Extrinsic Dopant Effects on Oxygen Vacancy Formation Energies in

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Extrinsic Dopant Effects on Oxygen Vacancy Formation Energies in ZrO2 with Implication for Memristive Device Performance Handan Yildirim, and Ruth Pachter ACS Appl. Electron. Mater., Just Accepted Manuscript • DOI: 10.1021/acsaelm.8b00090 • Publication Date (Web): 29 Mar 2019 Downloaded from http://pubs.acs.org on March 29, 2019

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ACS Applied Electronic Materials

Extrinsic Dopant Effects on Oxygen Vacancy Formation Energies in ZrO2 with Implication for Memristive Device Performance Handan Yildirim* and Ruth Pachter* Air Force Research Laboratory, Materials and Manufacturing Directorate, Wright-Patterson Air Force Base, Ohio 45433, USA

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*Corresponding authors: [email protected] [email protected] ACS Paragon Plus Environment

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ABSTRACT

Despite much progress in development of oxide-based resistive random-access memory (ReRAM) devices that have an inherent memory, and advantages in increased speed of operation, higher density, nonvolatility, ease of integration, and low power, many challenges remain, particularly relating to conductive filament (CF) formation and rupture, and associated device uniformity. Oxygen vacancies (Vos) play an important role for both the valence change memory (VCM), based on formation and rupture of Vo or oxygen ion-mediated CFs, and the electrochemical metallization mechanism (ECM), in which a metallic CF is formed by the cations of an active electrode. In this work, to provide guidelines for ReRAM device improvements, we investigated the role of dopants within the ZrO2 resistive switching layer. Density functional theory calculations for twenty dopants, which span a range of electron configurations, valence, and atomic radii, identified a preference towards either substitutional or interstitial doping, useful for considering VCM or ECM cells, respectively. The propensity towards reduction of Vo formation energies (OVFEs) to improve device performance was elucidated for all dopants, and found to be in good agreement with available experimental data, validating our predictions for dopant selection. Moreover, significantly reduced dopant formation energies were calculated in the presence of Vos for interstitially doped Ni, Cu, and Ag atoms, suggesting their facile incorporation into ZrO2 from the electrode, which can enhance the formation of metallic CFs in ECM cells. The concept of devices based on such a hybrid mechanism, can improve performance of ECM cells. We also found that the dopants affect OVFEs locally, enhance clustering of Vos near dopants, and enable spatial control of the conducting pathways. Finally, our electronic structure analyses, which provide information on the generation of mid-gap states, can motivate experimental analysis of the transport mechanism in the device.

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Keywords: Resistive random access memory (ReRAM), Oxygen vacancy formation energy, Ion doping, bulk ZrO2, Density Functional Theory (DFT), Resistive Switching (RS) uniformity. Introduction Memristive devices could offer significant advantages in comparison to existing memory systems by providing increased speed of operation, higher density, nonvolatility, ease of integration, and low power.1 Specifically, metal-insulator-metal sandwich-like stacks with a switching oxide between the electrodes that operate by ionic carriers, exhibit resistive switching (RS) in resistive random-access memory (ReRAM) devices. The underlying mechanism of operation in these devices varies, depending on the oxide layer and the electrodes, however oxygen vacancies (Vos) were shown to play an important role.2-3 In valence change memory (VCM) cells, RS is attributed to the formation and rupture of Vobased conductive filaments (CFs), while for electrochemical metallization mechanism (ECM) cells, RS is manifested by a conductive bridge formation and dissolution of cations of the active electrode. Yet, even though a basic understanding of RS has been established, many challenges in development of ReRAM devices remain,4 including non-uniformity of RS parameters, high switching voltage, low cycling endurance, and overall poor device uniformity.5 Current devices often suffer from large variation in the switching voltage that results from random growth/rupture of the CFs, which causes difficulty in the formation and rupture along the same path in each cycle. Improving the uniformity of operation voltage demands controllable mechanisms for CF growth. In addition, simplification of RS by eliminating the electroforming step is also desirable. Among binary oxides, HfO2 emerged as a promising candidate (e.g. see references6-7 and references therein) for ReRAM applications, and improved performance was demonstrated upon doping. Indeed, ion doping has been attracting increasing attention for modulating and improving ReRAM device performance. Experimental methods for doping include ion implantation, co-sputtering, or atomic layer deposition (ALD), which can affect ReRAM characteristics. For example, while co-sputtering results in a uniform distribution of dopants, ALD results in more localized regions of dopants. Efficient doping ACS Paragon Plus Environment

