Peierls distortion mediated reversible phasetransition in GeTe under pressureZhimei Suna,b,1, Jian Zhoua, Ho-Kwang Maoc,1, and Rajeev Ahujad,e

aDepartment of Materials Science and Engineering, College of Materials, and bFujian Provincial Key Laboratory of Theoretical and ComputationalChemistry, Xiamen University, 361005 Xiamen, China; cGeophysical Laboratory, Carnegie Institution of Washington, 5251 Broad Branch Road Northwest,Washington, DC 20015; dDepartment of Physics and Astronomy, Uppsala University, 75120 Uppsala, Sweden; and eDepartment of Materials andEngineering, Royal Institute of Technology, 10044 Stockholm, Sweden

Contributed by Ho-Kwang Mao, February 24, 2012 (sent for review December 21, 2011)

With the advent of big synchrotron facilities around the world,pressure is now routinely placed to design a new material ormanipulate the properties of materials. In GeTe, an importantphase-change material that utilizes the property contrast betweenthe crystalline and amorphous states for data storage, we ob-served a reversible phase transition of rhombohedral ↔ rocksalt ↔orthorhombic ↔ monoclinic coupled with a semiconductor ↔metal interconversion under pressure on the basis of ab initiomolecular dynamics simulations. This interesting reversible phasetransition under pressure is believed to be mediated by Peierls dis-tortion in GeTe. Our results suggest a unique way to understandthe reversible phase transition and hence the resistance switchingthat is crucial to the applications of phase-change materials innonvolatile memory. The present finding can also be expandedto other IV-VI semiconductors.

high pressure ∣ semiconductor chalcogenides ∣ semiconductor-metalinterconversion

Pressure-induced structural changes in matters are of greatinterest in many disciplines, such as in physics, materialsscience, and geophysics. For example, lithium transforms from ametal to a semiconductor insulator under high pressure (1),Ce3Al metallic glass converts to a face-centered-cubic crystalat high pressure, and the investigations at high pressures andtemperatures on the inner core contribute greatly to the under-standing of the Earth (2, 3). In phase-change materials, the re-cord media for phase-change random access memory (PCRAM)which is considered as the next-generation universal memory type(4), pressure can be used as a crucial tool to understand the struc-tural and material properties. PCRAM utilizes the large physicalproperty contrast between the crystalline and amorphous statesof phase-change materials, especially chalcogenide semiconduc-tors, to record information. Due to the large difference in densitybetween the crystalline and amorphous states, significant pres-sure is momentarily generated during the writing and erasing pro-cess in phase-change recording (5). On the other hand, pressure isalso a very useful thermodynamic variable to study phase stability.

Ge2Sb2Te5 (GST) and GeTe are important phase-change ma-terials for PCRAM applications (6, 7), where the rock salt struc-tured GSTand GeTe act as the zero state in the data storage. Thedifference between the two compounds in a rock salt structure isthat Ge, Sb and 20% vacancies occupy sodium positions in GST,yet there are no such intrinsic vacancies in GeTe. In the past fewyears, extensive work has been performed to understand thestructural changes under pressures for GST in order to unravelthe atomistic mechanisms of the phase-change recording (5, 8–11). The previous high-pressure studies show that pressure willinduce the amorphization of rock salt structured GST (5, 8–11),in which the intrinsic vacancies are believed to play an importantrole (8, 10). However, this principle cannot be applied to binarychalcogenide GeTe. Therefore, further investigation on the struc-tural evolution of vacancy-free rock salt GeTe under pressure isvital to elucidate the atomistic phase-change mechanism for a

comprehensive understanding on the phase-change switching.It is known that GeTe undergoes a series of structural phase tran-sition under pressures (12–15), where several intermediatephases were reported. However, the structural phase transitionsas well as the underlying driving force are not comprehensivelyunderstood partly due to the complexity of the intermediatestructures and the internal atomic distortions under pressure.More specifically for PCRAM applications, since the involvedphase-change area is in nanometers and the phase-change timescale is in nanoseconds, high-pressure study of phase-changematerials is limited by experimental techniques that can hardlyprovide details of the structural evolutions. In this respect, abinitio molecular dynamics (AIMD) simulations can provide anefficient and rather accurate way to “in situ” observe the struc-tural changes of matters under pressure. In addition, ab initio to-tal energy calculations help us to understand the correspondingproperty changes.

