Excitation-Assisted Disordering of GeTe and Related Solids with

Article pubs.acs.org/JPCC

Excitation-Assisted Disordering of GeTe and Related Solids with Resonant Bonding A. V. Kolobov,*,† P. Fons,† J. Tominaga,† and M. Hase§ †

Nanoelectronics Research Institute, National Institute of Advanced Industrial Science and Technology (AIST), Tsukuba Central 4, 1-1-1, Higashi, Tsukuba, Ibaraki 305-8562, Japan § Institute of Applied Physics, University of Tsukuba, 1-1-1 Tennodai, Tsukuba 305-8573, Japan ABSTRACT: GeTe and related phase-change alloys are characterized by resonant bonding, where the same p-orbitals are used to form bonds on both sides of the atom. In this work, we propose that inversion of the phase of the wave functions associated with electronic excitation plays a crucial role in structural phenomena, varying from ferroelectric-toparaelectric phase transition to amorphization. A special case of coherent phase-flips may generate layer-by-layer evaporation and fabrication of graphene-like layer structures of phase-change materials if appropriate excitation conditions are satisfied for single crystal excitation.

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bonding in the crystalline phase6−8 when elements withon averagefive valence electrons form six σ-bonds with the nearest neighbors using three p-orbitals; that is, bonds on each side of participating atoms are formed by sharing the same porbital. There are various ways to study bonding in solids using ab initio simulations, such as calculating the inverse participation ratio,9,10 the electron localization function,11 or the charge density difference (CDD).3,12 The present authors have chosen to use the charge density difference. As the name implies, the CDD is a difference in electron charge due to interactions between atoms. In particular, a CDD for a covalent bond is characterized by an increase in the charge density halfway between the participating atoms. This approach has been used to study bonding in both the ideal binary GeTe and the Sbdoped GeTe representing Ge−Sb−Te alloys.3,12 Depending on the details of the local structure, either threecenter two-electron (3c-2e) bonds or three-center four-electron (3c-4e) bonds can be created. To be more specific, in binary GeTe, a composition that possesses a pronounced bonding energy hierarchy between the shorter and longer Ge−Te bonds, the longer bonds are due to interaction between the back-lobes of the same p-orbitals that form the shorter bonds.3 In Ge−Sb−Te alloys, thanks to the presence of vacancies on Ge/Sb sites, Te atoms with unused lone-pair orbitals are created; the latter can rebond to a neighboring layer forming rather symmetric 3c−4e bonds.12 While there are some potentially important differences between 3c−2e and 3c−4e bonds, more important is their common feature; namely, the lobes of p-orbitals on both sides of the atom participate in

INTRODUCTION The quasibinary GeTe−Sb 2 Te 3 system (primarily the Ge2Sb2Te5 composition, or GST225) has been long used in optical memory devices such as rewritable DVD-RAM, and it is also a leading candidate for the nonvolatile electronic memory known as phase-change random-access memory (PC-RAM); last year Samsung and Micron started shipping these devices into the market. The basis of phase-change storage is a large property contrast between the crystalline and amorphous phases; the idea dates back to the 1960s.1 Nonvolatile memory devices are currently key elements of various electronics and portable systems (digital camera, solid state disks, smartphones, computers, e-books, tablets, etc.), and the market has been increasing exponentially over the past decade. In a PC-RAM device, when a voltage exceeding a certain value (a threshold voltage) is applied to the high-resistivity amorphous phase, the material switches into the low-resistivity crystalline (SET) phase. The process can be reversed (RESET) by applying another pulse, of appropriately chosen amplitude and duration, that reverts the structure to the amorphous phase. It has long been believed that the role of laser (current) pulses is solely to heat the material, either above the melting point for amosphization or above the crystallization temperature for the reverse process.2 Recently there has been growing experimental and theoretical evidence that electronic excitation can open a nonthermal amorphization channel.3,4 For a summary of athermal amorphization of chalcogenides, the interested reader is referred to a recent review.5 The characteristic features of phase-change materials that make them unique for memory applications are (i) the unusually high optical contrast between the crystalline and amorphous phases, (ii) stability of both crystalline and amorphous phases, and (iii) fast switching between the states. These properties have been associated with so-called resonance © 2014 American Chemical Society

Received: December 19, 2013 Revised: April 16, 2014 Published: April 16, 2014 10248

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bonding. Upon amorphization, resonant bonds are broken and the resulting amorphous phase is characterized by purely covalent bonds. In this work, we propose that phase-flip of the wave functions in GeTe and related materials, associated with electronic excitation, may play a crucial role in changing the bonding character and inducing disorder, varying from ferroelectric-toparaelectric transition to amorphization.