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can also be achieved by ion implantation with a proper choice of implantation dose and energy, so that the distribution and concentration of ions can be controlled. Gd-doped HfO2 resulted in improved ReRAM performance due to the suppressed randomness of the CFs, and a reduced oxygen migration barrier.8 For Au- and N-doped HfO2,9-10 a high resistance ratio, reliable data retention, and switching uniformity were established, resulting from suppressed stochastic formation of CFs. Among the Al-, Cu, and N-doped devices of HfO2,11 the Cu-doped device showed the best performance, and differences were explained by the formation of different types of CFs. Al- and Ti-doping of HfO2 was reported.12-13 It has also been shown that the performance was improved for a HfO2-based CBRAM (conductive bridging RAM) device with a Cu top electrode upon introduction of Vos, which facilitated the formation of Cu filaments.14 In addition, Al-, Cr-, and Cu-doped TiO2 showed a better switching uniformity and a lower set voltage due to enhanced Vo generation,15 also revealing that dopant effects can be tuned by the valence state of doped ions. N-doped Ta2O516 illustrated small SET/RESET voltages with reduced variations, and Si-doping promoted Vo formation and transport, giving rise to high endurance.17 Aldoped CeO218 demonstrated improved performance due to enhanced Vo generation, while systematic modulation of the concentration and mobility of the ionic carriers was reported for Gd-doped CeO2.19 Overall, ion doping can reduce variations of RS parameters, such as forming/SET voltages and resistance in the OFF state, and also eliminate the electroforming step. Doped devices exhibit improved device performance, with high device yields, low operating voltages, fast speed, large ON/OFF ratios, long retention time, and cycle/device uniformities. At the same time, interestingly, ZrO2,20 a wide band gap semiconductor, which has properties similar to those of HfO2, was less studied, although found suitable as an active layer in ReRAMs, attributed to its high dielectric constant, excellent electrical/chemical stability, and CMOS compatibility.21-24 We note that the main difference between Zr and Hf is that Zr has no f electrons, while Hf has a 4f subshell. The two elements have very similar atomic radii due to lanthanide contraction, but different electron affinities.25 In addition to VCM cells involving sub-stoichiometric ZrO2, ZrO2-based devices also include Cu/ZrO2/Pt, for which an ECM cell was identified with an active Cu electrode, and by ACS Paragon Plus Environment

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controlling the current compliance, volatile to nonvolatile RS conversion was demonstrated.26 An ECM mechanism was also found for Ni/ZrO2/TaN,27 with Ni as the top electrode in the CBRAM device,23 as well as for Ag/ZrO2/Pt.22 Doping has proven useful for a Cu/ZrO2/Pt memory cell, demonstrating a high resistance ratio, high speed of operation, and long retention time.28 Ti doping29 of ZrO2 removed electroforming, and variations in RS parameters were reduced by increasing Vo generation, while Gd-, Y-, Dy-, and Ce-doped ZrO2 devices30-31 also showed that trivalent ion-doped films have forming-free behavior due to an increased Vo concentration. However, understanding the chemistry and thermodynamics of dopants that could impact RS in ZrO2based ReRAMs is still lacking. First principles studies provide atomistic-scale insights, which are not always obtainable in experimentally deposited films that can have multiple defects and dopant interactions with vacancies and impurities, yet such studies are scant for ZrO2.32 On the other hand, investigations on dopant effects by density functional theory (DFT) were reported for HfO2,33-37 and also for other oxides, e.g. TiO2,38 and Ta2O5,39 where p-type dopants were predicted to promote lower forming voltages and improve retention properties. Effects of p-type doping on CF formation in HfO2 were reported,33 and Al-, Si-, and Ti-doped HfO2 was also studied,34 showing that only the nonstoichiometric oxide decreases the forming voltage. To potentially achieve improved performance of ZrO2-based ReRAMs upon doping, our goal in this work is to explore the effects of doping by DFT calculations. Following the investigation of dopant formation energies (DFEs), the effects of dopants on oxygen vacancy formation energies (OVFEs) were analyzed. DFT calculations were performed using a large set of dopants. The choice of dopants was based on the previous experimental studies of doped ZrO2, significantly expanding the dopant choices to ensure that they span a wide range of electron configurations, valences, electronegativities, and atomic radii, which provide chemical diversity for examining differences. DFEs of dopants in close proximity to Vos demonstrate a significant decrease, which can imply facile incorporation into the ZrO2 switching layer, enabling easier formation of cation-based CFs in CBRAM cells. Reduction in OVFEs in doped ZrO2 was demonstrated in all cases, but the magnitude of the variation differs, as dependent on the ACS Paragon Plus Environment

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dopant’s attributes, enabling guidance towards dopant selection for improvement of the characteristics of ECM or VCM type ZrO2-based ReRAMs. Electronic structure calculations revealed the generation of impurity states upon doping, which can provide insight into the electron transport mechanism in the device. Methods and Computational Details All calculations were performed using the Vienna ab-initio simulation package,40 applying the projector augmented-wave method to treat core and valence electrons. A plane wave energy cut-off of 520 eV was used in the spin-polarized calculations. Zr_sv and O pseudopotentials were employed (pseudopotentials used for each dopant are summarized in Table S.1.). Integration of the Brillouin zone was done with 4x4x4 and 2x2x3 k-point meshes for 2x2x2 (96 atoms) and 3x3x2 (216 atoms) supercells, respectively. Size effects on the formation energies showed minimal impact; therefore, all calculations were performed using the 2x2x2 supercell (Zr32O64). Atomic positions were relaxed until the Hellmann-Feynman force converged to within 0.01 eV/Å. Among the three common phases (monoclinic, tetragonal, and cubic) of bulk ZrO2, the monoclinic phase (m-ZrO2) is the most stable at room temperature and atmospheric pressure, as was also demonstrated theoretically,41 and was investigated in this study. To determine the appropriate exchangecorrelation functional to be used, a comparison of the lattice parameters and band gaps using several functionals was performed. The generalized gradient approximation (GGA) Perdew-Burke-Ernzerhof (PBE)42 and PBEsol,43 inclusion of a Hubbard-type on-site Coulomb correction,44 the hybrid functionals B3LYP45 and PBE0,46 as well as the range-separated hybrid Heyd-Scuseria-Ernzerhof (HSE06) functional,47 were considered. The results of the lattice constants and band gaps for undoped ZrO2 are summarized in Table 1 and Figure S.1. The hybrid functionals provided a benchmarking set for evaluating the performance of PBE, PBEsol, PBE+Ud, and PBE+Ud+Up results. The DFT+U approach was used first, with the correction applied to Zr 4d states only, using either Ueff (= U-J) of 4 eV or 8 eV with J=1 eV. Additionally, to account for localized O 2p hole states for low valence doped (substitutionally) metal oxides, the correction was also introduced to O 2p states. We used a Up value of ACS Paragon Plus Environment

