Polymorphism in amorphous Ge2Sb2Te5 ...

E*PCOS2010

Polymorphism in amorphous Ge2Sb2Te5: comparison of melt-quenched and as-deposited structures J. Akola 1,2,3, J. Larrucea 3, and R. O. Jones 1,4 Institut für Festkörperforschung, Forschungszentrum Jülich, D-52425 Jülich, Germany 2 Department of Physics, Tampere University of Technology, P.O. Box 692, FI-33101 Tampere, Finland 3 Nanoscience Center, Department of Physics, P.O. Box 35, FI-40014 University of Jyväskylä, Finland 4 German Research School for Simulation Sciences, FZ Jülich and RWTH Aachen, D-52425 Jülich, Germany [email protected] [email protected] 1

ABSTRACT Atomistic simulations on phase-change materials have focused on melt-quenched (MQ) samples, and both system size and quench time have posed challenges. We present here results of massively-parallel density functional (DF) simulations of the as-deposited (AD) amorphous structure of the prototype phase change material Ge2Sb2Te5. We have studied a 648-atom sample generated by computer-aided deposition at 300 K and compare the results with those for a 460-atom MQ sample we reported previously. The AD structure differs from MQ in essential ways: (1) Ge atoms are predominantly tetrahedrally coordinated, (2) homopolar and Ge-Sb bonds are more common and reduce the number of ABAB squares (A=Ge,Sb; B=Te), the characteristic building blocks of the material. The first observation resolves the contradiction between measured and calculated Ge-Te bond lengths, and the latter explains the large differences in crystallization speeds. Sb and Te are more highly coordinated than expected from the “8-N rule” (N is the number of valence electrons), and a-GST cannot be regarded as a covalent network glass. Key words: Density functional simulations, Ge2Sb2Te5, amorphous structure, melt-quenched, as-deposited

1. INTRODUCTION Phase change materials (PCMs) are chalcogenide alloys that can switch rapidly between the amorphous and crystalline phases. They are used extensively in rewritable high-density data storage, especially in optical recording [Digital Versatile Disc (DVD), Blu-ray Disc] [1]. PCMs function because the amorphous and crystalline phases have distinct electronic and optical properties, and the transition between them can occur on the timescale of nanoseconds [2,3]. The most common materials are GeTe-Sb2Te3 pseudobinary compounds, especially the composition Ge2Sb2Te5 (GST) doped alloys of SbxTe (x>2). The determination of the structures involved has challenged both theory and experiment. Extended x-ray absorption fine structure (EXAFS) data [4-6], x-ray diffraction (XRD) measurements [7], and x-ray photoelectron spectroscopy (XPS) [8] have provided important clues to the atomic structure of a-GST, but the local coordination of Ge atoms has remained controversial: EXAFS data indicate tetrahedrally coordinated Ge with considerably shorter bond lengths (2.61-2.63 Å) than in the crystal, while XRD measurements suggest predominantly octahedral bond angles for all atom types [7]. Density functional (DF) calculations [9-14] generally support the latter view (with some tetrahedral Ge) and identified four-membered rings with AB alternation (A=Ge,Sb; B=Te) as the crucial structural units of GST. A crucial question remains: Are theory and experiment studying the same structural phase (polymorph)? The deposited (AD, measured) structure may differ from the melt-quenched (MQ, calculated) structure, and there is indeed much evidence that AD and MQ samples show completely different crystallization speeds and characteristics [2,3,15]. We compare here the results of DF / molecular dynamics (MD) simulations of a 648-atom sample of a-GST generated by computer-aided deposition on a two-dimensional template with those obtained previously for an MQ sample (460 atoms), refined with respect to XRD and XPS data [14]. The structure and electronic properties are similar, but the AD sample has many tetrahedral Ge atoms and a considerable number of “wrong bonds” (homopolar and Ge-Sb bonds), which hamper crystallization. Our results for the Ge-Te bond lengths agree with EXAFS measurements [4-6]

and explain the apparent inconsistency between these measurements and earlier DF calculations. The method we describe should be useful in generating amorphous structures of other PCMs and semiconducting alloys.