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SIMULATION DETAILS All calculations have been done using the Vienna ab initio simulation package (VASP).13−16 The VASP carries out an iterative solution of the generalized Kohn−Sham equations of density functional theory, based on the minimization of the norm of the residual vector for each eigenstate, and it employs an efficient charge density mixing algorithm.15 Gradientcorrected functionals in the form of the Generalized Gradient Approximation PBE (GGA-PBE) by Perdew, Burke, and Ernzerhof were used. The VASP code makes use of the projector-augmented wave (PAW) method developed by Blöchl17 to describe the interaction between electrons and ions and a plane wave basis to expand the electronic wave functions. Our calculations were performed using the PAW method for all elements. The Ge PAW included the valence electrons 4s2 4p2 while, for Te, the 5s2 5p4 valence electrons were used. A plane wave basis with an energy cutoff of 250 eV was used. For all calculations a supercell of 48 GeTe atoms was employed. A 2 × 2 × 2 Monkhorst−Pack grid of k-points was used for integration of the Brillouin zone. Spin−orbit coupling effects were included. For the excited state calculations, band occupation was manually specified with the appropriate fraction of valence electrons (as specified in the text) being promoted to the lowest conduction band. A fully relaxed supercell with all electrons in the ground state was used as the starting structure for all excited state calculations.

Figure 1. Schematics of the formation of a σ bond using two aligned porbitals.

viewed as phase-flipping of the wave function subtended at one of the participating atoms. We now turn to the case of a resonantly bonded solid using the molecular-orbital ideas described above. Most such solids, such as As, Sb, GeTe, or GST alloys, are characterized by Peierls distortion that splits six identical bonds into subsets of three short (strong) and three long (weak) bonds.20 This is illustrated in Figure 2 (upper panel) for GeTe, where a CDD map for the ground state is shown. The increased electron density along the short bonds is indicative of covalent interaction. The interaction between the atoms along the longer interatomic distances is much weaker and ensured by the back-lobes of the same orbitals that are involved in the formation of the shorter bonds.3 Pronounced energy hierarchy between the short and long bonds allows one to consider the structure of GeTe as layered with shorter intralayer bonds and weaker interlayer bonds. In earlier publications, in discussion of the resonant bonding only the amplitudebut not the phaseof the wave function has been considered. Here we discuss the important role of the phase of the wave function. Indeed the phase of the wavefuction associated with a p-orbital is opposite on different sides of the atoms. An important point is that in the lowestenergy (ground) state of the system the minimum potential energy is achieved due to the formation of resonance bonds. In this case, the wave function phase outside the covalently bonded layers, corresponding to the antibonding configuration with respect to the intralayer Ge−Te bonds, simultaneously corresponds to the bonding configuration (same color orbitals) with respect to the interlayer Ge−Te distance, which ensures the attractive interaction between the layers (Figure 2, middle panel). It should be noted that it is this weak bonding along the longer interatomic distances that preserves the integrity of the crystal. The attractive interlayer interaction is only possible when the back-lobes involved have the same phase. At the same time, the layered GeTe structure may also be formed if the wave function phase is changed in every second layer, as shown schematically in the lower panel of Figure 2. In this case, the covalent bonds within the layers remain unchanged (for all layers) but the interaction between the layers changes to antibonding; that is, the forces keeping a three-dimensional crystal together disappear. If all wave functions change phase, the resulting structure is indistinguishable for the original one, namely, there is in-phase

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RESULTS AND DISCUSSION Phenomenological Description. Ground State. Before proceeding to excitation-assisted loss of long-range order in resonantly bonded solids, we would like to recall several fundamental facts regarding covalent bonding. A covalent bond is a bond in which two atoms share two electrons whose wave functions are in phase and interfere constructively. The two atomic orbitals in this case form a bonding molecular orbital. If, on the other hand, the two wave functions are out of phase, the interference is destructive, resulting is a zero electron density in between the atoms, and the corresponding molecular orbital is called antibonding. The two atoms in the antibonding state usually repel each other. This situation is demonstrated in Figure 1 for a prototypical p-orbital σ-bond. In a solid, bonding and antibonding molecular orbitals split into the valence and conduction bands, respectively. To describe the phase of the participating wave functions, the following convention is used. The phases of the wave functions are marked by “+” and “−” signs or, alternatively, by two different colors. When the two wave functions are in phase, the overlapped region has a “+ +” or “− −” configuration, which corresponds to the bonding state. When the two wave functions are out of phase, the overlapped region has a “+ −” or “− +” configuration, which corresponds to the antibonding state. Once such a system, such as a diatomic molecule, is optically excited, it can dissociate, H2 being a typical example18,19 Electronic excitation can thus be 10249

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Figure 3. Bonding configurations of GeTe in the ground state when Ge−Te interactions both within and between layers are in-phase. Blue and red colors correspond to two different phases of the p-orbital wave function.

