Analysis and simulation of the multiple resistive switching modes occurring in HfOx- based resistive random access memories using memdiodes Cite as: J. Appl. Phys. 125, 234503 (2019); https://doi.org/10.1063/1.5094864 Submitted: 06 March 2019 . Accepted: 30 May 2019 . Published Online: 21 June 2019 S. Petzold, E. Miranda, S. U. Sharath, J. Muñoz-Gorriz, T. Vogel, E. Piros, N. Kaiser, R. Eilhardt, A. Zintler, L. Molina-Luna, J. Suñé, and L. Alff ARTICLES YOU MAY BE INTERESTED IN Resistive switching phenomena: A review of statistical physics approaches Applied Physics Reviews 2, 031303 (2015); https://doi.org/10.1063/1.4929512 Multilevel HfO2-based RRAM devices for low-power neuromorphic networks APL Materials 7, 081120 (2019); https://doi.org/10.1063/1.5108650 Perspective: A review on memristive hardware for neuromorphic computation Journal of Applied Physics 124, 151903 (2018); https://doi.org/10.1063/1.5037835 J. Appl. Phys. 125, 234503 (2019); https://doi.org/10.1063/1.5094864 125, 234503 © 2019 Author(s). Journal of ARTICLE scitation.org/journal/jap Applied Physics Analysis and simulation of the multiple resistive switching modes occurring in HfOx-based resistive random access memories using memdiodes Cite as: J. Appl. Phys. 125, 234503 (2019); doi: 10.1063/1.5094864 Submitted: 6 March 2019 · Accepted: 30 May 2019 · View Online Export Citation CrossMark Published Online: 21 June 2019 S. Petzold,1,a) E. Miranda,2 S. U. Sharath,1 J. Muñoz-Gorriz,2 T. Vogel,1 E. Piros,1 N. Kaiser,1 R. Eilhardt,1 1 1 A. Zintler, L. Molina-Luna, J. Suñé, and L. Alff1 2 AFFILIATIONS 1 Institute of Materials Science, Technische Universität Darmstadt, Alarich-Weiss-Straße 2, 64287 Darmstadt, Germany 2 Departament d’Enginyeria Electrònica, Universitat Autònoma de Barcelona, 08193 Cerdanyola del Valles, Spain a) Author to whom correspondence should be addressed: petzold@oxide.tu-darmstadt.de ABSTRACT In this work, analysis and simulation of all experimentally observed switching modes in hafnium oxide based resistive random access memories are carried out using a simplified electrical conduction model. To achieve switching mode variation, two metal-insulator-metal cells with identical stack combination, but varying oxygen stoichiometry of the hafnia layer, namely, stoichiometric vs highly deficient, are considered. To access the individual switching modes, the devices were subjected to a variety of cycling conditions comprising different voltage and current ranges. For modeling the device behavior, a single or two antiserially connected memdiodes (diode with memory) were utilized. In this way, successful compact simulation of unipolar, bipolar, threshold, and complementary resistive switching modes is accom- plished confirming the coexistence of two switching mechanisms of opposite polarity as the basis for all observable switching phenomena in this material. We show that only calibration of the outer current–voltage loops with the memdiode model is necessary for predicting the device behavior in the defined region revealing additional information on the switching process. The correspondence of each memdiode device with the conduction characteristics of the individual top and bottom metal-oxide contacts allows one to assess the role played by each interface in the switching process separately. This identification paves the path for a future improvement of the device performance and functionality by means of appropriate interface engineering. © 2019 Author(s). All article content, except where otherwise noted, is licensed under a Creative Commons Attribution (CC BY) license (http:// creativecommons.org/licenses/by/4.0/). https://doi.org/10.1063/1.5094864 I. INTRODUCTION computing and is believed to be a suitable candidate for multibit Resistive random access memories (RRAMs) have been inten- operations, thanks to its multilevel storage capability. The plasticity sively studied during the last decade revealing promising characteris- exhibited by RRAM cells also enables mimicking neuronal net- tics such as fast switching speed in the subnanosecond region,1 low works8,9 with the RRAM cell acting as the electrical synapse,10 high- voltage operation, low power consumption,2 resilience toward ioniz- lighting its role in applications such as image recognition and ing radiation,3 and scalability4 below 10 nm. Consisting of a simple autonomous driving. Although extensively investigated and already metal-insulator-metal (MIM) structure and being manufacturable introduced in the market11 as early as in 2013, the underlying with complementary metal-oxide-semiconductor (CMOS) compati- switching mechanisms of valence change memory (VCM) cells are ble materials, e.g., hafnium or tantalum oxide makes RRAM not completely understood. The switching process relies on the for- back-end-of-line (BEOL) compatible and, thus, an interesting candi- mation (forming/set) and dissolution (reset) of a metal-rich atom- date for applications in the Internet of Things5 (IoT) fostering the sized pathway pictured as a conductive filament (CF). The filament so-called “More than Moore”6 approach. In general, RRAM enables formation requires an initial activation voltage that leads to a redistri- storage densities as small as 4F2 and 4F2/n through 3D stacking.7 bution of oxygen atoms which results in an increased local density Moreover, RRAM is investigated within the scope of in-memory of oxygen vacancies in the dielectric layer, thus creating a defect J. Appl. Phys. 125, 234503 (2019); doi: 10.1063/1.5094864 125, 234503-1 © Author(s) 2019 Journal of ARTICLE scitation.org/journal/jap Applied Physics band which enables local current transport through the dielectric. By overview of the investigated stack is depicted in Fig. 1(b) with applying an appropriate voltage protocol, part of the previously bright-field transmission electron microscope images for the Si removed oxygen is recaptured by the vacancy sites causing the (100)-substrate, the magnetron sputtered titanium nitride elec- rupture of the conductive filament thus increasing the resistance trode, and the tetragonal (left) and monoclinic (right) hafnia state of the device. In this way, the device can be reversibly switched layers, respectively. The platinum top electrode (TE) was deposited from a high resistance state (HRS) to a low resistance state (LRS) ex situ by magnetron sputtering. Therefore, the depicted Pt elec- and vice versa. A number of different factors, such as the oxygen trode is only a schematic representation of the actual polycrystal- affinity or roughness of the electrodes, the diffusion barriers for line platinum electrode. For the tetragonal hafnia layer (HfO1.5), oxygen transport in the dielectric, or the high local current densities the crystal size was found to be smaller and the interface to TiN resulting in Joule heating up to 1000 K,12 participate in or influence was found to be distinct compared to the monoclinic (HfO2) the switching mechanism making it a complex process hard to dis- hafnia layer. The impact of the oxygen content of the dielectric entangle. Therefore, a clear picture and understanding of the con- layer on the electronic structure can be seen by the low-loss elec- ductive filament in VCM is still missing. Although indirect probing tron energy-loss spectra depicted in Fig. 1(c), which shows a clear techniques, such as conductive atomic force microscopy, can be uti- difference between deficient and stoichiometric films. The elec- lized to verify and locate conductive filaments,13–15 it can only tronic structure fingerprints of stoichiometric m-HfO2 and oxygen render limited information. Opposed to conductive bridge RAM, a deficient t-HfO1.5 are in agreement with the literature.20,21 The direct imaging of the conductive filament via transmission electron electron energy loss near edge structure (ELNES) features in the microscopy is more complex since the filament is not based on spectra are denoted as α to η, which correspond to A to H in Ref. 21. nonhost cations (e.g., Cu), but on defects in the anion sublattice of The change in the electronic structure of the hafnia layer also the dielectric (oxygen vacancies). Although various approaches are affects the optical bandgap of the material. In Fig. 1(d), the being followed in order to gain further insight,16–19 a clear atomistic UV/Vis-absorption spectra of a deficient and stoichiometric amor- picture with a correlation to the switching characteristics is still not phous hafnia reference sample are depicted. By evaluating energy finalized. Hence, every new finding about the characteristics of the vs α2 plots, the bandgap of deficient hafnia is found to reduce by conductive filament in the switching process, which further improves the understanding of the resistive switching process, is important. So far, four different switching modes have been identified in the literature, namely, bipolar resistive switching (BRS), unipolar resistive switching (URS), threshold resistive switching (TRS), and complementary resistive switching (CRS). While the first two can be categorized as nonvolatile, i.e., memory type, the latter two can also be utilized for the volatile selector-type switching mechanisms. The BRS mode can be additionally differentiated to figure eight- wise (f8) and counter figure eight-wise (cf8) switching depending on the voltage polarity of the switching loop. In this study, a sim- plified behavioral model that clarifies how BRS-f8 and BRS-cf8, as well as CRS, can coexist in the same device and be transmuted into each other is reported. Within the proposed framework, the prereq- uisites necessary for observing both URS and TRS, which can be represented by the same approach and also transmuted to BRS under certain conditions, are also discussed. II. EXPERIMENTAL AND OXYGEN ENGINEERING The stacks used in this work (TiN/HfO2/Pt and TiN/HfO1.5/Pt) were grown using a custom designed molecular beam epitaxy (MBE) unit enabling the tuning