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A Combined Ab Initio and Experimental Study on the Nature of Conductive Filaments in Pt/HfO2/Pt Resistive Random Access Memory Kan-Hao Xue, Boubacar Traoré, Philippe Blaise, Leonardo R. C. Fonseca, Elisa Vianello, Gabriel Molas, Barbara De Salvo, Gérard Ghibaudo, Fellow, IEEE, Blanka Magyari-Köpe, Member, IEEE, and Yoshio Nishi, Life Fellow, IEEE
Abstract— Through ab initio calculations, we propose that the conductive filaments in Pt/HfO2 /Pt resistive random access memories are due to HfOx suboxides, possibly tetragonal, where x ≤ 1.5. The electroforming process is initiated by a continuous supply of oxygen Frenkel defect pairs through an electrochemical process. The accumulation of oxygen vacancies leads to metallic suboxide phases, which remain conductive even as ultranarrow 1-nm2 filaments embedded in an insulating HfO2 matrix. Our experiments further show that the filaments remain as major leakage paths even in the OFF -state. Moreover, thermal heating may increase the OFF -state resistance, implying that there are oxygen interstitials left in the oxide layer, which may recombine with the oxygen vacancies in the filaments at high temperature. Index Terms— Dielectric breakdown, electrochemical processes, hafnium compounds, metal-insulator structures, nanotechnology, semiconductor memories.
I. I NTRODUCTION
H
AFNIA (HfO2 ) is one of the leading candidates as the dielectric in resistive random access memories (RRAMs)
Manuscript received October 30, 2013; revised January 1, 2014, February 17, 2014, and March 15, 2014; accepted March 17, 2014. Date of publication April 7, 2014; date of current version April 18, 2014. This work was supported by the Nanosciences Foundation of Grenoble, France. The work of L. R. C. Fonseca was supported in part by the Brazilian Agency CNPq through the INCT/Namitec initiative. The calculations were performed on the Stanford National Nanotechnology Infrastructure Network Computing Facility supported by the National Science Foundation of USA. The review of this paper was arranged by Editor A. Schenk. K.-H. Xue was with the Institut de Microélectronique Electromagnétisme et Photonique et le Laboratoire d’Hyperfréquences et de Caractérisation, Grenoble 38016, France. He is now with the Laboratoire de Réactivité et Chimie des Solides, Université de Picardie Jules Verne, Amiens 80039, France (e-mail:
[email protected]). B. Traoré, P. Blaise, E. Vianello, G. Molas, and B. De Salvo are with CEA-LETI, Grenoble 38054, France (e-mail:
[email protected];
[email protected];
[email protected];
[email protected];
[email protected]). L. R. C. Fonseca is with the Center for Semiconductor Components, University of Campinas, Campinas 13083-870, Brazil (e-mail:
[email protected]). G. Ghibaudo is with the Institut de Microélectronique Electromagnétisme et Photonique et le Laboratoire d’Hyperfréquences et de Caractérisation, Grenoble 38016, France (e-mail:
[email protected]). B. Magyari-Köpe and Y. Nishi are with the Department of Electrical Engineering, Stanford University, Stanford, CA 94305 USA (e-mail:
[email protected];
[email protected]). Color versions of one or more of the figures in this paper are available online at http://ieeexplore.ieee.org. Digital Object Identifier 10.1109/TED.2014.2312943
[1], [2]. Since it already serves as the high permittivity dielectric layer in state-of-the-art CMOS [3], high-quality hafnia thin films can be conveniently obtained through ordinary atomic layer deposition (ALD) in compliance with the CMOS technology [4]. The core element of hafnia RRAM is a metal/HfO2 /metal capacitor [5], [6]. The resistive switching effect is initiated by an electroforming step, which consists of a high electric field (some MV/cm) applied across the hafnia thin film to create conductive paths by soft breakdown, rendering the memory cell conductive (the so-called ON-state). The electric current across the dielectric is limited by external circuits to avoid permanent damage. These conductive paths are named filaments and are only metastable since they can be ruptured by passing a large current. This phenomenon is called RESET since it recovers the dielectric property of the thin film, switching the cell to the so-called OFF-state. Subsequently, soft breakdown can occur by applying a voltage bias larger than the RESET voltage, albeit lower than the forming voltage, recreating the conductive paths. This process is called SET. The cell simply records bits 0 and 1 by the difference between its resistance states. Depending on the choice of top and bottom electrodes, hafnia RRAM can either be bipolar [7], i.e., the SET and RESET voltages take different signs, or nonpolar [5], when both SET and RESET occur under either positive or negative applied voltage. In nonpolar Pt/HfO2 /Pt memory cells, only two elements, Hf and O, ought to be associated with the SET/RESET mechanisms since Pt is an inert metal. Even though Pt is a catalyst for oxygen reduction [8], there is no reaction between Pt and O or Hf ions. However, the role of other electrodes in the switching mechanisms of bipolar cells like Ti/HfOx /TiN cannot be ruled out. The exclusion of the electrodes from the switching process suggests that the device physics of the Pt/HfO2 /Pt nonpolar cells may be simpler than otherwise, and as such, it deserves a first investigation. While a filamentary origin of conduction has been widely accepted for Pt/HfO2 /Pt RRAM cells, atomistic simulations of the actual filament structures are rare. Aspera et al. [9] reported fully occupied defect bands in monoclinic HfO2 (m-HfO2 ) with neutral O vacancy chains along the c-axis, but a partially occupied defect band if the vacancy chains are negatively charged. They attributed the conductive phase in HfO2 RRAM
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Fig. 1. Typical I –V curves obtained from a Pt/HfO x /Pt memory cell during the electroforming, RESET, and SET steps. Circles indicate the two major current drops during RESET and the smaller current drop during SET.
