Unveiling the structure and electronic characteristics of amorphous GeS for high performance threshold switching

Phase-change memory is technically mature nonvolatile memory due to the good performance in storage speed and endurance.^1–4 It utilizes the large contrast of reflectivity and resistivity induced by the fast and reversible transition between the crystalline and amorphous states of phase-change materials (PCM) to store the data.^5–7 To address the explosive growth of data, the 3-dimensional (3D) phase-change memory known as 3D XPoint is proposed, by integrating the PCM unit on an ovonic threshold switching (OTS) selector.⁸ Note that both PCM and OTS materials belong to chalcogenides, but OTS materials could realize the threshold switching behavior under electric field without obviously changing the amorphous configuration. Despite the great importance of OTS selector in high-density memory products, the underlying physics is still under debate, leading to the performance bottleneck of OTS devices. Hence, much attention has been attracted on the OTS materials.

The PCM is dominantly composed of the Te-based chalcogenide locating at the pseudo-line between GeTe and Sb₂Te₃ (Refs. 9–11). The fast transition between crystalline and amorphous states is ascribed to the structure similarity of the two phases.^12,13 Different from the PCM, the OTS materials always keep the amorphous states in the cyclic operation, thus requiring a high glass stability. The typical OTS material is amorphous (a-) GeSe, in which the local configurations deviate far from the crystalline state, making it difficult to crystalize.^14–17 To further improve the stability for high endurance, some alien elements, such as C,¹⁸ N,¹⁹ and Si,²⁰ were added to the a-GeSe. In addition, some attempts are carried out on other OTS materials, such as SiTe²¹ and GeTe₆ (Ref. 22), to optimize the OTS behaviors. The OTS mechanism is the key to the function realization of selectors, thus attracting much attention.^23–26 The pure electrical model proposed by Ielmini and Zhang pointed out that the mid-gap states located at the bandgap contribute to the electron migration and play an important role in the OTS mechanism.²⁶ Some studies claimed that the mid-gap states originate from the over-coordinated Ge configurations.^17,27,28 Our previous studies illustrated that the over-coordinated chalcogens could also generate the mid-gap states.^29–31 Recent studies revealed that the a-GeS also presents the OTS behavior and possesses ultrahigh driving current and large selectivity, making it an excellent candidate^32,33 for the high performance OTS selector. However, the understanding of the stability and the OTS behavior of a-GeS is still very limited until now.

In the work, we have studied the structure and electronic property of a-GeS in the amorphization process by ab initio molecular dynamics (AIMD) simulations. The results reveal that a-GeS is dominantly composed of Ge–S bonds. Both Ge- and S-centered clusters are mainly in the form of defective octahedrons in liquid (l-) GeS. When l-GeS is cooled to an amorphous solid, more Ge-centered octahedrons are formed and a small fraction of Ge-centered clusters change to the tetrahedrons, while the S-centered clusters deviate from the octahedral structures notably, leading to the high stability of a-GeS. In addition, the bandgap is increased and the localized states are reduced during the amorphization process, making the charges migrate through the bandgap difficult. Our studies clarify the stability and OTS behavior of a-GeS, which is helpful for the application as an OTS selector.

The studies were carried out by the AIMD simulations with the Vienna Ab initio Simulation Package (VASP) code based on the density functional theory (DFT).^34,35 The exchange correlation functional of the projector augmented-wave (PAW) method was adopted with the Perdew–Burke–Ernzerhof generalized gradient approximation (GGA-PBE).^36–38 During the AIMD simulations, only one Γ point was selected from the Brillouin zone, and the time step was set to 3 fs. The canonical (NVT) ensemble with the Nose-Hoover thermostat was applied to control the temperature and pressure.^39,40 Similar to our previous investigations on the amorphous systems,^29,30,41,42 a cubic box containing 100 Ge and 100 S atoms was built as the initial model; then, a melt-quenching method was utilized to obtain the a-GeS with a cooling rate of 33.3 K/ps. In the cooling process, the configurations under different temperatures were sampled to analyze the local structures. As for the bonding nature and electronic property, the energy cutoff was 500 eV and a 2 × 2 × 2 k-points grids were sampled in the Brillouin zone, the a-GeS was optimized at 0 K, with a force convergence of 0.02 eV.

