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6.1 Introduction

The resistive-switching memory (RRAM) is an emerging memory device based on the reversible change of resistance in an active material, usually a metal oxide (e.g., NiO, TiO2, HfO x , TaO x ) [1–5] or a chalcogenide glass (e.g., GeSe, GeS) [6, 7]. The change of resistance is generally due to the formation and the dissolution of a conductive filament (CF) with a size of a few nanometers. The CF is initially created by a dielectric breakdown process, similar to the one observed in silicon dioxide [8–10]. In metal oxides, the material degradation due to high field and high temperature during breakdown results in a local transformation of the insulating active layer into a conductive phase, e.g., a metal [11] or an oxygen-deficient region with relatively high conductivity [12, 13]. Figure 6.1 shows a scanning electron microscopy (SEM) image of a typical CF in a Pt–CuO–Pt RRAM, supporting the localized nature of the switching [2]. Other reports have indicated that the CF in TiO2 RRAM consists of Ti4O7, a Magneli phase of titanium oxide exhibiting metallic conductivity [12]. For reference, oxygen-deficient silicon oxide was also found at the breakdown spot of the gate dielectric in MOS devices [9, 10]. In chalcogenide-based RRAM, instead, the CF originates from electrodeposition of cations, such as Ag and Cu, from one electrode to the other due to field- and temperature-induced electrochemical reactions [6, 7]. These electrochemical devices are generally referred to as conductive-bridge memory (CBRAM) and can also feature silicon or metal oxides as active layers or electrolytes [14, 15].

Fig. 6.1
figure 1

SEM image of a conductive nanofilament, in a Pt–CuO–Pt resistive switching memories. Reprinted with permission from [2] (©2008 Elsevier Ltd.)

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The first observations of reversible switching in metal oxides date back to the 1960s, demonstrating electrically induced resistance change in NiO [16], TiO2 [17], and Nb2O5 [18]. Most recently, resistive switching was shown to take place in ternary oxides such as Cr-doped SrTiO3 [19] and ferroelectric Pb(Zr0.52Ti0.48)O3 (PZT) [20]. In the last decade, intensive industrial and academic research on RRAM devices has resurfaced for several binary metal oxides, such as NiO [21–24], TiO x [25–28], CuO x [29], HfO x [30, 31], and TaO x [32, 33]. These works have aimed at evaluating the potential of the new technology in terms of scalability in view of a possible replacement of Flash memories for high-density nonvolatile storage and memories. From this standpoint, RRAM is most attractive for ultrascaled nonvolatile memories below the 10 nm node, due to its low and controllable programming current and fast switching, resulting in a low switching energy. For instance, a programming current below 10 μA was reported thanks to the control of the CF size through a transistor in series with the RRAM device, in the so-called one transistor/one resistor (1T1R) structure [34–37]. Programming currents in the range of a few μA have also been reported in other instances [38–40]. On the other hand, programming times in the range of a few ns or even less have been reported [40–42]. As a reference, considering a programming current of 1 μA with a programming time of 1 ns with a programming voltage of 1 V, a switching energy of 1 fJ is obtained. For comparison, the switching time in SRAM and DRAM is in the range of 3–10 ns with a switching energy of around 10 pJ, which highlights the strong potential of RRAM as a possible replacement of both nonvolatile and computer (system) memories. The area scaling of RRAM also seems promising, given the small size of the CF, together with the reported capability to control the CF size through limitation of the programming current during the formation stage [36, 37].

Although promising from several different aspects, including area scaling, switching speed, and energy consumption, RRAM still faces some fundamental limits. First, industrial development of RRAM will be possible only if this technology is demonstrated to be scalable enough to cover two or three technology nodes, otherwise the return of the industrial investments would not be sufficient. Second, reliability issues are still not completely understood, particularly in terms of cycling endurance, namely the number of program/erase cycles that can be achieved in one cell, and data retention, namely the maximum lifetime of the memory state. In particular, the low cycling endurance might critically limit the applicability of RRAM for system memories replacing SRAM and DRAM. To best address such scalability and reliability issues, the physical mechanisms must be thoroughly understood and physically based models must be developed, thus allowing for accurate prediction of scalability and for improvement and optimization of reliability.

This chapter will cover the current status about the understanding of switching and reliability mechanisms in bipolar switching RRAM. First, memory operation, including formation and program/erase switching in unipolar and bipolar memory devices, will be described. Then, the microscopic mechanisms for the resistive switching will be discussed based on experimental results obtained from HfO x RRAM devices. A physical model for resistive switching will be shown, demonstrating the ability to predict switching parameters, such as resistance in the low resistance state and programming current as a function of operating conditions, such as the maximum current during CF formation. Finally, the reduction of switching time, switching energy, and CF size and their reliability implications will be addressed.

6.2 Unipolar, Bipolar, and Complementary Switching Characteristics

Figure 6.2 shows typical I–V characteristics including the resistive switching transitions for (a) unipolar, (b) bipolar, and (c) complementary switching operations. In all cases, two transitions can be identified, namely a set transition for achieving a low resistance state and a reset transition to achieve a high resistance state. The low and high resistance states will be referred to as set and reset states in the following. In unipolar switching (Fig. 6.2a), set and reset can be operated irrespective of the voltage polarity, while in bipolar switching set and reset are achieved under opposite polarities, e.g., positive voltage for set and negative voltage for reset (Fig. 6.2b). Complementary switching features instead set and reset transitions at both positive and negative polarity (Fig. 6.2c) [43]. Complementary switching was first introduced for ad hoc, antiserially connected RRAM stacks [44], then demonstrated as a fundamental switching mode in individual oxide layers in [43].

