Abstract
Phasechange materials exhibit fast and reversible transitions between an amorphous and a crystalline state at high temperature. The two states display resistivity contrast, which is exploited in phasechange memory devices. The technologically most important family of phasechange materials consists of GeSbTe alloys. In this work, we investigate the structural, electronic and kinetic properties of liquid Ge_{2}Sb_{2}Te_{5} as a function of temperature by a combined experimental and computational approach. Understanding the properties of this phase is important to clarify the amorphization and crystallization processes. We show that the structural properties of the models obtained from ab initio and reverse Monte Carlo simulations are in good agreement with neutron and Xray diffraction experiments. We extract the kinetic coefficients from the molecular dynamics trajectories and determine the activation energy for viscosity. The obtained value is shown to be fully compatible with our viscosity measurements.
Introduction
Due to continuously increasing demand on highdensity and fast datastorage devices, the interest in phasechange materials (PCMs) and their applications in nonvolatile data storage media is extremely high^{1,2,3}. The first work on PCMs dates back to 1968, when Ovshinsky reported on a sharp transition from high resistivity to low resistivity in amorphous Te_{48}As_{30}Si_{12}Ge_{10} induced by an electric field (electric switching)^{4}. However, another property of PCMs – the large contrast in the optical reflectivity between the amorphous and crystalline state – led to practical applications in the data storage media, namely in rewritable optical discs such as CDs, DVDs and Bluray discs. Many such devices are based on the GeSbTe (GST) PCM alloys from the pseudobinary line between GeTe and Sb_{2}Te_{3} compounds, discovered by Yamada et al.^{5}.
Recently, the development of the phasechange random access memory (PCRAM) has sparked renewed interest in the electric switching phenomenon. PCRAMs exploit the electronic contrast between the amorphous and crystalline state. It is plausible that these nonvolatile devices will be able to outperform and replace the Flash memory, whose miniaturization will soon come to an end due to physical limits. At present, GST alloys are among the most promising PCMs for highspeed, highreliability PCRAMs. In spite of intensive studies, however, a complete understanding of the switching phenomena and the property contrast at the atomic level, which is required for the development of new, better performing datastorage media, is still lacking. Furthermore, the elucidation of the relations between the chemical composition, atomic structure, bonding mechanism and resulting phasechange properties remains a challenge for physicists and material scientists.
Apart from the technological importance of PCMs, the peculiar combination of physical properties of the crystalline, amorphous and liquid state is of great scientific interest too^{1,2,3}. During the last years, significant progress has been made in the theoretical and experimental investigation of both crystalline^{6,7,8} and amorphous^{9,10,11,12,13,14,15,16,17,18} GST alloys, while our knowledge of the structural and dynamical properties of the liquid state is more limited^{19,20,21,22,23,24,25,26,27,28}. In particular, there are still open questions about the crystallinetoamorphous (amorphization) and amorphoustocrystalline (devitrification) phase transitions, which can be clarified only by a detailed study of the liquid state. In PCMbased devices, the amorphization process occurs due to local melting (by a laser or current pulse) and subsequent quenching from the melt. It has been recently understood^{29,30,31,32} that the high fragility of the supercooled liquid state of PCMs plays a key role in the devitrification process. Fragility describes the deviation of the temperature dependence of the viscosity η from the Arrhenius behaviour. The high fragility of PCMs is responsible for two essential properties of PCMs, namely the rapid crystallization at high temperature and the high stability of the amorphous phase at room temperature. Hence, knowledge of the atomic structure and the dynamics of GeSbTe alloys in the liquid and supercooled liquid state is indispensable for a complete comprehension of the phasechange processes.
Ab initio molecular dynamics (AIMD) simulations based on density functional theory (DFT) have been shown to yield models of PCMs which, overall, are in good agreement with experimental data. For standard generalizedgradientapproximation (GGA) functionals, the main discrepancy is the fact that the bond distances in liquid and amorphous PCMs are typically overestimated by 1–3%. A number of studies, including some of our own works^{12,13,33,34,35,36,37}, have shown that the complementary information provided by different experimental techniques such as Xray diffraction (XRD), neutron diffraction (ND) and extended Xray absorption fine structure (EXAFS) can be effectively combined and interpreted in the frame of the reverse MonteCarlo (RMC) simulation method^{38}. In particular, in refs 12,13, the RMC method was used to analyse XRD, ND and EXAFS data for amorphous Ge_{1}Sb_{2}Te_{4} and Ge_{2}Sb_{2}Te_{5} alloys. These studies have provided very detailed information on the local atomic structure of these amorphous systems.
