JOURNAL OF APPLIED PHYSICS 119, 134502 (2016)

Enhanced oxygen vacancy diffusion in Ta2O5 resistive memory devices due to infinitely adaptive crystal structure Hao Jiang1,2 and Derek A. Stewart1,a) 1

San Jose Research Center, HGST, a Western Digital company, San Jose, California 95135, USA Materials Science Program, University of Wisconsin, Madison, Wisconsin 53706, USA

2

(Received 31 December 2015; accepted 24 March 2016; published online 6 April 2016) Metal oxide resistive memory devices based on Ta2O5 have demonstrated high switching speed, long endurance, and low set voltage. However, the physical origin of this improved performance is still unclear. Ta2O5 is an important archetype of a class of materials that possess an adaptive crystal structure that can respond easily to the presence of defects. Using first principles nudged elastic band calculations, we show that this adaptive crystal structure leads to low energy barriers for inplane diffusion of oxygen vacancies in k phase Ta2O5. Identified diffusion paths are associated with collective motion of neighboring atoms. The overall vacancy diffusion is anisotropic with higher diffusion barriers found for oxygen vacancy movement between Ta-O planes. Coupled with the fact that oxygen vacancy formation energy in Ta2O5 is relatively small, our calculated low diffusion barriers can help explain the low set voltage in Ta2O5 based resistive memory devices. Our work shows that other oxides with adaptive crystal structures could serve as potential candidates for resistive random access memory devices. We also discuss some general characteristics for ideal C 2016 resistive RAM oxides that could be used in future computational material searches. V AIP Publishing LLC. [http://dx.doi.org/10.1063/1.4945579]

I. INTRODUCTION

Oxide-based resistance switching devices have attracted considerable attention due to their fast switching speed, low power, and potential use in future resistive random access memory (RRAM).1–3 Tantalum pentoxide (Ta2O5) is a leading candidate material for RRAM devices.4–6 Ta2O5 based resistance switches have shown high switching speed, long endurance, and low voltage, compared to memory devices using other materials.4–8 Recent studies have indicated that the resistance switching mechanism in transition metal oxides is due to the connection and disruption of conductive filaments inside the oxide.4–6,9–11 However, it is not currently clear why Ta2O5 demonstrates superior performance to other transition metal oxides. The active region of an oxide-based RRAM device consists of an oxide layer sandwiched between two electrodes. When a large voltage is applied across the device, the high electric field can generate oxygen vacancies in the oxide and also drive the drift of charged vacancies to create a conductive filament between the electrodes, changing the device to a low resistance state.9 The conductive filament consists of a region of high neutral oxygen vacancy concentration with high electrical conductivity. Applying an opposite electric field can drive the drift and reaction of oxygen vacancies, breaking the filament and restoring the high resistance state.4–6,12 Joule heating can also be used to activate vacancy diffusion at the end of the filament so that they combine with nearby oxygen interstitials, disrupting the conductive vacancy filament. While deposited RRAM oxide films are typically amorphous, there is also growing evidence for Ta2O5 a)

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and TiO2 that a polycrystalline region forms around the filament due to Joule heating.6,10,13,14 Therefore, the formation and diffusion of oxygen vacancies in both amorphous and crystalline Ta2O5 plays a key role in Ta2O5-based RRAM devices. A detailed study of the energy landscape for oxygen vacancies can help resolve the switching mechanism and provide key inputs such as vacancy activation energies for device-level models. The stable crystalline phase of Ta2O5 at low temperatures has been debated for many years due to experimental challenges in resolving the oxygen sublattice structure.15 Several theoretical studies have sought to identify the Ta2O5 crystal phase,16–20 and among the proposed structures, the k phase not only shows the lowest energy per formula unit16 but also agrees well with experimentally reported bond length distribution and bandgap.21 Previous studies16,22 have also found that the introduction of oxygen vacancies in the k phase led to significant long range atomic restructuring. The presence of many metastable Ta2O5 phases and the facile structural relaxation in response to defects can be explained by Ta2O5 possessing an adaptive crystalline structure.16,22,23 While the impact of this adaptive structure on vacancy formation has been studied,16,22 its effect on vacancy diffusion is still unknown. Therefore, understanding oxygen vacancy diffusion in this phase can shed light on the Ta2O5 conductive filament formation and disruption process. Greater insight into oxygen vacancy diffusion will also prove beneficial for other applications in photocatalysis24 and high-k dielectric layers.25 II. METHODS