Motivated by the above aspects, in this work, we have per-formed prolonged AIMD simulations on GeTe under pressure.The crucial findings of this work are that, unlike Ge2Sb2Te5,which amorphisized under pressures, rock salt GeTe remainsin a crystalline state and undergoes a reversible rhombohedral ↔rocksalt ↔ orthorhombic ↔ monoclinic phase transitioncoupled with a semiconductor-metal interconversion under theinvestigated pressure range. Our results show that this reversiblephase transition in GeTe under pressures is mediated by Peierlsdistortion based on the chemical bonding analysis.

Structural Changes Under PressuresWe started with ideal rock salt GeTe, for which the optimizedlattice parameter of 6.012 Å (Table 1) is in very good agreementwith that of experimental values of 5.93 ∼ 6.023 Å (16). Byapplying pressures up to 39 GPa, GeTe undergoes a series ofphase transition in the sequence of rock salt → rhombohedal →rock salt → orthorhombic → tetragonal → monoclinic (Table 1).On the other hand, if we allow larger deviations of δ ¼ 0.0253 Åand δ ¼ 0.1491 Å to fit the symmetry for the structures obtainedat 5.0 and 18.9 GPa (Table 1), respectively, we still obtain a rocksalt structure. Therefore, the rhombohedral (R3m) and orthor-hombic (Pmn21) structures are actually rhombohedrally andorthorhombically distorted rock salt phases, respectively. We cansee that the phase transition of GeTe under pressures is verycomplex, where several intermediate phases appear. The presentresults are in agreement with that of experimental work underpressures (14), where phase transitions from rhombohedral torock salt, pseudotetragonal, and orthorhombic structures havebeen reported. On decompression, the monoclinic phase is re-

Author contributions: Z.S. designed research; Z.S. performed research; Z.S. and J.Z.analyzed data; and Z.S., J.Z., H.-K.M., and R.A. wrote the paper.

The authors declare no conflict of interest.1To whom correspondence may be addressed. E-mail: zmsun@xmu.edu.cn, zhmsun2@yahoo.com, or hmao@ciw.edu.

This article contains supporting information online at www.pnas.org/lookup/suppl/doi:10.1073/pnas.1202875109/-/DCSupplemental.

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tained to 26 GPa, but showing different symmetry with that ofcompression (Table S1). Nevertheless, on decompression to am-bient conditions, we observed a phase transition in the sequenceof monoclinic → orthorhombic → rock salt → rhombohdedral(Table S1). The final rhombohedral structure obtained at ambientconditions can also be viewed as a rhombohedrally distorted rocksalt phase (Table 1).

During the phase transitions under compression, we found thatthe structure shows negligible changes and atoms basically vibratearound their original positions under pressures up to 18.9 GPa.While at 28.6 GPa, some pairs of Ge and Te atoms in the (001)planes move to the middle of adjacent layers along the [010] di-rection, resulting in six extra layers and thus a tetragonal symme-try (Fig. 1 A). With further increasing the pressure to 38.9 GPa,Ge and Te atoms move away from each other in the h111i direc-tion (Fig. 1B) showing large deviations from the original posi-tions, and the structure reveals a low symmetry as viewed fromthe h010i direction (Fig. 1C). The symmetry fitting unravels amonoclinic cell consisting of three units in the present used super-cell (Fig. 1C).

Pair correlation functions (PCF) and the distributions of bondangles and coordination numbers unravel details of the structureevolution in rock salt GeTe under pressures. For ideal rock saltGeTe, there is only one Ge-Te bond length (3.01 Å). At 5.0 GPa,

the Ge-Te bond splits into one shorter (2.84 Å) and one longer(3.03 Å) bond, and they become 2.80 and 2.92 Å at 10.6 GPa,respectively, showing a decreased difference between the twotypes of bonds. At above 18.9 GPa, the Ge-Te bond lengths mergeinto narrow distributions for the first nearest neighbors (Fig. 2A).The average Ge-Te bond lengths are 2.78, 2.72, and 2.69 Å for theorthorhombic, tetragonal, and monoclinic phases, respectively,indicating a small effect of pressures on the average Ge-Te bondsat high pressures. On the other hand, these three Ge-Te bondlengths are between a sum of perfect covalent radii 2.58 Å,and a sum of perfect ionic radii 2.94 Å (retrieved from http://www.webelements.com/germanium/atom_sizes.html and http://www.webelements.com/tellurium/atom_sizes.html), indicatingthat the chemical bonding in GeTe should be a combination ofthese two types of bonds. Furthermore, at above 28.6 GPa forthe tetragonal and monoclinic phases (Fig. 2A), the presence ofthe first peak at 2.62 Å in Ge-Ge PCF reveals the first Ge-Genearest neighbors; the first peaks in Te-Te PCF locate at 3.80and 3.50 Å for the tetragonal and monoclinic phases, respectively,

Fig. 1. Snapshot structure obtained at various pressures. (A) tetragonalphase at 28.6 GPa; (B) and (C) the monoclinic phase at 38.9 GPa viewed fromdifferent directions; (D) the finial structure showing a rhomhedral symmetryobtained by decompressing the monoclinic phase to ambient conditions. Thegreen spheres represent Ge atoms and the orange spheres represent Teatoms.