In this work, we investigate the atomic ordering in the liquid phase of Ge_{2}Sb_{2}Te_{5}, as well its electronic and kinetic properties, by combining AIMD simulations with experiments and RMC simulations. We use AIMD and a van der Waals density functional which includes nonlocal correlations^{39} (denoted as vdWDF2) to generate long trajectories at different temperatures, from which we extract the structural properties (including structure factors, pair and threebody correlation functions, and ring statistics), the electronic structure and the viscosity coefficients of the liquid state. These quantities are compared with experimental XRD data, neutron diffraction with Ge isotopic substitution data, and viscosity measurements. The AIMD structural models are also taken as input for refined RMC simulations. We show that the agreement between simulations and experiments is quite good. In particular, the mismatch between experimental and theoretical atomic distances is partially cured by the use of the vdWDF2 functional and the temperature dependence of the activation energy for the viscosity matches the experimental value nicely. We also discuss the discrepancies in the magnitude of the viscosity in relation to the approximations made in our simulations.
Results
Structural and electronic properties
The experimental neutron and Xray total structure factors S(q) for liquid Ge_{2}Sb_{2}Te_{5} measured at 923 K (which is close to the melting point, T = 900 K) are compared with AIMD and RMC structure factors in Fig. 1. As the AIMD models are more informative than the RMC configurations, the former are discussed in detail in the following. The AIMD models contain 540 atoms and their density is set to 0.030 Å^{−3}, which is an average over the values we determined experimentally by a high energy γray attenuation method in the temperature range considered (see Table 1). To generate the models, we employ the following procedure: we start from a random configuration and equilibrate the system at T = 3000 K for 30 ps. Then, we quench the system to the target temperature (925 K) and equilibrate for 30 ps. After equilibration, we compute the total partial distribution function g(r), as well as the six partial pair distribution functions g_{ij}(r) (where i and j indicate the atomic species) by averaging over 20 ps. The AIMD partial g_{ij}(r)’s are plotted in Fig. 2, together with the RMC fits. For the sake of comparison, we also perform AIMD simulations using a standard GGA functional and include the data in Figs 1 and 2. Notice that the three experimental data sets are not sufficient to separate the 6 partial correlation functions of this 3 component system. We calculate the neutron and Xray structure factor S(q) by combining the partial structure factors S_{ij}(q) (obtained from the Fourier transforms of the g_{ij}(r) functions) with the Xray and neutron diffraction weights. Similar to the experimental structure factors, the AIMD total S(q) curves exhibit a pronounced first peak and a smaller second peak. This is indicative of octahedral order, as discussed in ref. 21, where ND measurements were performed on several GST liquid alloys and compared with other octahedral liquids, as well as with selected tetrahedral liquids. For this purpose, the order parameter S ≡ S(q_{2})/S(q_{1}) was introduced, where q_{1} and q_{2} denote the position of the first and second peak^{21}. Our AIMD models yield S = 0.69. The intensity of the first and second peak of the theoretical S(q) is overestimated as compared to experiments. We also observe a small shift of the peaks to lower values of q. As far as the third and subsequent peaks are concerned, the agreement is excellent. Overall, the curves are closer to experimental values than those obtained using GGA functionals (except for the height of the first peak), which lead to an underestimation of the second peak and a pronounced shift of the third peak to lower diffraction vectors. Notice that there is very good correspondence of the RMC fits with the experimental datasets.
We also perform AIMD simulations at three other temperatures, namely at T = 852, 1024 and 1250 K. Since the melting temperature of Ge_{2}Sb_{2}Te_{5} is about 900 K, the lowest temperature considered corresponds to a slightly supercooled liquid phase. The total pair distribution functions g(r) are presented in Fig. 3, together with the structure factors, whereas the partial g_{ij}(r)’s at 852, 1024 and 1250 K are shown in the supplement, Figs S1–3. We also include the GGA curves at T = 926 K. The latter are in very good agreement with those of ref. 20. Due to the use of the vdWDF2 functional, which yields a better description of dispersive interactions, the g(r) functions exhibit more pronounced secondary peaks and deeper minima than those obtained from standard GGA calculations. In particular, the second peak at 4.055 Å and the first and second minima at 3.325 and 5.275 Å are better defined, indicating better resolved atomic connectivities and neighbour shells. Moreover, there is a shift of the first peak to smaller interatomic distances – 2.835 Å at 925K (vdWDF2 simulations), to be compared with 2.92 Å (GGA simulations) – which partially cures the tendency of GGA functionals to yield too long firstneighbour distances for amorphous and liquid PCMs. In refs 27,28, van der Waals semiempirical corrections^{40} to GGA functionals were shown to have similar effects on liquid GeTe_{4} and supercooled liquid Ge_{2}Sb_{2}Te_{5}.