of the oxygen content (crystal structure) of the functional hafnia layer in the full range from metallic hafnium to highly deficient (tetragonal) to stoichiometric (monoclinic) films. The oxygen content of the dielectric layer was FIG. 1. (a) X-ray diffraction pattern for the investigated stack consisting of controlled via the oxygen flow rate and radio frequency power of tetragonal (green) and monoclinic (purple) hafnium oxide. (b) Overview of the the radical source. For CMOS compatibility and for stabilization of Si/TiN/hafnia/Pt-stacks with stoichiometric HfO2 or oxygen deficient HfO1.5, the tetragonal and monoclinic phases of the 20 nm thick hafnia respectively. For silicon, TiN and Hafnia, representative TEM bright-field images layer, a growth temperature of 320 °C was chosen. The two-theta are depicted. (c) Electron energy-loss spectra for m-HfO2 and t-HfO1.5, respec- X-ray diffraction patterns for the predominantly tetragonal and tively, displaying their difference in electronic structure. (d) UV/Vis-absorption monoclinic hafnia stacks are depicted in Fig. 1(a). Further details spectra of amorphous, deficient, and stoichiometric hafnia reference samples. The optical bandgap reduces by 0.5 eV from stoichiometric (5.7 eV) to deficient about the oxide growth process and the quantitative evaluation of (5.2 eV) hafnia. the oxygen stoichiometry can be found in Ref. 20. A schematic J. Appl. Phys. 125, 234503 (2019); doi: 10.1063/1.5094864 125, 234503-2 © Author(s) 2019 Journal of ARTICLE scitation.org/journal/jap Applied Physics 0.5 eV compared to the stoichiometric hafnia layer resulting in optical bandgaps of 5.2 and 5.7 eV, respectively. In this work, the resistive switching behavior of highly deficient hafnia devices (HfO1.5) to fully oxidized, stoichiometric hafnia devices (HfO2) of 20 nm film thickness was investigated and compared. The electrical characterization was performed using a Keithley Semiconductor Characterization System 4200 (SCS 4200) by applying bias to the platinum top electrode (TE) while grounding the titanium nitride back electrode (BE). III. MEMDIODE MODEL The compact model considered here to deal with the different FIG. 2. (a) Typical current–voltage characteristic and memory state loop associ- conduction modes exhibited by our devices consists of a single ated with the memdiode model. In this case, the transition rates are different for memdiode structure, i.e., a diode with hysteretic properties, or in a positive and negative voltages. (b) Equivalent circuit model for the current equa- tion (1). R is the series resistance. The diodes are driven by the memory state combination of memdiodes. The memdiode model was originally of the device and one diode D is activated at a time. For (a) and (b), the green presented in Ref. 22 and later extended in Ref. 23. For the sake of curve represents current in neg. voltage direction (yellow—positive voltage completeness, here it is succinctly reviewed. Physically, the mem- bias). (c) Electrical symbol for the memdiode. diode represents the presence of a potential barrier that controls the electron flow. The conduction properties of this nonlinear device change according to the variation of this barrier. Because of the uncertainty in the area of the CF, instead of the potential barrier Equations (3) and (4) represent the transition from HRS to LRS and height, the current amplitude is used as the reference variable. vice versa and can be physically connected with the completion and Following a memristive approach, the proposed model relies on two destruction of the CF,22 respectively. ηþ and η are the transition equations, one for the electron transport expressed as a diode with a rates, and V þ and V  are the set and reset voltages. V is the voltage series resistance and a second equation for the memory state of the a time step before V. Γþ (V) and Γ (V) define the so-called hysteron device which is based on a hysteresis operator. The equation for the or memory map of the device which records the history of the I–V characteristic of a single memdiode M is given by device as a function of the applied voltage [see Fig. 2(a)]. The initial value λ0 determines whether the device starts in LRS (λ0 = 1) or HRS (λ0 = 0). λ calculated from (2) yields the transition from HRS to LRS I ¼ sgn(V){(αR)1 W{αRI0 (λ) exp[α(abs(V) þ RI0 (λ))]} and vice versa through a change in the properties of the diodes  I0 (λ)}, (1) depicted in Fig. 2(b). This λ is used in turn to compute the current given by (1). The final result is a current loop as that illustrated in Fig. 2(a). Notice that only one diode D within the memdiode is acti- where I0 (λ) ¼ Imin (1  λ) þ Imax λ is the diode current amplitude, α vated at the time depending on the applied bias polarity. Inverse cur- is a constant related to the particular features of the conduction rents are neglected. Additionally, time effects (pulsed measurements mechanism, and R is a series resistance. Equation (1) is the solution