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7 eV, which was found applicable for Al-doped SiO2 and Li-doped MgO for O 2p states along with the correction to Zr d states using a Ud value of 8 eV.48 We found that the PBEsol lattice parameters are in better agreement with experiment (< 1% for the lattice parameters a, b, and c) than PBE. The PBE+Ud calculations demonstrated that increasing Ueff enhanced the lattice parameters, but even for Ueff=4 eV, the values deviate both from experiment (3.03%, 1.98%, and 2.96%) and PBEsol results (2.56%, 1.68%, and 2.18%), for a, b, and c, respectively. Lattice parameters obtained using PBE0 and HSE06 were found to be close to the experimental values by 0.7%, 0.3%, and 0.99% for a, b, and c, respectively, while B3LYP predicted slightly larger lattice parameters (1.64%, 0.99%, and 1.96%), similar to those of PBE. Results using PBEsol demonstrated very similar values to those using PBE0 and HSE06 (see Figure S.1.), within 0.2%, 0.02%, and 0.15%. The PBEsol functional was therefore used for all calculations, but for the assessment of the effects of the exchange-correlation functional on the formation energies, we performed additional calculations using Hubbard U correction and B3LYP. To benchmark band gap predictions, we compared with the optical gap measured for m-ZrO2 by UVVIS for undoped stoichiometric ZrO2, of 5.09 eV.49 A fundamental band gap of 5.83 eV was reported using vacuum-ultraviolet (VUV) spectroscopy,50 which is consistent with electron energy loss spectroscopy (EELS) measurements.51 Calculated band gaps (see Table 1 and Figures S.1. and S.2.a) show that the PBE and PBEsol results of about 3.5 eV are underestimated, as expected due to the use of GGA functionals, agreeing with earlier reports (3.4-3.47 eV, 4.22 eV, see Table1). The values increase with the Hubbard U correction (3.94 eV, 4.39 eV for Ueff (Ud) =4 eV and 8 eV, respectively, and 4.56 eV for Ud=8 eV and Up=7 eV), however still smaller than the measured band gaps. As expected, the band gaps are improved when using hybrid functionals, namely of 5.04 eV, 5.30 eV, and 5.83 eV, using HSE06, B3LYP, and PBE0, respectively. The electronic density of states (DOS), decomposed by electron spin and atomic orbitals, were calculated using PBEsol, PBE+Ud, and also with B3LYP, a hybrid functional that resulted in an intermediate band gap, and provided the correct order for ZrO2 phases (vs. PBE0) in previous work,52 although the lattice parameters were less well reproduced (see ACS Paragon Plus Environment

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Figure S.1.). The results indicate that the upper valence band (VB) largely consists of O 2p character and the lower part of the conduction band (CB) is mostly composed of Zr 4d states. The VB top and CB bottom were similar for all functionals, including PBE0 and HSE06. Results and Discussion Cation Doped Stoichiometric ZrO2 – Dopant Formation Energies: To evaluate the propensity of mZrO2 towards doping, twenty cation dopants with varying electron configuration, valence, atomic radius, and Pauling electronegativity were considered, and based on valence electron numbers, they are classified as strong n-/p-type, weak n-/p-type, and isovalent dopants (see Table 2). A low doping concentration was assumed, therefore ensuring that the effect on structural changes is negligible. In addition to the most common substitutional doping configuration, the dopants considered may also occupy interstitial lattice positions, and we therefore explored both types of doping. In addition to substitutional doping at the Zr4+ site, interstitial doping was investigated by placing the dopant at predefined four initial interstitial sites, as determined by the lattice symmetry (see Figure 1.a). DFEs are calculated by Edop_form (M ~ Zr) = EM ~ ZrO2_dop - EZrO2_undop+µZr - µdopant

(substitutional doping)

(1),

(interstitial doping)

(2),

and Edop_form (M+ZrO2) = EM+ZrO2_dop -EZrO2_undop - µdopant

where the first and second terms on the right side of the equation are the energies of doped and undoped ZrO2, respectively, and µZr and µdopant are the chemical potentials/atom for Zr and dopant, respectively, calculated using the most stable bulk phases. By ranking the total energies and analyzing the structures for Cu- and Ni-doped ZrO2, the number of interstitial doping sites was reduced to two, e.g. sites P1 and P2 (Figure 1.a-b), which were then used to calculate DFEs for the remaining 18 dopants. Note that a thorough examination of the most stable sites for interstitial doping for each dopant might be useful, however, this is not only beyond the scope of this study, but also, the most probable/stable way for doping oxide films for ReRAM applications is likely through substitutional doping. Therefore, the role of interstitial doping calculations, which is based on two interstitial sites, is sufficient to explore any ACS Paragon Plus Environment

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effect they have on Vo formation energies as compared to substitutional doping. The energy difference between P1 and P2 was 0.25 eV and 1.04 eV for Cu and Ni doping, respectively, with P1 the more stable configuration. In the following, we primarily discuss the results for the P1 site. Size effects on DFEs were evaluated by considering 2x2x2 and 3x3x2 supercells, which indicated a minimal effect (see Figure S.3.a), and the 2x2x2 supercell was used henceforth. DFEs for substitutional and interstitial (P1) doping were also evaluated using PBE+Ud+Up, but the results showed qualitatively similar trends (Figure S.4.a-b). Differences in DFEs using PBE+Ud+Up vs. PBEsol are more pronounced for interstitial doping, which likely results from structural differences, but overall, the results illustrate that PBEsol captures the trends of the PBE+U results.Additionally, to examine any potential effect on doping trends of the dopant’s chemical potential (µdopant in Equation 2), which depends on an arbitrary reference state, we calculated relative formation energies by Erelative = Etot interstitial – (Etot substitutional - µZr)