Fig. 6.2
figure 2

Schematic current-voltage characteristics for the three switching modes of filamentary RRAMs, namely unipolar switching (a), bipolar switching (b), and complementary switching (c). Set/reset transitions occur independent of the bias polarity in unipolar switching, while they must be operated at opposite polarity in bipolar switching, e.g., set transition at positive polarity and reset transition at negative polarity. The maximum current flowing through the device after set is limited at a compliance current I C in both unipolar and bipolar switching. In complementary switching, set with no I C-limitation is followed by reset at the same polarity, allowing for the transition from a high resistive state to a different high resistive state. The two states differ by the position of the reservoir of conductive ions, see Fig. 6.3. Application of a negative sweep allows achieving the initial high resistive state through set and reset transitions

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In the unipolar-switching case, the I–V curve of the reset state (OFF state in Fig. 6.2a) displays a sudden set transition at a relatively large voltage, where the device achieves a low resistance through formation (or re-activation) of the CF. In general, a current compliance I C (“cc” in Fig. 6.2a), namely a limitation in the total current flowing through the device, is enforced during the set transition to prevent excessive growth of the CF which may eventually result in an irreversible breakdown [36, 37]. The I–V curve in the set state displays a reset transition at a reset voltage V reset and a reset current I reset. Reset is due to the dissolution of the CF, resulting in the transition to a high resistance state. No compliance is enforced during the reset current, thus allowing the necessary voltage and current to reach the values which are needed to dissolve the CF. The possible shape of the CF is schematically shown in Fig. 6.3 for the (a) set and (b) reset states. The conductive species are believed to diffuse radially or vertically from the CF at the hottest location during reset, as a result of thermally activated diffusion and migration [45].

Fig. 6.3
figure 3

Schematic illustration of the set and reset states in unipolar, bipolar, and complementary switching. Set state corresponds to a continuous CF in any case, while the reset state may differ depending on the polarity of the set/reset processes. In unipolar switching, set (a) and reset (b) states correspond to a continuous and interrupted CF, respectively, where filament breakdown is supposed to take place in the middle of the CF due to local temperature increase and consequent diffusion and oxidation. In bipolar switching, set (c) and reset (d) states correspond to a continuous and a interrupted filament, respectively, both with asymmetric structure due to the presence of a reservoir of conductive ions at one electrode (the top electrode in the scheme reported here). A negative applied voltage results in the transition from (c) to (d), as positively charged ions are attracted toward the top electrode by the electric field. In complementary switching, a positive applied voltage results in the transition from an initial reset state, corresponding to ions accumulated at the top electrode (e), to a set state, where ions are distributed along a continuous CF (f). A further increase of the applied positive voltage leads to the accumulation of conductive ions to the bottom electrode, thus resulting in a second reset state (g). Application of a voltage sweep with negative polarity results in the reverse transition, from (g) to (e) through set and reset transitions

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In the bipolar switching case, the I–V curves in Fig. 6.2b display instead the set transition at a relatively large, positive voltage, while the reset transition takes place under a relatively low negative voltage. Note that the polarity may change depending on the particular active material/stack and on the initial forming operation. However, bipolar switching always requires voltage polarity reversal for repeatable set and reset processes. Figure 6.3c, d show the set and reset states, respectively, assuming that a positive (negative) voltage applied to the top electrode results in set (reset) transition. Most of the conductive ions are believed to remain at the top electrode, resulting in an asymmetric (e.g., conical) shape of the CF in the set state. Set and reset transitions mostly take place through vertical ion migration, activated by the temperature in the direction of the electric field.

Finally, the complementary switching characteristics in Fig. 6.2c were recently demonstrated for bipolar switching devices such as HfO x RRAM [43]. In complementary switching, the set transition under positive voltage applied to the top electrode is not limited by any compliance, therefore the CF achieves a maximum size which is only limited by the amount of available conductive ions (e.g., hafnium ions Hf+ or oxygen vacancies V +O ) in the switching location. After completion of CF growth, the voltage is further increased, leading to the migration of conductive ions toward the negative (bottom) electrode and to a consequent deactivation of the CF, resulting in a reset transition at a relatively large voltage. After reset, almost all ions that contributed to the formation and growth of the CF are located at the bottom negative electrode side and the resistance is relatively high, given the absence of a continuous CF. A similar operation is then carried out under negative voltage applied to the top electrode, leading to ion migration from the reservoir located at the bottom electrode toward the top electrode. This leads to a set transition, i.e., CF nucleation and growth, followed by reset, i.e., CF dissolution due to further ion migration toward the top negative electrode [43]. The same sequence can be further repeated until a maximum number of cycles, limited by the endurance lifetime. Complementary switching was first demonstrated in ad hoc stacks, consisting of a metal–insulator–metal–insulator–metal (MIMIM) structure where the intermediate electrode served as the initial reservoir for cations (positively charge ions), e.g., Cu or Ag ions [44, 46]. The application advantage of complementary switching is that the two states encoding the logic bit have both high resistances, since they consist of the conductive ions being accumulated either toward the top or the bottom electrode. The absence of a low resistance state in the array allows purely passive crossbar arrays to be achieved without the need for any select device, e.g., diodes or threshold switches [47–57]. The two states can be recognized through the sensing of the current response to a positive voltage at the top electrode: a set/reset sequence is observed if ions are located at the top electrode, but not if they are at the bottom electrode, thus allowing the recognition of the internal logic state. Note that reading is destructive, since ions are displaced from their original location. Figure 6.3e–g shows the CF shape in the high resistance state with conductive ions at the top electrode in the set state and in the high resistance state with conductive ions at the bottom electrode, respectively. The application of a positive voltage to the high resistance state in Fig. 6.3e results in ion migration toward the bottom electrode, leading to the formation of a continuous CF (set state in Fig. 6.3f) and to the accumulation of ions at the bottom electrode (reset state in Fig. 6.3g). The reverse path is followed if a negative sweep is applied to the state in Fig. 6.3g.

A general question regarding unipolar, bipolar, and complementary switching is what mechanisms drive the set/reset transitions and what is the connection between the existence of a certain type of switching and the active material properties. In general, unipolar switching is attributed to thermochemical mechanisms, namely physical mechanisms driven by the temperature alone, with little or no role of the electric field direction [4]. Set is explained as a chemical reduction of the metal oxide, e.g., NiO → Ni + O, due to the high temperature achieved at the CF site during set. Reset is instead generally explained as the inverse chemical reaction, namely oxidation, e.g., Ni + O → NiO, occurring at the metal-rich CF due to the large local temperatures during voltage application [58]. Note that oxidation and reduction may generally occur in the same material system (e.g., NiO) depending on the temperature range, i.e., reduction and oxidation requires a relatively high and low temperature, respectively [4, 59, 60]. For bipolar switching, instead, the driving force for switching is believed to be the ion migration induced by the electric field and accelerated by the local temperature due to Joule heating [45, 61]. Typical unipolar switching materials are NiO [4, 11, 21–24, 34, 36, 37, 49, 62, 63], TiO2 [12, 27, 28], and TiON [64, 65], while bipolar switching materials include TiO2 [25–27, 32], HfO x [30, 31, 43], and WO x [40]. In several cases, a coexistence between unipolar and bipolar switching has been observed, namely materials capable of bipolar switching were demonstrated to feature also unipolar switching [38, 66–69].