2. METHOD OF CALCULATION The DF/MD simulations used the CPMD program (Born-Oppenheimer mode) [16,17], as described elsewhere [9,18]. We used a time step of 3.025 fs, scalar-relativistic pseudopotentials and periodic boundary conditions with a single point (k=0) in the Brillouin zone. The kinetic energy cutoff of the plane wave basis was 20 Ry, and we use a NoseHoover thermostat and a stable and efficient predictor-corrector algorithm. For the exchange-correlation energy Exc we adopted the PBEsol [19] approximation, which was developed originally for extended systems and surface energies and led to improved bond lengths and lattice constants for semiconductors. The simulations were carried out at 300 K, beginning with a random template of 36 atoms in an area of 27.61x27.61 Å2 (layer thickness 1.4 Å). These atoms were fixed during deposition to minimize relaxation effects near the base of the system. 17 layers of 36 atoms were then deposited on the sample and allowed to relax for 5-10 ps each. The vertical box dimension was adjusted for each layer to minimize the interaction with the slab replica (vacuum region 10 Å). Deposition took a total of 91 ps, and the result is shown in Fig. 1. There is limited mobility at 300 K, but some atoms mix with layers deposited previously, and the lower coordination of Te enhances its concentration at the surface. The final vertical dimension of the 648-atom sample is 15 % larger than in the bulk. The model AD system was then prepared by releasing the 32 template atoms and decreasing the vertical box size (19 steps at 300 K) to obtain a cubic supercell (size 27.61 Å, density 0.0308 atoms/Å3). The process lasted 67 ps in steps of 3-4 ps, and the system was equilibrated for 34 ps before data collection (25 ps). The pressure was small (2.9±1.8 kbar) at the final (experimental) density, and the final structure was optimized at 0 K [Figs. 1(c-d)].

Figure 1. As-deposited (AD) sample of GST at 300 K. (a) Top view after 17 added layers (648 atoms). The uppermost atoms within 1.2 nm are highlighted in color, and the red tetrahedra mark selected Ge atoms with tetrahedral coordination. Ge, red; Sb, blue; Te, yellow. (b) Side view of the final surface. (c-d) Two perspectives of final (compressed) bulk sample. The cavities (cyan isosurfaces) comprise 16.3 % of the total volume. The test particle radius for cavity analysis was 2.8 Å.

The MQ sample (460 atoms) is based on the RMC-refined geometry [14], which has a semiconducting band gap and reproduces the XRD structure factor S(Q) [14]. This structure does not correspond to a DF energy minimum, so we

performed a simulation at 300 K using the same functional (PBEsol) and atomic density as for AD. Initialization (5 ps, 300 K) was followed by data collection (35 ps). The MQ structure is 11 meV/atom more stable than AD and 58 meV/atom less stable than the rocksalt structure.

3. RESULTS & DISCUSSION The structure factors S(Q) for the AD and MQ samples are compared with experiment in Fig. 2. The curves for AD and MQ are strikingly similar, indicating that it will be difficult distinguish between these structures using XRD alone [20]. The agreement with the experiment is very good, although the calculated heights for the first two peaks (2.1 and 3.3 Å-1) are somewhat low, and the shape of the third peak differs slightly. The calculated structures are from DF/MD simulations at 300 K, and deviations from experiment are caused in part by the approximations in the Exc functional, as shown in Ref. [18]. The calculations reproduce the prepeak measured at 0.9-1.0 Å-1.

