Article pubs.acs.org/IC
Metastable Stacking-Polymorphism in Ge2Sb2Te5 Shixiong He, Linggang Zhu, Jian Zhou, and Zhimei Sun* School of Materials Science and Engineering, and Center for Integrated Computational Materials Engineering, International Research Institute for Multidisciplinary Science, Beihang University, Beijing 100191, China S Supporting Information *
ABSTRACT: Metastable rocksalt structured Ge2Sb2Te5 is the most widely used phase-change material for data storage, yet the atomic arrangements of which are still under debate. In this work, we have proposed metastable stacking-polymorphism in cubic Ge2Sb2Te5 based on first-principles calculations. Our results show that cubic Ge2Sb2Te5 is actually polymorphic, varying from randomly distributed vacancies to highly ordered vacancy layers; consequently, the electrical property varies between metallic and semiconducting. These different atomic stackings of cubic Ge2Sb2Te5 can be obtained at different experimental synthetic conditions. The concept of stacking-polymorphic Ge2Sb2Te5 provides important fundamentals for metastable Ge2Sb2Te5 and is useful for tuning the performance of the phase-change materials. initio calculations, Eom et al.9 obtained an opposing result that intrinsic vacancies have a tendency to distribute randomly at 4b sites. Recently, in 2016, Zhang et al.10,11 performed an atomicscale chemical identification experiment on GST that was obtained by the crystallization of the amorphous phase, and they demonstrated the existence of atomic disorder of Ge, Sb and vacancy at 4b sites and confirmed a gradual vacancy ordering process upon further annealing. Interestingly, in 2017, by high-resolution aberration-corrected scanning transmission electron microscopy, Hilmi et al.12 observed both randomly distributed vacancies and highly ordered vacancy layers in epitaxial cubic GST thin films synthesized by a pulsed laser deposition technique. It is worth to mention that such a similar debate exists in hexagonal GST, which is the stable phase for cubic GST.5,13−16 Obviously, the above conclusions about how Ge, Sb and vacancies arrange at 4b sites were derived from results obtained at different experimental or theoretical conditions; especially, the experimental conditions influence the conclusions drastically. These conditional atomic configurations make it natural for us to think that all of these reported structures might be stacking-polymorphs of cubic GST, and such an assumption of stacking-polymorph can be applied also to the stable hexagonal GST. The phenomena of polymorphs are common in many materials; for example, Ti3SiC2, a widely investigated highperformance ceramic material, has two polymorphs with the same space group P63/mmc, i.e., α- and β-Ti3SiC2. α-Ti3SiC2 is the normally obtained phase, which can transform to β-Ti3SiC2 at high temperatures where only the positions of Si atoms change.17 Another interesting example is polymorphic Cu, by different solution routes, two distinct polymorphic Cu(TCNQ)
1. INTRODUCTION Chalcogenide phase-change materials are widely used for optical memory, such as digital versatile disc random access memory (DVD-RAM). Recently, electrical data storage based on chalcogenides that is also referred to as phase-change random access memory (PCRAM) is considered as the most promising next-generation nonvolatile electronic memory.1−3 Among these chalcogenide alloys, Ge2Sb2Te5 (GST) exhibits the best performance for DVD-RAM in terms of speed and stability and has been investigated as the candidate recording material for prototype PCRAM.4 GST can exist in two crystalline phases, metastable cubic and stable hexagonal, while the phenomenon of fast reversible phase transition between cubic and amorphous GST is used for data storage, and the significant contrast in the electrical properties between cubic and amorphous GST is used for encoding the recorded information.5,6 Thus, extensive works have been performed to understand the structure of cubic GST in order to unravel the underlying mechanism of phase-change data storage. Cubic GST has a rocksalt symmetry, where the anion (4a) sites are fully occupied by Te atoms and the cation (4b) sites are occupied by Ge, Sb atoms and 20% intrinsic vacancies. Even after many years of experimental and theoretical studies, how atoms arrange at 4b sites seems still under debate. In a very early study, based on X-ray absorption fine-structure spectroscopy (EXAFS) studies, Yamada et al.7 proposed that Ge, Sb atoms and vacancies randomly occupy the 4b sites. Later, upon high-resolution transmission electron microscopy analysis, Park et al.8 put forward that Ge and Sb atoms tend to position themselves on specific planes. On the basis of ab initio total energy calculations, Sun et al.5 proposed that a totally ordered atomic configuration of the -Te-Ge-Te-Sb-Te-v-Te-Sb-Te-Gestacking along the [111] direction is the most stable structure, where “v” represents vacancy layers. Also, on the basis of ab © XXXX American Chemical Society