(3),

where the first and second terms on the right side of the equation are the total energies of the supercell with a dopant placed at an interstitial or substitutional site, respectively and µZr is the chemical potential of Zr in m-ZrO2. Calculated DFEs for substitutional and interstitial doping (Equations 1 and 2) using PBEsol are summarized in Figure 1.c, and the values are listed in Figure 1.d. Interstitial doping is more favorable for both strong p-type (alkaline earth Mg, Sr, and Ba) and n-type (Cu, Ag, and Ni) dopants. ΔDFEs (defined as the difference between the formation energy of substitutional and interstitial doping) are 4.84 eV, 2.46 eV, 1.66 eV for Mg, Sr, and Ba, respectively, and 8.77 eV, 7.99 eV, 7.09 eV for Ni, Cu, and Ag, respectively. The results vary to some extent by using other functionals (see Figure 1.d. and the caption for description of the functionals), however the general trend is consistent with the PBEsol values. The calculated DFEs (see Equation 2) for interstitial doping by strong p-/n-type dopants demonstrate an increasing order as Mg>Sr>Ba, and Ni>Cu>Ag, respectively, dependent on the atomic radius and electronegativity trends within the same group, where more electropositive dopants result in a lower interstitial DFE. A larger electronegativity, combined with the smallest atomic radius among the ACS Paragon Plus Environment

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weak p-type dopants, may have contributed to preference of the Al dopant towards interstitial doping (ΔDFE of 1.58 eV), and similarly for Sc with ΔDFE of 0.4 eV. Indeed, interstitial doping preference can be correlated with the atomic radius. On the other hand, among the same dopant group, Y, Gd, and La have a strong preference towards substitutional doping (ΔDFEs 1.0-1.6 eV). Dopant-O bonds are 2.07 Å, 2.18 Å and 2.20 Å for Sc, Y, and Gd, respectively, suggesting that Sc-O bonds are similar to those of undoped ZrO2, causing only small lattice distortions, while these bonds for Y and Gd are slightly larger. Within this category of dopants, the DFE for La-doped ZrO2 is higher (3.18 eV) than for the other dopants, as it has the largest radius, and lengthened La-O bonds, of 2.24 Å-2.26 Å (see Table S.2.). All the isovalent dopants studied have a preference towards substitutional doping, with DFEs smaller than 2 eV, except for Si (see Figure1.d.). Hf- and Ce-doped ZrO2 indicate the strongest substitutional doping preference, with ΔDFE ~ 4 eV, while the Ti-dopant has slightly larger DFEs. The DFE for Hfdoped ZrO2 is -0.66 eV, as Hf and Zr are similar elements, resulting in small structural changes upon doping (see Table S.2). The bond lengths between Hf and the two nearest oxygens (2.06 Å-2.05 Å) are closest to those of undoped ZrO2 (2.08 Å-2.07 Å). These bond lengths are 1.77 Å-1.74 Å for Si-doped ZrO2, showing appreciable distortion, similar to the distortion caused by the Al dopant (Table S.2). Si is the least favorable dopant among this group for substitutional doping, attributed to a combination of a relatively larger electronegativity and much smaller atomic radius. The Ce dopant has the second lowest DFE (0.43 eV), with the largest radius among the group, having Ce-O bonds of 2.14 Å-2.16 Å, somewhat larger than those of undoped ZrO2. Relative formation energies (Erelative in Equation 3) vs. dopant type are shown in Figure 1.e. (Erelative > 0 and Erelative < 0 refer to energetically favorable substitutional or interstitial doping, respectively). These results allow us to exclude the effect of the dopant’s chemical potential on doping preference (Figure 1.d). We note that both strong p- and n-type dopants prefer interstitial doping, and the largest relative formation energies are calculated for Hf and Ce, suggesting that for cases where the dopant’s valence is close to that of the host metal, a stronger tendency for substitutional doping occurs. Effects of ACS Paragon Plus Environment

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atomic radii on doping preference is also evident within a given dopant group (see Table 2 and Figure 1.e). To analyze the formation of impurity states in the forbidden gap upon doping, in particular for substitutional doping, electronic structures of doped ZrO2 were calculated at the PBEsol level. The total and dopant-projected DOS for isovalent, p-type, and n-type doped ZrO2 are summarized in Figure 2.a, 2.b, and 2.c. Contributions from Zr and O states to the DOS are shown in the left panel, and for the dopants in the right panel. Among the isovalent dopants (see Figure 2.a), the DOS show that for Si and Hf, the total DOS are similar to those of undoped ZrO2, with no impurity states in the forbidden gap (the Fermi level stays on top of the VB as in undoped ZrO2). The results are consistent with those using B3LYP (Figure S.5.a). For Ti, a small impurity state at about 2.8 eV above the Fermi level appears, mostly contributed by Ti (right panel), with a very small contribution from Zr and O (left panel). Cedoped ZrO2 however, indicates appearance of an impurity state above the Fermi level at approximately 2.3 eV, contributed primarily by O states, but also by Zr states. The dopant also contributes to the impurity state in this case, but its contribution is lower. These substitutionally stable dopants contribute mainly to the CBM (CB maximum), similar to undoped ZrO2, for which the CBM is mainly made of Zr states. A Bader53 charge analysis for undoped ZrO2 resulted in a charge of 9.45e on Zr, and 7.24e and 7.30e for the two O with 3-/4-fold coordination. For the Hf-doped structure, charges on the nearest neighbor (nn) O to the dopant are slightly reduced to 7.20e and 7.28e, suggesting a minimal change. For Ti- and Ce-doped ZrO2, the charges were reduced to 7.25e and 7.11e, and 7.26e and 7.19e, respectively, demonstrating a noticeable impact on the charge distribution, namely the local electronic structure, however the change is smaller for Si, with 7.23e and 7.42e, dependent on the local bond distribution of Si with nn O. The contribution from p-type dopants to the total DOS for (Figure 2.b) is mostly at the VBM (valence band maximum) region, originating mainly from O states. Two impurity states crossing over the Fermi level appear for Ba-doped ZrO2, contributed mostly by O states (left panel), as well as Ba states (right panel). Ba doping leads to reduction of the nn O charges to as low as 7.03e, with charges reduced to ACS Paragon Plus Environment