Fig. 3. Temperature dependence of the ON-state resistance for various samples using 1-mA compliance current. While the ON-state resistance shows some variability from sample to sample, the linear dependence of the ON resistance on temperature in all cases indicates metallic conduction.
Fig. 2. Dependence of the ON- and OFF-state resistances on cell area, for the same SET current compliance of 1 mA. The cell area has a little impact on the resistances of the ON and OFF states.
Fig. 4. Variation of the OFF-state resistance with temperature. The increased resistance after heating up to 200 °C remains high even after cooling back to room temperature.
to charged O vacancy chains. However, fixed charges are neutralized by the adjacent metal electrodes as soon as the metal–filament–metal conductive path is formed. Therefore, this explanation cannot account for the stability of the conductive filaments. In this paper, we combine experiments and atomistic simulations to investigate the switching mechanism of nonpolar Pt/HfO2 /Pt cells and propose possible stoichiometries for the filament structure.
The resulting OFF-state resistance depends on the depth of RESET, i.e., the maximum (or ending) voltage in the RESET operation. In Fig. 1, the RESET operation stops at 1 V. The subsequent SET procedure shows a minor RESET at 1.06 V, reflecting the fact that the previous RESET was not complete. The SET voltage is ∼2.8 V, lower than the electroforming voltage. Keeping the current compliance fixed, we have found that the memory cell area has a minor influence on the ON - and OFF -state resistances, as shown in Fig. 2. For the ON -state, this is an indication of the filamentary nature of the device in that state. For the OFF-state, this finding suggests that the remaining parts of the filaments, i.e., those not ruptured during the last RESET step, are critical conduction spots in the OFF -state. Fig. 3 shows metallic conduction for the ON -state as attested by the linear increase of the ON-state resistance on temperature rise. On the other hand, the OFF-state resistance is very sensitive to temperature variation. Fig. 4 shows that its resistance increases by nearly three orders of magnitude upon heating from room temperature to 200 °C. This large resistance change is permanent, remaining high even when the temperature is lowered. Because the Pt/HfO2 /Pt cell works in the nonpolar mode, SET/RESET may occur at either polarity. We have thus investigated the polarity symmetry of the I –V curves. Fig. 5(a) shows the statistical distribution of positive and negative RESET
II. E XPERIMENT Our RRAM cells consist of a Pt (25-nm)/HfOx (10-nm)/Pt (25-nm) capacitor. The Pt electrodes were deposited by sputtering, while the HfOx thin film was deposited by ALD at 350 °C. Typical I –V curves are shown in Fig. 1. In the initial electroforming step, the applied voltage was ramped up to 5 V. Next, during RESET, the voltage was increased from zero until a sharp current drop of two orders of magnitude took place at 0.7 V. Increasing the voltage further to 0.85 V, the current suffered another decrease of more than two orders of magnitude. Hence, the RESET procedure is generally not a one-step process in Pt/HfOx /Pt cells, in agreement with [10].1 1 In the work of Goux et al. [10] only a minority of their Pt/HfO /Pt cells 2 showed RESET behavior. However, the shown I –V curves for those cells with normal RESET behavior are similar to our results, both showing multistep RESET.
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Fig. 7. Location of a neutral O interstitial in m-HfO2 . The O interstitial is labeled 1 and has three Hf neighbors a, b, and c. The O ion labeled 2 is bonded to the same three Hf ions. All atomic positions were optimized.