and ramp rate effects) are not considered for present purposes but of a diode with series resistance and W is the Lambert function. Imin can be included as well using the extended model reported in Ref. 23. and Imax are the minimum and maximum values of the current The forward direction of the memdiode [see Fig. 2(c)] is defined amplitude, respectively. abs(V) is the absolute value of the applied so as to have positive V þ and negative V  [yellow and green curves bias, and sgn is the sign function. As I0 increases in (1), the I–V in Fig. 2(a)]. As an example, the model parameters used in Fig. 3(a) curve changes its shape from exponential to linear as experimentally for the BRS-cf8 curve are Imin = 5.0 ⋅ 10−6 A, Imax = 5.5 ⋅ 10−3 A, observed for this kind of devices. λ is a control parameter that runs α = 2.1 eV−1, R = 100 Ω, V+ = −2.02 V, V − = 0.7 V, η+ = −100 V−1, between 0 and 1 and is given by the recursive operator, η− = −5.2 V−1, and λ0 = 0. For the BRS-f8 curve [Fig. 3(c)], the n h   io model parameters are Imin = 6.5 ⋅ 10−5 A, Imax = 4.0 ⋅ 10−3 A, λðV Þ ¼ min Γ ðV Þ; max λ V ; Γþ ðV Þ ; (2) α = 2.1 eV−1, R = 250 Ω, V+ = 0.47 V, V− = −0.52 V, η+ = 100 V−1, η− = 12 V−1, and λ0 = 0. Notice that these electrical parameters can be connected to the physics through a proper choice of a particular where min and max are the minimum and maximum functions, conduction mechanism. It is worth mentioning that the model uses respectively. The positive and negative ridge functions in (2) are the outer I–V characteristic (major loop) as the calibration curve but defined as can deal with arbitrary input signals (minor loops). The compliance is simply introduced as a limit in the current magnitude given by (1). 1 Γþ (V) ¼ {1 þ exp[ηþ (V  V þ )]} (3) IV. RESULTS AND DISCUSSION and The experimental and simulated curves corresponding to the different switching modes detected in hafnia are summarized in Γ (V) ¼ {1 þ exp[η (V  V  )]}1 : (4) Fig. 3. The red curves are simulations while the green and yellow J. Appl. Phys. 125, 234503 (2019); doi: 10.1063/1.5094864 125, 234503-3 © Author(s) 2019 Journal of ARTICLE scitation.org/journal/jap Applied Physics FIG. 3. The blue dotted box includes the resistive switching curves associated with the stoichiometric HfO2-stack, while the black dotted box includes the curves of the deficient HfO1.5-stack, respectively. The stacks in the center (EC1, 2, and 3) represent the equivalent circuits used for simulating the corresponding switching modes (indi- cated by red arrows); M1 and M2 represent two memdiodes of opposite voltage polarity; the switching curves are named as follows: (a) counter figure eight-wise bipolar resistive switching (cf8-BRS); (b) unipolar resistive switching (URS); (c) figure eight-wise bipolar resistive switching (f8-BRS); (d) threshold resistive switching (TRS); (e) superimposed counter figure and figure eight-wise bipolar resistive switching (cf8 + f8-BRS); (f ) complementary resistive switching (CRS) also being a superposition of f8 and cf8-BRS; (g) and (h) extracted I–V curves for diodes M1 and M2 which when combined in series result in the CRS of (f ). Greenish curves represent experimental curves of bipolar nature and, therefore, are indicated as E-field assisted, while the yellowish curves represent experimental curves of unipolar nature and, therefore, are indicated as temperature assisted, respectively. # indicates the depicted cycle number. The red curves always represent the simulated curves of the model. J. Appl. Phys. 125, 234503 (2019); doi: 10.1063/1.5094864 125, 234503-4 © Author(s) 2019 Journal of ARTICLE scitation.org/journal/jap Applied Physics lines are experimental data with # indicating the depicted cycle number. A thorough description of the complete set of experiments carried out can be found in Ref. 20. The plots inside the blue dotted box are switching modes observed for the stoichiometric (HfO2) stack, namely, cf8-BRS [Fig. 3(a)], URS [Fig. 3(b)], and TRS [Fig. 3(d)]. The plots inside the black dotted box correspond to the switching curves for the highly deficient hafnia (HfO1.5) stack, namely, f8-BRS [Fig. 3(c)], a combination of cf8- and f8-BRS [Fig. 3(e)], and CRS [Fig. 3(f )]. Altogether, the two considered stacks show all observed resistive switching modes reported in the literature for HfOx, whereby only one material parameter was changed, namely, the initial oxygen vacancy concentration. We found that all switching modes associated with the stoichiometric sample can be simulated using a single memdiode as illustrated in the schematic EC1 in Fig. 3. Nevertheless, for the deficient stack an additional memdiode with opposite polarity (EC2 and EC3 in Fig. 3) is required for fitting the experimental curves. This dis- tinction indicates that for the deficient stack case an additional switching phenomenon is superimposed to the observed cf8-BRS behavior corresponding to the stoichiometric stack, which was found to result in the observed