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7.14e and 7.03e for Mg- and Sr-doped ZrO2, respectively. The DOS for Al-, Sc-, Gd-, and La-doped ZrO2 show half metallicity, with the VB for one spin orientation partially filled, but there is a gap for the other spin orientation. The DOS obtained using PBEsol for Al-doped ZrO2 are similar to those calculated with the B3LYP functional (Figure S.5.a). For all these dopants, reduction in the O nn charges is minimal (7.21e). Conversely, for n-type dopants (Figure 2.c), the DOS show that the Fermi level moves up into the band gap, particularly for V, Nb, Ta, Cr, and Mo, and the impurity states lie within the band gap below the CB. The DOS also illustrate that generally, impurity states that appear close to the CBM are for dopants with a higher valence, whereas for dopants with a lower valence, these states tend to move to lower energies, close to the VBM. For V-, Nb-, Mo-, Cr-, and Ta-doped ZrO2, the impurity states appear within the gap close to the CBM, contributed mainly by dopant states, along with some contributions from both O and Zr states. Similarly, for Cu, Ag, and Ni dopants, the impurity states are in mid gap and close to the VBM, contributed by dopant states, as well as with some contributions from O and Zr states. For Ag-, Cu-, and Ni-doped ZrO2, nn O charges are reduced to as low as 7.0e, while for the V-, Nb-, Ta-, Mo-, and Cr dopants, the values are 7.12e, 7.20e, 7.17e, 7.17e, and 7.12e, respectively. Based on the interplay between the electron configuration of the dopants, valence electrons, and atomic radius, which can cause local distortions, the resulting order of doping preference towards substitutional doping is Hf > Ce > Ti > Y > Gd > Ta > Nb > La > Si, and for interstitial doping the order is Sc > Mg > Ni > V > Al > Cr > Cu > Mo > Sr > Ag > Ba. Dopants in bold indicate DFEs of 2.5 eV or less. Dopants preferring substitutional doping could be favored for ReRAM devices that exhibit a VCM mechanism, e.g. upon Ce, Ti, Y, or Gd doping, while dopants that favor interstitial doping could facilitate an ECM mechanism, e.g. Ag, Cu, and Ni. Indeed, in addition to the formation of a Cu filament in a Cu/ZrO2/Pt cell, generation of a Ni filament was demonstrated for a Ni/ZrO2/TaN device, prior to annealing and incorporation of oxygen defects.27 This observation supports our result on interstitial doping preference for Ni, and may also imply that for cases where Vos are incorporated postprocessing, filament formation is facilitated. Indeed, in an experimental study for HfO2-based CBRAM ACS Paragon Plus Environment

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with a Cu top electrode, a substantial improvement was established during post-HfO2 deposition annealing in vacuum, which was attributed to the considerable amount of Vos that reduced the energetic cost for Cu insertion, thereby facilitating the formation of Cu filaments.14 Our calculations also suggest that doping of the switching layer with dopants that lower the OVFEs, can ease filament formation by facilitating cation incorporation from the electrode into the oxide layer. Considering these observations, nn Vo effects on DFEs (interstitial (P1)) were calculated for Cu, Ag, and Ni, which can lead to CF formation in CBRAM devices. A single Vo (4-fold site) was first introduced into the oxide, and in the optimized structure the dopant (at P1 site) was brought next to Vo as the 1st nn, because it is the most stable structure. We then calculated the DFEs for this configuration. Following that, a second Vo was introduced into the 4-fold site, and the dopant was brought as the 1st nn to both Vos, and the DFE was calculated. The resulting DFEs of Cu, Ag, and Ni dopants with Vo presence in comparison to doped stoichiometric ZrO2 are summarized in Table 3, demonstrating noticeable decreases with Vo presence nearby each dopant. The changes in DFEs were similar for Cu and Ag, but larger for Ni. These results, therefore, confirm the experimental observations that increased Vos in the resistive switching layer will enhance the insertion of cations, as demonstrated for the Ni/ZrO2/TaN system, prior to annealing and incorporation of oxygen defects.27 Cation Doped Non-stoichiometric ZrO2 – Oxygen Vacancy Formation Energies: Doping of the switching oxide layer can improve ReRAM device performance by tuning the formation energy, concentration, distribution, and drift/diffusion of Vo defects that assist in forming the CFs, as dependent on the underlying mechanism of ReRAM device operation. During the electroforming step, the applied field reduces the OVFEs, which leads to an increase in Vo concentration in the switching layer before the conductive path forms. Therefore, the forming voltages applied to generate Vo will be affected by the OVFE values. The stoichiometry can be monitored and controlled during doping, or by postprocessing. To provide dopant selection strategies for determining the optimal dopants for ZrO2-based memory cells, OVFEs were calculated for all the dopants considered. The OVFEs were calculated for an undoped supercell as the reference by ACS Paragon Plus Environment

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EVo_undop_form = EwVo_undop - EPrist_undop + µO