Received: August 2, 2017
A
DOI: 10.1021/acs.inorgchem.7b01970 Inorg. Chem. XXXX, XXX, XXX−XXX
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Inorganic Chemistry were obtained, which displayed bistable switching behavior.18 Even amorphous SiO2 also has amorphous polymorphs with two substantially different amorphous states.19 Therefore, we took further close analysis on the different conclusions about the atomic configurations of metastable cubic GST which were obtained at different experimental conditions and arrived at the assumption that metastable GST is actually stacking-polymorphic. These stacking-polymorphs of GST might provide more options for designing novel phase-change materials. In this work, we have performed systematic ab initio calculations on all the possible stacking configurations of cubic GST, including the point-defect atomic stacking and layer stacking, and our results demonstrate that cubic GST is stacking-polymorphic both with randomly distributed vacancies and with highly ordered vacancy layers. The electronic structures and the physical properties of polymorphic GST vary between semiconductor and metal, and the different stacking-polymorphic GSTs can be obtained at different experimental synthetic conditions.
Table 1. Calculated Total Energy and Lattice Parameters for Metastable Stacking-Polymorphs in Ge2Sb2Te5 energy (eV/atom)
a (Å/atom)
atomic arrangement
PBE
vdW-D2
PBE
vdW-D2
aa bb cc dd ee
−3.776 −3.759 −3.770 −3.766 −3.718
−4.117 −4.098 −4.109 −4.102
6.106 6.157 6.120 6.151 6.149
5.943 5.900 5.925 5.922
a
a: -Te-Ge-Te-Sb-Te-v-Te-Sb-Te-Ge- stacking along [111]. bb: -TeSb-Te-Ge-Te-v-Te-Ge-Te-Sb- stacking along [111]. cc: -Te-Ge-Te-SbTe-v-Te-Ge-Te-Sb- stacking along [111]. dd: -Te-Ge/Sb-Te-Ge/SbTe-v-Te-Ge/Sb-Te-Ge/Sb- stacking along [111], wherein Ge and Sb atoms are mixed in the same layer. In (a)−(d), “v” represents a vacancy layer. ee: An SQS where Ge, Sb atoms and vacancies randomly occupy the 4b cation sites.
2. COMPUTATIONAL METHODS Our calculations were carried out within the framework of density functional theory (DFT) as implemented in the Vienna Ab initio Simulation Package (VASP).20 The projector augmented wave (PAW) potentials21 were used with the generalized gradient approximations22 (GGA) of the Perdew−Burke−Ernzerhof23 (PBE) exchange-correlation functional, where 4s24p2 for Ge, 5s25p3 for Sb, and 5s25p4 for Te were treated as valence electrons in the pseudopotentials. A cutoff energy of 300 eV was chosen for the plane-wave expansion of wave functions, and convergence with respect to self-consistent iterations was achieved when the total energy difference between cycles was less than 1 × 10−5 eV. The k-point of 5 × 5 × 2 automatically generated with their origin at Γ point and the tetrahedron method with Blöchl corrections24 were used. The k-point grid has been tested to be sufficient to obtain the converged results. To take the van der Waals (vdW) forces into account for better describing the weak Te−Te interactions, a semiempirical dispersion potential was added to the conventional Kohn−Sham DFT energy in the scheme of the DFT-D2 method.25,26 Crystal orbital Hamilton population27 (COHP) analyses were performed by the TB-LMTO-ASA28,29 code and GGA functional.30 The total and partial density of states (DOS) were calculated for the equilibrium structure. The PHONOPY code31 was performed to calculate the phonon frequencies through the supercell approach32 (SCA) as well as the density functional perturbation theory33 (DFPT) where supercells containing 108 atoms and 12 vacancy sites and 5 × 5 × 2 k-points were used. The VESTA package34 was used to analysis the electron localization function35 (ELF), and the Bader charge analysis36−38 was performed for the chemical bonding interactions.