6.3 Bipolar Switching Characteristics

Figure 6.4 shows the measured I–V characteristics for a bipolar switching RRAM with HfO x active oxide and TiN as electrode material in both the top and bottom contacts [70]. The thickness of the oxide layer was 20 nm, and the electrical switching was initiated by a forming stage at about +3 V (not shown). Set and reset transitions were observed under positive and negative voltage, respectively. The figure shows three I–V characteristics with a set/reset transition for increasing current compliance I C enforced during the set transition, namely I C = 0.5, 0.75, and 1 mA. The set transition occurs almost abruptly at about 0.5 V. Immediately after set, the current is limited to I C while the voltage drop across the device reaches a value V C of about 0.4 V. The resistance of the device in the set state is given by:

Fig. 6.4
figure 4

Measured I–V characteristics for a bipolar switching RRAM, consisting of a TiN/HfO x /TiN MIM stack with a 20 nm thick HfO x layer. Set and reset take place under positive and negative polarity, respectively. Set takes place at V set, then the current flowing during the set transition is externally limited to a compliance current I C. Increasing I C results in a decrease of the set-state resistance R and an increase of the reset current I reset. Note the rather constant voltage V C = RI C at the end of the set transition. The reset voltage V reset is also almost constant and similar to V C

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$$ R = {V_{\rm{C}}}{/}{I_{\rm{C}}}, $$
(6.1)

and is thus inversely proportional to I C given the almost constant V C = 0.4 V. At negative voltage, the reset transition is initiated at a reset voltage V reset, which is almost constant around 0.4 V, thus roughly equal to V C. The reset current I reset is therefore approximately given by:

$$ {I_{\rm{reset}}} = \eta {I_{\rm{C}}}, $$
(6.2)

with η ≈ 1, given that I reset = V reset/R ≈ V C/R = I C [61].

These findings are generally observed in most oxide-based RRAM devices, as summarized in Fig. 6.5a, b [45, 61]. Figure 6.5a, b show the measured set state resistance and the reset current, respectively, as a function of I C under DC-mode switching. Several oxide-RRAM materials are shown in the figure, including NiO [34, 37], TiO x [71], HfO x [30], and HfO x –ZrO x [72]. Data in Fig. 6.5a agree with the inverse proportionality between R and I C in Eq. (6.1), with V C = 0.4 V, while data in Fig. 6.5b confirm Eq. (6.2). The figures also report data for one transistor/one resistor (1T1R) structures, where the RRAM was in series with a MOS transistor to control the current flowing in the device during set [30, 34, 36, 37]. Data from 1T1R devices generally feature a smaller I reset, thanks to the absence of current overshoot exceeding I C during the set transition [36, 61, 73]. Note that data in the figures align on the same trend irrespective of the active material (NiO, HfO x , TiO x , etc.), of the switching mode (unipolar or bipolar switching), and of the cell structure (single MIM, 1T1R device). The independence of V C and η in Eqs. (6.1) and (6.2) on the active material suggests a universal switching kinetic for the formation of the CF, with little or no dependence on the metal oxide composition [45, 61].

Fig. 6.5
figure 5

Measured resistance R in the set state (a) and reset current I reset (b) as a function of I C, for both unipolar and bipolar switching and for several metal oxides, including NiO [21, 34, 36, 37], TiO x [71], HfO x [30], and HfO x –ZrO x [72]. The resistance is inversely proportional to I C according to Eq. (6.1), while I reset is proportional to I C according to Eq. (6.2). Note that all data follow the same universal line, irrespective of the switching mode or active material. Reprinted with permission from [45] (© 2011 IEEE)

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6.4 Time-Resolved Switching Characteristics

To gain more insight into the set transition described by Eq. (6.1) and into the universal switching characteristic, where V C does not significantly depend on the material or switching mode, time-resolved switching experiments have been carried out. In these experiments, set pulses with voltage amplitude V A were applied to a RRAM device with a load resistance R L in series, as illustrated in Fig. 6.6. The initial state was a reset state with resistance around 5 kΩ. A sequence of pulses with increasing pulsewidth was applied and the resistance R of the device was measured after each pulse. Between each set pulse, no reset pulse was applied, thus allowing tracking of the cumulative effect of set pulses for increasing time. The voltage across the cell during each set pulse V was also evaluated as:

Fig. 6.6
figure 6

Schematic illustration of the device layout for the time-resolved measurement of the set transition. The RRAM device is connected with a load resistance R L to limit the current during set. A pulse with voltage V A is applied, with a voltage drop V at the RRAM device. Reprinted with permission from [74] (©2011 IEEE)

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$$ V = \frac{R}{{R + {R_{\rm{L}}}}}{V_{\rm{A}}}, $$
(6.3)

where R is the resistance measured after the corresponding set pulse.

Figure 6.7 shows the measured R as a function of time for R L = 1 kΩ (a), 2.2 kΩ (b) and 5 kΩ (c) and for increasing applied voltage V A, from 1 to 3.5 V, for HfO x -based RRAM devices [74]. Figure 6.7d–f show the corresponding estimated V across the RRAM. Note the extremely wide time range in the experiments, from 100 ns to 1 s, which was possible thanks to a logarithmic increase of pulsewidth in the sequential set experiment [74]. In general, R decreases for increasing set time, as a result of the formation (nucleation) and growth of the CF. The set process becomes faster for increasing V A, as expected due to the voltage-accelerated kinetics of filament growth. The resistance at the end of the set transient at 1 s increases for increasing R L: This is similar to the compliance effect seen in Fig. 6.4, where a decreasing I C (corresponding to an increase of R L, since a larger R L provide more limitation to the current through the device) results in a larger R at the end of set.