CRS [Fig. 3(f )] and combined f8 + cf8-BRS [Fig. 3(e)], respectively. The switching mechanism associated with the opposite polarity is operating in a lower voltage regime and thus can be isolated by choosing the appropriate voltage program. This consideration results in the f8-BRS switching behavior shown in Fig. 3(c). EC2 also consists of two antiserially connected memdiodes, but since the voltage program has been reduced only M2 is activated, while M1 simply acts as a series resis- tor. If the voltage span is increased (from −2.7 to +2.7 V), the second memdiode comes into play affecting the I–V curve [see Fig. 3(e)] which qualitatively is the superimposed switching behav- ior depicted in Figs. 3(a) and 3(c), respectively, and also depicted in the equivalent circuit EC3 as the series combination of M1 and M2. Notice how the proposed model is able to capture the repeti- tive hump in the positive side of the I–V curve in Fig. 3(e). If the FIG. 4. Simulated switching behavior of the deficient HfO1.5 stack in the positive voltage protocol is further increased with respect to that shown in voltage direction. (a) Applied voltage vs time, (b) current vs time, and (c) current Fig. 3(c), the set event in the f8-switching is followed by the reset vs voltage of the f8 + cf8 switching operation. Note that (c) is the composition of event in the cf8-switching for the positive voltage direction, while (a) and (b). By limiting the operation voltage to 1.3 V, the CRS can be isolated which is correlated to the set of the f8-switching (M2—Pt|HfOx) followed by the for the negative voltage direction the set event in the cf8-switching reset of the cf8-operation (M1—TiN|HfOx). By further increasing the operation is followed by the reset event in the f8-switching thus resulting in voltage, the reset of the cf8-operation is driven forward further resetting the the CRS mode [see Fig. 3(f )]. Therefore, all switching modes attrib- device to a higher resistance state. uted to the deficient HfO1.5-stack [Figs. 3(c), 3(e), and 3(f )] can be represented by two memdiodes in series as depicted in the sche- matic EC3. Model results for an arbitrary input signal (sinusoidal in this case) displaying the interplay of f8-set and cf8-reset resulting resistance [M1 (TiN|HfOx)]. By stopping the reset process at 1.3 V, in the CRS are depicted in Fig. 4. In (a) and (b), voltage- and CRS can be produced. By further increasing the operation voltage, current vs time characteristics of the f8 + cf8 switching operation the reset process of the cf8-operation can be carried on to higher are depicted, respectively. Due to an appropriate calculation of the resistance levels of the HRS resulting in the observed f8 + cf8 f8 + cf8 switching operation, any input signal within the calibration switching operation. region is feasible and renders fitting output data. The input does For the investigated stacks, the superimposed switching modes not need to be linear. Figure 4(c) is the composition of (a) and (b). with opposite polarity can be attributed to the effects occurring at When the operation voltage is limited to 1.3 V, the CRS mode can the two oxide interfaces, namely, Pt/HfOx and HfOx/TiN. While be isolated within the f8- and cf8-BRS switching operation of the TiN is able to form bonds to oxygen of ionic-covalent character HfO1.5 stack. Below 1 V, the set in the f8-operation dominates the forming titanium oxynitride24 (TiON), and which has been sug- device behavior resulting in a decrease of the overall device resis- gested in the literature to participate in the switching process,25 plati- tance being attributed to memdiode M2 (HfOx|Pt). Beyond 1 V, num is classified as an inert material showing catalytic properties. the reset in cf8-operation is activated overall increasing the device Therefore, the binding energy of oxygen at the Pt/HfOx-interface is J. Appl. Phys. 125, 234503 (2019); doi: 10.1063/1.5094864 125, 234503-5 © Author(s) 2019 Journal of ARTICLE scitation.org/journal/jap Applied Physics considerably lower than for the TiN/HfOx-interface.26,27 The model also accounts for the occasionally observed TRS mode observed f8-switching is thus attributed to the electric field domi- which coexists with the URS mode [see Fig. 3(d)]. TRS is ascribed nated storage and recapture of the mobile oxygen ions at the to a thermal runaway process, e.g., insufficient heat dissipation,33 Pt-interface, occurring at lower operation voltages with opposite resulting in the formation of an unstable filament. polarity (including lower on/off ratios) than the cf8-switching which Additional information on each memdiode (each interface we attribute to the interaction with the TiN-interface. As can be seen behavior) can be easily extracted in the case of CRS since almost from Fig. 3, only for the deficient stack combination, the Pt-interface identical parameters for both opposite devices are considered. This also actively participates in the switching process (M1 + M2), while is