Fig. 5. (a) Cumulative distribution function of the magnitudes of RESET voltages for various samples from the same batch, comparing the positive and negative RESET cases. (b) Cumulative distribution function of positive SET voltages for various samples. Before the SET operation, the OFF-states were obtained by either positive or negative RESET.
the Perdew–Burke–Ernzerhof [19] functional. The formation energy of an O vacancy or interstitial with charge q is defined as E for = E D − E 0 ± μ O + q (E V + E F + V )
(1)
where E D is the energy of the defective supercell, E 0 is the energy of the defect-free supercell, μO is the O chemical potential, E V is the top of valence band level, E F is the Fermi level measured from the top of valence band, and V is the average potential shift due to the introduction of the defect. In an oxygen-rich environment, μO is usually set as a half of the value obtained for an O2 molecule. The plus sign in front of μO is for O vacancies, while the minus sign is for O interstitials. In this paper, we assumed an O-rich environment, which better approaches the growth process of our samples. Fig. 6. Formation energies of O vacancies (V O ) and O interstitials (Oi ) in m-HfO2 , where only the charge states with the lowest energy are shown. Inset: unit cell of m-HfO2 with all O sites named. Here and in the following figures, big green balls represent Hf, while small red balls represent O.
voltages in the same batch of samples, while Fig. 5(b) shows the statistical distribution of SET voltages for the OFF-states in samples with positive and negative preRESET. These results support a polarity-independent nature for SET and RESET. The device cycling test data can be found in [11], which shows relatively stable RON but variable ROFF . This is consistent with other previous reports on the Pt/HfOx /Pt system [12]. III. A B I NITIO C ALCULATIONS Here, we identify through simulations the energetically favorable HfOx stoichiometries that may fit the conductivity characteristics of the ON-state. Our calculations were based on density functional theory [13] as implemented in plane-wavebased Vienna Ab Initio Simulation Package [14], [15], using projector augmented-wave [16], [17] pseudopotentials. The unit cell and the naming adopted for the O atoms are indicated in the inset of Fig. 6. The plane wave cutoff energy was 500 eV, which converged well for all compounds considered. Monkhorst–Pack [18] k-meshes were utilized for sampling the Brillouin zone. To investigate point defects, a 2 × 2 × 2 supercell with 96 atoms was set up. The generalized gradient approximation was used for the exchange-correlation energy, within
A. Bulk The m-HfO2 unit cell parameters were optimized to minimize residual forces and residual pressure. Our calculated parameters are a = 5.146 Å, b = 5.195 Å, c = 5.255 Å, and β = 99.68°, where β is the angle formed between the a and c vectors (the inset of Fig. 6). These values are in agreement with the previous results [20]–[22]. In all defect calculations, the atomic positions were fully optimized to minimize the residual forces, while the volume of the supercell was kept fixed at multiples of the unit cell. B. Point Defects The formation energy of a neutral O vacancy in m-HfO2 is 7.00 eV, located at the four-coordination O(B) site. Analysis of charged vacancies reveals that the +1 charged O vacancies are unstable, while the +2 charged O vacancies are preferred over neutral vacancies when the Fermi level is near the valence band maximum (VBM), as shown in Fig. 6. Moreover, the +2 charged O(A) vacancy (E for = 1.22 eV) is energetically more favorable over the +2 charged O(B) vacancy (E for = 1.80 eV) by 0.58 eV. These results are consistent with the former calculation in [21]. The calculated formation energy of a neutral O interstitial is 1.05 eV. Its location in the HfO2 matrix is shown in Fig. 7, where it is identified as O #1. Fig. 7 also marks its closest neighbor, identified as O #2, which forms bonds with the same three Hf ions as O #1 does. O #1 and O #2 display the same Bader charge (−0.72e). For charged interstitials, the formation
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TABLE I R ELATIVE E NERGY P ER HfO C HEMICAL F ORMULA FOR VARIOUS HfO P HASES
Fig. 8. Configuration of the ground-state O Frenkel defect pair in m-HfO2 . The charged O vacancy is indicated by an ellipse and the charged O interstitial is indicated by an arrow. All atomic positions were optimized.