Figure 1. Total density of states of metastable stacking-polymorphs in Ge2Sb2Te5; herein, the graph in the right-hand dashed box is the magnification of the TDOS of these stackings around Ef (the left-hand dashed box).
Information). In addition, if some Ge and Te atoms, or Sb and Te atoms, exchange sites, there should be some Ge−Ge, Sb−Sb, Ge−Sb, and Te−Te homopolar bonds, which will reduce the stability of these structures, and hence, these cases of such anti-site disordered stacking GST are not considered. Table 1 lists the calculated total energy and lattice parameters for the five stacking configurations of GST with and without vdW correction. Due to the absence of vdW interaction between the adjacent Te-Te layers in stacking e, we employed the same PBE pseudopotential without vdW corrections for the five stacking structures in order to compare stacking e with other vacancy ordered structures. Some conclusions can be drawn based on the results in Table 1. First, stacking a is the most stable structure and stacking e is the least stable structure; moreover, the ordering of vacancies lowers the total energy of the system, agreeing with experimental results and our previous work.5,39 It is interesting to note that the largest energy difference is between stackings a and e which is only about 58 meV/atom, and all the vacancy ordered stacking structures are more stable than the totally disordered stacking structure. On the other hand, the energy difference between the Ge/Sb mixed configuration (stacking d) and the most stable configuration (stacking a) is only 10 meV/atom; that is to say, the Ge/Sb
3. RESULTS AND DISCUSSION We started from the following five kinds of atomic arrangements for cubic GST, which include almost all possible atomic arrangements: (a) -Te3-Ge-Te2-Sb-Te1-v-Te1-Sb-Te2-Ge(stacking a); (b) -Te3-Sb-Te2-Ge-Te1-v-Te1-Ge-Te2-Sb(stacking b); (c) -Te3-Ge-Te2-Sb-Te1-v-Te1-Ge-Te2-Sb(stacking c); (d) -Te3-Ge/Sb-Te2-Ge/Sb-Te1-v-Te1-Ge/SbTe2-Ge/Sb- (stacking d); herein, Ge and Sb atoms randomly occupy in the same (111) layer, for stackings a to d, “v” represents vacancy layers and all atoms stack along the [1 1 1] direction; (e) Special quasirandom structure (SQS, stacking e); herein Ge, Sb atoms and vacancies randomly occupy the 4b cation sites. Supercells consisting of 108 atoms with 12 vacancy positions are used for stackings a to d and 144 atoms with 16 vacancies for stacking e (Figure S1 in the Supporting B
DOI: 10.1021/acs.inorgchem.7b01970 Inorg. Chem. XXXX, XXX, XXX−XXX
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Inorganic Chemistry
Figure 2. Partial density of states of (a) stacking a, (b) stacking b and band structures of (c) stacking a, (d) stacking b; herein, the lines represent normal orbitals and dots describe the weighted orbitals of VBM and CMB, where the larger the dot, the more weight to VBM or CBM.