Table 1. The fitted symmetry and lattice parameters for GeTe at various pressures, where the maximum deviation (δ in Å) is the atomicdeviation from the original positions in the rock salt symmetry

Pressure (GPa) Symmetry Lattice parameters (Å)

0 (0 K) Fm3̄m a ¼ b ¼ c ¼ 6.0125.0 (a) Fm3̄m (δ ¼ 0.0839); (b) R3m (δ ¼ 0.0011) a ¼ b ¼ c ¼ 5.8633 a ¼ b ¼ c ¼ 4.146, α ¼ β ¼ γ ¼ 60°10.6 Fm3̄m (δ ¼ 0.0253) a ¼ b ¼ c ¼ 5.716718.9 (a) Fm3̄m (δ ¼ 0.1491); (b) Pmn21 (δ ¼ 0.0014), Orthorhombic (a) a ¼ b ¼ c ¼ 5.5667 (b) a ¼ 3.9362, b ¼ 5.5667, c ¼ 11.808728.6 P42cm (δ ¼ 0), tetragonal a ¼ b ¼ 16.25, c ¼ 5.416738.9 P21∕c (δ ¼ 0.0012), Monoclinic a ¼ b ¼ 15.80, c ¼ 5.2667Dec. (a) Fm3̄m (δ ¼ 0.1345) (b) R3m (δ ¼ 0.0022) a ¼ b ¼ c ¼ 6.06 a ¼ b ¼ c ¼ 4.285, α ¼ β ¼ γ ¼ 60°The phase obtained at 0 GPa is the optimized structure at 0 Kelvin (K). Dec. referres to the structure obtained by decompressing the monoclinic phases to

ambient conditions (room temperature and 0 pressure).

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Fig. 2. (A) The bond length distribution for the Ge-Te, Ge-Ge, and Te-Tebonds and (B) The bond angle distributions around Ge and Te for the orthor-hombic (at 18.9 GPa), tetragonal (at 28.6 GPa), and monoclinic (at 38.9 GPa)phases.

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which is the second nearest neighbor pairs. Therefore, large dis-placements of Ge atoms occurred during phase transition underpressures. As seen from the distributions of bond angle aroundGe and Te (Fig. 2B) at 18.9 GPa, the angles locate at around 90°and 176°, revealing a distorted rock salt structure; at 28.6 GPa, afew small peaks located at around 60°, 70°, 128°, and 149° appearbeside the main peaks at around 90° and 177°; at 38.9 GPa, themain peak at approximately 90° splits into two peaks locatingat around 82° and 97° for Ge and at 82° and 99° for Te atoms,showing the relative large displacement of Ge and Te, which isin agreement with the structure analysis (Fig. 1C). Nevertheless,the presence of two more peaks at around 60° and 133° suggeststhe relative large displacement of Ge atoms during phase transi-tion, which can be further supported by the distribution of coor-dination numbers (Fig. S1). The coordination number for Teremains approximately 6 under pressures up to 38.9 GPa, whilethat for Ge increases with increasing pressure at above 28.6 GPa.

Electronic StructuresThe above reversible phase transformation is accompanied by areversible semiconductor-metal transition. The original rock saltGeTe is a narrow gap semiconductor (Fig. S2A) with a band gapof approximately 0.4 eV, which is higher than the estimated valueof 0.1–0.2 eV suggested from concentration dependence of sus-ceptibility mass but lower than the value of 0.7–1.0 eV observedfrom optical absorption edges (17). Further, the valence band be-low the Fermi level is dominated by Te 5p and Ge 4p states withcontributions from Ge 4s states (Fig. S2B), showing a Ge4p-Te5pcovalent bonding character in rock salt GeTe. By gradually apply-ing hydrostatic pressures to rock salt GeTe, the valence band max-imum and conduction band minimum move toward the Fermilevel, resulting in the transition from a semiconductor to a metal(Fig. 3A). Compared to rock salt GeTe, more Ge 4s electrons

contribute to chemical bonding at high pressures as seen fromthe increased states below the Fermi level (Fig. 3B). The statesat the Fermi level consist of Ge 4s4p and Te 5p electrons with thep electrons dominate (Fig. 3B), suggesting that the conductionstill mainly results from the p electrons.