Density functional (DFT) electronic-structure calculations were done using the Quantum Espresso package with 119, 134502-1

C 2016 AIP Publishing LLC V

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ultrasoft pseudopotentials.26 Plane wave and charge density energy cutoffs were 110 Ry and 880 Ry, respectively. We used the Perdew-Burke-Ernzerhof (PBE) generalized gradient approximation (GGA) for exchange and correlation. DFT calculations underestimate the bandgap of metal oxides and DFTþU can partially corrected this. However, previous works have shown that DFT produces similar trends in formation energy (e.g., predict the most stable configuration)27–29 and transition barriers (within 0.1 eV) compared to DFTþU.27,29,30 Prior work has also found that DFTþU can lead to metastability of electronic states along the transition path which can make nudged elastic band calculations difficult to converge.31 Therefore, given our focus on atomic configuration and migration of oxygen vacancies, we use DFT to eliminate the need for adjustable U values. Due to the adaptive nature of the k phase,16 a 3  3  3 supercell was required to capture the structural changes induced by the vacancies and their migration. In this work, we use the nudged elastic band (NEB) approach to calculate the energy barriers for vacancy migration. The NEB is a well established technique that has been shown to provide activation energies in good agreement with experiment for cases ranging from interstitial migration in silicon32 to vacancy diffusion in metal oxides (e.g., TiO2,33 ZnO,27 and Al2O334). However, some care in the choice of calculation parameters is required to achieve accurate results. For this work, we use the climbing image variant35 of the nudged elastic band approach (CI-NEB) which does a better job at finding saddle point configuration and the height of the transition barrier. CI-NEB calculations were done on large well-converged supercells to minimize any residual strain that could affect convergence of the NEB calculations. We also use the generalized gradient (GGA) functional which has been shown to provide better agreement with experiment for transition barrier energies than the local density approximation (LDA).32 III. RESULTS A. Oxygen vacancy formation

Figure 1 inset shows a 3  3  3 supercell of the k phase Ta2O5. There are 3 different oxygen sites: 2 coordinated inplane (2f), 3 coordinated in-plane (3f), and 2 coordinated inter-plane (bwp). Given the adaptive nature of the k phase,16 there may exist different configurations for each vacancy site. To explore the energy landscape, we conduct structural relaxation of each vacancy site with small displacements of nearby atoms. Our calculations revealed three different configurations for 2f vacancy (Figs. 2(a)–2(c)), and only 1 configuration for 3f (Fig. 2(e)) and bwp vacancy. In addition, the atomic configurations around some vacancies change when the defects become charged. For the þ2 charged 2f-a vacancy, two nearest 2-coordinated oxygen atoms become 3-coordinated to compensate for the extra charge (Fig 2(d)). For configuration 2f-b and 2f-c, there is no significant change in bonding between neutral and charged states. For 3f vacancy, the stable bonding configuration differs for the neutral and charged states (Figs. 2(e) and 2(f)).

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FIG. 1. The formation energy of oxygen vacancies versus Fermi energy. Inset shows an in-plane view of the k phase with Ta (green), in-plane O (red), and inter-plane O (blue).

In general, we find that our relaxed configurations are similar to previous studies16,22 for atomic positions near the vacancy. However, we did not observe the predicted shifts in atomic positions far from the vacancy that were reported in earlier studies.16,22 These differences in the long-range atomic positions could be due to the use of smaller supercell sizes in the prior works. Small supercells can lead to increased interactions between the vacancy and its periodic images, resulting in significant atomic rearrangement. We also found that a large 3  3  3 supercell was necessary to identify the three stable 2f vacancy structures. Differences in choice of exchange-correlation and plane-wave cutoff could also affect the final relaxed vacancy configuration. A more detailed comparison of our relaxed structures with previous works is included in the supplementary materials.36 The vacancy formation energy is given by Ef ¼ Edef  Elatt  lO þ qðVBM þ F þ DVÞ;

(1)

where Edef is the energy of the supercell containing an oxygen vacancy, Elatt is the energy of the pristine lattice, lO is the oxygen chemical potential for oxygen rich conditions, q is the oxygen vacancy charge state, VBM is the valence band maximum (VBM) energy, F is the Fermi level measured from VBM, and DV is the change of VBM induced by defects. We find that DV is within 0.02 eV, which is negligible in formation energy calculations. The formation energies are listed in Table I. The formation energy for charged vacancies depends on the Fermi energy in the oxide. The formation energy for charged vacancies are listed for the case where the Fermi energy is at the VBM to highlight the minimum possible vacancy formation energy. We find the 2f-c vacancy to be the most stable configuration among all three 2f sites for both neutral and þ2 charged states. For the þ1 charge state, the formation energy of these vacancy sites are similar, so active transformation among them would be expected at room and elevated temperature. Similar to prior work by Lee et al.16 which used GGA, we find the 3f vacancy site to be the most stable neutral vacancy