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(4),

where the first and second terms on the right side of the equation correspond to the total energies of undoped ZrO2 with and without Vo, respectively. The oxygen chemical potential was taken to be half of the total energy of a free, isolated, spin polarized O2 molecule in the triplet state, namely μO (= ½ E(O2)). The effect of dopant-Vo distances on the OVFEs was investigated by placing the dopant at the 1st nn site to Vo, and also furthest away from it. For most dopants, the closest dopant-Vo configuration was most favorable (except for two cases with a small difference), and therefore adopted in all calculations (see Table S.3.). The OVFEs and the position of Vo defect states with respect to the VBM in undoped ZrO2 are summarized in Table S.4. The supercell size effect on the OVFEs was also evaluated for a few select dopants, by using a 3x3x2 supercell. Similar trends were obtained, with deviations of less than 0.1 eV. The same trends also hold for OVFEs obtained using PBE+Ud and B3LYP (see Figure 3.d). The OVFE values for a 4-fold (3-fold) coordinated Vo were 6.29 eV (6.16 eV), with the former more stable by 0.13 eV. Therefore, the OVFEs were evaluated for 4-fold Vo in all cases. By using the PBE+Ud (Ueff =4 eV, and 8 eV) and B3LYP functionals, values of 6.48 eV, 6.62 eV, and 6.33 eV, were obtained, respectively. DOS for undoped ZrO2 with a 4-fold Vo using PBEsol, PBE+Ud, and B3LYP are summarized in Figure S.2.b. Appearance of new states in the forbidden gap that correspond to Vo is noted, having a doubly occupied one-electron energy level deep in the forbidden gap, strongly localized at the vacancy site, formed mostly by Zr states. The electrons can hop between these localized defect states that may contribute to the conduction in the ReRAM device. Projected DOS for Zr suggest that reduced Zr mainly contributes to the CB tail. The mid-gap states hybridized between Zr 4d and O 2p consist mostly of d orbitals. For doped ZrO2, the OVFEs were calculated for a neutral 3-/4-fold coordinated Vo that is introduced as the 1st nn of the dopant (see Figure 3.a) by EVo_dop_form = EwVo_dop - EPrist_dop + µO

(5),


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where the first and the second terms correspond to the energies of doped supercells with and without Vo, respectively. The results of the OVFEs are summarized in Figure 3.b-c (values are listed in Figure 3.d). All calculated OVFEs in the presence of dopants were found to decrease more strongly for substitutional than for interstitial doping, with the degree of reduction dependent on the dopant’s attributes. Interestingly, strong p-n/-type dopants, which have preference towards interstitial doping, in stoichiometric ZrO2, cause a significant decrease in the OVFEs (ΔOVFE, relative to the stoichiometric ZrO2 value of 6.29 eV), with values up to 4.5 eV (Mg > Sr > Ba > Ni > Cu > Ag), where Mg shows the largest reduction of 5.8 eV. Substituting Zr4+ with p-type dopants creates an electron-deficient region in the ZrO2 lattice, where the holes will receive electrons from nearby oxygen ions, which can be oxidized to an oxygen atom. The local electron deficiency can also weaken the metal-oxygen bonds in this case, and facilitate energetically favorable Vo formation. When the OVFEs decrease significantly, as is the case for strong p-type dopants, the interplay between OVFE decrease and RS efficiency is to be considered. The substitutional doping of the alkaline-earth dopants with very low OVFEs (≤ 1 eV), for example, may suggest spontaneous formation of such phases as MgZrO3, SrZrO3, and BaZrO3, but even if no phase change is induced, Vos could stay tightly bound to the dopants, possibly forming non-switchable conducting pathways. On the other hand, a study on switching characteristics of Mg-doped HfO2 with varying Mg concentration showed a decrease in the forming voltage, improvement in device repeatability, and increased conduction, attributed to the increase in Vo concentration as a result of Mg2+ substitution of Hf4+.54 Similarly, increase in ion conductivity was also reported for ZrO2 stabilized with low valence oxides, e.g. MgO, CaO, and Y2O3.55 These can motivate further experimental validation in using these dopants to improve ZrO2-based memory cells. In comparison to the strong p-type dopants, the reduction in OVFEs is generally lower for weak ptype dopants due to the difference in the degree of perturbation induced in the electronic structure, leading to reduced OVFEs of ~ ½ of that of the undoped oxide. Our results are consistent with ACS Paragon Plus Environment

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measurements for Al-doped ZrO2, where the forming voltage distribution was found narrower in the doped oxide, and uniformity was improved. The smallest change in OVFEs upon substitutional doping is shown for isovalent and weak n-type dopants. The least effective dopants in reducing OVFEs are Hf and Ce, having the same valence as Zr, and very similar atomic radii to Zr, hence minimal perturbation upon substitution. ΔOVFEs (up to 1.5 eV) were calculated for Ce (0.5 eV) > Ta > Nb > Ti > Hf > V > Mo that are either isovalent or weak n-type dopants, and the remaining dopants exhibit an intermediate change. Experimentally, complete removal of the electroforming step as a result of enhanced Vo concentration for Y-, Gd-, and Dy-doped ZrO2 was demonstrated,31 while for Ce-doped ZrO2 films, the uniformity of the CF during the forming process increased by mitigating further oxygen vacancy generation,30 and the device required electroforming,31 consistent with our results. Changes in the electronic structure of doped ZrO2 with a neutral Vo are summarized in Figure 4.a, 4.b, and 4.c. The DOS for isovalent dopants (Figure 4.a) illustrate that the Fermi level moves up into the band gap, and an occupied defect level appears, similar to undoped ZrO2 with a neutral Vo. Defect states are mostly contributed by Zr near Vo in all cases. Corresponding results using the B3LYP functional for Al and Hf doping (Figure S.5.d) are similar to those of PBEsol. For Ti- and Ce-doped ZrO2, in addition to the defect state observed at the Fermi level (also contributed by dopant states in all cases), there are additional impurity states above the Fermi level close to the CBM. For weak p-type dopants, the Fermi level moves up into the band gap, except for Al-doped ZrO2 (B3LYP provides similar results, see Figure S.5.c). For the strong p-type dopants Mg, Sr, and Ba, defect states appear within the band gap near the CB (Figure 4.b), mainly contributed by Zr, but also by the dopants. Vo defect states appear at the Fermi level and above it, close to the CBM. These states are mostly contributed by Zr and the dopants. When p-type dopants reside near a neutral Vo, which leaves two excess electrons and compensate the dopant, vacancy defect states in the band gap are not fully occupied. For n-type dopants with a neutral Vo as the 1st nn (DOS in Figure 4.c), the Fermi level moves up into the band gap, and defect states that were mostly located near the CB region are now split, occupying both the upper and lower (occupied) part of the band gap. The upper part of the spectrum is ACS Paragon Plus Environment