We evaluate the average coordination number (CN) for each atomic species by integrating the corresponding partial distribution function up to the first minimum (see Table 2). The total and partial CNs increase with temperature. We observe a significant number of GeGe and GeSb bonds, as evidenced by the corresponding partial CNs included in Table 2. Recently, some of us have explained the presence of GeGe bonds in the liquid phase of the parent compound GeTe as due to the small heat of formation of this compound^{41}. These very bonds turn out to be responsible for the presence of tetrahedral structures in rapidly quenched amorphous GeTe^{41,42}. We expect that similar behaviour occurs for Ge_{2}Sb_{2}Te_{5}. TeTe bonds are also present in the liquid state but their number decreases more drastically upon quenching to the amorphous state^{14,15}. If one compares our CNs for Ge_{2}Sb_{2}Te_{5} with previous results in the literature, one observes deviations from the values at T = 900 K provided in ref. 20. These discrepancies stem from the use of different functionals and the different cutoff distances employed. There are also some deviations between our data at T = 852 K and the CNs at T = 822 K provided in ref. 28, which indicate that the Grimme corrections give a larger fraction of GeGe and GeSb bonds than vdWDF2 functionals.
We also compute the bond angle distributions (BADs) (shown in Fig. 4) and the angularlimited threebody correlations (ALTBCs) from the AIMD trajectories (see Fig. 5). We consider both total BADs and partial BADs resolved for different central atoms. All of the total distribution functions display a peak centered at 90°, which is indicative of predominant (defective) octahedral coordination. The height of the peak decreases with increasing temperature. At the same time, the probability of observing bond angles below 80° and above 110° becomes more significant. The partial BADs for central Te are similar to the total ones, whereas the Sb BADs display a narrower main peak. On the other hand, the main peak of the Ge BADs is shifted to larger angles, especially at lower temperatures. This shift is due to the presence of a fraction of Ge atoms with tetrahedral coordination, characterized by bond angles around 104°. These structures contain at least one GeGe or GeSb bond. In fact, the BADs resolved over different atomic sequences shown in the supplement (Figs S4–7) clearly indicate that all the sequences containing GeGe or GeSb are peaked at angles around 105°–110°.
The ALTBC expresses the probability of having a bond of a given length r_{1} almost aligned with a bond of length r_{2}. We include angular deviations smaller than 25° in the calculation of the probability. The ALTBC distributions exhibit two peaks corresponding to alternating short and long bonds, indicative of Peierls distortion. Interestingly, the distortion appears to decrease upon increasing temperature. More specifically, the height of the two peaks decreases, as well as the distance between them. Partial ALTBC plots are shown in Figs S8–12. Similar effects have been previously observed in liquid GeTe and have been ascribed to the progressive transition from a semiconducting to a metallic liquid^{43}. To further elucidate this phenomenon, we calculate the electronic density of states (averaged over 10 time steps) at different temperatures. This quantity indeed shows a pseudogap at the Fermi energy at low temperatures, whereas, at higher temperatures, the dip tends to disappear (see Fig. 6).
Finally, we compute the primitive ring statistics, which provides information about the intermediate range order. The relevant histograms are shown in Figs S13 and S14. We have calculated the number of rings both for fixed cutoff (3.2 Å) and by employing the cutoffs determined from the partial distribution functions included in Table 2. The most common ring structure is the 5membered ring, as already discussed in ref. 28 for the supercooled liquid state. This is particularly evident if a fixed cutoff is used. In amorphous GST, 4membered rings are instead predominant^{14,15,16}. However, 4membered rings become more numerous at the highest temperature considered (1250 K). Large rings up to 12membered rings are abundant as well. Overall, an increase in the number of short and long rings is observed with increasing temperature, but only if variable cutoff lengths are used. We also consider ABAB rings, where A stands for Ge or Sb atoms and B denotes Te atoms. In amorphous GST, these rings constitute the majority of 4membered rings. In our models of the liquid state, the fraction of 4membered ABAB rings oscillates around 15–25% (using variable cutoffs) and 10–15% (for fixed cutoff).