Fig. 6.7
figure 7

Measured R and V for increasing load resistance R L = 1 kΩ (a, d), 2.2 kΩ (b, e), and 5 kΩ (c, f). The resistance was measured in a broad time scale from 10 ns to 1 s at increasing V A. The resistance drop reflects the formation and growth of the CF, where the growth rate increases for increasing V A. The final R increases with R L due to the decreasing compliance current. Note the universal character of the measured V across the cell, suggesting that V is the controlling parameter for the CF growth process. Reprinted with permission from [74] (© 2011 IEEE)

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The resistance limitation effect in Fig. 6.7a–c can be understood by considering the time and V A dependence of the voltage V across the cell as a function of time in Fig. 6.7d–f. Here, the RRAM voltage follows a unique function of time, which is independent from V A and R L. These results reveal that voltage is the controlling parameter for the filament growth process during set. In fact, V adjusts to a given value V C(t) at any time, irrespective of V A and R L, where V C is dictated by the filament growth kinetics in the material. The self-adjustment of the RRAM voltage is due to the presence of a negative feedback by the presence of a load resistance in series with the cell [75]: as the CF grows, its resistance decreases, thus the voltage across the device decreases due to Eq. (6.3). The growth process thus quenches itself, resulting in a self-limiting growth kinetics. Note that, if no load resistance is put in series with the RRAM device, no negative feedback is enforced, thus leading, in principle, to an unlimited growth of the CF. (In real devices, other limitation mechanisms take place, as already demonstrated by the complementary switching behavior described in Sect. 6.3.)

The results in Fig. 6.7d–f highlight the meaning of the constant V C at the end of the set transient in DC set experiments in Figs. 6.4 and 6.5: In particular, note in Fig. 6.7d–f that V is close to V C = 0.4 V at t = 1 s, at the end of the set experiment. V C has therefore the meaning of the natural voltage across the cell, which results from the CF growth in presence of a negative feedback, due, e.g., to a load resistance R L in series with the cell in Fig. 6.7, or to a current compliance I C in Figs. 6.4 and 6.5. Data in Fig. 6.7d–f also reveal that V C depends on the set time, e.g., a larger V C is expected for decreasing set time.

The universal behavior of V in Fig. 6.7d–f provides evidence for a voltage-controlled growth process in oxide-based RRAM. The voltage-controlled nature of the set transition results from the strong (e.g., exponential) dependence of the growth rate on voltage. In fact, such a strong dependence allows for a quick readjustment of the voltage across the cell at any given time during set. To gain more insight into the fundamental law governing the voltage dependence of the CF growth process, we have measured the set time t set and the reset time t reset as a function of cell voltage V. Set/reset times were estimated as the times for which the resistance decreases/increases by 50 % from the initial value. Figure 6.8 shows the time-resolved resistance change during reset in HfO x RRAM, starting from a low-resistance set state and for increasing V A between 0.6 and 1.2 V. No load resistance was applied during reset as already noted in Sect. 6.2, so that V = V A. The reset time decreases for increasing V A, revealing a similar voltage-controlled nature as evidenced for the set transition. Figure 6.9a shows the measured t set/t reset as a function of the cell voltage V, estimated by Eq. (6.3) with R L = 0 for reset. Both t set and t reset follow approximately the same dependence, with a strong dependence on voltage. In fact, t set and t reset change by ten decades upon a voltage increase from about 0.3 V to about 1.25 V, e.g., roughly a factor 4 [74]. These results are in agreement with similar data for RRAM devices based on the migration of Ag cations [75] and based on TiO x resistive switching [3]. Note, in particular, that the t set and t reset does not feature an exponential behavior on voltage, thus indicating that a simple F-model for set/reset is not sufficiently accurate. To understand the fundamental law driving set and reset kinetics, t set and t reset are shown in Fig. 6.9b as a function of 1/kT, where k is the Boltzmann constant and T is the local temperature at the localized filament [74]. The local temperature was evaluated from the Joule heating model described by:

Fig. 6.8
figure 8

Measured R as a function of time during reset for increasing V A. No load resistance was applied in series with the cell. The reset time, corresponding to a 50% increase of R, is marked on the figure, indicating an almost exponential decrease of t reset for increasing voltage

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Fig. 6.9
figure 9

Measured set and reset times, evaluated as a 50% resistance decrease or increase, respectively, as a function of voltage (a) and as a function of 1/kT (b), where T is the local temperature at the CF evaluated from the Joule heating formula of Eq. (6.4). The exponential dependence on 1/kT suggests that set/reset processes are due to temperature-activated mechanisms obeying an Arrhenius law

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$$ T = {T_0} + \frac{{{R_{\rm{th}}}}}{R}{V^2}, $$
(6.4)

where R th is the effective thermal resistance at the localized CF and T 0 is the temperature of the device (i.e., room temperature) [62, 75, 76]. The thermal resistance R th was evaluated as:

$$ {R_{\rm{th}}} = \frac{1}{{8{k_{\rm{th}}}}}\frac{{4L}}{{\pi {\phi^2}}}, $$
(6.5)

where k th is the thermal conductivity in the CF, L is its length, assumed equal to the oxide thickness, and φ is the diameter of the filament, assumed to have a cylindrical shape. The factor 8 in the denominator of Eq. (6.5) is obtained by solving the Fourier differential equation in the presence of a distributed Joule dissipation [76, 77]. The electrical resistance is given by a formula similar to Eq. (6.5), except for replacing 1/(8k th) with the electrical resistivity ρ. As a result, the ratio between thermal and electrical resistance in Eq. (6.4) can be written as:

$$ \frac{{{R_{\rm{th}}}}}{R} = \frac{1}{{8\rho {k_{\rm{th}}}}}. $$
(6.6)

For the T estimation in Fig. 6.9, a ratio R th/R = 1,500 kV−2 was assumed, corresponding to a thermal conductivity k th = 20 JK−1 cm−1 s−1, similar to the thermal conductivity of bulk hafnium, and an electrical resistivity ρ = 400 μΩ cm, which is about 30 times larger than bulk hafnium value. Such a large enhancement of electrical resistivity can be understood by the nonmetallic character of the CF, generally associated with a suboxide phase such a Ti4O7 in the case of TiO x RRAM [12, 13]. Also, one should consider that the electrical resistivity may be largely affected by significant surface and defect scattering at the nanoscale CF, as a result of the Fuchs–Sondheimer formula [78]:

$$ \rho = {\rho_{\rm{bulk}}}\left( {1 + \frac{3}{4}\frac{\lambda }{\phi }\left( {1 - p} \right)} \right), $$
(6.7)

where ρ bulk is the bulk electrical resistivity, λ is the electron mean free path, and p is the specularity factor, namely, the probability for elastic scattering at the surface of the CF. For instance, an electrical resistivity ρ = 380 μΩ cm, and thus close to the value used to estimate R th/R in Eq. (6.6), can be obtained for a Hf nanoscale filament of size φ = 1 nm, assuming λ = 28 nm and p = 0.5 [61, 78]. This supports the choice of electrical resistivity in the CF.