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mainly contributed by Zr states that are near Vo, while the lower part mostly governed by the contribution from the dopant states.

Conclusions In summary, our computational investigation on the effect of dopants on ZrO2-based ReRAMs demonstrated agreement with available experimental data, thus validating guidance for device performance improvement. Analysis of stoichiometric ZrO2 revealed differences between the DFEs for substitutional vs. interstitial doping, dependent on the electron configuration and atomic radius, with an ordering of Hf > Ce > Ti > Y > Gd > Ta > Nb > La > Si, and Sc > Mg > Ni > V > Al > Cu > Cr > Mo > Sr > Ag > Ba, respectively. These results can guide dopant selection for facile incorporation within ZrO2, dependent on the type of RS mechanism considered. Dopants that prefer substitutional doping could be suitable for ReRAMs that exhibit a VCM mechanism, e.g. upon Ce, Ti, Y, or Gd doping, while dopants that favor interstitial doping could facilitate an ECM mechanism. Importantly, to select optimal dopants for achieving ReRAM device improvement, these results have to be combined with an assessment of the propensity towards OVFE reduction. The reduction in OVFEs was the largest for substitutionally doped strong p- and n-type dopants, specifically Mg > Sr > Ba > Ni > Cu > Ag, due to changes in the electronic structures, while interstitial doping does not lead to significant change in OVFEs. For both substitutional and interstitial doping, the smallest change in OVFEs was encountered for isovalent and weak n-type dopants. Additionally, we argue that generation of Vos in the oxide layer either by introducing dopants that lower the OVFEs or through changing oxide growth conditions, can facilitate cation-based CF formation for CBRAM cells. We confirmed this suggestion by demonstrating that DFEs for interstitially doped ZrO2 with Ni, Cu, and Ag in the presence of Vos are significantly reduced. Therefore, we conclude that the concept of a hybrid CBRAM device, assisted by generation of Vos in the switching layer, can improve device performance. For VCM cells, Mg doping, a strong p-type dopant, can also be considered for improvement, and has proven useful in a ACS Paragon Plus Environment

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HfO2-based device.54 However, very low OVFEs, e.g. less than ~ 1 eV, may lead to spontaneous formation of new phases, dopant-Vo complexes, or trapping of Vo, which could limit the kinetics of recombination, successive switching and formation of non-switchable conducting pathways, providing an interesting motivation for experimental validation of such ZrO2-based cells. The Y, Gd, Sc, and La weak p-type dopants indicated the largest decrease in OVFEs, of about half of that of undoped ZrO2, in agreement with experimental observations, which demonstrated removal of the electroforming step. For Ce-doped ZrO2 films, the uniformity of the CF during the forming process increased by mitigating further Vo generation, and the device required electroforming, consistent with our results. Our results also revealed that dopants affect OVFEs locally, enhancing Vo clustering, suggesting that spatial control of CFs can be enabled. Localized Vo-based CFs can reduce variations in RS parameters, and suppress stochastic formation of the CF, which will allow better RS control, resulting in a high resistance ratio, RS uniformity, and uniformity for forming/set voltages, hence overall device performance improvement. Finally, our electronic structure analyses can motivate analysis of the transport mechanism in memristive devices, as has been performed for SrTiO3, where mid-gap states were characterized by soft X-ray resonant electron spectroscopy,56 and used to discern the transport mechanism. Supporting Information Chemical potential/atom for all dopants and Zr, comparison of lattice parameters calculated using different functionals and structural doping configurations, OVFEs for Vo introduced nearby or away from select dopants and for a Vo using different functionals, total and projected DOS for stoichiometric and nonstoichiometric undoped ZrO2 with a neutral Vo, size effects on DFEs and OVFEs, the effect of Vo position w.r.t dopant on OVFEs. This information is available free of charge. Author Information *Handan Yildirim: [email protected] *Ruth Pachter: [email protected] ACS Paragon Plus Environment

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Acknowledgements The computational resources and helpful assistance provided by the AFRL DSRC are gratefully acknowledged. H.Y. acknowledges an NRC Research Associateship Programs (RAP) Fellowship. Table 1. Comparison of the lattice parameters (a, b, and c) and band gaps (Eg) for undoped m-ZrO2 bulk obtained using different functionals. Computational results from other studies are in square parentheses.