Figure 2. Upper panel: Charge density difference map for the ground state of GeTe calculated using CASTEP, where an increased electron density shown as a red cloud represents a strong covalent-like interaction along the shorter interatomic distance. Middle panel: Schematics of the wave function phase in the ground state (bonding configurations for both intra- and interlayer atoms). Lower panel: Schematics of the wave function phase in the excited state (antibonding configuration for the interlayer atoms). Opposite phases of the wave functions are shown by red and blue colors. In the ground state, the wave functions are in phase for both short and long Ge−Te interatomic distances, making the overall structure stable. In the excited state, the interaction within layers has bonding character (red vs red in the lower layer and blue vs blue in the upper layer) while that between the layers (the longer interatomic distances) is antibonding (red vs blue).

Figure 4. Phase flip resulting in rupture of two interlayer bonds and the formation of a stronger bond between the original layers and consequent local relaxation. The neighboring orbitals shown by open ovals have different phases represented by different colors and are in an antibonding configuration.

Excited State. We now consider the system in the excited state. As mentioned above, electronic excitation results in phase-flips of some of the wave functions. Imagine that the wave functions subtended at atoms A and B flip phases (Figure 4). As a result, two short interlayer bonds are broken (the originally bonding orbitals change to anti bonding configuration) and a longer interchain bond is strengthened, which results in local atomic relaxation. When multiple such phaseflips occur, some of the longer and shorter bonds swap, while some others are broken altogether. As a result, the shorter and longer bonds are no longer coherent in space and the structure becomes on average “cubic”,21 while preserving locally the shorter and longer bonds.22,23 This process may be the underlying origin of the ferroelectric-to-paraelectric phase

interaction along both the shorter and longer interatomic distances as shown in Figure 3(a) and (b), where shorter bonds are shown by thick lines and longer bonds are shown by thin lines. Red and blue colors correspond to different phases of the wave functions. This schematic representation is more convenient for visualization purposes and will be used in below, where the structural changes resulting from electronic excitation are schematically shown in Figures 4−6. 10250

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loss of the long-range order. Alternatively, once a certain amount of disorder is accumulated in the system through electronic excitation (with a concomitant temperature increase), the remaining weaker (longer) bonds may break as a result of thermal vibrations. In other words, both electronic excitation and thermal vibrations can lead to the material’s amorphization. Note that in both cases melting of the crytal that involves rupture of strong covalent bonds is not required. When the system is excited at low level, the phase-flips are likely to be uncorrelated. However, with increasing excitation level, correlation between various flips can be expected and, in particular, one especially interesting possibility exists. If the wave function phase changes such that the covalent bonding within layers alternate between “+ +″ and “− −″ (Figure 2, lower panel and Figure 6) there is no difference in bonding within different layers since in both cases the wave function at the center of the shorter bond is in phase. At the same time, the interlayer bonding nature along the longer interatomic distances changes drastically. What used to be weak bonding “− −″ configurations in the ground state changes to antibonding “+ −″ configurations. The net result of this change is repulsion between pairs of atoms in the excited state that were interacting attractively in the ground state. As a result, the ordered system can dissociate (preserving the short covalent bonds) resulting in the loss of long-range order. While experiments on laser dissociation of molecules25,26 have been performed by various groups, similar studies for (resonantly bonded) solids are complicated by the following circumstances. In order to observe a detectable effect in a solid, the number of excited electrons should represent a significant fraction of the total valence electrons. For example, when semiconductors such as Si melt athermally, at least 10% of the valence electrons have to be simultaneously excited.27,28 Such high excitation levels necessarily lead to the temperature rise making it difficult to distinguish between pure electronic and thermal effects. Additionally, the excited state properties can only be measured within very short times (less than the characteristic recombination time of nonequilibrium charge carriers), making femtosecond laser excitation a technique of choice. DFT Calculations. The alternative to use simulations is also complicated. While density functional theory in most cases provides excellent results for the ground state, simulations of solids in the electronically excited state remains a great challenge. Such calculations by time-dependent density functional theory (TDDFT) method29 usually limit the simulation time to no more than 100 fs. In contrast, most of the dynamic processes involved in phase change have a time scale significantly larger than 1 ps. For this reason, the authors of4,30 focused on the qualitative features rather than the quantitative results. Therefore, they simplify the study by removing electrons from the high-lying valence band states according to the strength of the excitation. In analogy to defect study, the authors used a jellium background charge to compensate for the loss of charged carriers. While this approach has certain serious deficiencies, it is nonetheless attractive to use it to get some insights into the electronic structure in the excited state. We performed similar calculations by removing a certain fraction of electrons from the valence band and placing them into the conduction band within the VASP package. The proposed mechanism of phase-reversal between the alternating layers requires 50% of the electrons to be transferred to the

Figure 5. Low level excitation resulting in loss of coherency between the shorter and longer bonds (upper panel) may eventually lead to rupture of the remaining longer bonds (lower panel).