Figure 1 shows the total density of states (TDOS) mainly in the valence band energy range for the five stacking-polymorphs of cubic GST, where the most prominent difference is at the band gap. The polymorphs of stackings a and c have a narrow band gap at the Fermi level (EF) of 0.29 and 0.11 eV, respectively, while polymorphs of stackings b, d, and e have no band gap at EF. Thus, it is expected that the electrical properties of the five polymorphs from stackings a to e are different. It is interesting to note that such similar behaviors are observed in the experimental work by Park et al.,40 where the property changes of cubic GST from insulating to metallic behavior are coupled with the structure changes by applying an electrical current. The calculated partial density of states (PDOS) and electronic band structures for the polymorphs of stackings a and b are displayed in Figure 2. Analysis of the PDOS reveals the origin of the differences observed in TDOS. As seen in Figure 2a for stacking a, the valence electron states just below the Fermi level consist mainly of p−p coupling between Te and Ge and p−p coupling between Te and Sb. This conclusion is supported by further analyzing the band structure of stacking a as shown in Figure 2c, where the valence-band maximum (VBM) is mainly dominated by Te 5p states and the conduction-band minimum (CBM) mainly consists of p states from Ge and Sb. For stacking b, the difference is obvious as shown in Figure 2b,d, where the valence electron states mainly consist of p−p coupling between Te and Sb, and obviously the p states of Te and Sb make the major contribution to the band edges. Furthermore, the distinct difference between stackings a and b is that the former has a direct band gap and the latter has no band gap. The difference in properties of various stacking-polymorphic GST can be further understood by an analysis of their chemical bonding. Herein, the COHP analyses are performed taking all interactions with r < 3.5 Å into account, the results of which are shown in Figure 3. Ideally, the −COHP takes a positive value for bonding, a negative one for the antibonding state, and zero
mixed configuration is highly possible to observe experimentally, in line with the direct study on atomic stacking of rocksalt GST by high angle annular dark field scanning transmission electron microscopy (HAADF-STEM) combined with atomic energy-dispersive X-ray (EDX) mapping.11 Second, the calculated lattice parameters for the five configurations are very close to each other, with that of PBE (vdW-D2) being slightly larger (smaller) than that of the experiment of 6.02 Å.8 Consequently, all of these configurations are energetically possible structures for cubic GST. Actually, experimental results can support this conclusion; for example, in the experiment of Zhang et al.,10 the vacancy ordering in rocksalt GST varies with the annealing time and temperature. As GST was annealed at 150 °C for 30 min just after being crystallized from the amorphous phase, HAADF-STEM images display randomly distributed vacancies, which may correspond to the structure of stacking e, while, upon further annealing, the vacancies are gradually segregated onto specific (111) planes, showing a gradually ordered process like the structures from stackings e to a. The above results suggest that GST have many configurations where Ge, Sb and vacancies may arrange in a completely disordered state or ordered stacking at the 4b sites of rocksalt GST. In other words, all of these configurations are actual stacking-polymorphs of GST, which can be obtained at different synthetic conditions. One can image that a complete vacancy disordered structure (stacking e) would be obtained when amorphous GST just crystallizes into a cubic state, while, with further annealing GST at a certain temperature, there would be a gradual vacancy ordering process, and cubic GST would finally transform into any configuration among stackings from d to a. Nevertheless, in terms of energy, in addition to the mostly ordered configuration (stacking a), the Ge/Sb mixed structure (stacking d) would be the highly observed configuration by appropriate experimental technique as discussed above. In the following, we will perform extensive analyses of electronic structure and chemical bonding for the five stacking-polymorphs of cubic GST. C
DOI: 10.1021/acs.inorgchem.7b01970 Inorg. Chem. XXXX, XXX, XXX−XXX
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Figure 4. Phonon dispersion relations along high-symmetry lines of metastable stacking-polymorphs in Ge2Sb2Te5. (a) Stacking a; (b) stacking b.