Methods

a, b, c (Å)

Eg (eV)

PBE

5.225, 5.269, 5.420 [5.199, 5.301, 5.343]57

3.524 [3.40, 3.47, 4.22]57

PBEsol

5.176, 5.229, 5.362

3.507

PBE+Ud (Ueff =4 eV)

5.312, 5.317, 5.479

3.935

PBE+Ud (Ueff =8 eV)

5.391, 5.362, 5.532

4.389

5.310, 5.319, 5.423

4.560

PBE0

5.186, 5.230, 5.370 [5.187, 5.248, 5.326]51

5.833 [6.09] 51

B3LYP

5.237, 5.264, 5.423 [5.246, 5.270, 5.405]51

5.542 [5.61]51

HSE06

5.187, 5.230, 5.370

5.040 [5.14]49

PBE+Ud+Up eV and Up=7 eV)

(Ud =8

5.83 (VUV)50 5.2-5.8 (EELS)51, 5.0949 Ueff corresponds to U-J and Ud and Up indicate Hubbard corrections to the Zr 4d and O 2p orbitals, respectively. Experiment

5.151, 5.212, 5.31758


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Table 2. Common oxidation states, electron configuration, atomic radius (r), and electronegativity of the dopants considered, along with the host metal, Zr. Dopant (M)

Common Oxidation State

Electron

r (pm)

Electronegativity

Configuration

4+

[Kr] 4d25s2

175

1.33

Mg

+2

[Ne] 3s2

141

1.31

Sr

+2

[Kr] 5s2

195

0.95

Ba

+2

[Xe] 6s2

215

0.89

Al

+3

[Ne] 3s23p1

121

1.61

Sc

+3

[Ar] 3d14s2

170

1.36

Y

+3

[Kr] 4d15s2

190

1.22

Gd

+3

[Xe] 4f75d16s2

196

1.20

La

+3

[Xe] 5d16s2

207

1.10

Si

+2, +4

[Ne] 3s23p2

111

1.90

Ti

+2, +3, +4

[Ar] 3d24s2

160

1.54

Hf

+4

[Xe] 4f145d26s2

175

1.30

Ce

+3, +4

[Xe] 4f15d16s2

204

1.12

Zr – host metal strong p-type

weak p-type

isovalent – Zr like

weak n-type Cr

+2, +3, +6

[Ar] 3d54s1

139

1.66

Mo

+4, +6

[Kr] 4d55s1

154

2.16

V

+2, +3, +4, +5

[Ar] 3d34s2

153

1.63

Nb

+3, +5

[Kr] 4d45s1

164

1.60

Ta

+5

[Xe] 4f145d36s2

170

1.50

strong n-type Ni

+2, +3

[Ar] 3d84s2

124

1.91

Cu

+1, +2

[Ar] 3d104s1

132

1.90

Ag

+1

[Kr] 4d105s1

145

1.93


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Table 3. Dopant formation energies (DFEs in eV) calculated using PBEsol for interstitially doped Ag,

DFEs @ P1

Cu

Ag

Ni

no Vo

3.599

5.214

2.369

1Vo

2.705

3.870

1.350

2Vo

1.477

2.401

0.619

Cu, and Ni, with and without Vo presence in ZrO2 bulk.


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Figure 1. Illustration of interstitial doping sites (green and red balls represent Zr and O atoms, respectively, and magenta balls illustrate the positions of an interstitial dopant) for the a) energetically most stable interstitial configuration (P1), b) second energetically most stable interstitial configuration (P2) in m-ZrO2, c) Comparison of DFEs – calculated as defined by Equations 1 and 2 for substitutional (S) and interstitial (P1 and P2) doping using the PBEsol functional, d) DFE values for substitutional and interstitial doping calculated using PBEsol, PBE+Ud with two different Ueff value (square and curled parentheses for Ueff = 8 eV and 4 eV, respectively) and with the B3LYP functional shown for values with double parentheses, e) Relative dopant formation energy Erelative = Etot interstitial – (Etot substitutional - µZr), calculated using PBEsol, where for dopants with Erelative > 0 or Erelative < 0, substitutional or interstitial doping are more favorable, respectively.


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Figure 2. Total and projected DOS for substitutionally doped stoichiometric ZrO2 for a) isovalent, b) ptype, and c) n-type dopants. Projected DOS presented on the right panels are for the dopants (filled areas with red) shown by zooming into the CBM and VBM regions for clarity. The Fermi level is set to zero and shown by the dashed line.


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1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


Figure 3. a) Illustration of m-ZrO2 (green and red balls represent Zr and O atoms, respectively) with 3-/4fold coordinated Vo and the dopant (magenta open circle) substitutionally replacing Zr as the 1st nn of Vo (shown by a solid arrow), b) OVFEs calculated as defined in Equations 3 and 4 with a dopant as 1st nn of Vo for interstitial (P1 and P2) doping, c) OVFEs for substitutional (S) doping with a dopant as 1st nn of Vo calculated using the PBEsol functional, and d) Actual values of OVFEs for substitutional and interstitial doping calculated using PBEsol, PBE+Ud with two different Ueff values (shown by square and curled parentheses with Ueff = 8 eV and 4 eV, respectively), and with the B3LYP functional shown with double square parentheses. PBE+Ud calculations are performed for substitutional and P1 doping, and B3LYP for substitutional doping for select dopants. Cyan and magenta bars in b-c show OVFEs in undoped m-ZrO2 for 3-/4-fold coordinated Vo.

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1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


Figure 4. Total and projected DOS of substitutionally doped ZrO2 with a neutral Vo introduced as the 1st nn of the dopant for a) isovalent, b) p-type, and c) n-type dopants. Projected DOS presented on the right panels are for the dopants (filled areas with red) shown by zooming into the CBM and VBM regions for clarity. The Fermi level is set to zero and shown by the dashed line.

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