Kinetic properties
The diffusion coefficients are computed by applying Einstein’s formula,
where 〈r^{2}(t)〉 is the meansquared distance over which the atoms have moved in the time interval t. The latter quantity is calculated by averaging over time and particles. The viscosity η is obtained from the diffusion coefficients using the StokesEinstein relation,
where R_{hyd} is the hydrodynamic radius. We estimate R_{hyd} from the simulations of GeTe carried out in ref. 31. We expect that R_{hyd} for Ge_{2}Sb_{2}Te_{5} should not differ significantly from the GeTe value. Notice that the StokesEinstein relation may break down at low temperatures close to the glass transition temperature due to the high fragility of the supercooled liquid state of GeTe and Ge_{2}Sb_{2}Te_{5}^{29,31}. Nonetheless, the relation is definitely valid in the weakly supercooled regime and above the melting temperature. In the temperature interval considered, the viscosities range from 1.6 mPa s to 4.8 mPa s. These values are larger than the experimental viscosities we have measured by the method of oscillating cup, as shown in Fig. 7 (see also Table S1 for the experimental data and Figs S15–19 for the meansquared displacement plots). The latter quantities vary between 0.8 and 2.0 mPa s in the temperature range between 901 K and 1253 K. In the next section, we discuss possible origins of the mismatch. Nonetheless, we point out that the experimental and theoretical activation energies E_{a} are very similar. Fitting the two data sets with the Arrhenius equation , where η_{0} is a constant representing the asymptotic viscosity at infinite temperature, k_{B} is the Boltzmann constant, and T is the absolute temperature, one obtains η_{0} = 0.140 mPa s, E_{a} = 0.256 eV (simulations) and η_{0} = 0.063 mPa s, E_{a} = 0.266 eV (experiments). The fit quality of R^{2} = 0.99205 for the experimental data (R^{2} = 0.98963 for fit of the AIMD results) shows that the Arrhenius law describes the temperature dependence of the dynamic viscosity for liquid Ge_{2}Sb_{2}Te_{5} very well.
Discussion and Conclusions
In this work, we have determined the structural and dynamic properties of liquid Ge_{2}Sb_{2}Te_{5} in the temperature range between and 850 K and 1250 K. For this purpose, we have performed AIMD and RMC simulations, as well as neutron and Xray diffraction, oscillatingcup viscometer and γray attenuation experiments. In our AIMD simulations, we have mainly employed the vdWDF2 functional^{39}, which includes nonlocal correlations and, thus, provides a better description of van der Waals interactions than standard local and semilocal functionals. In ref. 41 vdWDF2 simulations were shown to yield accurate models of amorphous GeTe. Our work indicates that this functional is also suitable to describe the liquid state of PCMs. Recently, semiempirical van der Waals corrections^{40} in combination with gradientcorrected functionals have been employed to investigate liquid^{27} and amorphous^{44} GeTe_{4}, as well as selected GeSbTe liquids with high Te content^{28}. These corrections have also been shown to improve the level of agreement between calculations and experiments for said chalcogenides, although, for amorphous GeTe, their inclusion appears to be less effective^{41}. Qualitatively speaking, both semiempirical and ab initio van der Waals functionals lead to more sharply defined atomic connectivities and neighbour shells.
As far as the dynamical properties are concerned, there is qualitative, but not quantitative, agreement between simulations and experiments, in that the experimental viscosities are smaller than the theoretical ones in the temperature range considered. An important source of discrepancy probably lies in the approximations inherent in the exchangecorrelation functional employed. In principle, even small deviations between the experimental and computational energy barriers for migration, E_{a}, can lead to large deviations in the diffusion coefficients and viscosities. Our results indicate that the two activation energies differ by less than 5%. Interestingly, there are large differences in the prefactors η_{0}: the theoretical estimate is more than twice as large as the experimental one. Nevertheless, we should point out that the theoretical E_{a} and η_{0} are affected by significant statistical uncertainties because of the small number of data points. It is not obvious what the effect of nonlocal functionals or Grimme corrections on the kinetic properties should be. In fact, for liquid GeTe_{4}, the latter corrections yield smaller diffusion coefficients and, thus, larger viscosities than plain GGA simulations^{27}. This point deserves further investigation. Another source of error is the finite size effects due to the periodic boundary conditions. These effects originate from the fact that a diffusing particle sets up a slowly decaying hydrodynamic flow, which, in a periodic system, brings about an interference between the particle and its periodic images^{45}. Consequently, one obtains smaller diffusion coefficients as compared to the “real” values corresponding to the thermodynamic limit. Hence, larger simulation cells are expected to reduce the discrepancy with experiments. A third error source is caused by the use of thermostats. This technical point is discussed in the Methods section.
Importantly, the small (hightemperature) activation energy for viscosity we have obtained, E_{a} = 0.256 eV, is in agreement with previous results about similar phasechange materials^{29,30,31}. Notice that, at lower temperatures, in the deep supercooled regime, there is a dramatic change in the activation energy. This behaviour is due to the high fragility^{29} of Ge_{2}Sb_{2}Te_{5} and is ultimately responsible for the remarkable stability of the amorphous state at room temperature a crucial property for applications of PCMs in memory devices.