Figure 2. (a) Structure factor S(Q) of AD (black) and MQ (blue) samples at 300 K, and XRD (red). The calculated S(Q) are shifted by 0.4. (b) Electronic DOS of AD and MQ samples. Vertical dashed line marks band gap separating the σ-band with Te-5s character. The electronic densities of states (DOS) in AD and MQ are very similar, with band gaps of 0.2-0.3 eV at the Fermi energy. The DOS profiles are in satisfactory agreement with XPS data [8], the most significant difference being near the DOS minimum around -10 eV between two σ-bands. This minimum has merged in AD as the neighboring peak (with Te-5s character) weakens when Te-Te bonds are formed (Fig. 3). This is consistent with the XPS profile. The projections onto atomic orbitals (p-DOS) are not significantly different. The partial distribution functions (PDFs) of the a-GST samples are shown in Fig. 3. Ge-Te and Sb-Te bonds dominate in GST (AB alternation). EXAFS measurements [4-6] have shown that Ge-Te distances shrink upon amorphization (2.61-2.63 Å), suggesting that Ge might have tetrahedral coordination. This differs from earlier DF simulations [9-11], which found mostly (distorted) octahedral configurations for Ge with Ge-Te bonds of 2.77-2.78 Å. Tetrahedrally

bonded Ge atoms also occur. The discrepancies in the Ge-Te bond length appear to have two causes: (a) Most approximations for Exc tend to overestimate bond lengths by 2-3 %, but the use of the PBEsol functional here reduces this error (in MQ the Ge-Te PDF maximum is at 2.72 Å). (b) Sample preparation is crucial: AD has more tetrahedral Ge atoms, and the Ge-Te maximum shifts to 2.69 Å. Finally, a restriction to tetrahedral structures leads to a maximum in the Ge-Te PDF at 2.65 Å, within 1 % of the EXAFS result. This is consistent with the PBEsol calculations of semiconductor lattice constants [19]. Ge-Ge bonds (2.52 Å), which correspond mainly to tetrahedral Ge atoms here, agree well with experiment (2.47±0.03 Å) [5].

Figure 3. Partial distribution functions of AD (black) and MQ (red) at 300 K. The blue curves were calculated for cGST at 300 K [9] and have been scaled by a factor of 0.25.

Sb-Te bond lengths change little upon amorphization, and the first maximum of AD and MQ is at 2.89 Å. The other PDFs show clear differences between the samples, since the number of ``wrong bonds'', i.e. homopolar and Ge-Sb bonds that do not occur in c-GST, is significantly larger for AD. This is reflected in the Ge-Te and Sb-Te PDFs (AB bonds) as weaker first maxima and emerging second maxima at 4.2 Å. The corresponding partial coordination numbers (Table 1) show that Ge and Sb have twice as many wrong bonds (1.1 on average) as Te (including Te-Te bonds), although the Te concentration is larger than those of Ge and Sb combined. Deposition does not favor particular bonding configurations, and this is a further evidence of the unfavorable nature of Te-Te bonds in a-GST.

The reduced chemical alternation is also demonstrated in the fraction of atoms that participate in the ABAB rings (squares) and are essential for the rapid phase transition. There are fewer such rings in the AD structure. The total coordination numbers for AD (evaluated from the PDFs) are 4.2, 3.7, and 2.8 for Ge, Sb, and Te, respectively. Earlier work [9,10,14] has indicated that the total coordination numbers of Sb and Te in a-GST do not satisfy the “8-N rule” of covalently bonded networks, and additional support for this conclusion is found by calculating the bond orders (number of chemical bonds) for each interatomic connection via the overlap of wave functions. The Ge-Te and Sb-Te bond orders have maxima at 0.9 indicating nearly covalent single bonds (1) shifted from the broader c-GST maxima at 0.6. The change in the bond strengths reflects modifications in the electronic properties upon crystallization and is related to the structural medium range order (Jahn-Teller deformation in c-GST, resonance effects) [21]. The chemical coordination of Ge, Sb, and Te is 3.7-3.8, 3.6 and 3.1, respectively, for both samples. Sb and Te are clearly overcoordinated with respect to the “8-N rule”.