Figure 6. Bonding configurations of GeTe with correlated phase-flips resulting in the destabilization of the 3D structure and its layering.

transition taking place in GeTe around 705 K. Indeed, the band gap of GeTe is ca. 0.3 eV and the thermal energy of 0.07 eV (corresponding to 705 K) is sufficient to excite a significant amount of electrons across the band gap. The origin of the ferroelectric-to-paraelectric phase transition may thus lie in the electronic excitation of the system rather than in thermally induced structural disorder as was proposed earlier.22,23 The spatial randomization of the distribution of the shorter and longer bonds at higher excitation levels deduced from the proposed model and schematically shown in Figs 3−5 is in perfect agreement with the experimental and simulational results for the structural evolution in GeTe22,23 and Ge8Sb2Te11 at elevated temperatures.24 Upon an increased level of the electronic excitation, more and more phase-flips take place (Figure 5). Consequently more and more bonds break eventually leading to complete disappearance of the longer Ge−Te bonds and concomitant 10251

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between the covalently bonded GeTe buckled layers leaving the latter intact. As a result, upon cessation of excitation, the layers can easily readjust, reforming the crystalline phase. On the other hand, in polycrystals, the short covalently bonded fragments from different grains that are randomly oriented can interact with each other forming a continuous random network, which requires significantly higher energies to recrystallize. The amorphization should be easier at higher temperatures where the rhombohedral distortions are stochastic and loss of long-range order results in significant relaxation of the covalently bonded structure. It is thus predicted that short femtosecond pulses that can amorphise a polycrystalline sample can only induce transient disordering in a single crystal. Furthermore, different response to the electronic excitation of the nominally rather similar binary GeTe with 3c-2e bonds and GeSbTe with 3c-4e is expected. If selective generation of antibonding configurations is experimentally realized, this would additionally open an interesting possibility of layer-by-layer evaporation of resonantly bonded solids allowing for fabrication of graphene-like structures.

antibonding state, a number that certainly cannot be considered as a perturbation on the ground state. We have thus limited our simulations to the concentration of the excited electrons up to 10%. Figure 7 shows the CDD maps for the increasing degree of excitation. In the ground state, the obtained CDD is very

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SUMMARY In summary, it is argued that the phase of the wave function plays a crucial role in the stability of crystals with resonant bonding. Electronic excitation that flips the phase of the wave function changing interaction between certain pairs of atoms from bonding to antibonding can lead to structural instabilities and subsequent amorphization. The proposed ideas are suppported by DFT simulations and open a new vision of the mechanism of phase change in GeTe-based memory alloys.

Figure 7. CDD maps calculated using VASP for GeTe with a different number of valence electrons (percent marked in the corresponding panels) promoted to the conduction band, demonstrating a change in the bonding (a)symmetry between the shorter and longer Ge−Te interatomic distances.

similar to the one reported previously using the CASTEP package;3,12 that is, there is a pronounced asymmetry in interaction between Ge and Te atoms along the short and long Ge−Te interatomic distances. As a small amount of electrons (2.5% to 5%) is transferred into the conduction band, the bonding asymmetry decreases; that is, the structure becomes more “cubic”. Interestingly, as the concentration of excited electrons is further increased (10%), the bonding asymmetry re-appears in agreement with the proposed idea of correlated phase-flips. This behavior, while strange at the first glance, is actually in perfect agreement with the experiment, when Peierls distortion, associated with the bonding asymmetry, was observed at low temperatures (zero excitation level), disappeared at higher temperatures (low excitation level) and then re-entered as the temperature was further increased and the material melted (high excitation level); the authors referred to this as “re-entrant Peierls distortion”.31 The observed increase in the bonding asymmetry upon higher excitation levels, is also in agreement with the experimental observation that the shorter Ge−Te bond remains essentially unchanged (in binary GeTe22) or becomes shorter (in Ge2Sb2Te53,32) with increasing temperature, when the material expands33 and interatomic distances would be expected to increase. The observed result demonstrates that the volume expansion proceeds due to elongationi.e. weakeningof the longer bonds. Experimental studies to verify this proposal are currently underway using an ultrafast optical laser pump and X-ray free electron laser probe experiments. These studies are expected to provide direct information on the femtosecond scale structural response of phase-change materials to electronic excitation. In particular, one would expect single crystal GeTe and polycrystalline samples to respond differently. Indeed, in a single crystal, electronic excitation weakens the interaction

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AUTHOR INFORMATION

Corresponding Author

*E-mail: [email protected]. Tel.: +(81.298) 861 2636. Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS The authors acknowledge partial support from the X-ray Free Electron Laser Priority Strategy Program of MEXT, Japan (Projects 12013011 and 12013023).

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REFERENCES

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