Segregation energy trends and their charge state dependence were established for Group II to Group VI substitutional metal dopants in HfO2 using density functional theory. Corroborating the segregation energy with dopant-oxygen bond lengths and charge state stability, strong effects are predicted for Group II and Group III p-type dopants, which can easily reverse their segregation trend due to −2 charge state preference. Transitions between segregation and isolation may occur around 1.5 eV above the valence band maximum, with the exception of Al, which remains barely stable in its segregated form. In Al-doped HfOx, the switching characteristics of filaments formed near Al dopants show subtle changes and the OFF state data retention is degraded. A comprehensive assessment on configurational Al-VO interaction, charge state dependence, and migration energy changes points to the fact that to achieve OFF state data retention improvements, it will be necessary to engineer the filament interaction with Al to stabilize configurations that favor vacancy filament dissolution. Another mode of failure can result from subsequent charge trapping during the operation of the device, which ultimately prohibits the filament dissociation.
The evolution of information technology industry toward meeting the ever increasing processing demand in personal computers, smart phones, pads, and Internet of Things (IoT) application devices1,2 has been a strong driver for the adoption of new adjacent memory technologies with cost-effective solutions for data storage. As the physical dimension of devices are further scaled down to a few nanometers, overcoming the physical and performance limitations of conventional memories becomes essential to meet the demand of novel applications. Among the new non-volatile memory technologies for use in solid-state drives, field-programmable gate arrays (3D-FPGA), and neuromorphic computing, the resistive random-access memory (RRAM) devices have been getting important traction lately and are becoming of central interest to the semiconductor research community.3,4 RRAM devices are scalable and compatible with CMOS processes and have multiple substantial advantages over other emerging memory technologies which include simple fabrication processes, low power dissipation, and fast read/write performance.5–7 For a large-scale integration of RRAM devices; however, it is necessary to reach a superior control of device characteristics, solve the operation challenges related to switching-parameter variability, cycling endurance, and data retention, and improve the batch-to-batch, device-to-device, and cycle-to-cycle variability.8–10
To date, various RRAM device structures had been considered, which can be categorized by the heterogeneous combination of various materials or by the underlying switching operation, which can be either interfacial or filamentary. On the interfacial switching side, significant advancements in improving the device characteristics have come around by engineering tunnel barriers and band offsets that facilitate low power device switching. On the filamentary side, it is widely adopted that the device operation relies on both electronic and ionic dynamics around the localized conductive channels which occur within a few nanometers’ radius and are strongly influenced by quantum phenomena like electron tunneling and local atomic charge delocalization.11,12 Near these nanoscale filaments, large temperature gradients were previously reported,13,14 in addition to chemical and electrical potential alterations of exponential nature that govern the ionic and electronic conduction.
The filamentary switching phenomenon is inherently an atomistic process; therefore, the device characteristics are strongly dependent upon local material properties which are not easily obtainable from measurements. Computational studies from atomistic simulations to kinetic Monte Carlo,13 analytic descriptions,14,15 and compact models are crucial to elucidate these effects at various levels and to link the fundamental local properties of materials with their macroscopic device characteristics. The ab initio calculations of bulk-like properties, such as formation energies, diffusion coefficients, and defect states, provide an assessment for static behavior, and then, they can be treated as local quantities varying in space and time in multiscale approaches.
As fabricated, binary oxide-based filamentary RRAM cells are typically in an insulating state. An electrical forming process step is used to break down the oxide layer, causing the RRAM cell to acquire its switching capacity. After forming, the resistance of the cell can be switched between high resistance state (HRS) and low resistance state (LRS) values using voltages of different magnitudes, durations, and polarities.15,16 Forming free devices would be preferred for their integration into the CMOS process, and on this front, recent advancements on device structure optimizations targeting device and filament scaling issues had shown promising results.17 However, some of the proposed improvements in performance also increase the vulnerability to the stochastic motion of individual ions, leading to what is more generally known as the “voltage-time dilemma.”