Table 1. Partial coordination numbers evaluated from the PDFs (Fig. 3) by applying a bond cutoff of 3.2 Å. Sample

as-deposited (AD)

melt-quenched (MQ)

Experiment (Ref. [5])

N(Ge-Ge)

0.47

0.33

0.6±0.2

N(Ge-Sb)

0.59

0.26

N(Ge-Te)

3.09

3.55

N(Sb-Sb)

0.54

0.56

N(Sb-Te)

2.59

2.88

N(Te-Te)

0.49

0.26

3.3±0.5

2.8±0.5

The bond angle distributions for each element [Fig. 4] provide further information about the local environment. X-SbX angles [Fig. 4(b), X arbitrary] show characteristic octahedral bond angles (a dominant peak at 90º and enhanced weight near linear configurations, 180º). The AD and MQ samples differ little in this case. For Te, the maximum around 90º again dominates, but the weight is small after 120º. AD and MQ differ somewhat in the shape of the X-TeX distribution. X-Ge-X distributions resemble those of Sb, but the maxima shift to larger values (MQ: 94º, AD: 100º) and broaden. The shift of X-Ge-X distributions towards the tetrahedral value (109.47º) can be demonstrated by varying bond cutoffs from 2.7 to 3.2 Å [Fig. 4(c)], and a restriction to bonds less than 2.7 Å in AD yields a maximum consistent with tetrahedral configurations. The differences in Ge-centered bond angles [Fig. 4(a)] raise the question: Do the numbers of tetrahedrally coordinated Ge atoms in the two samples differ? Analysis of coordination numbers at 300 K shows that fourfold coordination is enhanced in AD (70 %, AD; 59 %, MQ). If we classify fourfold coordinated Ge atoms as “tetrahedral” if all bond distances are below 3.0 Å and the average bond angle over 100º, the fraction of tetrahedrally coordinated Ge atoms at 300 K is significantly higher for AD (58 %) than MQ (36 %). Deposition begins with low-coordinated surface atoms (at smaller density) and favors fourfold coordination (70 %). Ge atoms are then likely to adopt a tetrahedral coordination, as seen in Fig. 1 near the sample surface,.

Figure 4. (a,b,d) Bond angle distributions of AD (black) and MQ (red) samples. The bond cutoff is 3.2 Å and the octahedral (90º) and tetrahedral (109.47º) values are shown by vertical dashed lines. Panel (c) shows the effect of varying the bond cutoff from 2.7 to 3.2 Å for Ge-centered configurations.

4. CONCLUSION DF/MD simulations at 300 K of the as-deposited phase of a-GST (AD, 648 atoms, over 200 ps) have been compared with a previously published melt-quenched structure (MQ, 460 atoms) [14]. Ge atoms have crucially different environments: predominantly tetrahedral in AD and distorted octahedral in MQ. The PBEsol functional gives improved results, and we can explain the apparent contradiction between the calculated and measured (EXAFS) GeTe bond lengths. Wrong bonds in the AD sample reduce the number of ABAB squares, which nucleate crystallization. Their absence in AD explains the much slower phase transition. Both samples display a tendency of reducing the number of Te-Te bonds, and MQ is 11 meV / atom more stable than AD. Their structure factors and electronic properties are similar, so that distinguishing between them using XRD remains a challenge.

REFERENCES 1. M. Wuttig and N. Yamada, “Phase-change materials for rewriteable data storage”, Nature Mater. 6 (2007) 824, and references therein.