Particularly, the average COHP value of stacking b is slightly lower than that of stacking e, which can imply that the vacancy ordering has little influence on depleting antibonding states. To investigate the stability of stacking-polymorphs in GST, we have carried out the phonon dispersion curves of stackings a and b along the high-symmetry lines in the first Brillouin zone (FBZ), which are displayed in Figure 4. One thing we noticed in our calculations is that there are some negative frequencies in phonon dispersions for both stackings a and b. The imaginary phonon dispersions are related to the negative stress tensor, which indicates the dynamic instability of the optimized structure. Actually, cubic GST is a metastable phase, and the stable crystalline phase of GST is hexagonal; therefore, imaginary phonon dispersions are reasonable for stackings a and b. As amorphization of cubic GST will result in an increase in the lattice parameters, we can infer that, when the amorphization of GST occurs, the position of negative frequencies would take priority. On the other hand, it is worth to mention that negative phonon dispersions were observed in many other materials which can exist stably, such as single quintuple Bi2Te3 and Bi2Se3 films and bulk materials studied by Cheng et al.41 Besides many similarities, some obvious differences between stackings a and b can be seen. For stacking a as shown in Figure 4a, the imaginary phonon dispersions are mainly distributed around the high symmetry points of Γ (0, 0, 0), K (1/3, 1/3, 0), and H (1/3, 1/3, 1/2). For stacking b as seen in Figure 4b, the imaginary phonon dispersions distribute in everywhere except for the area along M (1/2, 0, 0) to K (1/3, 1/3, 0) and L (1/2, 0, 1/2) to H (1/3, 1/ 3, 1/2) directions. The distribution range of imaginary phonon dispersions for stacking a is far less than that for stacking b. This can further confirm that the atomic arrangement of stacking a is more stable. On the other hand, to verify the mechanical stability of the stacking-polymorphs in GST, we have calculated the elastic constants cij for stackings a and b by a step-by-step stress−strain method.42 On the basis of the Born’s stability criteria43,44 of c11 − c12 > 0 and (c11 − c12)c44 − 2c214 > 0 2 for the shear stability and (c11 + c12)c33 − 2c13 > 0
Figure 3. COHP diagrams. (a) Te1−Sb bonds (red), Te2−Sb (blue), Te2−Ge (green), Te3−Ge (pink) of stacking a. (b) Te1−Sb bonds (red), Te2−Sb (blue), Te2−Ge (green), Te3−Ge (pink) of stacking b. Inset: Magnification of dashed box. (c) Average bonds of stacking a, stacking b, and stacking e. All interactions with r < 3.5 Å were taken into account, and the average was normalized to a single bond.
for the nonbonding state. The COHP diagrams of the Te−Sb bonding and Te−Ge bonding in stacking a are shown in Figure 3a; it is obvious that there are strong Te−Sb and Te−Ge bondings in stacking a due to the large bonding regions below the Fermi level. Both Te−Sb and Te−Ge bondings fall into nonbonding regions around the Fermi level, which confirms an electronic stability. However, for stacking b as shown in Figure 3b, only the Te2−Ge bonding falls into nonbonding regions at the Fermi level, whereas Te1−Ge, Te2−Sb, and Te3−Sb bonding slightly fall into antibonding regions which lead to a slight internal stress. According to molecular orbital theory, the antibonding states at high energy reflect an electronic instability; hence, it can explain the higher cohesive energy of stacking b in contrast to stacking a. In order to rule out the effect of vacancies, we visualize the bonding and antibonding states for the structures of stackings a, b, and e by plotting averaged COHP (Figure 3c). The average bond strength is in terms of the averaged COHP value, we can see the nearly similar averaged COHP values for the three polymorphic GST, except for a small difference at around the Fermi level. D
DOI: 10.1021/acs.inorgchem.7b01970 Inorg. Chem. XXXX, XXX, XXX−XXX
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Figure 5. ELF projected on the (1 1 0) plane for (a) stacking a, (b) stacking b and ELF values between Te and Ge (Sb) atoms for (c) stacking a, (d) stacking b. All the graphs are under the same saturation levels, and the interval between the contour lines is 0.20.
analyze the covalent bonding character in GST, we employed the line ELF distribution between Te and Ge (Sb) atoms for stackings a and b (see Figure 5c,d, respectively). For stacking a as seen in Figure 5c, Te1−Sb is the strongest bond with ELF = 0.68; the strength of Te2−Sb, Te3−Ge, and Te2−Ge bonds decline in turn with the ELF value decreasing from 0.58 to 0.56 and to 0.51, also showing a small difference in bonding strength among these three bonds. For stacking b as seen in Figure 5d, the difference in bonding strength among these four bonds is significant, with the ELF value varying from 0.73 to 0.38, demonstrating rather larger inhomogeneous character in bonding strength in stacking b compared to stacking a. In stacking b, the Te1−Ge bond is the strongest (ELF = 0.73) and the Te2−Ge bond is the weakest (ELF = 0.38); this large difference indicates that the Te2−Ge bond is easy to break and hence results in phase transition. That is to say, stacking b is less stable than stacking a, which agrees well with our above analyses. The ionic character of GST can be analyzed by estimating the charge transfers among the constitute elements in stackings a and b as listed in Table 2 by performing the Bader charge analysis. It is clearly seen that the ionic charges in stackings a and b can be presented as (Ge0.40+)2(Sb0.54+)2(Te0.38−)5 and (Ge0.33+)2(Sb0.49+)2(Te0.32−)5, respectively. Therefore, the charge transfers from Ge and Sb to Te atoms are 0.80 e and 1.08 e for stacking a, respectively, whereas these amounts are 0.66 e and 0.98 e for stacking b, indicating that the ionicity of chemical bonds in stacking a is slightly stronger than that in stacking b. Meanwhile, there are only a few charge transfers from Ge and Sb atoms to Te atoms for these two types of atomic arrangements. These tiny charge transfers reveal very weak ionic bonding interaction in stacking-polymorphs in GST. Finally, to explore the possible phase transition among the stacking-polymorphs in GST, we have calculated the diffusion energy curves by artificially disordering stackings a and b.
