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Abstract
Chalcogenide phase-change materials (PCMs) are promising candidates for nonvolatile memory and neuromorphic computing devices. The recently developed Ge2Sb2Se4Te1 alloy shows superior properties in terms of low optical loss and higher thermal stability with respect to the flagship Ge2Sb2Te5 alloy, making this new quaternary alloy a suitable candidate for high-performance optical switches and modulators. In this work, we carry out ab initio calculations to understand how selenium substitution modifies the local structure and the optical response of the amorphous quaternary alloys. We consider four amorphous Ge2Sb2SexTe5-x (GSST) alloys with x = 1 to 4 and show that the substitution of selenium content induces a gradual reduction in the calculated refractive indices, which is in agreement with experimental observation. This improvement on optical loss stems from the increased band gap size, which is attributed to the larger Peierls-like distortion and the stronger charge transfer in the Se-richer amorphous GSST alloys.
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1. Introduction
In response to the drastically increased demand on data storage and processing, new materials based non-volatile memory and neuro-inspired computing are being extensively investigated [1–4]. Chalcogenide phase-change materials (PCMs) are one of the leading candidates for these applications [5–15]. As pioneered by Intel and Micron, the PCM-based 3D cross-point products are already commercially available, known as storage-class memory [16]. The core materials in use are the Ge-Sb-Te alloys along the GeTe–Sb2Te3 pseudo-binary line [17–21]. These alloys can be switched rapidly and reversibly between the crystalline and amorphous phases by adding external electrical or optical pulses. The pronounced change in electrical resistivity or optical reflectivity between the two solid-state phases is used to encode digital information. This property contrast has been explained by the changes in bonding mechanism [22–27] and the degree of disorder upon phase transition [28–31].
Regarding optical applications, the Ge-Sb-Te alloys, in particular, Ge2Sb2Te5 (abbreviated as GST in the following), was firstly used as rewritable optical disks in 1990s [17]. Later on, GST was integrated with silicon waveguides [32–34], which opened up the possibility to develop on-chip photonic phase-change devices with much improved storage density beyond the diffraction limit. In addition to photonic memory [35,36] and neuro-inspired computing [37,38], GST also holds the promise for various nanophotonic applications, such as color rendering and nanopixel displays [39], phase-change antennas and metasurfaces [40–43] and others [44–46]. However, GST is not a suitable candidate for optical modulators, due to the high optical loss caused by strong inter-band absorption in the visible to near-infrared spectrum and free carrier absorption at longer wavelengths [47,48].
By properly alloying Se into GST, Ge2Sb2Se4Te1 (GSS4T1) alloy [48,49] was recently developed, which showed a very broad transparency window (1–18.5 µm). This quaternary alloy was exploited in various low-loss designs of optical switches and modulators [48–54], as well as meta-surfaces [55]. Binary alloys Sb2Se3 [56,57] and Sb2S3 [57–60] were also investigated for low-loss applications. Very recently, a thorough theoretical work was done to understand the changes in structural and optical properties in the binary antimony sesquichalcogenide alloys [61]. In this work, we evaluate whether the presence of germanium and mixture of selenium and tellurium could lead to further changes in the optical properties of the quaternary amorphous alloys. We performed systematic ab initio molecular dynamics (AIMD) simulations of four GSST compounds, namely, Ge2Sb2Se1Te4, Ge2Sb2Se2Te3, Ge2Sb2Se3Te2 and Ge2Sb2Se4Te1 (abbreviated as GSS1T4, GSS2T3, GSS3T2 and GSS4T1), to understand the origin of the reduced optical loss in the quaternary alloys.