energy of the −1 charged O interstitial is 2.91 eV, while for the −2 charged, it is 3.37 eV, for the Fermi level at the VBM. The −2 charged interstitial becomes more favorable for the Fermi level higher than 1.17 eV from the VBM (Fig. 6), while the −1 charged interstitial is unstable throughout the bandgap. Fig. 6 also shows that the energetically favorable O Frenkel pair consists of a +2 charged O vacancy and a −2 charged O interstitial. To verify this idea, we carried out O Frenkel pair calculations in the same 2 × 2 × 2 supercell, with one O(B) vacancy and one O interstitial occupying various locations. For each configuration, all atomic positions were fully optimized. The ground-state Frenkel pair defect model is shown in Fig. 8. The Bader charge for the O interstitial is −1.30e, close to the average O Bader charge (−1.36e), and very different from its value for the isolated neutral O interstitial calculated before (−0.72e). Allowing for charged vacancies and interstitials, the formation energy of the Frenkel pair is 4.71 eV. We have also identified a metastable configuration for the Frenkel pair in the same 2 × 2 × 2 supercell, where the formation energy is at a local minimum. It consists of the same O(B) vacancy, but with the O interstitial located at the O #1 site shown in Fig. 7. This pair does not exchange charge, contrary to the configuration described previously where the formation energy is at a global minimum. Indeed, the Bader charge on the O interstitial of this metastable pair is −0.73e, close to half the average O Bader charge, −1.37e, and almost the same as the isolated single O interstitial charge, −0.72e. The formation energy of this Frenkel pair is 8.21 eV, slightly higher than that of an isolated neutral O vacancy (7.00 eV) plus an isolated O interstitial (1.05 eV). While this O Frenkel pair costs more energy, it may be relevant in the ON-state of an RRAM cell where fixed charges must be neutralized in order for the filament to grow. In addition to forming a Frenkel pair, the O interstitial may also migrate to the Pt electrode, occupying an interstitial position in the metal. The calculated formation energy of the combined neutral O vacancy in HfO2 and O interstitial in bulk Pt is 7.91 eV. This value is larger than the charged Frenkel pair (4.71 eV). Finally, it is worth mentioning that the existing grain boundaries may serve as segregation paths for both O vacancies and interstitials. Our previous calculation [23] employing a 5 (310)/[001] grain boundary model for cubic HfO2 (c-HfO2) revealed a 2.06-eV energy gain for a single-neutral O vacancy to migrate from the HfO2 bulk to the grain boundary. For a neutral O interstitial, the energy gain due to
segregation is 0.35 eV. In this paper, we do not consider grain boundaries, though they may become preferential sites for resistive switching [24], [25] due to lower vacancy formation energies. C. Conductivity of HfOx Suboxides At present, there is still no clear experimental evidence of the exact filament composition in HfO2 RRAM. Metal Hf is energetically very stable, but its stoichiometry is far from the initial HfO2 or HfO2−x compositions. Another possible candidate is a conductive suboxide, an example of which being the Magnéli phase Tin O2n−1 (typically Ti4 O7 ) that accounts for the conductive phase in TiO2 RRAM [26]. The fact that Ti4 O7 is very close to TiO2 in stoichiometry suggests that once some conductive suboxide phases are reached locally, a sharp current rise appears, where the filament grows fast aided by Joule heating [27]. This scenario stimulates the investigation of suboxides as the composition of conductive filaments in HfO2 RRAM. Here, we investigate possible crystal structures of HfOx with various stoichiometries (1 ≤ x ≤ 2) and their electronic properties. Previously, we predicted the ground state of Hf2 O3 to be the tetragonal P4m2 phase with a semimetal electronic structure, and showed that Hf4 O7 is not responsible for metallic conduction [22]. Recently, Puchala and van der Ven [28] predicted a hexagonal ZrO ground state. Following their work, we calculated the energies of various HfO crystal structures (Table I).2 To account for possible small energy differences between crystals, we adopted the Heyd–Scuseria–Ernzerhof (HSE06) hybrid functional [29] for more accurate static total energy calculations. The ground-state HfO belongs to the hexagonal space group P62m (h-HfO), and is an isomorph of hexagonal ZrO. We identified another low-energy HfO phase with space group P42 /mmc, which can be viewed as tetragonal Hf2 O3 (t-Hf2 O3 ) with one missing O per primitive cell (Fig. 9). The densities of states (DOS) of hcp Hf metal, h-HfO, tetragonal HfO (t-HfO), t-Hf2 O3 , and m-HfO2 are compared in Fig. 10. While h-HfO is a semiconductor with a small bandgap of 0.23 eV, t-HfO shows finite DOS at the Fermi level. Hence, metallic conduction emerges in some tetragonal suboxides Hf2 O3 or HfO, indicating that sufficient substoichiometry 2 The orthorhombic structure was obtained by removing one oxygen atom in the tetragonal Hf2 O3 unit cell followed by full relaxation, but the missing oxygen is on a different site from the tetragonal HfO case.