Table 2. Average Values of Bader Charge Transfers for Metastable Stacking-Polymorphs in Ge2Sb2Te5 Δq (e) atomic arrangement
Ge
Sb
Te
aa bb
0.40 0.33
0.54 0.49
−0.38 −0.32
a a: -Te-Ge-Te-Sb-Te-v-Te-Sb-Te-Ge- stacking. bb: -Te-Sb-Te-Ge-Tev-Te-Ge-Te-Sb- stacking.
corresponding to the volume collapse, our calculated elastic constants cij (Table S1 in the Supporting Information) satisfy the above criteria, which confirm the mechanical stability of metastable GST. Further analyses on the electron localization function (ELF) reveal rather strong covalent bonding in stacking-polymorphs of GST, since the maximal values of ELF are 0.91 for stacking a and 0.93 for stacking b that exceed 0.9 as shown in Figure 5. The values of ELF vary between 0 and 1 where ELF = 1 represents perfect covalent bonds and the covalent bonding is the strongest.45 Meanwhile, the covalence of stacking b is stronger than that of stacking a due to the greater maximal values of ELF. In Figure 5a, it is clear that stacking a is rather strong covalent bonded. Banana-shaped nonbonding electrons are tightly bound to Te1 and Sb atoms, whereas spherical shaped nonbonding electrons are at the core of Ge, Te2, and Te3 atoms, which shows strong Te1−Sb and weak Te2−Sb, Te2−Ge, and Te3−Ge bonds. For stacking b as seen in Figure 5b, banana-shaped nonbonding electrons are tightly bound to Te1 and Ge, Te2 and Ge atoms, and spherical shaped nonbonding electrons are at the core of Sb and Te3 atoms, which shows strong Te1−Ge, Te2−Ge bonding and weak Te2−Sb, Te3−Sb bonding. As for the adjacent Te atoms, there is no direct bonding in both stackings a and b, suggesting vdWtype weak Te1−Te1 bonding. In order to further qualitatively E
DOI: 10.1021/acs.inorgchem.7b01970 Inorg. Chem. XXXX, XXX, XXX−XXX
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back to the Ge atomic layer is extremely small (Eact = 0.005 eV); nevertheless, the structure with one Ge atom placed in the Te-Te vacancy layer for disordered stacking b can exist stably after relaxation. The energy barrier (Eact = 0.035 eV) for the diffusion of two Ge atoms from the Te-Te vacancy layer back to the Ge atomic layer is slightly higher than that in disordered stacking a, suggesting that the ordering of vacancies is easier in disordered stacking a than in disordered stacking b. Even though the energy barrier for the ordering process is low, it needs driving-force energy by applying temperature or electrical current to trigger the transition and cannot spontaneously happen. Meanwhile, the reverse amorphization processes are much more difficult for stacking a than stacking b. That is to say that, for stacking a, its ordering process is easier than and its disordering process is more difficult than that of stacking b. Moreover, the structures of stackings c and d can be regarded as the mixture of stackings a and b. Therefore, these results can support our above assumption that a vacancy disordered metastable-stacking GST can transform into any one of the vacancy ordered configurations among stackings from a to d with annealing the structure at various conditions, and could be used to improve the stability of phase-change memory devices by controlling the working current to remove the intermedium of polymorphic GST.