Data for t set and t reset in the Arrhenius plot of Fig. 6.9b display an almost linear behavior, thus suggesting that the set/reset process for filament growth and dissolution obeys a strong temperature activation, driven by the local temperature increase due to Joule heating. Also, the similarity between t set and t reset suggests that set/reset mechanisms have the same nature, e.g., the temperature-activated ion migration driven by the electric field at a localized spot. The voltage application during the set/reset pulse might thus have two important roles (1) providing the necessary Joule heating to allow completion of the filament growth/dissolution in a sufficiently short time, thanks to the Arrhenius temperature activation in Fig. 6.9b, and (2) providing the necessary electric field needed to drive ion migration in the correct direction, thus allowing to either fill an existing high-resistance gap through ion migration, to nucleate and grow a CF during set, or open a high resistance gap by ion migration during reset. Note finally that set and reset times display a weak difference at small voltages and temperatures. In particular, t set is generally larger than t reset at small voltages, or, equivalently, the set voltage V set is generally larger than the reset voltage V reset for the same time scale of the set/reset experiment. This is also clear from Fig. 6.4, where V set is around 0.6 V, with a smaller V reset of about 0.44 V. This can be understood by the fact that set is initiated by nucleation, where the CF must be initially formed through ion migration across a high resistance gap. Such an initial condition differs significantly from the one in the reset process, starting from a continuous CF with low resistance. In particular, one may expect that the initial temperature is larger in the continuous CF with respect to the disconnected CF, as a result of the change in electrical resistance in Eq. (6.4): the relatively larger value of R in the set state, compared to the reset state, results in a smaller local temperature due to Joule heating, for the same applied voltage. In addition, one should consider that, in the set state, only the ion migration is accelerated by the temperature at the tip of the broken CF, which may be significantly smaller than the maximum temperature evaluated by Eq. (6.4). As a result, a resistance-dependent overvoltage must be supplied to the reset state to initiate the set transition. Generally, the larger the resistance, the larger the voltage needed to trigger set, according to Eq. (6.4). Note that one should also consider the change in the thermal resistance, which might possibly compensate the increase of R in Eq. (6.4). However, thermal resistance changes are believed to be less marked, due to the phonon contribution to thermal conduction in the quasi-insulating gap.

6.5 Physical Mechanism for Bipolar Switching

The previous experimental analyses have pointed out the following evidences:

  • Set is a voltage-controlled process, where the filament growth kinetics is a strong function of voltage, thus the voltage across the cell follows a universal evolution with time in the presence of a load resistance or current compliance system.

  • Set and reset processes share the same fundamental physical mechanism, since similar set/reset times are observed as a function of voltage across the device.

  • Set and reset processes are temperature accelerated through an Arrhenius law, where the local temperature increase due to Joule heating allows for the completion of CF growth/dissolution mechanisms in an extremely short time, e.g., few ns or even sub-ns time scales.

These evidences point to a fundamental role of ion migration during set/reset processes. Ion migration, in fact, accounts for the bipolar character of switching, since ions are pushed and retracted toward one electrode during set and reset process, respectively, thus allowing for the filling and opening of a depleted gap with high resistance. Ion migration obeys also a temperature-accelerated kinetics, due to thermally activated ion hopping among localized states [61, 75, 79, 80]. In this perspective, it should be noted that Eqs. (6.1) and (6.2), which control the I C dependence of set and reset voltage and currents, are found not only in oxide-based RRAMs (e.g., see Fig. 6.5), but also in conductive-bridge RAM (CBRAM), namely RRAM devices which rely on the migration of Ag or Cu. Such metallic ions are supplied from one of the electrodes and migrate through a high resistance layer, typically a chalcogenide glass [6, 7, 75] or an oxide layer [14, 15]. For reference, Fig. 6.10 shows the measured R (a) and the measured I reset (b) as a function of I C, for CBRAM devices based on Ag migration in GeSe and on Cu migration in SiO x [15]. Data for HfO x RRAM are also shown for reference [30]. Results obey Eqs. (6.1) and (6.2), although with V C ≈ 0.2 V and η ≈ 0.5, and thus smaller than the values obtained from oxide-RRAM in Fig. 6.5. While the smaller values of V C and η can be understood by different values of the activation energy for set and reset, the validity of Eqs. (6.1) and (6.2) suggests that the same physical mechanisms control set/reset processes in both oxide-based RRAM and CBRAM. Since the latter obviously rely on ion migration for CF formation/disruption, the same mechanisms is strongly supported as the key physical phenomenon driving set/reset in oxide-RRAM.

Fig. 6.10
figure 10

Measured and calculated R (a) and I reset (b) as a function of I C, for HfO x -based RRAM devices [30] and CBRAM devices based on Ag:GeSe or Cu:SiO2 [15]. All material systems display similar behaviors in agreement with Eqs. (6.1) and (6.2), suggesting common mechanisms for set/reset in RRAM and CBRAM devices. The figure also shows calculations according to the model described in Sect. 6.6. Reprinted with permission from [74] (© 2011 IEEE)

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Figure 6.11 shows the physical picture for resistive switching in oxide-based RRAM, which is compatible with the experimental evidence gained so far. The figure shows snapshots during the set process, illustrating the nucleation (a, b) and growth (c, d) stages of the CF. The initial state corresponds to a broken CF, where conductive species (e.g., Hf ions and/or oxygen ions and/or oxygen vacancies in HfO x ) have been accumulated toward the top electrode by a previous reset process under negative voltage. The application of a positive voltage at the top electrode drives the ions toward the bottom electrode, resulting in the formation of a CF nucleus, i.e., the smallest continuous connection of the two electrodes through conductive species, and its subsequent growth. Electrical conduction through the CF results in Joule heating and a temperature increase, thus accelerating the growth process. As the filament grows, its resistance decreases, thus resulting in a decrease of the voltage across the oxide layer according to Eq. (6.3), if a compliance system or a load resistance is connected to the device during set. The resulting voltage reduction quenches the driving force for ion migration, thus slowing down the growth process. If no compliance or series resistance is present in the circuit, the growth process will take place until all ions in the reservoir at the top electrode are used in the CF. From this point, further ion migration might result in a reduction of the CF size and in accumulation of the ions toward the bottom electrode, thus resulting in a reset process. This has been indeed demonstrated in HfO x -based RRAM devices and is the basis for the complementary switching operation described in Sect. 6.1. For an interrupted set process described by Fig. 6.11, the reset process can be described by the same sequence but in reverse order, namely from d to a.