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Fig. 9. Atomic structures of tetragonal Hf2 O3 (left), tetragonal HfO (middle), and hexagonal HfO (right). Fig. 11. Tetragonal Hf2 O3 filament (regions inside the circles) embedded in HfO2 . All atomic positions were optimized.
Fig. 10. Density of states of (a) hcp Hf, (b) h-HfO, (c) t-HfO, (d) t-Hf2 O3 , and (e) m-HfO2 calculated with the HSE06 functional. The Fermi level (or highest occupied molecular orbital in the cases of h-HfO and m-HfO2 ) is indicated by the vertical lines.
is required (x ≤ 1.5 in HfOx ). On the other hand, not all but some particular tetragonal substoichiometric phases show metallic conduction. Hf2 O3 (x = 1.5) holds the first stoichiometry for which HfOx may be metallic. Recently, McKenna [30] has shown through zero temperature ab initio calculations that HfOx (0.2 < x < 2) may decompose into HfO0.2 and m-HfO2 . Nevertheless, the filaments in RRAM samples correspond to metastable phases, which are affected by changes of electrical stress. In addition, a suboxide may be more stable than the hcp-Hf/m-HfO2 mixture as the entropy terms are considered in the Gibbs free energy. Moreover, tetragonal HfOx (1.5 ≤ x ≤ 1.7) samples have been obtained [31] without decomposing into hcp-Hf (or HfO0.2 ) and m-HfO2 . In summary, while the exact composition of the filament is still an open question, we believe that conductive suboxides are strong and realistic candidates. D. Embedded Filament Models Despite the established metallic or semimetallic conduction in HfOx suboxides for x ≤ 1.5, it is still unresolved whether a suboxide conductive filament remains as such when embedded in HfO2 . In this section, we analyze two filament models consisting of a narrow core conductive suboxide region and a surrounding HfO2 matrix. Notice, however, that the simple compositions assumed in our models do not necessarily correspond to a true filament composition as experimental evidence still lacks. For simplicity, we choose the c-HfO2 phase as the matrix. The two core/matrix models have a t-Hf2 O3 core and a zinc
Fig. 12. Zinc blende HfO filament (regions inside the circles) embedded in cubic HfO2 . All atomic positions were optimized.
blende HfO (zb-HfO) core, respectively (our choice of the zb-HfO core model is discussed below). The size of the core filaments is ∼ 1 nm × 1 nm × 0.5 nm embedded in a 2 nm × 2 nm × 0.5 nm c-HfO2 matrix (the dimensions of the matrix coincide with the dimensions of the supercells in these calculations). In either model, the matrix is stress free but the core is stressed to fit in the space carved in the matrix. With the cores in place, all the atomic positions, including those in the host, were fully optimized to minimize residual forces. While zb-HfO is not a low-energy HfO phase, it offers the great benefit that its lattice constant is very close to c-HfO2 and its structure is easily derived by removing half of the O atoms from c-HfO2 . On the contrary, lattice mismatch between c-HfO2 and t-Hf2 O3 seems inevitable. The resulting stresses, which in (x, y, z) directions are (5.6, −43.6, −18.8) kBar for the t-Hf2 O3 core model and (−6.3, 12.3, −6.3) kBar for the zb-HfO core model, confirm our expectation. Therefore, the two models may roughly be regarded as one with and one without stress, respectively. Considering the heavy calculation load, the local density approximation was adopted here as the exchange-correlation functional. Fig. 11 shows the relaxed atomic structures of the t-Hf2 O3 filament model. The core filament region has been rotated to better fit the host. Due to stress induced by the core, the host region deviates from the initial cubic phase, approaching the more energetically favorable monoclinic phase. Fig. 12 shows the relaxed atomic structures of the zb-HfO filament model, where both the core and the host regions retain the cubic symmetry.
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Fig. 15. Schematic representation of the switching mechanism in Pt/HfO2 /Pt RRAM devices. Blue (dark gray) regions have the stoichiometry HfOx with x ≤ 1.5.
IV. D EVICE M ODEL A. Electroforming Fig. 13. Site-projected DOS on the Hf atoms A–I (Fig. 11) ranging from one tetragonal Hf2 O3 core center to another, passing by the cubic HfO2 matrix.
Fig. 14. Site-projected DOS on the Hf atoms A–H (Fig. 12) ranging from one zinc blende HfO core center to another, passing by the cubic HfO2 matrix.