2. S. Raoux, H.-Y. Cheng, M. A. Caldwell, and H.-S. P. Wong, “Crystallization times of Ge-Te phase change materials as a function of composition”, Appl. Phys. Lett. 95 (2009) 071910. 3. S. Raoux, R. Shelby, B. Munoz, M. Hitzbleck, D. Krebs, M. Salinga, M. Woda, M. Austgen, K.-M. Chung, and M. Wuttig, “Crystallization times of as-deposited and melt-quenched amorphous phase change materials”, E*PCOS 2008 Proceedings (2008). 4. A. V. Kolobov, P. Fons, A. I. Frenkel, A. L. Ankudinov, J. Tominaga, and T. Uruga, “Understanding the phase-change mechanism of rewritable optical media”, Nature Mater. 3 (2004) 703. 5. D. A. Baker, M. A. Paesler, G. Lucovsky, S. C. Agarwal, and P. C. Taylor, “Application of Bond Constraint Theory to the Switchable Optical Memory Material Ge2Sb2Te5”, Phys. Rev. Lett. 96 (2006) 255501; M. A. Paesler, D. A. Baker, G. Lucovsky, A. E. Edwards, and P. C. Taylor, “EXAFS study of local order in the amorphous chalcogenide semiconductor Ge2Sb2Te5”, J. Phys. Chem. Solids 68 (2007) 873. 6. P. Jovari, I. Kaban, J. Steiner, B. Beuneu, A. Schöps, and A. Webb, “Wrong bonds in sputtered amorphous Ge2Sb2Te5”, J. Phys.: Condens. Matter 19 (2007) 335212. 7. S. Kohara, K. Kato, S. Kimura, H. Tanaka, T. Usuki, K. Suzuya, H. Tanaka, Y. Moritomo, Matsunaga, N. Yamada, Y. Tanaka, H. Suematsu, and M. Takata, “Structural basis for the fast phase change on Ge2Sb2Te5: Ring statistics analogy between the crystal and amorphous states”, Appl. Phys. Lett. 89 (2006) 201910. 8. J.-J. Kim, K. Kobayashi, E. Ikenaga, M. Kobata, S. Ueda, T. Matsunaga, K. Kifune, R. Kojima, and N. Yamada, “Electronic structure of amorphous and crystalline (GeTe)1−x (Sb2Te3)x investigated using hard xray photoemission spectroscopy”, Phys. Rev. B 76 (2007) 115124. 9. J. Akola and R. O. Jones, “Structural phase transitions on the nanoscale: The crucial pattern in the phase change materials Ge2Sb2Te5 and GeTe”, Phys. Rev. B 76 (2007) 235201; “Binary alloys of Ge and Te: order, voids, and the eutectic composition”, Phys. Rev. Lett. 100 (2008) 205502; “Density functional study of amorphous, liquid and crystalline Ge2Sb2Te5: Homopolar bonds and/or AB alternation?” J. Phys.: Condens. Matter 20 (2008) 465103. 10. S. Caravati, M. Bernasconi, T. D. Kühne, M. Krack, and M. Parrinello, “Coexistence of tetrahedral- and octahedral-like sites in amorphous phase change materials”, Appl. Phys. Lett. 91 (2007) 171906. 11. J. Hegedüs and S. R. Elliott, “Microscopic origin of the fast crystallization ability of Ge–Sb–Te phase-change memory materials”, Nature Mater. 7 (2008) 399. 12. S. Caravati, M. Bernasconi, T. D. Kühne, M. Krack, and M. Parrinello, “Unravelling the Mechanism of Pressure Induced Amorphization of Phase Change Materials “, Phys. Rev. Lett. 102 (2009) 205502. 13. K. B. Borisenko, Y. Chen, S. A. Song, and D. J. H. Cockayne, “Nanoscale Phase Separation and Building Blocks of Ge2Sb2Te5N and Ge2Sb2Te5N2 Thin Films”, Chem. Mater. 21 (2009) 5244. 14. J. Akola, R. O. Jones, S. Kohara, S. Kimura, K. Kobayashi, M. Takata, T. Matsunaga, R. Kojima, and N. Yamada, “Experimentally constrained density-functional calculations of the amorphous structure of the prototypical phase-change material Ge2Sb2Te5”, Phys. Rev. B 80 (2009) 020201(R). 15. See, for example, J. H. Coombs, A. P. J. M. Jongenelis, W. van Es-Spiekman, and B. A. J. Jacobs, “Laserinduced crystallization phenomena in GeTe-based alloys. I. Characterization of nucleation and growth”, J. Appl. Phys. 78 (1995) 4906; J. Park, M. R. Kim, W. S. Choi, H. Seo, and C. Yeon, “Characterization of amorphous phases of Ge2Sb2Te5 phase-change optical recording material on their crystallization behavior”, Jpn. J. Appl. Phys. 38 (1999) 4775; P. K. Khulbe, E. M. Wright, and M. Mansipur, “Crystallization behavior of as-deposited, melt-quenched, and primed amorphous states of Ge2Sb2.3Te5 films”, J. Appl. Phys. 88 (2000 ) 3926; M.-H. Kwon, B.-S. Lee, S. N. Bogle, L. N. Nittala, S. G. Bishop, J. R. Abelson, S. Raoux, B.