Chemical Bonding AnalysisThe values of charge transfer obtained by a Bader charge analysiscode (18, 19) can give us an estimation of the ionic bondingcharacter. The estimated average charge around Ge and Te inGeTe under ambient condition and various pressures are listedin Table 2. The results show that Ge denotes electrons to Te,which indicates an ionic character in GeTe. Furthermore, distor-tions induce more electron transfer from Ge to Te, for example,the charge transfer for rock salt GeTe both at ambient conditionsand high pressure (10.6 GPa) is more or less the same (Table 2),while slight distortion of either rhombohedral or orthorhombicwill increase the charge transfer to 0.343 e and 0.497 e, respec-tively, suggesting the increased ionic proportion in the chemicalbonding of GeTe with distortions. By gradually decompressingthe monoclinic cell to ambient conditions, the average chargetransfer is 0.448 e and 0.444 e for the rhombohedral with a latticeparameter of 6.06 Å and 6.02 Å, respectively, showing a slighteffect of the lattice parameters on the charge transfer at ambientconditions.

Electron localization function (ELF) (20, 21) analysis canprovide a rather quantitative understanding on the chemicalbonding in GeTe under pressures (a detailed explanation of ELFis given in the figure caption of Fig. 4; briefly, the higher the ELFvalue between atoms, the stronger the covalent bond). The ELFin Fig. 4A–C reveals a character of alternately strong and weakcovalently bonded square rings, which is in contrast to that ofideal rock salt GeTe where evenly distributed chemical bondsare observed (Fig. S3). The character of alternately strong andweak covalent bonds unravels the presence of Peierls distortionin the high-pressure GeTe phases, which has been reported inliquid GeTe (22). Considering there are 10 electrons per atompair in GeTe, but 12 electrons are required to saturate the octa-hedrally coordinated chemical-bonds, there are not sufficientnumbers of electrons to satisfy the orbitals requirement forcovalent bonding, and hence the six bonds are not equal. Further,going from Fig. 4 A–C for the high-pressure phases ofrhomobohedral → rock salt → octahedral, the strength of weakbonds increases with pressures, and finally results in three strongcovalent bonds in one Ge-Te square ring in orthorhombic GeTe.The results show that before GeTe completely loses its rock saltsymmetry, the character of Peierls distortion gradually weakenswith increasing pressures and according to this it should finallydisappear at certain pressures. Even though nearly all bondsare equally strong and the Peierls distortion character is not ob-vious in most parts of the structure at 28.6 GPa (Fig. 4D), a smallpart of the structure consists of highly distorted square rings andhence again results in the alternate strong and weak covalentbonds (Fig. 4E). As a result, the distorted rock salt phase trans-forms to a tetragonal symmetry. The results show that rock saltGeTe with equally bonded Ge-Te bonds is not stable and Peierlsdistortion will release the repulsive energy and stabilize the struc-ture. Therefore, with increasing pressures distorted rock salt

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Fig. 3. (A) The total density of states for the phases obtained at variouspressures. The phases at 5.0, 10.6, and 18.9 GPa have a rhombohedral, rocksalt, and orthormbic symmetry; (B) Partial density of states for Ge and Teatoms in the orthorhombic phase at 18.9 GPa.

Table 2. The calculated average charge (in electron or e) of Ge andTe for the various GeTe phases under pressures

0 GPa 5.0 GPa 10.6 GPa 18.9 GPa 28.6 GPa 38.9 GPa Dec.

Ge q (e) 3.6722 3.657 3.6723 3.503 3.592 3.631 3.552Te q (e) 6.3278 6.343 6.3277 6.497 6.408 6.368 6.448

q refers to charges and Dec. refers to the phase obtained by decompressingthe high pressure monoclinic phase to ambient conditions. Herein thesubscripts 2, 3, 8, 7 are the fourth digits after the decimal point.

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GeTe transforms to low-symmetry phases to keep the Peierlsdistortion. According to this rule, GeTe should collapse to evenlow-symmetry phase with further increasing pressures, which isconfirmed by the phase transition to monoclinic at 38.9 GPa.The typical ELF for GeTe at 38.9 GPa (Fig. 4F) reveals highlydistorted square rings bonded by alternately strong and weakcovalent Ge-Te bonds and hence results in the Peierls distortioncharacter in the monoclinic phase.