The forming process itself had been explained by the formation of oxygen vacancy clusters which give rise to charge carrier delocalization and conducting channels.18–20 However, the driving forces of vacancy migration and filament formation are still unclear and difficult to investigate from experiments. To explain the effects of electronic charges and impurities on the formation of conductive filaments in binary transition metal oxides, theoretic assessments in systematic ab initio studies have been put forward in TiO2, NiO, HfO2, and Ta2O5 RRAMs.18–32 Key results included the following: (1) identifying the charge trapping process under applied voltage to facilitate and drive the formation of conductive filaments; (2) predicting the diffusion of oxygen into the conductive filament to induce “OFF” state; (3) proposing a charge-assisted atomic diffusion mechanism to explain the oxygen vacancy dynamics during the cycling operation of the resistive switching; and (4) addressing the viability of selective metal dopant technologies on improving switching properties of RRAM devices. Additional effects include the formation of oxygen vacancies induced by interfacial oxygen diffusion into the electrodes during deposition and forming processes.23 Depending on the type of electrode used, interfacial oxygen vacancy formation can be associated with bulk vacancy creation to form and stabilize the filament. Moreover, extrinsic dopant atoms can impact both bulk and interfacial processes and alter the diffusion mechanism and filament robustness. It is therefore of increased interest to understand the critical issues on filamentary switching related to metal doping, and in this paper, as a first step, we study the bulk effects related to dopant induced oxygen vacancy formation and device retention.
II. COMPUTATIONAL METHODOLOGY
The electronic structure for various dopants in monoclinic HfO2 (m-HfO2, space group P21/c) was obtained from spin-polarized density functional theory (DFT) calculations as implemented in the Vienna Ab Initio Simulation Package (VASP),33–35 employing the projector augmented-wave method.36 A 2 × 2 × 2 gamma-centered Monkhorst-Pack grid was used for k-point sampling, and all ions were relaxed until forces were less than 0.01 eV/Å per ion. To maximize accuracy and performance, we employed the local density approximation (LDA) + U method in the Dudarev approach,37 which has been previously used for calculations on rutile TiO2,18,38 monoclinic HfO2,32,42 and Ta2O5.24,47 The onsite Coulomb corrections used were Ud = 6.6 eV on Hf 5d orbitals and Up = 9.5 eV on O 2p orbitals. This approach has achieved comparable accuracy to quasiparticle excitations (GW) and hybrid functional methods39,40 for bandgaps and defect transition levels, while retaining the computational efficiency of local density approximation (LDA) or generalized gradient approximation (GGA) based calculations. In the unit cell of m-HfO2, there are 12 atoms: 4 sevenfold-coordinated Hf, 4 threefold-coordinated (3C) O, and 4 fourfold-coordinated (4C) O atoms. In this study, we used 3 × 3 × 3 supercells measuring about 15 Å × 15 Å × 15 Å of monoclinic HfOx with 106 Hf, 210 O, and up to 2 dopant atoms. The 3C-VO was found to be more stable in filamentary arrangements than 4C-VO;42 therefore, the VO filament is formed by removing six three-coordinated (3C) oxygens. The dopants were systematically introduced on substitutional Hf sites. For the retention study of Al:HfO2, the Al dopant stability was assessed for both substitutional and interstitial sites.
The segregation energy was defined as the net change in energy when two dopant ions move from far apart to close together,
for Eseg < 0 eV dopants favor segregation.
III. RESULTS AND DISCUSSION
A. Dopant segregation trends in HfO2
Impurity doping by transition metals as well as hydrogen and nitrogen had been previously considered as a potential strategy to fine tune the characteristics of HfOx-based RRAM devices.41–47 Some of the early studies were mainly targeting the reduction of forming voltages toward achieving forming-free behavior. It has been pointed out that Hf-like dopants (such as Zr, Ti, and Si) can be used for a moderate reduction of oxygen vacancy formation energy without yielding a significant change in switching parameters.32,42 Weak p- and n-type (Al, La, Ta, W, etc.) dopants on the other hand were predicted to produce a large formation energy reduction and facilitate the formation of more stable filaments. The experimental data32 indicated that for these dopants the required forming/switching voltages were reduced and enhanced uniformity was achieved, but these advantaged came at the cost of ON/OFF ratio deterioration. Moreover, strong p- and n-type dopants (Sr, Ni, Cu) were shown to drastically change the switching parameters and further reduce the ON/OFF ratio. The mechanisms by which the dopants alter the characteristics can be viewed as opening up additional conductive channels and repopulating states with excess electrons introduced by n-type dopants. In the p-type case, lowering the occupied levels in the bandgap and shifting the Fermi energy level toward the valence band reduces the oxygen vacancy formation energy. In both cases, the filament conduction mechanism through gap states was strongly disrupted by the introduction of dopants. This phenomenon coupled with the adjacent high resistance state stability reduction can explain the ON/OFF ratio deterioration observed experimentally. Moreover, it was put forward that by further increasing the doping concentration and enhancing the dopant-filament interaction a more significant change in device characteristics can be obtained,32,42 which ultimately provides another degree of freedom in tuning RRAM device characteristics. Therefore, in order to move forward, a critical aspect is to determine which dopants might prefer to segregate in HfO2 in order to establish whether a high concentration of dopants might be in the center of conductive filaments’ nucleation.