Fig. 6.11
figure 11

Schematic illustration of the filamentary growth process based on ion migration during set. In a reference HfO2 RRAM, ion migration results in filament nucleation (a, b) and successive growth (c, d), leading to a resistance drop during set transition. The reverse sequence applies for describing the reset process of filament dissolution. Reprinted with permission from [61] (© 2011 IEEE)

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6.6 Physical Model for Bipolar Switching

The set transition illustrated in Fig. 6.11 can be given a simple analytical description through the experimental evidence for ion migration driven by field and the local temperature [61, 74]. According to this model, the size of the CF increases with time according to the following growth equation:

$$ \frac{{{\text{d}}\phi }}{{{\text{d}}t}} = A{{\text{e}}^{{ - \frac{{{E_{\rm{A}}}}}{{kT}}}}}, $$
(6.8)

where E A is the activation energy for ion migration and A is a preexponential coefficient. The model is justified by noting that the filament growth takes place through ion migration from the reservoir to the CF, and thus is limited by the migration process. The latter is thermally activated through the Arrhenius law, as already evidenced from experiments shown in Fig. 6.9. From this perspective, A may be a rather complicated function of ion diffusivity in the considered active oxide or grain boundaries, the filament length L, and the composition/volume of the ion reservoir (pure metallic phase, oxygen deficient oxide, etc.). The local temperature T in Eq. (6.8) can be obtained by the Joule heating in Eq. (6.4), while the activation energy decreases due to the applied field as a result of the barrier lowering effect. This is shown in Fig. 6.12, where the potential profile along the active oxide layer is depicted for zero and nonzero applied voltages [45, 75]. Application of a voltage V across the oxide layer results in a lowering of the barrier according to:

Fig. 6.12
figure 12

Schematic illustration of the voltage-induced lowering of the energy barrier for ion hopping during filamentary growth/dissolution. Ions hop among potential wells through thermal excitation over potential barriers of amplitude E A0. The voltage V lowers the barrier by an amount qαV, thus enhancing migration in the direction of the electric field. Reprinted with permission from [45] (© 2011 IEEE)

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$$ {E_{\rm{A}}} = {E_{{{\rm{A}}0}}} - q\alpha V, $$
(6.9)

where E A0 is the zero-field activation energy and α is a constant [45, 75]. Substitution of Eqs. (6.4) and (6.9) in Eq. (6.8) results in:

$$ \frac{{{\text{d}}\phi }}{{{\text{d}}t}} = A{{\text{e}}^{{ - \frac{{{E_{{{\rm{A}}0}}} - q\alpha V}}{{k\left( {{T_0} + {{{{R_{\rm{th}}}}} \left/ {R} \right.}{V^2}} \right)}}}}}, $$
(6.10)

which shows that application of a voltage has two enhancement effects on the growth rate, namely the barrier lowering and the Joule heating. Note that, while the model fully describes the growth process, it cannot account for the nucleation process, where the initial high-resistance gap is filled by ions. However, this approximation is largely acceptable because (1) the nucleation process only results in a minor overvoltage of V set with respect to V reset, of about V set − V reset = 0.15 V in Fig. 6.9, and (2) the correlation between R and I C in Fig. 6.5a depends on the latest steps of the filament evolution, largely in the growth regime when the model in Eq. (6.10) already applies. Therefore, to understand and account for the set/reset characteristics in Figs. 6.5 and 6.7, the growth model provides sufficient physical accuracy.

The reset process can be modeled by Eq. (6.10) with a simple change in the sign of the preexponential coefficient A, to describe a decrease in size of the CF, instead of a growth. Such a reset model fully accounts for the Joule heating and filament evolution in the initial stages of the reset process, when there is a continuous CF connecting the two electrodes. On the other hand, the model may fail in describing the later stages of reset, when the gap opening results in a change in the thermal and electrical description of the filament. However, the model fully accounts for the calculation of parameters V reset and I reset in Fig. 6.5b, which are responsible for the initiation of the reset process.

6.7 Simulation Results

Figure 6.13 shows measured and calculated resistance and voltage across the cell for different load resistance R L = 1 kΩ (a, d), 2.2 kΩ (b, e), 5 kΩ (c, f). Data are the same as in Fig. 6.7, while calculations were performed with Eq. (6.10) assuming E A = 1.2 eV, A = 1 ms−1 and α = 0.3 [74]. The value chosen for the activation energy is in agreement with the energy barrier for diffusion and migration observed in various oxide systems, including NiO [62, 63, 76] and Gd-doped MoO [80]. Such a value should be viewed as the energy barrier for ion migration according to the schematic of Fig. 6.12. The value used for the barrier lowering coefficient α is similar to previous analysis [75, 79]. The choice of each of these values will be later sustained by individual comparisons with data. The calculations in the figure account very well for experimental data, in terms of voltage acceleration of the set process, where the increase of V A results in an increase of the growth speed revealed by the decrease of the resistance, and of the compliance effect, where the increase of R L results in a stronger limitation of the current, thus limiting the final size of the CF. In particular, note that the model accounts for the universal dependence of V on t in Fig. 6.13d–f, irrespective of the applied voltage and load resistance. This is because the growth rate in Eq. (6.10) is a strong function of V, thus enabling a regulation of the voltage across to the device thanks to the negative feedback loop, where any filament growth results in a decrease of voltage.

Fig. 6.13
figure 13

Measured and calculated R and V for increasing load resistance R L = 1 kΩ (a, d), 2.2 kΩ (b, e), and 5 kΩ (c, f). Calculations were performed using Eq. (6.10) with parameters E A0 = 1.4 eV, α = 0.3, and A = 1 m s−1. The model accounts for (1) the voltage acceleration of filament growth, (2) the dependence on R L due to current limitation, and (3) the universal time evolution of V, due to the exponential dependence of filament growth on V. Reprinted with permission from [74] (© 2011 IEEE)