The dynamics property is displayed in Fig. S1 of the supplementary material, and the atomic mobility is very high at 1000 K and is notably reduced at 300 K, suggesting the transition from liquid to solid. The total pair correlation function g(r) is shown in Fig. 1(a). At 1000 K, a prominent peak is observed at ∼2.41 Å, hinting the distance range of short-range order (SRO) in l-GeS. Meanwhile, a smaller peak is observed at ∼3.62 Å, suggesting the existence of medium-range order (MRO). As the temperature decreases, both of the two peaks become sharper, and their heights are enhanced, indicating that both the SRO and MRO are enhanced in the amorphization process. Figure 1(b) shows the partial g(r) of Ge–S configuration. Only one peak is observed at ∼2.41 Å, which is in line with the first peak of total g(r). It reveals that the Ge–S bonding is the important component of the SRO. The partial g(r) of Ge–Ge configuration is shown in Fig. 1(c). Two peaks are observed in the cooling process. Different from the total g(r), the first peak located at ∼2.65 Å is relatively small, while the second peak located at ∼3.70 Å is notable, indicating that the contribution of Ge–Ge configuration to the SRO is relatively small, but to the MRO is very large. The partial g(r) of S–S configuration is shown in Fig. 1(d). The main peak is located at ∼3.56 Å, which is close to the second peak in total g(r), revealing that the S–S configuration also plays an important role in the MRO. Then, it is inferred that the SRO in a-GeS originates from the Ge–S and Ge–Ge bonds, while the MRO stems from the Ge–Ge and S–S configurations.

The coordination numbers (CN) of Ge and S atoms are shown in Figs. 2(a) and 2(c), respectively. CN of Ge–S and Ge–Ge configurations is 2.68 and 0.30 at 1000 K and increases gradually with the decreasing temperature. At 300 K, they become 2.82 and 0.38, respectively, making the total CN of Ge reaches 3.20. It is clear that Ge atoms prefer to bonding with S atoms due to different electronegativity between these two elements. From Fig. 2(b), CN of S–S configuration is close to zero; then, the CN of S atom is dominantly ascribed to the S–Ge configuration. CN of S–Ge configuration is 2.68 at 1000 K and increases to 2.82 at 300 K. From the coordination condition, it is demonstrated that the a-GeS is composed of a large fraction of Ge–S bonds and a small fraction of Ge–Ge bonds.

Figures 2(c) and 2(d) show the distributions of CN for Ge and S atoms, respectively. CN of Ge concentrates on 2, 3, and 4 at 1000 K. As the temperature decreases, the fraction of CN = 2 decreases prominently while those of CN = 3 and CN = 4 increase, indicating that the Ge-centered clusters tend to form the higher coordinated configurations in the amorphization process. From Fig. 2(d), CN of S is also distributed at 2, 3, and 4 under 1000 K. During the amorphization process, the fractions of both CN = 2 and CN = 4 are reduced, while that of CN = 3 is enhanced. Interestingly, the fractions of CN = 3 are very large in both Ge- and S-centered configurations, agreeing with the cases in crystalline (c-) GeS (seen in Fig. S2 of supplementary material).

Figure 3(a) shows the bond-angle distribution function (BADF) of Ge-centered clusters. The principal peak is found at ∼93° under 1000 K, reminding us of the distorted octahedron. As the temperature decreases to 300 K gradually, the peak shifts right to 94°, and its height is obviously enhanced, revealing that more Ge-centered octahedrons with distortions are formed. Figure 3(b) shows the BADF of S-centered clusters. The principal peak is located at ∼92° at 1000 K, presenting the octahedral feature. As the temperature decreases, the peak moves right to ∼105° at 300 K, and the density is increased. It indicates that the S-centered clusters tend to form the defective octahedrons in l-GeS but gradually deviate from the octahedral structure in the amorphization process. From Fig. S2 of supplementary material, the BADF of Ge-centered clusters is located at ∼83° and ∼113° while the cases of S-centered clusters are located at ∼97° and ∼113°. Clearly, the bond angle relations of both Ge- and S-centered clusters in a-GeS are distinctly different from the crystalline state, which can prevent the crystallization of the glass.

The primitive rings are usually used to characterize the MRO in amorphous state.^11,44 By using the RINGS code,⁴⁷ the ring distributions of GeS at 1000 and 300 K are computed, as shown in Figs. 3(e) and 3(f), respectively. There are many fourfold and sixfold rings at 1000 K, with the fractions of 42.5% and 18.6%. As for the a-GeS at 300 K, the fraction of fourfold ring is reduced to 27.8%, while the fractions of fivefold and sixfold rings are enhanced to 22.8% and 21.9%, respectively. As only fourfold rings exist in the c-GeS (seen Fig. S2 in supplementary material), the similarity of MRO between the a- and c-GeS is reduced in the amorphization process.

