Anharmonic Effects in Ge2Sb2Te5 and Consequences on Thermodynamic Stability

TL;DR

Ge$_2$Sb$_2$Te$_5$ (GST) phase-change materials exhibit thermally driven phase transitions that challenge harmonic vibrational theories. The authors quantify anharmonicity using the metric $\sigma$, comparing harmonic PES from phonons to PES from AIMD at 300 K for two hexagonal stackings, Petrov and Kooi–de Hosson (KDH), with and without van der Waals corrections. They find strong dependence of $\sigma$ on stacking and dispersion treatment, with Petrov-PBEsol+vdW(TS) yielding the largest anharmonicity ($\sigma \approx 0.41$) and Ge as the most anharmonic element, while KDH is comparatively more thermodynamically stable. By employing the quasi-harmonic approximation, they demonstrate significant thermal lattice expansion in Petrov and only modest changes in KDH, underscoring the necessity of going beyond harmonic descriptions for GST thermodynamics and suggesting avenues for improving predictive models with machine-learned interatomic potentials. Together, these results emphasize the critical role of anharmonicity and vdW interactions in GST's phase-change behavior and stability, with implications for accurate modelling of thermal transport and phase kinetics. $F$ and related vibrational terms are treated within $F = \frac{1}{2} \sum_{qj} \hbar \omega_{qj} + k_B T \sum_{qj} \ln \left[ 1 - \exp\left( -\frac{\hbar \omega_{qj}}{k_B T} \right) \right]$, and the anharmonicity metric is $\sigma = \sqrt{ \frac{\sum_{I,\alpha} \langle (F_{I,\alpha}^A)^2 \rangle_t}{\sum_{I,\alpha} \langle (F_{I,\alpha})^2 \rangle_t}}$.

Abstract

Chalcogenide materials are an important class of phase change material (PCMs) owing to their employment in digital memory solutions. Chalgogenide materials have applications in phase change random access memory (PCRAM) due to their ability to reversibly cycle between crystalline and amorphous states, and of these materials Ge2Sb2Te5 (GST) is of particular interest due to its speed, stability and low crystallisation temperatures. GST possesses two stable crystalline polymorphs, cubic and hexagonal (trigonal system). Studies show that phenomena such as heat transport and thermal lattice expansion drive the phase-change nature of these materials. These phenomena are not incorporated in the harmonic approximation, which is a popular model for describing vibrations in solids. Through ab initio density functional theory (DFT), we computationally investigate the anharmonic behaviour of pristine GST, without vacancies or defects, while considering the various stacking models that exist and inclusion of van der Waals (vdW) interactions in our modelling. We present the vibrational analysis of different stacking models in GST; Petrov and Kooi-De Hosson (KDH) models and the quantification anharmonic behaviour. Our results demonstrate the importance of incorporating anharmonic and dispersion effects when modelling GST, especially in the choice of stacking models, along with implications for phenomena relating to phase-change behaviour.

Figures (8)

• Figure 1: Nine atom unit cells of KDH and Petrov structures of Ge$_2$Sb$_2$Te$_5$ (see text). Where A, B, and C denote different stacking positions with the unit cell and blue, purple, and orange spheres represent atoms of Ge, Sb, and Te, respectively. (Colour online)
• Figure 2: Potential energy surface ($V(\mathbf{R})$), harmonic approximation ($V^{(2)}(\mathbf{R})$), and the deviation between the two, defined as anharmonicity ($V^{A}(\mathbf{R})$) shaded in green.
• Figure 3: Workflow for computing anharmonicity metric, $\sigma$, with FHI-vibes.
• Figure 4: Total anharmonicity, $\sigma^A$, for Petrov and KDH structure models.
• Figure 5: Anharmonicity resolved by element, $\sigma^A_E$, for Ge, Te, Sb in Petrov and KDH model.