Figs. 13 and 14 show the site-projected partial DOS (PDOS) on some selected Hf atoms, starting from the center of one core region, going through the host, and finishing at the center of the neighboring core region. In both models, the core regions remain metallic, with no bandgap opening near the Fermi level. However, the zb-HfO model has greater DOS at the Fermi level. In the host region, the DOS are similar to bulk c-HfO2 , despite the appearance of some low-intensity gap states. Indeed, even though atoms E, F, and G in the t-Hf2 O3 core model (Fig. 13), and atoms C, D, E, and F in the zb-HfO core model (Fig. 14) are in the dielectric host, their PDOS do not generally show clean bandgaps. Only for the Hf atoms most distant from the filaments, namely F/E in the former/latter model, the PDOS show a clean bandgap. To sum up, these results indicate that conduction in an O-deficient filament is possible even for extremely narrow 1 nm × 1 nm filament cross section.
Based on our ab initio results, we propose a two-stage scenario for electroforming in Pt/HfOx /Pt cells, as shown schematically in Fig. 15. In our model, initially charged O Frenkel pairs near the cathode (or the front tip of the filament if the filament is already partially created) are the origin of filament generation. Electron injection from the cathode plays the essential role of neutralizing the O vacancies that can then aggregate without the Coulomb repulsion of the charged state. Meanwhile, the charged highly mobile O interstitials quickly migrate to the anode under the external electric field. At the anode, these interstitials exchange their charges with the electrode as soon as their distance from the anode is short enough to allow for electronic tunneling. This is the end of the first stage of electroforming where one or a few conductive channels are created, followed by a sharp increase of local currents. In the second stage, Joule heating increases the temperature in the vicinity of these conductive channels, promoting defect generation. Hence, the filaments expand laterally, increasing their cross section [32] until the total current reaches the external current compliance. From energetic point of view, the formation of charged O Frenkel pairs at A (Fig. 15) requires 4.71 eV per pair in stoichiometric HfO2 . The final state after steps A–C consists of one neutral O vacancy near the cathode plus one neutral O interstitial near the anode. Moreover, two elementary charges are transferred from the cathode to the anode. Due to the external bias, this charge transfer provides an energy gain as the Fermi level in the cathode is higher than in the anode. On the other hand, the formation energy of one well-separated neutral Frenkel pair is E gen = 8.05 − 2V − E col (eV)
(2)
where V is the applied bias, the factor of two is related to the two electrons transferred from the cathode to the anode, and E col is the energy loss due to ionic inelastic collisions during the O2− transport. The formation energy of an isolated neutral O vacancy is 7.00 eV, while that of a neutral O interstitial is 1.05 eV, summing up to 8.05 eV. Therefore, from (2) and provided that E col is small, charge transport by the O ion at an external bias of 1.7 V or more makes the neutral Frenkel pair more energetically favorable than the charged
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Frenkel pair. Equation (2) also predicts that at about 4 V, continuous generation of O neutral Frenkel pairs costs almost no energy, leading to the electroforming process. Since the O vacancies near the cathode are neutral, they may accumulate to form suboxide phases, resulting in filament formation. These estimations are based on the pure stoichiometric m-HfO2 phase, while initial substoichiometry or grain boundaries may lower the required voltage. While the supply of O Frenkel pairs starts at the cathode side, the filament extends toward the anode during electroforming. Hence, the locations of electron injection and of O Frenkel pair generation are not fixed, but are instead at the filament growing tip (named virtual cathode in [33]), which is under dynamic evolution during electroforming. Aside from the energetic point of view, a minimum electric field is also essential for the electrical migration of O2− in the oxide. For thick oxide films, this electric field criterion may require a larger applied voltage, overcoming the minimum bias criterion discussed above. Notice also that in our model electronic charging is indispensable to the RRAM switching, similar to [34]. B. Reset We propose further that the electroforming step creates a few local filaments whose stoichiometry is HfOx with x ≤ 1.5, as shown in Fig. 15. The missing O2− ions migrate to the Pt anode or stay in HfO2 near the anode as interstitials. As a high current passes through, the