In summary, the amorphous networks in a-Sb₂Te and a-Sb₂Te₃ mostly comprise defective octahedral motifs. A snapshot of the amorphous structure of a-Sb₂Te is shown in Fig. 4, where the most predominant structural motifs are represented by balls and sticks.

Fig. 3

Angle distribution functions of amorphous Sb₂Te and Sb₂Te₃

Fig. 4

Snapshot of amorphous Sb₂Te. The most common structural motifs are represented by balls and sticks

The distribution of primitive rings, which describes the medium-range order in the amorphous network, is shown in Fig. 5 for both systems. For a-Sb₂Te₃, four-membered rings are prevalent (18 %), in agreement with [24], whereas five-membered rings are the most common in the model of a-Sb₂Te (18 %), though the number of four-membered rings is only slightly smaller (15 %). Similar results hold for AIST [14]. The majority of the four-membered rings in a-Sb₂Te₃ (82 %) have SbTeSbTe alternation. This is not the case in a-Sb₂Te (25 %). In a-Sb₂Te, the fraction of larger rings (between six- and 14-membered) is quite significant. Interestingly, in a-Sb₂Te₃ the distribution of rings is even broader, and several very large rings are present. This result is in line with the low average coordination number of Te atoms in a-Sb₂Te₃.

Fig. 5

Statistics for primitive rings in amorphous Sb₂Te and Sb₂Te₃ (ring length is the number of atoms in the ring)

We also calculated the volume occupied by cavities in the two amorphous systems using the method developed in [27], which is implemented in the program VNP [28]. Atomic radii are set equal to 50 % of the average bond length for each species, whereas the radius of the test sphere is set to 1.3 Å. The fraction of the total volume occupied by the voids is 18 % in a-Sb₂Te₃ and 2 % in a-Sb₂Te. Furthermore, we computed the distribution of the volume of the cavities for the two amorphous systems (see Fig. 6). In agreement with [24], we found that the number of cavities in a-Sb₂Te₃ is large, as is their average size. On the other hand, there are only a few cavities in a-Sb₂Te, and they are small. The large concentration of voids and large rings in a-Sb₂Te₃ may be partly due to the fact that, for this system, we used the theoretical value for the density computed in [24] (we used an experimental one for a-Sb₂Te instead see "Methods"). Nevertheless, these results clearly indicate a more open structure in a-Sb₂Te₃.

Fig. 6

Distributions of cavity volume for amorphous Sb₂Te and Sb₂Te₃

In conclusion, our study shows that amorphous Sb₂Te mostly consists of defective octahedral structures, as also seen in the case of Sb₂Te₃. In contrast to the latter, however, a-Sb₂Te has a less open structure, as evidenced by the smaller number of large rings and cavities.

Methods

The amorphous phases of both Sb₂Te and Sb₂Te₃ were generated by quenching from the melt. A novel, Car–Parrinello-like scheme [29] was adopted for our AIMD simulations. This method was implemented in the CP2K suite of programs [30, 31]. The generalized gradient approximation (GGA) to the exchange–correlation potential [32] and scalar-relativistic Goedecker pseudopotentials [33] were used. The Kohn–Sham orbitals were expanded in a triple-zeta plus polarization Gaussian-type basis set, whereas the charge density was expanded in plane waves with a cutoff of 300 Ry. 270-atom models were considered for both alloys. Because of the large sizes of the models, the Brillouin zone was sampled at the Γ point only. The time step for the simulations was 2 fs. The systems were first randomized at very high temperature (3,000 K) for 14 ps, and then equilibrated at the (experimental) melting temperature for 30 ps, quenched from the melting temperature to 300 K within 30 ps, equilibrated at 300 K for 30 ps, and finally quenched to 10 K in 20 ps. Geometry optimization was also performed, starting from the low-temperature MD trajectory. The atomic density of Sb₂Te was set to the experimental value of 0.0309 atoms/ų (we used the atomic density of Sb₂Te doped with Ag and In, as determined in [13], thereby assuming that the small amount of Ag and In does not change the atomic density significantly). Due to the lack of experimental data on the density of Sb₂Te₃, we used the theoretical value of 0.0271 atoms/ų, as determined in [24].