2. Computational details
The amorphous models were generated by AIMD simulations following a standard melt-quench protocol [62]. For each GSST composition, three amorphous models with independent thermal history were generated. Each model contains 360 atoms in a cubic simulation box. All three models were used for the structural analyses of every GSST composition. The second-generation Car-Parrinello scheme [63], as implemented in the CP2K package [64], was used in combination with the Goedecker pseudopotentials [65] and the Perdew–Burke–Ernzerhof (PBE) functional [66]. The Brillouin zone was sampled at the Γ point only. The canonical (NVT) ensemble was used, along with a time step of 2 fs. The electronic structure and optical response calculations were made using the Vienna Ab-initio Simulation Package (VASP) [67]. The VASP calculations were performed using the PBE functional and the projector augmented-wave (PAW) pseudopotentials [68] with an energy cutoff of 500 eV. For optical response calculation, a 2×2×2 k-point mesh was used. The chemical bonding analyses were conducted using the LOBSTER code [69–72], which extracts relevant information from VASP calculations.
3. Results and discussion
Figure 1(a) shows the atomic structures of the four GSST amorphous models. The theoretical lattice edge was determined to be 23.24, 23.17, 22.92 and 22.89 Å (all the models show a small pressure value below 2 kbar), corresponding to a mass density value of 5.17, 4.97, 4.86 and 4.61 g/cm3, respectively. These calculated mass density values are smaller than that of amorphous GST [73]. Figure 1(b) shows the total radial distribution functions (RDFs) of the four amorphous alloys. A clear shift in the first peak position (from ∼2.8 to ∼2.6 Å) and second peak (from ∼4.1 to ∼3.9 Å) of RDF is found with the increase of Se concentration. A shoulder in RDF is observed for the intermediate compositions at ∼2.6 Å (GSS2T3) and ∼2.8 Å (GSS3T2), in addition to their primary peaks. This structural difference stems from the fact that the prevalent bond lengths of Sb-Se ∼2.6 Å and Ge-Se ∼2.5 Å are invariably shorter than Sb-Te ∼2.9 Å and Ge-Te ∼2.7 Å in the four amorphous alloys, as evidenced by the partial RDF analysis shown in Fig. 1(c) (GSS4T1) and Figure S1 (others). In addition to the major heteropolar bonds, “wrong” bonds are consistently observed in amorphous GSST alloys, similar to amorphous GST [74–78]. In particular, visible RDF peaks for Ge-Ge, Ge-Sb, Sb-Sb and Te-Te are consistently observed at short interatomic distances below 3 Å. Overall, the enriched Se concentration results in a more compact amorphous structure.
Fig. 1. (a) Amorphous structures of four GSST alloys. Green, orange, red and blue spheres represent Ge, Sb, Se and Te atoms, respectively. (b) Total radial distribution functions (RDFs) for each alloy. (c) Partial RDFs and bond populations (BAB) of amorphous GSS4T1.
We also carried out detailed bonding analysis using crystal orbital overlap population (COOP) method [79] to obtain further understanding on the four amorphous GSST alloys. The calculated bond populations of atomic pairs between atom A and atom B (BAB) [80–82] are shown in Fig. 1(c) and Figure S1. The bond population refers to the integration of the projected COOP on individual atomic contacts along the energy scale up to the Fermi level, which is regarded as an indicator for the strength of covalent interaction between a pair of atoms. The distribution of bond population shows a systematic increase in bond strength as the interatomic distance decreases. In particular, the Ge-Se bonds are much shorter and stronger, and get more abundant in the Se-richer GSST alloys. The distribution of coordination number and angular distribution functions in amorphous GSST alloys are overall similar to those in amorphous GST (Figure S2), and the local structures are also dominated by defective octahedral motifs, except for a minor fraction (25-32%) of tetrahedral Ge units. However, the quaternary alloys are compositionally more complex than the ternary one. Taking into account the shorter and stronger Se-based chemical bonds, and their increased fraction in the Se-richer GSST alloys, the structural barrier for crystallization should be increased, giving rise to a higher crystallization temperature.