generated heat raises the local temperature and activates the O interstitials, which then recombine with the filament near the anode, causing it to rupture. At this stage, the whole device, or one particular filament, switches to its high resistance state (RESET). Notice that in our model temperature is the main reason for RESET, thus a simple thermal treatment may indeed trigger or accelerate the RESET procedure. In particular, even in the OFF-state, heating may cause further recombination of O vacancies and the remaining O interstitials within the hafnia thin film. Therefore, an incomplete RESET during normal device operation could take place since the main mechanism is thermally activated recombination. At the end of RESET, the small amount of current still flowing through does not generate enough heating to trigger further recombination. External heating, however, can induce more O vacancy–interstitial recombination, playing the role of a larger current. Therefore, external heating further increases the OFF-state resistance. This model explains the experimental results shown in Fig. 4. C. Multiple-Filament Reset The nature of the filaments has been carefully examined through conductive atomic force microscopy and highresolution transmission electron microscopy (HRTEM). Celano et al. [35] identified many filaments in one Hf/HfO2 /TiN RRAM device. More recently, Chen et al. [36] used in situ HRTEM to dynamically observe filament evolution in a Pt/ZnO/Pt RRAM, and also reported multiple filaments. These experimental findings are consistent with our measured multistep RESET shown in Fig. 1. In the ON-state,
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many filaments may simultaneously conduct, but due to their different cross sections, their conductances vary. A large cross section or low-resistance filament will first break since a stronger Joule heating occurs in its neighborhood. This explains the initial large current drop, when the most currentcarrying filament breaks. Smaller filaments require higher voltage in order to generate sufficient heat. Notice that while the rupture of the larger cross-sectional filaments takes place with increasing bias, the current flowing through the smaller cross-sectional filaments continues to increase. Their rupture leads to further decrease of the current, though in smaller steps. D. Set When a subsequent higher voltage is applied to the soft breakdown occurs in the broken filament regions, generating O vacancy–interstitial defect pairs. One or more disconnected regions of the filaments reconnect, allowing current to flow. As in electroforming, the cross section of the filaments is modulated by the compliance current, as proposed in [32]. OFF -state,
V. C ONCLUSION We have shown through experiments and ab initio simulations that the conductive state in nonpolar Pt/HfO2 /Pt RRAM cells can be explained by local suboxide HfOx filaments, where x is close to or below 1.5. The initial electroforming step not only promotes charge injection, but also stabilizes neutral O Frenkel pairs against charged O Frenkel pairs. This is important for filament formation that results from the accumulation of neutral O vacancy clusters. As the flow of electric current increases, high temperature leads to O vacancy–interstitial recombination, and thus RESETs the device. The OFF-state resistance may further increase by thermal heating, indicating that there are O interstitials available near the suboxide filaments to recombine with O vacancies present in the filaments. The multiple current steps measured during RESET support our multiple-filament model, where the low-resistance filaments are the first to rupture, followed by the rupture of smaller cross-sectional filaments at higher applied voltages. R EFERENCES [1] H. Akinaga and H. Shima, “Resistive random access memory (ReRAM) based on metal oxides,” Proc. IEEE, vol. 98, no. 12, pp. 2237–2251, Dec. 2010. [2] K.-L. Lin, T.-H. Hou, J. Shieh, J.-H. Lin, C.-T. Chou, and Y.-J. Lee, “Electrode dependence of filament formation in HfO2 resistive-switching memory,” J. Appl. Phys., vol. 109, no. 8, pp. 084104-1–084104-7, Apr. 2011. [3] J. Robertson, “High dielectric constant gate oxides for metal oxide Si transistors,” Rep. Progress Phys., vol. 69, no. 2, pp. 327–396, Feb. 2006. [4] S. Tirano et al., “Accurate analysis of parasitic current overshoot during forming operation in RRAMs,” Microelectron. Eng., vol. 88, no. 7, pp. 1129–1132, Jul. 2011. [5] H. Y. Lee et al., “Electrical evidence of unstable anodic interface in Ru/HfO x /TiN unipolar resistive memory,” Appl. Phys. Lett., vol. 92, no. 14, pp. 142911-1–142911-3, Apr. 2008. [6] L. Goux et al., “Evidences of oxygen-mediated resistive-switching mechanism in TiN/HfO2 /Pt cells,” Appl. Phys. Lett., vol. 97, no. 24, pp. 243509-1–243509-3, Dec. 2010.