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FIG. 2. In-plane neutral 2 coordinated vacancy configurations are shown in (a) 2f-a, (b) 2f-b, and (c) 2f-c. The þ2 charged 2 coordinated in-plane vacancy (2f-a) is shown in (d). Neutral and þ2 charged 3 coordinated (3f) vacancy configurations are given in (e) and (f). Ta and O atoms are in green and red, respectively. Blue arrows denote atomic displacement.

in k Ta2O5. However, in contrast to Lee et al.,16 we predict that the 2f-c vacancy site has a lower formation energy (5.33 eV) than the neutral bwp vacancy (5.51 eV). Our predicted 2f-a formation energy (5.74 eV) is close to the 2f formation energy (5.9 eV) reported in Lee et al.,16 so their structural relaxation may have led to a 2f-a configuration. This work did not provide a figure of their relaxed 2f structure. Differences in the supercell size (as noted earlier) and plane-wave cutoff could also lead to differences in predicted vacancy formation energies. Guo and Robertson22 calculated vacancy formation energies in k Ta2O5 from first principles using a screened TABLE I. The formation energies of neutral and charged oxygen vacancies are given for different sites in k Ta2O5. The formation energies for charged vacancies are listed for the case where the Fermi energy is at the VBM to highlight the minimum possible vacancy formation energy. Neutral

Configuration 2f-a 2f-b 2f-c 3f bwp

This study (eV) 5.74 5.44 5.33 4.99 5.51

Prior works (eV) 5.9016 and 4.3822 4.4016 and 6.2522 5.6016 and 7.322

þ1 charges þ2 charged This study (eV) (eV) 2.89 2.79 2.90 2.88 2.97

0.69 0.55 0.29 0.34 0.49

exchanged (sX) hybrid functional. As noted in Table I, there are key differences in our predicted formation energies for neutral vacancies and those in Ref. 22. While Guo and Robertson22 also predict that the in-plane vacancy formation energies are less than for bwp sites, they find the 2f vacancy to have a much lower forming energy (4.38 eV) than the 3f site (6.25 eV). The differences in vacancy formation energy could be due to the smaller 2  2  3 supercell used in the prior work. The lattice parameters used to construct the supercell in Ref. 22 were based on GGA calculations and a subsequent relaxation of the atomic positions was done using the screened exchange hybrid functional. Predicted lattice constants and bond lengths using sX are typically smaller than those predicted using GGA.37 This could lead to contraction of atomic bonds and strain in the supercell, which could affect the predicted vacancy formation energies. The different relative formation energies could also be due to differences in the electronic structure predicted by the two functionals (GGA vs sX). The formation energy of oxygen vacancies as a function of F is shown in Fig. 1, where the 2f lines represent the lowest formation energy of all three 2f vacancy sites in neutral and charged states. When F is below 2.4 eV, both þ2 charged 2f and 3f vacancies are very stable against other charged or neutral sites. As F increases above 2.4 eV, the neutral vacancy at 3f sites becomes the most stable state. The þ1 charged states are energetically unfavorable over the

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J. Appl. Phys. 119, 134502 (2016)

FIG. 3. Pathways for in-plane migration (a) from a 3f vacancy to a 2f vacancy and (b) from a 2f vacancy to a 3f vacancy. Blue arrows denote atomic displacements. Panel (c) shows pathways from 3f vacancy to neighboring 3f or 2f vacancy where transitions are noted by blue and black arrows, respectively.

entire F window, therefore, our following CI-NEB transition barrier calculations only focus on neutral and þ2 charged defect states. Guo and Robertson22 also found that þ2 charged oxygen vacancies were stable for all sites for F less than 2.4 eV. However, they predicted that the þ2 charged 3f vacancies are the most stable for F below 2.4 eV and neutral 2f oxygen vacancies are stable for F above this. They also predicted oxygen vacancies at all sites would spontaneously form for F within approximately 0.3 eV of the valence band maximum. The possible factors that could lead to these differences were already noted for the neutral vacancy formation energies.