4. CONCLUSIONS In conclusion, we have investigated various atomic stackings in cubic Ge2Sb2Te5 by means of ab initio calculations. By comparing the calculated total energy and lattice parameters of five stacking configurations with the experimental values, we propose that cubic GST has many stacking-polymorphs actually, which consist of randomly distributed vacancies or highly ordered vacancy layers. A similar conclusion of stackingpolymorphs can be extended to the stable hexagonal GST as well. For the stacking-polymorphs of cubic GST, there exist rather strong covalent bonds and very weak ionic bonding interactions. Meantime, the stacking-polymorphic GST exhibits different electronic properties varying between semiconducting and metallic. The GST stacking-polymorphs can be obtained under different experimental synthetic conditions. The energy barrier for the ordering process is low, showing that the disordered metastable-stacking GST can gradually transform into the ordered phase under specific annealing conditions. The insight obtained from this study would be helpful for unraveling the underlying mechanism of phase-change data storage and provides more options for designing novel phase-change materials.
Figure 6. Diffusion energy curves of disordered stacking a with (a) two Sb atoms moved from the Te-Te vacancy layer to the Sb atomic layer and disordered stacking b with (b) one Ge atom, (c) two Ge atoms moved from the Te-Te vacancy layer to the Ge atomic layer, where the peak position is defined as the activation energy (Eact). The insets are the atomic structures of stacking a in (a) and stacking b in (b) and (c). The Ge, Sb, and Te atoms are colored blue, red, and green, respectively.
Whichever for stacking a with Sb atoms moved from the Sb atomic layer to the Te-Te vacancy layer and stacking b with Ge atoms moved from the Ge atomic layer to the Te-Te vacancy layer, the structures correspond to disordered stackings of cubic GST. As seen in Figure 6, the peak position of the diffusion energy curve is defined as the activation energy (Eact), which quantifies the lowest energy needed (energy barrier) for the diffusion of Sb or Ge atoms from one site to another. When disordering stacking a by manually moving one Sb atom from the Sb atomic layer to the Te-Te vacancy layer, the Sb atom will automatically move back to the Sb atomic layer after relaxation. Hence, we further manually move two Sb atoms from the Sb atomic layer to the Te-Te vacancy layer, as seen in Figure 6a; the Eact value is very low of 0.026 eV, indicating that the diffusion of Sb atoms from the Te-Te vacancy layer to the Sb atomic layer is very easy. However, for the reverse process, the energy needed for the diffusion of Sb atoms from the Sb atomic layer to the Te-Te vacancy layer is high (3.371 eV), which shows that the ordering of vacancies is much easier than the disordering process. A similar conclusion is obtained for the case of stacking b as shown in Figure 6b,c. As seen in Figure 6b, the energy barrier to overcome for the interstitial Ge diffusing
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ASSOCIATED CONTENT
S Supporting Information *
The Supporting Information is available free of charge on the ACS Publications website at DOI: 10.1021/acs.inorgchem.7b01970. Figure S1: Five kinds of atomic arrangements for cubic Ge2Sb2Te5. Table S1: The estimated elastic constants for metastable stacking-polymorphs in Ge2Sb2Te5 (PDF)
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AUTHOR INFORMATION
Corresponding Author
*E-mail:
[email protected]. ORCID
Linggang Zhu: 0000-0003-2514-4177 F
DOI: 10.1021/acs.inorgchem.7b01970 Inorg. Chem. XXXX, XXX, XXX−XXX
Article
Inorganic Chemistry
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Zhimei Sun: 0000-0002-4438-5032 Notes
The authors declare no competing financial interest.
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ACKNOWLEDGMENTS
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REFERENCES
This work is financially supported by the National Key Research and Development Program of China (Grant No. 2017YFB0701700), the National Natural Science Foundation for Distinguished Young Scientists of China (Grant No. 51225205), and the National Natural Science Foundation of China (No. 61274005).
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DOI: 10.1021/acs.inorgchem.7b01970 Inorg. Chem. XXXX, XXX, XXX−XXX
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DOI: 10.1021/acs.inorgchem.7b01970 Inorg. Chem. XXXX, XXX, XXX−XXX