Methods
Abinitio molecular dynamics simulations
The AIMD constantvolume (NVT) simulations are carried out with the QUICKSTEP code included in the CP2K package^{46}. We use the very efficient AIMD method developed by Kühne et al.^{47} This method is intrinsically dissipative and is employed in combination with Langevin thermostats, so that the simulations sample the canonical ensemble^{47,48}. Notice that, in general, stochastic thermostats can affect the dynamical properties of the system significantly. CP2K uses a mixed Gaussian and planewave basis set. In our simulations, KohnSham orbitals are expanded in a Gaussiantype basis set of triplezeta plus polarization quality, whereas the charge density is expanded in plane waves, with a cutoff of 300 Ry. Scalarrelativistic Goedecker^{49} pseudopotentials are used. The Brillouin zone is sampled at the Γ point.
Reverse MonteCarlo simulations
Reverse Monte Carlo simulation is performed using rmc++ code^{50}. The simulation box consists of 20250 atoms. Starting atomic configuration is a random distribution of atoms with the following minimum interatomic distance allowed in the model: 2.1 Å for GeGe, 2.2 Å for GeTe and GeSb, 2.4 Å for SbSb, TeTe, and SbTe. The atoms are moved randomly to optimize the fit to the experimental XRD and ND structure factors and to all of six partial pair distribution functions obtained by AIMD simulations.
Samples preparation
The Ge_{2}Sb_{2}Te_{5} master alloys are prepared from proper quantities of pure elements (all 99.999%). An alloy for isotopic substitution neutron diffraction is prepared from ^{70}Ge (enrichment 96.5%) and natural Sb and Te. Because of the high vapour pressure of Sb and Te, the alloys are synthesized in closed quartz ampoules. The ampoules are previously evacuated and filled with Ar to a pressure of about 250 mbar at room temperature. The alloys are melted and homogenized by isothermal heating at 1073 for 5 hours.
Xray diffraction experiment
Xray diffraction experiment is carried out at the BW5 experimental station^{51} at the DORIS synchrotron storage ring, DESY, Hamburg, Germany. The sample is filled and sealed into a thinwalled quartz glass capillary (diameter −2 mm, wall thickness–about 0.02 mm). The sample is heated by a halogen spotlight heater. The energy of the Xray radiation is 123.5 keV. The size of the incident beam is 1 × 4 mm^{2}. Raw data is corrected for detector deadtime, background, polarization, absorption, variations in detector solid angle, and incoherent scattering. The corrected intensity is normalized to a FaberZiman^{52} total structure factor using Xray atomic form factors given by Waasmaier and Kirfel^{53}.
Neutron diffraction with isotopic substitution
Neutron diffraction measurements are carried out at the Near and InterMediate Range Order Diffractometer^{54} (NIMROD) at the ISIS Second Target Station Facility of the Rutherford Appleton Laboratory, Oxford, UK. The samples are sealed under vacuum in quartzglass tubes (4.95 mm outer diameter and 0.38 mm wall thickness) made for nuclear magnetic resonance spectroscopy (Hilgenberg GmbH, Malsfeld, Germany). The quartzglass tube with the sample is inserted in a vanadium cylindrical cell (diameter of 6 mm; wall thickness of 40 μm), which is then placed in the middle of a vertical resistanceheating furnace. The sample temperature is kept constant with an accuracy of ±1 K during the isothermal measurements. The beam size is 8 × 30 mm^{2}. Timeofflight data are collected over a range of diffraction vector q between 0.1 and 30 Å^{−1}. However, the useful range of q is limited to about 15 Å^{−1} because of the neutron absorption resonances in the sample occurring at high energies. ND measurements are also performed for the empty quartzglass tube, the empty furnace, the empty spectrometer and the 6 mm thick vanadium rod for the purpose of instrument calibration and data normalization. Raw data are treated using the Gudrun program^{55} based upon algorithms in the ATLAS package^{56}.
Density measurements
The density of liquid Ge_{2}Sb_{2}Te_{5} alloy is determined by a high energy γray attenuation method. About 110 Mbq of ^{137}Cs is used as a γray source of 662 keV and a NaI scintillation counter is used as a γray detector. Ge_{2}Sb_{2}Te_{5} specimen is sealed in an ampoule made of fused quartz with a diameter of 1.1 cm and a length of 2.388 ± 0.002 cm. The length of the ampoule is determined by measuring the linear attenuation coefficient of Hg at room temperature. The linear attenuation coefficients for pure elements are measured using freshly powdered specimens compressed into a cylindrical steel tube. They are 0.007005 ± 0.000004 (m^{2}/kg) for Ge, 0.007329 ± 0.000008 (m^{2}/kg) for Sb and 0.007182 ± 0.000003 (m^{2}/kg) for Te. The uncertainty of the experimental values associated with counting statistics is less than 0.11%. The total experimental uncertainty is estimated to be less than 0.5%^{57}.