diffusion barrier is 0.38 eV. The low energy barriers and coordinated atomic movements for vacancy migration inplane in Ta2O5 support the hypothesis that the adaptive crystal structure benefits defect migration. Inter-plane transition from bwp vacancy to 2f or 3f inplane vacancies was also calculated (see Fig. S2 in the

B. Vacancy migration barrier

The adaptive crystal structure of Ta2O5 implies that vacancies may migrate through low energy barriers via shuffling rearrangement of neighboring atoms. By conducting CI-NEB calculations to connect different vacancy sites, several low barrier transition pathways for in-plane and interplane migration are revealed. For in-plane migration, both neutral and charged states show similar diffusion pathways. A full migration path starts with a 3f vacancy (ground state in neutral state), as shown in Fig. 3(a), that diffuses through a coordinated atom movement (blue arrows) to reach a neighboring 2f vacancy site (Fig. 3(b)). The next transition to a neighboring 3f vacancy site (Fig. 3(c)) also features coordinated atom movement. This site is symmetry equivalent to the beginning 3f vacancy. Note that the former and latter 3f-2f transitions are different in the view of atomic movement and therefore different in transition barriers. Now starting from the 3f site in Fig. 3(c), the vacancy can either repeat this 3f-2f-3f pathway by atomic movements indicated with the black arrows, or it can move directly to a neighboring 3f vacancy site by single atom movement, shown by the blue arrow. A movie of the in-plane transition is shown in Fig. S1 of the supplementary material.36 The energy landscape of these transitions for both neutral and charged vacancies is shown in Fig. 4(a). For the neutral state, the in-plane diffusion barrier is 0.70 eV, and for the charged state, the

FIG. 4. In-plane (a) and inter-plane (b) energy landscapes.

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supplementary material36). The energy landscape for transitions in neutral and charged states is shown in Fig. 4(b). The lowest inter-plane transition barrier for neutral state vacancy is 1.26 eV following 2f-bwp-2f pathway, and the lowest barrier for þ2 charged state vacancy is 0.75 eV following the same pathway. The barrier of inter-plane transitions is much higher than that of in-plane transitions in both neutral and charged states. The vacancy diffusion coefficients were calculated using D ¼ D0exp(–Ea/kT) where D0 is 8.6  107 cm2/s, as suggested by Nakamura et al.,38 Ea is the migration barrier, k is Boltzmann constant, and T is temperature. The calculated diffusion coefficient for þ2 charged oxygen vacancy at RT is 3.5  1013 cm2/s in-plane and 2.2  1019 cm2/s inter-plane. The in-plane diffusion coefficient is 106 times larger than that of inter-plane diffusion, regardless of the D0 chosen. To put this in perspective, it will take in-plane oxygen vacancies 7 ms to diffuse 1 nm at RT, while it will take over six hours for oxygen vacancies to diffuse 1 nm perpendicular to the Ta-O planes. Therefore, oxygen vacancy diffusion in the k phase is highly anisotropic, and we predict that in-plane diffusion should be much faster than inter-plane diffusion. It is important to note that the formation of a vacancy filament occurs due to the drift of charged oxygen vacancies in the presence of an applied electric field E. In some cases, the applied fields across the RRAM oxide region can be large enough to distort the energy landscape for vacancy diffusion and reduce the migration energy barrier in the field direction. The vacancy drift velocity, vd, has a non-linear dependence on the applied electric field and can be related to the ab-initio migration barrier using the expression for high field ionic transport,39,40 vd  expðEa =kTÞsinhðqaE=2kTÞ, where q is the vacancy charge and a is the effective length of the potential barrier. This implies that the filament forming voltages in k Ta2O5 for electric fields applied along the Ta-O plane should be lower than the forming voltages for electric fields applied perpendicular to the Ta-O plane. Several recent studies41–43 have developed vacancy drift-diffusion models for filament formation in resistive RAM devices, and the formation and migration barriers calculated in this work can be incorporated into these larger scale models.