illustrated in Figs. 3(f)–3(h). In Figs. 3(g) and 3(h), the individ- for the stoichiometric stack only the TiN-interface is considered to ual I–V curves for M1 and M2 are plotted. The combined result be active in BRS (M1). This can be explained by the different oxygen is shown in Fig. 3(f). In this case, model parameters for M1 content in the hafnia layers resulting in a different electroforming are Imin = 6.0 ⋅ 10−4 A, Imax = 9.0 ⋅ 10−3 A, α = 2.2 eV−1, R = 70 Ω, process, thus influencing the conductive filament. Due to the defic- V+ = 0.6 V, V− = −0.6 V, η+ = 100 V−1, η− = 15 V−1, and λ0 = 0, iency of oxygen by oxygen engineering28,29 in the HfO1.5-stack, the while for M2: Imin = 6.0 ⋅ 10−4 A, Imax = 7.0 ⋅ 10−3 A, α = 2.2 eV−1, voltage used to electroform the device is found to be in the range of R = 10 Ω, V+ = 0.37 V, V− = −0.4 V, η+ = 100 V−1, η− = 10 V−1, and the operation voltages for set and reset, thus considered “forming- λ0 = 1. Notice that the initial memory states for M1 and M2 are the free.” Due to the pre-existent oxygen deficiency, in principle, opposite. Further insight into the role of interfaces within the resis- no further creation of oxygen vacancies—but rather a redistribution tive switching process can be achieved by analyzing the potential of oxygen in the dielectric layer is necessary for the formation of a drops in each memdiode. A detailed analysis of one CRS switching conductive pathway resulting in a cylindrical-shaped filament (as cycle is depicted in Fig. 5. In Fig. 5(a), the green and red curves are schematically shown in Fig. 3, EC2 and EC3, respectively). the experimental and simulated current-time characteristics, respec- Additionally, it was found that the f8-switching could be further sta- tively. The black curve in Fig. 5(b) corresponds to the applied trian- bilized by applying a two-step forming process, starting by a first gular voltage sweep. The blue and cyan curves are the voltage drops forming step in the positive voltage direction (oxygen moving across M1 (TiN|HfOx) and M2 (Pt|HfOx), respectively. Notice that toward Pt), followed by a second step in the negative voltage direc- the distribution of voltages is by no means intuitive. This kind of tion (oxygen moving toward TiN). On the other hand, no pre- analysis is of utmost relevance since one can pinpoint the role of existent oxygen vacancies facilitate the switching process for the each interface in the switching process and, therefore, theoretically stoichiometric HfO2-stack. This means that every oxygen vacancy modify their properties for the appropriate target. The same needs to be created first, resulting in the storage of oxygen at the TiN-interface. In this case, a higher forming voltage of about −7 V is required, resulting in higher current overshoots, and in turn in stronger Joule heating effects, with a consequent more vigorous breakdown of the dielectric layer. This generates a less uniform con- ductive filament (likely conical-shaped) with a single active interface in the subsequent switching loops. As described above, the single or the two-memdiode model used for simulations is of wide range applicability. Here, we related the observed superimposed switching mechanisms to the different interfaces but the distinctive behavioral analysis can also be extended to other systems such as multilayer stacks, e.g., TiN/HfO2/Hf/HfO2/TiN which have been shown to exhibit CRS due to two antiserially connected resistor elements.30 For the stoichiometric HfO2-stack, URS was also identified. While BRS operates in both voltage polarities, URS is detected only for positive bias. It has been reported in the literature31 that URS and BRS are the result of different dominating physical processes which are for the case of BRS more E-field dominated and for the case of URS more dependent on thermal effects. Thermal effects can arise from the local temperature increase associated with the high current densities and high local electric fields within the filament or in the case of a ruptured filament with the virtual elec- trode emission. Thereby, instead of field driven migration of FIG. 5. (a) Current- and (b) voltage-time evolution within one switching cycle of oxygen (as in the case of BRS), effects such as Fick’s diffusion and the CRS mode [as depicted in Fig. 2(f )]. (a) The green curve is the experimen- Soret31,32 forces dominate the oxygen transport accounting for ion tal current evolution, while the red curve represents the simulated current transport along concentration and temperature gradients, respec- through both memdiodes. (b) The black curve represents the applied voltage tively. In this case, oxygen displacements are likely to be more program starting at 0 V toward −1.2 V, followed by a linear voltage increase up lateral within the dielectric layer rather than directed toward the to +1.2 V and down to 0 V. The cyan and blue curves are the corresponding voltage drops at the individual TiN|HfOx (M1) and Pt|HfOx (M2) interfaces (mem- electrodes. Still, this behavior can be modeled by solely making use diodes), respectively. of one memdiode with positive V+ and V−. The single memdiode J. Appl. Phys. 125, 234503 (2019); doi: 10.1063/1.5094864 125, 234503-6 © Author(s) 2019 Journal of ARTICLE scitation.org/journal/jap Applied Physics procedure can be applied to the other cases investigated, but this 4 Z. Zhang, Y. Wu, H. S. P. Wong, and S. S. Wong, “Nanometer-scale HfOx requires more sophisticated algorithms for the model parameters RRAM,” IEEE Electron Device Lett. 34(8), 1005–1007 (2013). extraction. 