Upon decompressing the monoclinic structure to ambient con-ditions following the reverse compression route, the monoclinicphase retains to 26.4 GPa but with different symmetry (Fig. S4),all the other structures are restored at the same volumes, showinga reversible phase transition (Table S1). We believe that this in-teresting reversible phase transition is mediated by the effect ofPeierls distortion in GeTe. Furthermore, the final structure atambient conditions has a rhombohedral or distorted rock saltsymmetry for different lattices of a ¼ 6.02 and a ¼ 6.06 (Table 1and Table S1), showing excellent agreement with that of experi-ments. The distorted rock salt structure also reveals alternatestrong and weak Ge-Te bonds (Fig. S5), indicating the Peierls dis-tortion character. Therefore, we believe the reversible phasetransition in GeTe should be mediated by Peierls distortions.The same conclusion can be expanded to IV-VI semiconductorsand the Ge-Sb-Te phase-change materials as well.

Computational MethodsOur ab initio molecular dynamics (AIMD) calculations wereperformed within the framework of density functional theoryas implemented in the Vienna ab initio simulation package(VASP) (23). The interatomic forces were computed quantummechanically using projector augmented wave potentials withinthe local density approximation (24). Gaussian smearing with abroadening value of 0.1 eV and one gamma point were appliedfor the AIMD simulations. For the relaxation of ions and static abinitio total energy calculations, the projection augmented wavepotentials within the generalized gradient approximations of Per-dew-Burke-Ernzerhof and the k-points of 2 × 2 × 2 automaticallygenerated with Gamma symmetry were used (25). We used a cut-off energy of 131.4 eV for the potentials in the AIMD simulationsand that of 218.7 eV in the static calculations. The d electrons

have also been considered as valence electrons for the high-pres-sure AIMD simulations, however, the analysis on density of statesshows that the d electrons located at the lowest values, and hencetheir contribution to chemical bonding, can be ignored, therefore,the results shown in the paper are AIMD simulations without delectrons. The charge transfer of GeTe at various pressures wasestimated by the Bader charge analysis code (18, 19).

The initial cell of rock salt structured GeTe consisted of 216atoms with an optimized cell size of a ¼ b ¼ c ¼ 18.042 Å.The system was then subjected to increasing pressures by gradu-ally reducing the volume in several steps (V∕V0 ¼ 0.9266, 0.859,0.7930, 0.7305, 0.6716). Each simulation at a fixed volume lasted86 ps. In order to compare with the previous results of Ge2Sb2Te5(8), the compression temperature was set at 100 K during com-pressing and at 300 K for decompressing, where the temperaturewas controlled using the algorithm of Nosé (26). The obtainedstructure at each volume was under further ionic relaxation at0 K before performing static calculations to obtain the structureand electronic structure information.

ConclusionsOur study suggests the importance of Peierls distortion in the re-versible phase transition of GeTe under pressure. The presentrule can be applied to the other similar IV-VI semiconductorsand shed new light on the mechanism of phase-change recording.Furthermore, we suggest that Peierls distortion plays an impor-tant role in the chalcogenide phase-change materials where un-saturated bonds exist, which might be an important merit whensearching for new phase-change materials.

ACKNOWLEDGMENTS. This work is supported by National Natural ScienceFoundation of China (60976005) and the Outstanding Young ScientistsFoundation of Fujian Province of China (2010J06018), and the financial sup-port from National Key Basic Research Program of China (973 Program,2012CB825700) is also acknowledged. The work of H.-K.M. was supportedby Energy Frontier Research in Extreme Environments Center (EFree), anEnergy Frontier Research Center funded by the U.S. Department of Energy,Office of Science, Office of Basic Energy Sciences under Award NumberDE-SG0001057. R.A. thanks VR, Sweden, for financial support. Z.S. thanksDr. Andreas Blomqvist for performing some calculations.

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Fig. 4. Contour plots of electron localization function (ELF) projected on the (001) planes for various phases under pressures. (A) the rhombohedral phase at5.0 GPa; (B) the rock salt phase at 10.6 GPa; (C) the orthorhombic phase at 18.9 GPa; (D) and (E) the tetragonal phase at 28.6 GPa, where (E) shows the (001)plane truncated at the same position as (A) to (C), and (D) shows the (001) plane just below (E); (F) typical ELF contour plot for the monoclinic phase truncated atthe same position as (A) to (C). The values of ELF vary between 0 and 1, showing the type and strength of the bond. For example, ELF ¼ 1 represents perfectcovalent bonds and any values between 0.5 and 1 reveal covalent bonds of various bonding strength, although ELF ¼ 0.5 gives a metallic system. The scale isfrom 0 (blue) to 1 (red) and the interval is 0.2.

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