Viscosity measurements
The dynamic viscosity of liquid Ge_{2}Sb_{2}Te_{5} alloy is measured using an oscillatingcup viscometer described elsewhere^{58}. The sample is sealed in a quartz crucible with 22.5 mm inner diameter under Ar atmosphere as above. The ampoule is inserted into a graphite holder connected to a torsion wire. The oscillating unit is situated in a highvacuum chamber with a Mowire resistance heater and appropriate shielding. The temperature of the sample is measured with uncertainty of about ±5 K by a thermocouple placed at the bottom of the sample holder. The damped torsion oscillations excited by a PCcontrolled mechanical unit are detected by means of a laserbeam/photodiode unit. The system is heated at a rate of 5 K min^{−1} to 1253 K, held for 1 hour at the constant temperature for homogenization, and cooled at a rate of 1 K min^{−1}. Ten to twelve oscillations are registered for each measured point during cooling of liquid Ge_{2}Sb_{2}Te_{5} alloy down to a solidification point at 900 K. The dynamic viscosity of the melt is determined from the measured oscillations using an equation given by Roscoe et al.^{59} and modified by Brooks et al.^{60}. The relative uncertainty of the dynamic viscosity is less than 10%, as estimated by Gruner et al.^{58}. The measurements repeated several times showed a very good reproducibility.
Additional Information
How to cite this article: Schumacher, M. et al. Structural, electronic and kinetic properties of the phasechange material Ge_{2}Sb_{2}Te_{5} in the liquid state. Sci. Rep. 6, 27434; doi: 10.1038/srep27434 (2016).
References
Wuttig, M. & Yamada, N. Phasechange materials for rewriteable data storage. Nat Mater 6, 824–832 (2007).
Raoux, S., Welnic, W. & Ielmini, D. Phase change materials and their application to nonvolatile memories. Chem Rev 110, 240–267 (2010).
Zhang, W. et al. Densityfunctional theory guided advances in phasechange materials and memories. MRS Bulletin 40, 856–865 (2015).
Ovshinsky, S. Reversible electrical switching phenomena in disordered structures. Phys Rev Lett 21, 1450–1453 (1968).
Yamada, N. et al. High speed overwritable phase change optical disk material. Jpn J Appl Phys 26, 61–66 (1987).
Nonaka, T. et al. Crystal structure of GeTe and Ge2Sb2Te5 metastable phase. Thin Solid Films 370, 258 (2000).
Matsunaga, T. & Yamada, N. Structural investigation of GeSb2Te4: A highspeed phasechange material. Phys Rev B 69, 104111 (2004).
Wuttig, M. et al. The role of vacancies and local distortions in the design of new phasechange materials. Nat Mater 6, 122–128 (2007).
Kolobov, A. V. et al. Understanding the phasechange mechanism of rewritable optical media. Nat Mater 3, 703–708 (2004).
Kohara, S. et al. Structural basis for the fast phase change of Ge2Sb2Te5: Ring statistics analogy between the crystal and amorphous states. Appl Phys Lett 89, 201910 (2006).
Akola, J. et al. Experimentally constrained densityfunctional calculations of the amorphous structure of the prototypical phasechange material Ge2Sb2Te5 . Phys Rev B 80, 020201 (2009).
Jóvári, P. et al. ‘Wrong bonds’ in sputtered amorphous Ge2Sb2Te5 . J Phys: Condens Matter 19, 335212 (2007).
Jóvári, P. et al. Local order in amorphous Ge2Sb2Te5 and GeSb2Te4 . Phys Rev B 77, 035202 (2008).
Caravati, S., Bernasconi, M., Kühne, T. D., Krack, M. & Parrinello, M. Coexistence of tetrahedral and octahedrallike sites in amorphous phase change materials. Appl Phys Lett 91, 171906 (2007).
Akola, J. & Jones, R. O. Structural phase transitions on the nanoscale: The crucial pattern in the phasechange materials Ge2Sb2Te5 and GeTe. Phys Rev B 76, 235201 (2007).
Hegedüs, J. & Elliott, S. R. Microscopic origin of the fast crystallization ability of Ge–Sb–Te phasechange memory materials. Nat Mater 7, 399–405 (2008).
Mazzarello, R., Caravati, S., AngiolettiUberti, S., Bernasconi, M. & Parrinello, M. Signature of tetrahedral Ge in the Raman spectrum of amorphous phasechange materials. Phys Rev Lett 104, 085503 (2010).