The calculated segregation energies for substitutional cation dopants are shown in Fig. 1 as a function of dopants’ charge state. In Group II (Sr and Ba), the strong p-type dopants have an increased tendency to segregate in all charge states. However, weak p-type dopants from Groups IIIA, B (Al, Sc, Y, and In), while they show moderate segregation trends for positive, neutral, and −1 charge states, in −2 charge state with the introduction of excess electrons in the system, the trend is reversed and dopants favor isolation. Goups IVA, B (Si, Ge, Sn, Pb, Ti, and Zr) and VA, B (Nb, Ta, and Sb) tend to have no preference for segregation or isolation in their neutral state but show slight isolation trends in their positive and negative charge states. A clear anomaly from these groups is +2 Pb which favors stronger segregation. Finally, Groups VIA, B (Mo, W, and Te) prefer isolation in their positive and neutral charge states; however, negative charges induce stabilization of segregated configurations.
Corroborating now the above trend in segregation energies with the average bond length of dopants with nearby oxygen ions (D–O) in their neutral charge state, a clear correlation is noted for Group II where larger lattice distortions are detected in the immediate neighborhood of the dopants (Fig. 2). It is interesting to note that the segregation energy correlation to the lattice distortions originates mostly from the first oxygen coordination shell shared between the dopants, while dopant-dopant (D–D) bond lengths reach equilibrium distances comparable to Hf-Hf. Group II, Sr and Ba, consisting of strong p-type dopants induce also drastic reductions in the oxygen vacancy formation energies, since the behavior of dopants’ segregation energies reported in Fig. 1 mirrors that of dopant effects on isolated VO formation energies reported in Fig. 11 of Ref. 32. Therefore, the bond length data from Fig. 2, the trends in oxygen vacancy formation, and dopant segregation tendency indicate that the degree of disruption a dopant causes to the immediate surrounding lattice and the local charge balance are the key factors driving the process of VO formation and segregation.
Another aspect of interest is the charge state stability of dopants induced by charge injection, as described by the Fermi energy (EF) position between the HfO2 valence band maximum (VBM) and conduction band minimum (CBM). As shown in Fig. 3, irrespective of the relative position of two dopants to each other, for Groups II, IIIA, B, and IVA, B, the stability of +2 states is limited to the <1 eV region just above the valence band, while for VA, B, the stability region is significantly larger with a width of ∼3 eV. For Groups VIA, B, these regions are reduced for Mo and Te to about ∼1.5 eV; however, W presents a +2 stability up to 2 eV. For neutral charge state stability, Groups IVA, B stand out with large stability regions of 4 eV observed for Si, Ge, Sn and 5 eV for Zr, while the smallest of about 2.5 eV is for Ti. In Groups VIA, B, Te also exhibits moderate neutral stability of about 3 eV and Mo and W of about 2 eV. All the other elements from the Groups IIA, IIIA, B, and VA, B are barely stable in their neutral charge states, indicating that with excess charge introduction the drastic transitions from +2 to −2 may induce large perturbations in device operation especially if the additional charge is exchanged with oxygen vacancies.
Finally, coupling the trends observed for segregation energies and charge state stability, it becomes clear that the dominating effects for strong (Group IIA) and weak (Groups IIIA, B) p-type dopants originate from their increased preference for −2 charge state stability. Excess charge introduction in the system will alter their segregation preference and induce transitions toward isolation ∼1.5 eV above VBM with the exception of Al, which barely remains stable in its segregated configuration. Nevertheless, negligible changes in segregation/isolation trends are observed for Groups IVA, B (the Hf-like dopants) and no change for Groups VA, B and VIA, B (weak n-type dopants) which consistently favor isolated dopants. Therefore, the large effects predicted for weak p-type dopants, i.e., changes in their charge state stability and segregation preference may cause filament instability due to dopants diffusion around the conductive channels and induce degradation of RRAM device performance cycles.