Next, we evaluate the impact of Se substitution on optical properties of amorphous GSST alloys. We calculated frequency-dependent dielectric functions within the independent-particle approximation, which was shown to be adequate to characterize the optical contrast between crystalline and amorphous PCMs [83–87]. Figure 2(a) shows the real (ε1) and imaginary (ε2) parts of the dielectric function of the four amorphous GSST alloys. With gradual Se substitution, the peak height of both ε1 and ε2 is continuously reduced, accompanied by a blueshift of the peak position. As shown in Fig. 2(b), the refractive index (n) and extinction coefficient (k) were obtained based on the calculated dielectric functions:
As the Se concentration increases, a systematic reduction in both n and k over the spectrum of 500 nm – 2.5 µm is observed, covering the typical working wavelengths for optical and photonic applications. It is evident that the extinction coefficient falls down to nearly zero around the 1550 nm telecommunication C-band in amorphous GSS4T1, which makes it a suitable candidate for low-loss optical modulators at this wavelength range. These findings are in good agreement with the experimental results [49].
Fig. 2. Calculated optical properties of amorphous GSST. (a) The real (ε1) and imaginary parts (ε2) of the dielectric function below photon energy of 6 eV. (b) The refractive index (n) and extinction coefficient (k) in the spectrum range between 500 nm and 2500 nm.
With the increase of Se content, the energy bandgap is enlarged from ∼0.42 eV in amorphous GSS1T4 to ∼0.73 eV in amorphous GSS4T1 (Fig. 3(a)). Note that DFT calculation at the PBE functional level typically underestimates the size of bandgap, and the use of hybrid functional is expected to give more accurate results. Nevertheless, this increase in bandgap size is in line with the measured optical bandgap values [88]. ε2 is composed of joint density of states (JDOS) and transition dipole moment (TDM) [83,84], which account for the amount of possible inter-band excitations and the transition probability for each possible excitation, respectively. With the increasing concentration of Se, the JDOS values decrease due to the widened bandgap (Fig. 3(b)), while the major chunk of TDM values (in the range of 1–6 eV) nearly overlap for the four alloys (Fig. 3(c)). Near the band edge region (0.5–1 eV), Se-poor compositions show some higher TDM values, which could also contribute to ε2. Overall, the change in JDOS profiles plays a major role in altering ε2, in terms of both peak position and peak height. Since the optical extinction coefficient k is determined mostly by ε2 (Eq. (2)), the reduced optical loss in Se-richer GSST alloys originates from the varied JDOS profiles, which is a direct consequence of bandgap widening. The above optical and electronic structure analyses were repeated using two additional amorphous models for each GSST composition (see Figure S3). Despite some numerical differences, the trend remains the same.
Fig. 3. Electronic structures. (a) The calculated density of states (DOS), (b) joint density of states (JDOS) and (c) transition dipole moment (TDM) of the four amorphous GSST alloys.
Finally, we discuss the underlying mechanism for bandgap widening in amorphous GSST alloys, which is mainly attributed to the enlarged Peierls-like distortion (PD) upon Se substitution. PD refers to the formation of long and short bonds in a nearly aligned pair of atoms (as sketched in Fig. 4(a)), which opens up a bandgap in semiconductors. For instance, each atom of crystalline GeTe has all equal bonds of ∼3.01 Å in the cubic phase, but three short bonds of 2.85 Å and three long bonds of 3.28 Å in the rhombohedral phase [89]. The corresponding long / short bond ratio is increased from 1.00 to 1.15, giving rise to an increase in gap size by 0.23 eV. In amorphous phase, high angular disorder is present and an angular limited three-body correlation (ALTBC) scheme has been developed to quantify the degree of PD [90]. As displayed in Fig. 4(a), all the atomic pairs with a bond angle larger than 155° were collected from the amorphous trajectories at 300 K over 10 ps for each GSST composition, and the distribution of short / long bond correlation around Ge atoms and around Sb atoms was plotted in a 2D map. The ALTBC shows a clear shift of the correlation peak of short / long bonds around Ge atoms from 2.83/3.40 Å in GSS1T4 to 2.55/3.56 Å in GSS4T1, corresponding to an increase in long / short bond ratio from 1.2 to 1.4. Regarding the bonding environment around Sb atoms, the major peak in ALTBC is flattened in range of 3.1/3.1 Å to 2.95/3.38 Å in GSS1T4, and becomes much sharper in GSS4T1 at 2.76/3.34 Å. We note that the reinforced PD leads to an increase in band gap size in amorphous GeTe and GST upon glass relaxation at room temperature [90–93], and such aging effects result in a well-known resistance drift issue [94–98]. It has been revealed by mechanical spectroscopy experiments that Se substitution in amorphous GeTe drives a transition in relaxation scheme [99]. Further investigations of aging effects on optical and electrical performance in amorphous Ge-Se-Te and Ge-Sb-Se-Te alloys are anticipated. Besides PD, the increase in ionicity upon Se substitution may also contribute to the variation of bandgap in the amorphous quaternary alloys. As shown in Fig. 4(b), the average Mülliken charge of Se (–0.31) is generally larger than that of Te (–0.11) in all four alloys. Given the enriched Se concentration, the average Mülliken charges of Ge and Sb are increased from (+0.07, +0.28) in GSS1T4 to (+0.21, +0.46) in GSS4T1.