J. Appl. Phys. 119, 134502 (2016)

average value of in-plane (0.7 eV) and inter-plane (1.26 eV) migration barrier is 0.98 eV, which is in reasonably good agreement with the experimental value. Our results show that positive charge can significantly lower both the formation energy and the migration barrier of oxygen vacancies in k Ta2O5. The formation energy and migration barrier for þ2 charged oxygen vacancies are only 0.29 eV and 0.38 eV, respectively, which implies the easy formation and fast diffusion of these defects. Previous work48 has also shown that vacancies are in the þ2 charged state for most electrode materials and our study also shows a wide energy window of Fermi energies that favors the formation of þ2 charged vacancies. Therefore, the low formation and migration energies due to the adaptive structure combined with the preference to stay in the þ2 charged state should contribute to the low forming and fast set/reset rate reported for Ta2O5 RRAM devices. The high endurance of Ta2O5 RRAM devices may also benefit from the enhanced mobility of the oxygen vacancies. Figure 5 shows the lowest oxygen vacancy formation energy and migration barrier of 4 candidate RRAM materials in crystalline phase. The formation energy and diffusion barrier of þ2 charged oxygen vacancies in k-Ta2O5 are much lower compared to other transition metal oxides, and this could explain the fast transition speed (2 ns) in Ta2O5 RRAM.6 Forming, set, and reset voltages are highly dependent on device size, measuring method, etc., and therefore parameters for different materials based devices reported in literatures are not directly comparable to each other. Here, we predict the operating voltages of Ta2O5 RRAM devices would be lower than other oxide based devices if the same device size and measuring process can be maintained. This also implies a computational route for identifying promising RRAM materials. Oxides with low oxygen vacancy formation energy and migration barrier could lead to low-voltage and fast RRAM devices. Oxides with adaptive crystal structures similar to Ta2O5 represent an important class to study.

IV. DISCUSSION

Our calculated migration barriers are in agreement with recently reported experimental and simulation results. A recent first principle study of amorphous Ta2O544 found that the diffusion barrier of oxygen vacancies in the optimum charge state varies from 0.3 to 1.0 eV, which covers our results for þ2 charged state of 0.38 eV for in-plane and 0.75 eV for inter-plane migration. Using isotope oxygen tracers, Nakamura et al.38 measured an average oxygen atom diffusion barrier of 1.2 6 0.1 eV in amorphous Ta2O5. As the k phase transforms into an amorphous state, the in-plane oxygen vacancy migration barrier should rise because of the loss of the crystalline adaptive structure, and the inter-plane barrier should drop because of connections to more oxygen atoms in closer distance. With this hypothesis and considering that oxygen atoms move as part of vacancy diffusion, the

FIG. 5. Lowest oxygen vacancy formation energy and migration barrier of four candidate RRAM materials in crystalline phase. All formation energies are calculated using GGA under oxygen-rich condition 33,45,46 with F ¼ 0. Migration barriers are from GGA calculations except for Al2O3 (LDA).33,34,47

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An interesting finding of this study is the prediction that the oxygen vacancy diffusion in the k phase is anisotropic with faster in-plane diffusion than inter-plane diffusion. In fact, several proposed crystal phases of Ta2O5 share the same structural feature of layers connected by 2 coordinated inter-plane oxygen atoms (e.g., hexagonal d and b phase17 and the 11 formula unit model16). This implies the vacancy diffusion in these phases is also anisotropic with faster inplane diffusion. This anisotropy is particularly important for applications where crystalline Ta2O5 is used, e.g., a controlled crystal orientation can lead to a fast or slow mass transport of carriers related to oxygen atoms. Further experimental studies on vacancy diffusion in crystalline Ta2O5 could help provide new insight into this issue. V. CONCLUSIONS

We have calculated the oxygen vacancy formation energy and migration barriers in k phase Ta2O5 from first principles. The most stable vacancy site was found to be inplane site with minimum formation energy of 4.99 eV for neutral state and 0.29 eV for þ2 charged state. Given the adaptive crystalline structure, the lowest migration barrier path was found to be an in-plane coordinated atomic movement diffusion with a energy barrier of 0.70 eV for neutral state and 0.38 eV for þ2 charged state. Charged oxygen vacancies in k-Ta2O5 demonstrate both low formation energy and low migration barrier compared to the neutral vacancies and vacancies in other candidate RRAM oxides. The low migration barrier for charged vacancies due to the adaptive crystal structure should lead to a lower operating voltage compared to other oxide RRAM devices and also helps explain the fast switching rate for Ta2O5 based RRAM devices. The diffusion of oxygen vacancies in k phase was also found to be anisotropic with faster in-plane diffusion than inter-plane diffusion. This feature may be of particular interest in applications where crystalline Ta2O5 is used. ACKNOWLEDGMENTS

The authors gratefully acknowledge helpful discussions with B. Magyari-K€ope, J. Childress, and J. Read. 1

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