Welnic, W. et al. Unravelling the interplay of local structure and physical properties in phasechange materials. Nature Mater 5, 56–62 (2006).
Sun, Z. et al. Local structure of liquid Ge1Sb2Te4 for rewritable data storage use. J Phys: Condens Matter 20, 205102 (2008).
Akola, J. & Jones, R. O. Density functional study of amorphous, liquid and crystalline Ge2Sb2Te5: homopolar bonds and/or AB alternation? J Phys: Condens Matter 20, 465103 (2008).
Steimer, C. et al. Characteristic ordering in liquid phasechange materials. Adv Mater 20, 4535–4540 (2008).
Delheusy, M. et al. Structure of liquid Tebased alloys used in rewritable DVDs. Physica B: Condens Matter 350, E1055–E1057 (2004).
Kolobov, A. V. et al. Liquid Ge2Sb2Te5 studied by extended xray absorption. Appl Phys Lett 95, 241902 (2009).
Bichara, C., Johnson, M. & Gaspard, J. P. Octahedral structure of liquid GeSb2Te4 alloy: Firstprinciples molecular dynamics study. Phys Rev B 75, 060201 (2007).
Caravati, S., Bernasconi, M. & Parrinello, M. Firstprinciples study of liquid and amorphous Sb2Te3 . Phys Rev B 81, 014201 (2010).
Otjacques, C. et al. Dynamics of the negative thermal expansion in tellurium based liquid alloys. Phys Rev Lett 103, 245901 (2009).
Micoulaut, M. Van der Waals corrections for an improved structural description of telluride based materials. J. Chem. Phys. 138, 061103 (2013).
FloresRuiz, H. et al. Effect of tellurium concentration on the structural and vibrational properties of phasechange GeSbTe liquids. Phys Rev B 92, 134205 (2015).
Orava, J., Greer, A. L., Gholipour, B., Hewak, D. W. & Smith, C. E. Characterization of supercooled liquid Ge2Sb2Te5 and its crystallization by ultrafastheating calorimetry. Nat Mater 11, 279–283 (2012).
Salinga, M. et al. Measurement of crystal growth velocity in a meltquenched phasechange material. Nat Commun 4, 2371 (2013).
Sosso, G. C., Behler, J. & Bernasconi, M. Breakdown of StokesEinstein relation in the supercooled liquid state of phase change materials. Phys Stat Sol (b) 249, 1880–1885 (2012).
Zhang, W. et al. M. How fragility makes phasechange data storage robust: insights from ab initio simulations. Sci Rep 4, 6529 (2014).
Kaban, I. et al. Structural studies on Terich GeTe melts. J Phys Condens Matter 18, 2749 (2006).
Kaban, I., Jóvári, P., Hoyer, W. & Welter, E. Determination of partial pair distribution functions in amorphous Ge15Te85 by simultaneous RMC simulation of diffraction and EXAFS data. J NonCryst Solids 353, 2474–2478 (2007).
Kaban, I., Jóvári, P. & Petkova, T. Structure of GeSe4In and GeSe5In glasses. J Phys Condens Matter 22, 404205 (2010).
Rátkai, L. et al. Microscopic origin of demixing in Ge20Se x Te80−x alloys. J Alloy Comp 509, 5190–5194 (2011).
Chrissanthopoulos, A. et al. Structure of AgIdoped Ge–In–S glasses: Experiment, reverse Monte Carlo modelling, and density functional calculations. J Solid State Chem 192, 7–15 (2012).
McGreevy, R. L. & Pusztai, L. Reverse Monte Carlo simulation: A new technique for the determination of disordered structures. Mol Simulat 1, 359–367 (1988).
Lee, K., Murray, E. D., Kong, L., Lundqvist, B. I. & Langreth, D. C. Higheraccuracy van der Waals density functional. Phys Rev B 82, 081101 (2010).
Grimme, S. Semiempirical GGAtype density functional constructed with a longrange dispersion correction. J Comput Chem 27, 1787–1799 (2006).
Raty, J.Y. et al. Aging mechanisms in amorphous phasechange materials. Nat Commun 6, 7467 (2015).
Deringer, V. L. et al. Bonding nature of local structural motifs in amorphous GeTe. Angew Chem Int Ed 53, 10817–10820 (2014).
Raty, J.Y. et al. Evidence of a reentrant Peierls distortion in liquid GeTe. Phys Rev Lett 85, 1950 (2000).
Bouzid, A. et al. Role of the van der Waals interactions and impact of the exchangecorrelation functional in determining the structure of glassy GeTe4 . Phys Rev B 82, 134208 (2015).
Yeh, I.C. & Hummer, G. Systemsize dependence of diffusion coefficients and viscosities from molecular dynamics simulations with periodic boundary conditions. J Phys Chem B 108, 15873–15879 (2004).