The snapshot of a-GeS is shown in Fig. 4(a), in which Ge and S atoms are randomly distributed in the simulation cell, making the a-GeS distinctly different from the crystalline state (seen in Fig. S2 of supplementary material). Figure 4(b) shows the distributions of Bader charges. The average Bader charge of Ge atom is 3.2 while that of S atom is 6.8, indicating that Ge atoms transfer electrons to S atoms. The crystal orbital Hamilton populations (COHP) of a-GeS are calculated by the LOBSTER code,^48,49 as seen in Fig. 4(c). The –COHP of Ge–Ge bond is positive while that of Ge–S bond is negative below the Fermi level, suggesting that the Ge–Ge bonds are in the bonding states while the Ge–S bonds possess the antibonding interaction. By integrating the COHP below the Fermi level, the integrated COHP (ICOHP) is obtained, as seen in Fig. 4(d), which is corresponding to the formation energies of chemical bonds. Apparently, the formation energy is decreased as the bonding length increases gradually. The locations of blue stars correspond to the first peaks of partial g(r) in Figs. 1(b) and 1(c), respectively. The formation energies of the Ge–S and Ge–Ge bonds are 3.70 and 3.61 eV, respectively. The Ge–S bonds are stronger than Ge–Ge bonds in a-GeS, and the Ge–Se bonds in a-GeSe, thus leading to the high stability of the glass.³⁰ 

Figures 5(a) and 5(b) show the total density of states (DOS) and inverse participation ratio (IPR) of a-GeS at 1000 and 0 K, respectively. The bandgap is relatively small in l-GeS but increases to ∼1.39 eV in a-GeS, which is smaller than the experimental result due to the typical underestimation of bandgap in DFT calculation.³² Usually, a small value of IPR represents a delocalized configuration, while a large value corresponds to a localization condition.⁵⁰ The charges during the localization configuration usually possess the high mobility, thus contributing to the threshold switching behavior.²⁶ The values of IPR near the bandgap are obvious in l-GeS at 1000 K; thus, the charges possess the high mobility, resulting in a good electrical conductivity. As for the a-GeS at 300 K, the localized states are mainly located at the edges of valence and conduction bands, which are smaller than the cases in l-GeS. It is probably due to the smaller localized states and larger bandgap in a-GeS that leads to an ultrahigh ovonic threshold switching voltage.³² 

The associated projected DOS (PDOS) is shown in Figs. 5(c) and 5(d), respectively. At 1000 K, the valence band near the Fermi level is dominantly composed of the p states of Ge and S atoms, forming the p–p bonds. From Fig. 5(a), there are many localized states in l-GeS, suggesting that the localized states mostly originate from the p–p bonds.⁵¹ The conduction band of l-GeS consists of the s and p states of Ge and the p state of S. For the PDOS at 0 K, the valence band is mainly composed of the s and p states of Ge and the p state of S, indicating that the sp³ hybrid bonds are formed in addition to the p–p bonds. The conduction band still consists of the s and p states of Ge and the p state of S, but the densities are reduced. As the sp3 hybrid bond is stronger than the p–p bond, the tetrahedral structures can further stabilize the amorphous configuration.

In summary, we have studied the structure and electronic characteristics of a-GeS by using the AIMD simulations. The results reveal that the a-GeS is composed of a large fraction of Ge–S bonds and a small proportion of Ge–Ge bonds. Both Ge- and S-centered clusters tend to form the octahedral structures in the liquid state. During the cooling process, more Ge-centered octahedrons are formed and a small fraction of Ge-centered clusters change to the tetrahedrons, and the S-centered structures gradually deviate from the octahedron. Meanwhile, CN of both Ge and S atoms is enhanced. The formation energies of Ge–S and Ge–Ge bonds are very large, presenting the high chemical stability. It is probably due to the stable chemical bonds and the highly coordinated configurations different from the crystalline phase that leads to the high stability of a-GeS. In addition, the bandgap is relatively large and the localized states are prominently reduced in a-GeS in contrast to l-GeS, making the electrons difficult to jump from valence band to conduction band via the mid-gap states; thus, the a-GeS presents an ultrahigh ovonic threshold switching voltage. Our studies provide an in-depth understanding of the structure and electronic property of a-GeS, which may speed up the applications of a-GeS in the industry of advanced memory.