5 D. Ielmini, “Resistive switching memories based on metal oxides: Mechanisms, reliability and scaling,” Semicond. Sci. Technol. 31(6), 063002 (2016). 6 T. Hino, T. Hasegawa, K. Terabe, T. Tsuruoka, A. Nayak, T. Ohno, and V. CONCLUSION M. Aono, “Atomic switches: Atomic-movement-controlled nanodevices for new In summary, it was shown that all reported switching modes types of computing,” Sci. Technol. Adv. Mater. 12(1), 013003 (2011). 7 S. Yu, H. Y. Chen, B. Gao, J. Kang, and H. S. P. Wong, “HfOx-based vertical for VCM-type RRAMs, in particular, for HfOx-based devices, can resistive switching random access memory suitable for bit-cost-effective three- be closely described by a simplified electrical conduction model. To dimensional cross-point architecture,” ACS Nano 7(3), 2320–2325 (2013). model all experimentally observed switching modes, the interface 8 M. Ziegler, C. Wenger, E. Chicca, and H. Kohlstedt, “Tutorial: Concepts for behavior was represented by one or two opposite-biased memdio- closely mimicking biological learning with memristive devices: Principles to des in series with appropriate initial conditions. While URS, TRS, emulate cellular forms of learning,” J. Appl. Phys. 124(15), 152003 (2018). 9 f8- and cf8-BRS can each be described by a single memdiode, the G. Pedretti, V. Milo, S. Ambrogio, R. Carboni, S. Bianchi, A. Calderoni, and observed CRS is only accessible by choosing the optimal voltage D. Ielmini, “Stochastic learning in neuromorphic hardware via spike timing region of the superimposed f8 + cf8-BRS and needs to be described dependent plasticity with RRAM synapses,” IEEE J. Emerg. Sel. Top. Circuits by two memdiodes. The separation of effects occurring at both Syst. 8(1), 77–85 (2018). 10 S. Petzold et al., “Gradual reset and set characteristics in yttrium oxide interfaces strongly supports the qualitative physical picture dis- based resistive random access memory,” Semicond. Sci. Technol. 34(7), 075008 cussed in Ref. 20. Interestingly, the proposed approach can also be (2019). used to represent other stack combinations, for example, bilayer or 11 M. Xiangchao et al., “A 16 Mb RRAM test chip based on analog power system multilayer stacks.30,33 By modeling, we were able to extract infor- with tunable write pulses,” in 2015 15th IEEE Non-Volatile Memory Technology mation on the individual interfaces, such as the potential drop dis- Symposium (NVMTS) (IEEE, 2015). tribution (and, therefore, their resistance evolution), which can be 12 E. Yalon, S. Cohen, A. Gavrilov, and D. Ritter, “Evaluation of the local temper- used in the future for engineering and fine tuning the switching ature of conductive filaments in resistive switching materials,” Nanotechnology process of these devices. To further improve the demonstrated 23(46), 465201 (2012). 13 behavioral model, additional cycle to cycle variation, stepwise U. Celano, L. Goux, A. Belmonte, K. Opsomer, A. Franquet, A. Schulze, transitions, temperature effects, and pulse operation applicability C. Detavernier, O. Richard, H. Bender, M. Jurczak, and W. Vandervorst, “Three-dimensional observation of the conductive filament in nanoscaled resis- could be implemented in future. tive memory devices,” Nano Lett. 14(5), 2401–2406 (2014). 14 M. Lanza, “A review on resistive switching in high-k dielectrics: A nanoscale ACKNOWLEDGMENTS point of view using conductive atomic force microscope,” Materials 7(3), 2155–2182 (2014). The work leading to this publication has been undertaken in 15 H. Bae, B. C. Jang, H. Park, S. H. Jung, H. M. Lee, J. Y. Park, S. Jeon, G. Son, the framework of the WAKeMeUP project which received funding I. Tcho, K. Yu, S. U. Im, S. Choi, and Y. Choi, “Functional circuitry on commer- from the Electronic Components and Systems for European cial fabric via textile-compatible nanoscale film coating process for fibertronics,” Leadership Joint Undertaking in collaboration with the European Nano Lett. 17(10), 6443–6452 (2017). Union’s H2020 Framework Programme (H2020/2014-2020) and 16 H. Du, C. L. Jia, A. Koehl, J. Barthel, R. Dittmann, R. Waser, and J. Mayer, National Authorities, under Grant Agreement No. 783176. This “Nanosized conducting filaments formed by atomic-scale defects in redox-based work was supported by Deutscher Akademischer Austauschdienst resistive switching memories,” Chem. Mater. 29(7), 3164–3173 (2017). 