Cheong, and K.-B. Kim, “Nanometer-scale order in amorphous Ge2Sb2Te5 analyzed by fluctuation electron microscopy”, Appl. Phys. Lett. 90 (2007) 021923; K. Do, D. Lee, H. Sohn, M.-H. Cho, and D.-H. Ko, “Crystallization behaviors of laser induced Ge2Sb2Te5 in different amorphous states”, J. Electrochem. Soc. 157 (2010) H264. 16. R. Car and M. Parrinello, “Unified approach for molecular dynamics and density functional theory”, Phys. Rev. Lett. 55 (1985) 2471. 17. CPMD V3.13: © IBM Corporation 1990-2009; © MPI für Festkörperforschung, Stuttgart 1997-2001 (http://www.cpmd.org ). 18. J. Akola and R. O. Jones, “Structure of amorphous Ge8Sb2Te11: GeTe-Sb2Te3 alloys and optical storage”, Phys. Rev. B 79 (2009) 134118. 19. J. P. Perdew, A. Ruzsinszky, G. I. Csonka, O. A. Vydrov, G. E. Scuseria, L. A. Constantin, X. Zhao, and K. Burke, “Restoring the density-gradient expansion for exchange in solids and surfaces”, Phys. Rev. Lett. 100 (2008) 136406. 20. M. Naito, M. Ishimaru, Y. Hirotsu, R. Kojima, and N. Yamada, “Direct observation of Ge2Sb2Te5 recording marks in the phase-change disk”, J. Appl. Phys. 107 (2010) 103507. 21. B. Huang and J. Robertson, “Bonding origin of optical contrast in phase-change memory materials”, Phys. Rev. Lett. 81 (2010) 081204(R).

Biographies J. Akola studied Physics at the Universities of Helsinki and Jyväskylä, Finland, obtaining his Ph.D. at Jyväskylä under Matti Manninen. After five years as a Post-doctoral Researcher at the Forschungszentrum Jülich, Germany, he returned in 2005 to the Nanoscience Center in Jyväskylä. He is currently working as Academy Research Fellow in the Tampere University of Technology and leads a group in Molecule and Materials Modeling. His fields of interest include classical, tight-binding, and density functional simulations of materials, nanoparticles, and biological systems. J. Larrucea studied theoretical chemistry in the University of Oulu, Finland, and in the University of Donostia, Basque Country, Spain, obtaining his Ph.D. at Donostia under Jesus M. Ugalde. He is working as a post-doctoral fellow in the Nanoscience Center of the University of Jyväskylä, and his research interests include modeling of semiconductor materials (PCMs) and related clusters. R. O. Jones obtained his B.Sc. Hons (Physics) at the University of Western Australia in Perth and his Ph.D. at the University of Cambridge, England under Volker Heine. He spent three years as a Post-doctoral Associate at Cornell University before joining the FZ Jülich. His main focus for over 30 years has been on density functional theory and its applications to a wide range of ordered and disordered systems (solids, surfaces, atomic clusters, molecules, polymers, biological molecules, … ).