XUE et al.: COMBINED AB INITIO AND EXPERIMENTAL STUDY ON THE NATURE OF CONDUCTIVE FILAMENTS
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[31] R. R. Manory, T. Mori, I. Shimizu, S. Miyake, and G. Kimmel, “Growth and structure control of HfO2−x films with cubic and tetragonal structures obtained by ion beam assisted deposition,” J. Vac. Sci. Technol. A, vol. 20, no. 2, pp. 549–554, Mar. 2002. [32] D. Ielmini, “Modeling the universal set/reset characteristics of bipolar RRAM by field-and temperature-driven filament growth,” IEEE Trans. Electron Devices, vol. 58, no. 12, pp. 4309–4317, Dec. 2011. [33] R. Waser, R. Dittmann, G. Staikov, and K. Szot, “Redox-based resistive switching memories-nanoionic mechanisms, prospects, and challenges,” Adv. Mater., vol. 21, nos. 25–26, pp. 2632–2663, Jul. 2009. [34] K. Kamiya, M. Y. Yang, B. Magyari-Köpe, M. Niwa, Y. Nishi, and K. Shiraishi, “Vacancy cohesion-isolation phase transition upon charge injection and removal in binary oxide-based RRAM filamentarytype switching,” IEEE Trans. Electron Devices, vol. 60, no. 10, pp. 3400–3406, Oct. 2013. [35] U. Celano, Y. Y. Chen, D. J. Wouters, G. Groeseneken, M. Jurczak, and W. Vandervorst, “Filament observation in metal-oxide resistive switching devices,” Appl. Phys. Lett., vol. 102, no. 12, pp. 121602-1–121602–3, Mar. 2013. [36] J.-Y. Chen et al., “Dynamic evolution of conducting nanofilament in resistive switching memories,” Nano Lett., vol. 13, no. 8, pp. 3671–3677, Jul. 2013.
Kan-Hao Xue received the B.S. and M.S. degrees in electronic engineering from Tsinghua University, Beijing, China, and the Ph.D. degree in electrical engineering from the University of Colorado, Colorado Springs, CO, USA, in 2010. He was involved in ab initio modeling of HfOx RRAM in Grenoble, France, from 2011 to 2013. He has authored and co-authored 19 articles, 12 as the first author, in international refereed journals.
Boubacar Traoré received the bachelor’s degree in electrical engineering from the University of Pretoria, Pretoria, South Africa, and the master’s degree in electronic systems from ESIEE Engineering, Paris, France, in 2009 and 2011, respectively. He is currently pursuing the Ph.D. degree at CEA-LETI, Grenoble, France, researching resistive RAM.
Philippe Blaise, photograph and biography not available at the time of publication.
Leonardo R. C. Fonseca received the Ph.D. degree in applied mathematics from the State University of New York at Stony Brook, Stony Brook, NY, USA, in 1996. He was with Motorola Semiconductors engaged in research on field emission flat displays and high-K dielectrics. He is currently an Associate Researcher with the University of Campinas, Campinas, Brazil. His current research interests include first principles simulations of devices and materials.
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Elisa Vianello received the Ph.D. degree in microelectronics from the University of Udine, Udine, Italy, and the Polytechnic Institute of Grenoble, Grenoble, France, in 2009. She has been a Scientist with the Advanced Memory Technology Laboratory, CEA-LETI, Grenoble, since 2011.
Gérard Ghibaudo (F’13) received the Ph.D. degree in electronics and the State Thesis degree in physics from the Grenoble Institute of Technology, Grenoble, France, in 1981 and 1984, respectively. He entered the Centre National de la Recherche Scientifique, France in 1981 and is now Director of Research. His current research interests include electronic transport, oxidation of silicon, MOS device physics, fluctuations, low-frequency noise, and dielectric reliability.
Gabriel Molas received the Ph.D. degree in nanoelectronics in 2004. He joined LETI, Grenoble, France, as a Research Engineer in 2004. Until 2011, he was involved in the processing and integration of innovative charge trap memory devices. In 2011, he moved to resistive RAM, including CBRAM and OXRAM.
Blanka Magyari-Köpe (M’06) received the Ph.D. degree in physics from the Royal Institute of Technology, Stockholm, Sweden, in 2003. She is currently a Senior Research Engineer with the Department of Electrical Engineering, Stanford University, Stanford, CA, USA. Her current research interests include understanding the RRAM switching mechanism, and on the atomic control of nanointerfaces among metallic, insulating, and semiconducting materials.
Barbara De Salvo received the Ph.D. degree in microelectronics from the Polytechnics Institute of Grenoble, Grenoble, France. She managed the Advanced Memory Technologies Laboratory at LETI, Grenoble, from 2008 to 2013. She is currently involved in the development of 10-nm and beyond fully depleted SOI CMOS technologies with IBM, Albany, NY, USA, as a LETI Assignee.
Yoshio Nishi (LF’87) received the Ph.D. degree in electronics engineering from the University of Tokyo, Tokyo, Japan. He is a Professor of Electrical Engineering with Stanford University, Stanford, CA, USA. His current research interests include nanoelectronic devices and physics for resistive change memory, and new device structures and materials.