VandeVondele, J. et al. Quickstep: Fast and accurate density functional calculations using a mixed Gaussian and plane waves approach. Comput Phys Comm 167, 103–128 (2005).
Kühne, T., Krack, M., Mohamed, F. R. & Parrinello, M. Efficient and accurate CarParrinellolike approach to BornOppenheimer molecular dynamics. Phys Rev Lett 98, 066401 (2007).
Kühne, T., Krack, M. & Parrinello, M. Static and dynamical properties of liquid water from first principles by a novel CarParrinello like approach. J Chem Theory Comp 5, 235–241 (2009).
Goedecker, S., Teter, M. & Hutter, J. Separable dualspace Gaussian pseudopotentials. Phys Rev B 54, 1703–1710 (1996).
Gereben, O., Jóvári, P., Temleitner, L. & Pusztai, L. A new version of the RMC++ Reverse Monte Carlo programme, aimed at investigating the structure of covalent glasses. J. Optoelectron. Adv. M. 9, 3021–3027 (2007); Code and executables are available at http://www.szfki.hu/~nphys/rmc++/opening.html.
Poulsen, H. F., Neuefind, J., Neumann, H.B., Schneider, J. R. & Zeidler, M. D. Amorphous silica studied by high energy Xray diffraction. J NonCryst Solids 188, 63–74 (1995).
Faber, T. E. & Ziman, J. M. A theory of the electrical properties of liquid metals. III. The resistivity of binary alloys. Philos Mag 11, 153–173 (1965).
Waasmaier, D. & Kirfel, A. New analytical scatteringfactor functions for free atoms and ions. Acta Crystallogr A 51, 416–431 (1995).
Bowron, D. T. et al. NIMROD: The Near and InterMediate Range Order Diffractometer of the ISIS second target station. Rev Sci Instrum 81, 033905 (2010).
Soper, A. K., Gudrun, N. & Gudrun, X. Programs for correcting raw neutron and Xray diffraction data to differential scattering cross section. Rutherford Appleton Laboratory Technical Report, RALTR2011013, 2011.
Hannon, A. C., Howells, W. S. & Soper, A. K. ATLAS: A suite of programs for the analysis of timeofflight neutron diffraction data from liquid and amorphous samples. Inst Phys Conf Ser 107, 193–211 (1990).
Tscuchiya, Y. Molar volume and thermodynamics of the structural change of liquid SeTe system. J Phys Soc Jpn 57, 3851–3857 (1988).
Gruner, S. & Hoyer, W. A statistical approach to estimate the experimental uncertainty of viscosity data obtained by the oscillation cup technique. J. Alloy Comp. 480, 629–633 (2009).
Roscoe, R. & Bainbridge, W. Viscosity determination by the oscillating vessel method I: theoretical considerations. Proc Phys Soc 72, 576–584 (1958).
Brooks, R. F., Dinsdale, A. T. & Quested, P. N. The measurement of viscosity of alloysa review of methods, data and models. Meas Sci Technol 16, 354–362 (2005).
Acknowledgements
We are indebted to W. Zhang for useful discussions. This work has been financially supported by the German Research Foundation DFG (Contracts Nos Ka3209/61 and Ma5339/21). We also acknowledge the computational resources granted by JARAHPC from RWTH Aachen University under project JARA0089, as well as funding by the DFG within the collaborative research centre SFB 917 “Nanoswitches”. P. Jóvári was supported by NKFIH (National Research, Development and Innovation Office) Grant No. SNN 116198. Part of this research was carried out at the light source DORIS III at DESY, Hamburg, a member of the Helmholtz Association (HGF). The experiments at the ISIS Pulsed Neutron and Muon Source were supported by a beamtime allocation from the Science and Technology Facilities Council (experiment RB1610107, DOI: 10.5286/ISIS.E.79111252). We thank T. F. Headen, P. McIntyre and A. Sears for support during neutron diffraction experiments.
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M.S. performed the AIMD modeling. P.J. and H.W. carried out the RMC simulations. H.W., P.J., T.G.A.Y. and I.K. performed the diffraction and oscillatingcup experiments, whereas Y.T. performed the density measurements. Analysis of the data was carried out by all the authors. The paper was written by R.M. and I.K. with contribution of all coauthors. The project was initiated by R.M. and I.K.
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Schumacher, M., Weber, H., Jóvári, P. et al. Structural, electronic and kinetic properties of the phasechange material Ge_{2}Sb_{2}Te_{5} in the liquid state. Sci Rep 6, 27434 (2016). https://doi.org/10.1038/srep27434
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DOI: https://doi.org/10.1038/srep27434
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