17 (DAAD) and the Deutsche Forschungsgemeinschaft under Project A. Zintler, U. Kunz, Y. Pivak, S. U. Sharath, S. Vogel, E. Hildebrandt, No. AL 560/13-2. Funding by the Federal Ministry of Education H.-J. Kleebe, L. Alff, and L. Molina-Luna, “FIB based fabrication of an operative Pt/HfO2/TiN device for resistive switching inside a transmission electron micro- and Research (BMBF) under Contract No. 16ESE0298 is gratefully scope,” Ultramicroscopy 181, 144–149 (2017). acknowledged. E.M. acknowledges support from MINECO, Spain 18 K. H. Xue and X. S. Miao, “Oxygen vacancy chain and conductive filament for- (Project No. TEC2017-84321-C4-4-R) and WAKeMeUP project. mation in hafnia,” J. Appl. Phys. 123(16), 161505 (2018). Also, funding from DFG under Grant Nos. MO 3010/3-1 and AL 19 C. Li, B. Gao, Y. Yao, X. Guan, X. Shen, Y. Wang, P. Huang, L. Liu, X. Liu, 560/21-1 and the European Research Council (ERC) “Horizon J. Li, C. Gu, J. Kang, and R. Yu, “Direct observations of nanofilament evolution 2020” Program under Grant No. 805359-FOXON is gratefully in switching processes in HfO2-based resistive random access memory by in situ acknowledged. TEM studies,” Adv. Mater. 29(10), 1602976 (2017). 20 S. U. Sharath, S. Vogel, L. Molina-Luna, E. Hildebrandt, C. Wenger, J. Kurian, M. Duerrschnabel, T. Niermann, G. Niu, P. Calka, M. Lehmann, H. Kleebe, REFERENCES T. Schroeder, and L. Alff, “Control of switching modes and conductance quanti- 1 A. C. Torrezan, J. P. Strachan, G. Medeiros-Ribeiro, and R. S. Williams, zation in oxygen engineered HfOx based memristive devices,” Adv. Funct. Mater. “Sub-nanosecond switching of a tantalum oxide memristor,” Nanotechnology 27(32), 1700432 (2017). 22(48), 485203 (2011). 21 M. P. Agustin, L. R. C. Fonseca, J. C. Hooker, and S. Stemmer, “Scanning 2 C. H. Cheng, C. Y. Tsai, A. Chin, and F. S. Yeh, “High performance ultra-low transmission electron microscopy of gate stacks with HfO2 dielectrics and TiN energy RRAM with good retention and endurance,” in 2010 IEEE International electrodes,” Appl. Phys. Lett. 87(12), 121909 (2005). Electron Devices Meeting (IEDM) (IEEE, 2010), pp. 19.4.1–19.4.4. 22 E. Miranda, “Compact model for the major and minor hysteretic I–V loops in 3 S. Petzold, S. U. Sharath, J. Lemke, E. Hildebrandt, C. Trautmann, and L. Alff, nonlinear memristive devices,” IEEE Trans. Nanotechnol. 14(5), 787–789 (2015). “Heavy ion radiation effects on hafnium oxide based resistive random access 23 G. A. Patterson, J. Suñé, and E. Miranda, “Voltage-driven hysteresis model for memory,” IEEE Trans. Nucl. Sci. 1-1 (2019), see https://ieeexplore.ieee.org/ resistive switching: SPICE modeling and circuit applications,” IEEE Trans. stamp/stamp.jsp?tp=&arnumber=8688490&tag=1. Comput. Aided Des. Integrated Circuits Syst. 36(12), 2044–2051 (2017). J. Appl. Phys. 125, 234503 (2019); doi: 10.1063/1.5094864 125, 234503-7 © Author(s) 2019 Journal of ARTICLE scitation.org/journal/jap Applied Physics 24 N. C. Saha and H. G. Tompkins, “Titanium nitride oxidation chemistry: 29 S. U. Sharath, T. Bertaud, J. Kurian, E. Hildebrandt, C. Walczyk, P. Calka, An x-ray photoelectron spectroscopy study,” J. Appl. Phys. 72(7), 3072–3079 P. Zaumseil, M. Sowinska, D. Walczyk, A. Gloskovskii, T. Schroeder, and L. Alff, (1992). “Towards forming-free resistive switching in oxygen engineered HfO2−x,” Appl. 25 X. Guan, S. Yu, and H. S. P. Wong, “On the switching parameter variation of Phys. Lett. 104(6), 063502 (2014). 30 metal-oxide RRAM—Part I: Physical modeling and simulation methodology,” D. J. Wouters, L. Zhang, A. Fantini, R. Degraeve, L. Goux, Y. Y. Chen, IEEE Trans. Electron Devices 59(4), 1172–1182 (2012). B. Govoreanu, G. Kar, G. Groeseneken, and M. Jurczak, “Analysis of comple- 26 J. H. Weaver and H. P. R. Frederikse, CRC Handbook of Chemistry and Physics mentary RRAM switching,” IEEE Electron Device Lett. 33(8), 1186–1188 (2012). (CRC Press, Boca Raton, 1977), Vol. 76, pp. 12–156. 31 J. J. Yang, D. B. Strukov, and D. R. Stewart, “Memristive devices for comput- 27 B. Avasarala and P. Haldar, “Electrochemical oxidation behavior of titanium ing,” Nat. Nanotechnol. 8(1), 13 (2013). 32 nitride based electrocatalysts under PEM fuel cell conditions,” Electrochim. Acta S. Kumar, C. E. Graves, J. P. Strachan, E. M. Grafals, A. L. D. Kilcoyne, 55(28), 9024–9034 (2010). T. Tyliszczak, J. Weker, J. Nishi, and R. S. Williams, “Direct observation of local- 28 S. U. Sharath, M. J. Joseph, S. Vogel, E. Hildebrandt, P. Komissinskiy, ized radial oxygen migration in functioning tantalum oxide memristors,” Adv. J. Kurian, T. Schroeder, and L. Alff, “Impact of oxygen stoichiometry on electro- Mater. 28(14), 2772–2776 (2016). forming and multiple switching modes in TiN/TaOx/Pt based ReRAM,” Appl. 33 E. Linn, R. Rosezin, C. Kügeler, and R. Waser, “Complementary resistive Phys. Lett. 109(17), 173503 (2016). switches for passive nanocrossbar memories,” Nat. Mater. 9(5), 403 (2010). J. Appl. Phys. 125, 234503 (2019); doi: 10.1063/1.5094864 125, 234503-8 © Author(s) 2019