B. Data retention issues in Al doped HfO2−x
Al doping, in particular, has received increased attention lately and has been reported to successfully reduce forming voltages and improve the uniformity of ON and OFF state resistances.48–50
Experimental studies pointed out enhanced ON state retention in HfAlOx over HfOx50 and previous calculations found the formation of filaments around Al impurities to be energetically favorable.32,42 Therefore, based on both theoretical and experimental observations, the ON state performance of Al-doped HfOx is strongly indicating the desired characteristics. However, the OFF state retention has been raising concerns about the viability of Al-doped HfOx devices. Frascaroli et al.51,52 found that by increasing Al doping concentration OFF state retention yielded sharp device failures. OFF state activation energies of Al-doped and un-doped HfOx extracted from experiments yielded a reduction to 1.1 eV from 1.5 eV and were attributed to the OFF state retention degradation with Al doping. Migration barriers of oxygen vacancies around Al ions calculated previously53 shown a significant barrier reduction of Vo back-diffusion to the filament when Al ions are present near conductive filaments, indicating also OFF state instability. In order to fully understand the Al effect on the retention degradation, a detailed investigation into Al and oxygen vacancy effects on their charge state stabilization and segregation trends in the substoichiometric oxide is therefore necessary. From Sec. III A, Al dopants in all charge states were found to prefer clustering together, reducing the formation energy by 0.35 eV.
To achieve a comprehensive understanding of the OFF state retention issues in Al doped HfO2, first the stability of a single Al ion on substitutional and interstitial sites was assessed, and formation energies are shown in Fig. 4. At low EF, Al will prefer the interstitial site; however, for EF > 1.35 eV, the Hf substitutional site becomes more favorable up to the CBM. Given the wider stability of cation substitution, we will use this profile throughout this section.
Now, for the interaction study between Al dopants and VO, various configurations have been considered as shown in Fig. 5(a). Two Al ions were initially positioned in nearby substitutional locations, and the VO formation energy was assessed to find the most stable configuration. For case 1: VO is strongly interacting with both Al ions, while for case 2 and case 3: VO is placed next to one Al ion, but far from the other Al ion. In Fig. 5(b), case 1 shows the lowest formation energy, indicating that the most favorable position for an oxygen vacancy is as VO2+ next to two Al ions. This configuration may represent the seed of the filament formation, since the formation energy of VO is significantly lowered relative to its isolated configuration far from the segregated Al ions. In addition, the electron density of states plotted in Fig. 5(c) indicates no defect level is generated in case 1 and the local charge neutrality is satisfied. For an in-depth understanding of this mechanism, a further analysis of the electron localization function of Al:HfO2 relative to undoped HfO2 is shown in Fig. 6 supporting that (1) a strong Hf 5d electron localization is observed on the oxygen vacancy site in the undoped case; (2) when Al ions are near the oxygen vacancy, there are no residing electrons on the VO site. Since Al ions are weak p-type dopants, essentially electron depletion occurs from the oxygen vacancy site toward Al, in the neutral charge state. This can be altered, however, by the application of an external voltage and excess electron injection in the system, in which case the vacancy site becomes populated (Fig. 6). Tracking the charge state of VO’s is of increased interest from the filament formation/rupture point of view, since VO2+ was established to be preferred only in isolated cases,27–29 while filaments would be composed of VO1+ or VO0. Moreover, previously VO2+ were found to be more mobile and favor isolation; thus, the filament can be switched to the OFF state.42 On the other hand, when vacancies are recaptured in the filament to establish the ON state, their close interaction will require a transition to charge states VO1+ or VO0 due to charge delocalization in the conductive channels. Therefore, the transition VO2+–>VO0 can be viewed as the signature process that induces the filament formation and rupture and consequently changes the resistance. From kinetics point of view, VO1+ and VO0 are also less mobile than VO2+ because of their preference for charge delocalization and strong vacancy-vacancy interactions.32,42 Figure 7 shows the schematic transition between the ON and OFF states when Al is close to the filament and the transition from VO0–>VO+2 during the switching process.