Fig. 4. Peierls-like distortion and charge analyses. (a) The angular-limited three-body correlation (ALTBC) analysis for amorphous GSST. The upper and lower panels present the bond distributions around Ge and Sb atoms, respectively. Two atomic pairs are sketched to show a Te-Ge-Te pair with large PD and a Te-Sb-Te pair with small PD. (b) Mülliken charges of each atom in amorphous GSST. All atoms from the three models are shown for each composition. The dashed lines indicate the average values.
4. Conclusion
In summary, we carried out ab initio calculations to investigate the structural and optical properties of amorphous GSST alloys with varied Se/Te ratio. The enrichment of shorter and stronger Se-based bonds results in more compact amorphous structures and better structural stability of Se-richer GSST alloys. The calculated optical profiles, including dielectric functions, refractive index and extinction coefficient, show a systematic reduction as the selenium content increases. This behavior is explained by the decreased joint density of states resulting from the enlarged bandgap upon selenium substitution. The larger bandgap value is attributed mostly to the enlarged Peierls-like distortion in Se-rich GSST alloys. Regarding Se substitution in the crystalline phase, the degree of metavalent bonding is expected to be weakened [22–26], resulting in a smaller contrast window in optical properties between the amorphous and crystalline phase of Se-rich GSST [49]. Similar trend in bonding character and optical profiles upon Se substitution holds for the parent phase—GeTe [100]. In addition, the change in crystallization kinetics [101] along the GeTe–GeSe pseudo-binary line was also thoroughly investigated, guiding materials optimization for high-performance phase-change applications. At last, we suggest that the composition of GSST could be further optimized for better amorphous stability and smaller optical loss by incorporating sulfur, either to replace selenium or tellurium, because such trend was already observed in the parent binary alloys Sb2Se3 and Sb2S3 [57,61]. However, it is important to keep in mind that replacing tellurium in GST with lighter chalcogens also slows down the programming speed, weakens the cycling endurance and reduces the optical contrast window. Therefore, a balanced composition should be considered for practical applications.
Funding
111 Project (BP2018008); National Natural Science Foundation of China (61774123).
Acknowledgements
W. Z. thanks the support of the National Natural Science Foundation of China (Grant No. 61774123) and 111 Project 2.0 (BP2018008) for their support. The authors acknowledge the support of the International Joint Laboratory for Micro/Nano Manufacturing and Measurement Technologies and the HPC platform of Xi’an Jiaotong University, and the Hefei Advanced Computing Center.
Disclosures
The authors declare that there are no conflicts of interest related to this article.
Competing Interests. The authors declare no competing interests.
Data availability
Data underlying the results presented in this paper are not publicly available at this time but may be obtained from the authors upon reasonable request.
Supplemental document
See Supplement 1 for supporting content.
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