Next, we turn to study the Al interaction with a formed VO filament corresponding to the schematics in Fig. 7. Three Al–Al configurations next to the VO filament were considered as shown in Fig. 8(a): (1) for type 1, the Al dopants are in the (010) plane, along the VO filament, with a nearest Al–Al distance of 3.38 Å; (2) for type 2, the Al dopants are in the (100) plane along the VO filament, with a nearest Al–Al distance of 3.65 Å; (3) for type 3, the Al dopants are in the (001) plane, perpendicular to the filament, with a nearest Al–Al distance of 4.54 Å. The corresponding formation energies are shown in Fig. 8(b), which strongly indicate that type 2 Al configuration is the most favorable. In addition, for the latter case, the filament has enhanced conductivity as illustrated by the charge delocalization in the partial charge density plot in Fig. 8(a) and depicts ON state-like behavior in Al doped HfO2 and the formation of a robust filament exhibits ON state data retention improvements.
For the OFF state, on the other hand, we need to have a better understanding of the association and disassociation processes of VO’s and how they are altered in the presence of Al dopants. Similar configurations to type 1, type 2, and type 3 described above are now investigated to simulate the switching to an OFF state-like configuration by two VO’s in the neighborhood of two segregated Al ions. One VO is next to two Al as in Fig. 5(a) case 1. Figures 9(a)–9(c) depict the partial charge density distribution plots corresponding to the associated and disassociated states for the three configurations. The observed OFF state failure mechanism is attributed to the reformation of VO clusters induced by the rupture process instability. Implicitly, in this process, the oxygen vacancies are restricted by Al to change their charge states to +2, therefore cannot reduce their out-diffusing migration energy barrier,53 and are recaptured. This conclusion is supported by the low VO association energies for all charge states in type 1 arrangement shown in Fig. 9(d), indicating that a filament can become more stable in the presence of Al dopants and this comes at the expense of an unstable disassociation process. This effect can therefore serve as an explanation for the poor OFF state retention observed experimentally in Al:HfOx devices.51,52 On the other hand, for type 2 and type 3, in the +2 charged state, the VO disassociation can become favorable over association indicating partial stability of the OFF state and possibly improved data retention. The transition points are near 4 eV in the bandgap, slightly higher than in the undoped HfOx case at 3 eV [Fig. 9(g)], pointing to enhanced stability in the +2 charge state in Al:HfOx. Finally, the relative stability and filament robustness is assessed in Fig. 9(h) for all configuration types, and it is found that type 2 and type 3 are slightly stabilized over type 1.
In conclusion, to achieve enhanced RRAM device operation and OFF state data retention improvement in Al doped HfOx, it will be necessary to avoid the metastable type 1 configuration or restabilize the Al distribution from type 1 to type 2 or type 3, possibly by either annealing or preconditioning the device. We believe similar findings to be also relevant to other binary transition metal oxides currently considered as potential RRAM switching materials, since previous results indicated similarities between dopant induced vacancy formation energy trends in HfO2,32 TiO2,21 and Ta2O5.54
Segregation energy, dopant-oxygen bond lengths, and charge state stability trends draw attention on strong effects introduced by Group II and Group III p-type dopants which can easily reverse their segregation trend due to −2 charge state preference. Charged induced segregation to isolation transitions may occur around 1.5 eV above the valence band maximum, with the exception of Al, which remains barely stable in its segregated form. A comprehensive assessment on the configurational Al-VO interaction in Al doped HfOx was performed to elucidate the OFF state degradation. Charge state dependence and migration energy changes point to the fact that to achieve OFF state data retention improvements, it will be necessary to engineer the filament interaction with Al to stabilize configurations that favor vacancy filament dissolution.
This work was funded by the Stanford Non-Volatile Memory Technology Research Initiative. The computational work was carried out on Computer Clusters belonging to the Extreme Science and Engineering Discovery Environment (XSEDE),55 which is supported by National Science Foundation Grant No. ACI-1548562, and also on the Center for Nanoscale Materials Computer Cluster supported by the U. S. Department of Energy, Office of Science, Office of Basic Energy Sciences, under Contract No. DE-AC02-06CH11357.