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Figure 6.14 shows the calculated I–V curve during set and reset for increasing values of I C = 7 μA, 166 μA and 2.4 mA. Simulations were performed assuming a 1T1R structure, where the saturated current in the MOS transistor was given by I sat = KV 2OD /2, with K = 700 μA cm−2. V OD represents the overdrive voltage, namely, the gate voltage minus the threshold voltage of the MOS transistor. The current compliance is thus given by the saturated MOS current and was changed in the simulations by changing the gate voltage at the MOS transistor. A voltage V A = 0.8 V was applied during set from a reset state consisting of a high resistance state with an initial filament of φ N  = 0.5 nm diameter. During set, the current increases due to filament growth and the consequent decrease of resistance. Once the saturated current is approached, the voltage across the device decreases similar to Eq. (6.3) (although no load resistance can properly be defined in the case of nonlinear MOS characteristics). After 1 s, which was the maximum set time in the calculation, the voltage reached a value V C of about 0.4 V, and thus the final resistance obeys Eq. (6.1). During reset the MOS transistor was biased to a large conductivity to allow negligible series resistance in the 1T1R. The device current increases according to the I–V curves in the final set state until reset takes place at V reset, which is slightly larger than V C. As a result, the reset current I reset is only slightly larger than I C, thus satisfying Eq. (6.2). Note the abrupt current drop in the calculations, which is due to the rapid decrease of CF size and the consequent increase of resistance as the temperature reaches the critical value for the onset of ion migration.

Fig. 6.14
figure 14

Calculated I–V characteristics for set and reset at increasing I C = 7 μA, 165 μA, and 2.4 mA. A 1T1R structure was assumed in the calculations, with a constant applied voltage V A = 0.8 V during set and a voltage sweep during reset. Reprinted with permission from [61] (© 2011 IEEE)

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Figure 6.15 shows the measured and calculated R (a) and I reset (b) as a function of I C, for several oxide-based RRAM in the literature [21, 30, 34, 36, 37, 71, 72]. Calculations were done assuming a total time of 1 s during set and a sweep rate of 2 V s−1 during reset, corresponding to DC switching. Calculations in Fig. 6.15a, b satisfy Eqs. (6.1) and (6.2), respectively, for set and reset, as a result of the voltage-controlled set/reset kinetics. Calculations were done at variable E A = 0.9, 1.2 and 1.5 eV, while A and α were kept unchanged. A decrease of E A leads to a weak decrease in V C: This is because the energy barrier decreases enhances ion migration, thus a lower temperature (hence voltage) is needed to sustain filament growth at any given time. The voltage thus readjusts to a smaller value during set under the negative feedback condition of Eq. (6.3). However, the change of V C is relatively small, about 0.03 V for a 0.1 eV change of E A in the range considered. Such a small sensitivity of set characteristic to E A might explain why most oxide materials display the same V C in Fig. 6.15a. Note also that the similarity between I reset and I C, namely η ≈ 1 in Eq. (6.2), can be attributed to the fact that set and reset processes rely on the same physical mechanism, namely temperature and field activated ion migration. This ensures that the same voltage (hence temperature) is needed to activate migration during either set or reset, irrespective of the polarity, thus causing V reset = V C. As a consequence, the reset I reset is also approximately equal to I C, as already stated in Eq. (6.2) where η ≈ 1.

Fig. 6.15
figure 15

Measured and calculated R in the set state (a) and reset current I reset (b) as a function of I C, for both unipolar and bipolar switching and for several metal oxides, including NiO [21, 34, 36, 37], TiO x [71], HfO x [30, 74], and HfO x –ZrO x [72]. Calculations by the filament growth model accounts for Eqs. (6.1) and (6.2) describing the I C dependence of R and I reset, respectively. The constant voltage V C is due to the voltage regulation effect during set under a limited current compliance, as shown in Figs. 6.13 and 6.14. The similar values for I reset and I C are due to the common nature of set and reset mechanisms, driven by the same activation energy E A0. The universal R and I reset behaviors are due to the weak dependence on E A0, as shown by calculations for variable energy barrier. Reprinted with permission from [61] (© 2011 IEEE)

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To better understand the set mechanism, and in particular the universal time evolution of the voltage across the cell during set, one may consider rewriting Eq. (6.10) in the following way:

$$ {\text{d}}t = {A^{{ - 1}}}{\text{d}}\phi {{\text{e}}^{{\frac{{{E_{\rm{A}}}}}{{k\left( {{T_0} + {{{{R_{\rm{th}}}}} \left/ {R} \right.}{V^2}} \right)}}}}} = {A^{{ - 1}}}{\text{d}}\phi {{\text{e}}^{{\frac{{{E_{\rm{A}}}}}{{k{T_0}\left( {1 + {{{\beta I_{\rm{C}}^2}} \left/ {{{\phi^4}}} \right.}} \right)}}}}}, $$
(6.11)

where E A has been assumed a constant for simplicity, an ideal current limitation to a constant I C = V/R was considered and the parameter β has been introduced, given by:

$$ \beta = \frac{{2\rho {L^2}}}{{{\pi^2}{k_{\rm{th}}}{T_0}}}. $$
(6.12)

The integration of Eq. (6.11) leads to:

$$ {t_{\rm{P}}} = \int_{{{\phi_N}}}^{{{\phi_{\rm{set}}}}} {{\text{d}}\phi {A^{{ - 1}}}{{\text{e}}^{{\frac{{{E_{\rm{A}}}}}{{k{T_0}\left( {1 + {{{\beta I_{\rm{C}}^2}} \left/ {{{\phi^4}}} \right.}} \right)}}}}}} = \int_{{{\phi_N}}}^{{{\phi_{\rm{set}}}}} {f\left( \phi \right){\text{d}}\phi }, $$
(6.13)

where t P is the total duration of the set pulse, f(φ) is the function within the integral, and φ set is the final diameter of the filament at the end of the set transition. The function f(φ) in Eq. (6.13) cannot be integrated analytically. Figure 6.16 shows the calculated function f as a function of φ (a) and the corresponding integral, namely the duration of the set time (b), for three values of the current compliance I C = 1, 10 and 100 μA. Both φ and its integral are steeply increasing functions of the diameter, which indicates that the filament growth under constant I C extends over several decades of time with relatively little increase of diameter. The integral of Eq. (6.13) can be found by interpolation of the calculated curves at the total set time t P, and the result is shown for t P = 1 s, corresponding to a typical DC switching experiment. In all cases, the resulting φ set is found in the steep region of the integral of Fig. 6.16b. From inspection of Eq. (6.13), one may expect that the condition t P = 1 s is satisfied by a critical value of the term C 2 = βI 2C /φ 4 in the denominator of the exponent. This is demonstrated by the inset of Fig. 6.16, showing the extracted φ set as a function of I C and showing that φ set is proportional to I 0.5C . Note that latter can be viewed as R ∝ φ −2 ∝ I −1C , namely Eq. (6.1). The physical meaning of the parameter C = β 0.5 I C/φ 2 controlling the exponent in the integral of Eq. (6.13) can be understood by a simple elaboration, showing that:

Fig. 6.16
figure 16

Calculated function f in the integral of Eq. (6.13) (a) and time t resulting from the integration of the same equation (b) for increasing I C = 1, 10, and 100 μA. The curves of calculated t for a set time t P = 1 s indicate the final filament size after set transition, as shown in the inset as a function of I C. The proportionality φ set ∝ I 0.5C is consistent with R ∝ I −1C , thus providing a physical basis for the empirical formula in Eq. (6.1)

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$$ C = \frac{{{\beta^{{0.5}}}{I_{\rm{C}}}}}{{{\phi^2}}} = \frac{{R{I_{\rm{C}}}}}{{\sqrt {{2{k_{\rm{th}}}\rho {T_0}}} }} = \frac{V}{{\sqrt {{2{k_{\rm{th}}}\rho {T_0}}} }}, $$
(6.14)

namely C is proportional to V through a constant (2k th ρT 0)−1. Therefore, Eq. (6.13) indicates that there is a correspondence between V across the cell and time during the set transition. This is shown in Fig. 6.17, showing C ∝ V as a function of time for the three values of I C in Fig. 6.16: C (hence V) follows a universal function of time, irrespective of the current compliance, in agreement with results shown in Fig. 6.13.

Fig. 6.17
figure 17

Calculated parameter C = β 0.5 I C φ −2 as a function of time according to Eq. (6.14), for increasing I C. The independence from I C accounts for the universal time evolution of voltage in Fig. 6.13

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6.8 Switching Time and Energy

Switching speed and switching energy are among the most important properties defining the performance of a new device for low power, high speed integrated circuits. Figure 6.18 shows the calculated reset time t reset as a function of V (a) and as a function of 1/kT (b). The figure also shows experimental data for set and reset times (same data as in Fig. 6.9). The same parameter values for E A, A, and α in Fig. 6.13 were used, while three different CF sizes were used, corresponding to R = 220 Ω, 10 kΩ, and 400 kΩ. The model accounts very well for the switching times in both the voltage and Arrhenius plots. In particular, the Arrhenius behavior, which is a key feature in the filament growth model, is clearly indicated by data aligning on a straight line in Fig. 6.13b. A more detailed analysis reveals that the data and calculations in Fig. 6.13b are slightly nonlinear: this can be understood by the voltage-induced barrier lowering, which results in a decrease of E A (i.e., a flattening of the curve in the Arrhenius plot) for increasing voltage, hence decreasing 1/kT. These results also provide a direct way to extract the microscopic parameters for ion migration from experimental data, namely the activation energy E A can be extracted from the slope of data in the Arrhenius plot and the barrier lowering coefficient α can be extracted from the curvature of data in the Arrhenius pot. The figure also compares calculations for different initial sizes of the filament, showing that a smaller CF requires a shorter time for reset. Given the symmetry between set and reset, the same conclusion might be drawn for the set transition, provided that set is conducted at constant voltage as assumed for reset in Fig. 6.13. No dependence on final filament size is instead expected when variable CF sizes are achieved through different compliance levels, such as in Figs. 6.4 and 6.7. A reduction of set/reset times by roughly a factor 40 is expected for an increase of resistance from 220 Ω to 400 kΩ. This factor reflects the difference in the initial diameter φ set of the filament, which can be estimated as (400 kΩ/220 Ω)0.5 ≈ 40. In fact, according to the filament growth model, the reset time can be given by the formula [76]:

Fig. 6.18
figure 18

Measured set and reset times, as a function of V (a) and 1/kT (b), where T is the local temperature at the switching location. Calculations of the reset time are also shown for increasing R = 220 Ω, 10 kΩ, and 400 kΩ. Note that the curve in the Arrhenius plot is not perfectly linear, as a result of the voltage-induced energy barrier lowering. Adapted from [74] (© 2011 IEEE)

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$$ {t_{\rm{reset}}} = \frac{{{\phi_{\rm{set}}}}}{{2{v_{\rm{G}}}}}, $$
(6.15)

where v G is an effective growth velocity. Eq. (6.15) indicates that, for any given voltage, the reset time should be proportional to the initial filament size φ set.

Figure 6.19 shows the calculated reset energy E reset as a function of voltage for the three resistance values used in Fig. 6.18. Data for an initial resistance of 220 Ω are also shown for reference. The energy was calculated by the integral:

Fig. 6.19
figure 19

Measured and calculated set/reset energy as a function of V for R = 220 Ω, 10 kΩ, and 400 kΩ. The energy largely decreases for increasing V, due to the switching times decreasing almost exponentially in Fig. 6.18, and for increasing R, as a result of the decreasing I in Eq. (6.16). Adapted from [74] (© 2011 IEEE)

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$$ {E_{\rm{reset}}} = \int_{\rm{reset}} {VI{\text{d}}t} = \int_{\rm{reset}} {\frac{{{V^2}}}{R}{\text{d}}t}, $$
(6.16)

that is the integral of dissipated power in time during the reset transition. Note that only the energy dissipation in the device is considered in Eq. (6.16), while more energy could be dissipated at the series transistor/resistance or at the select device. The set energy E set dissipated in the device is equal to E reset for a constant voltage set, since set is just a reversed reset process in this case. For an I C-controlled set, such as in Fig. 6.14, the E set is expected to be even smaller than E reset, because, although V could be higher to provide the nucleation overvoltage, the transition becomes faster at high voltage according to the exponential relationship in Eq. (6.10), therefore reducing the product V 2dt in Eq. (6.16).

Results in Fig. 6.19 suggest two ways to efficiently reduce the reset energy in RRAM: First, E reset decreases significantly for increasing voltage, as a result of the almost exponential enhancement of transition speed with voltage in Eq. (6.10). Second and most importantly, reducing the size of the CF results in a remarkable reduction of E reset at a given voltage, thanks to the increase of R in Eq. (6.16). From the figure, reset energies of the order of 10 fJ can be achieved by reset at about 1 V on a RRAM device with 400 kΩ resistance, corresponding to 2.5 μA reset current and 5 ns switching.

6.9 Scaling Challenges

From the results in Figs. 6.18 and 6.19, CF size control and reduction appears as an effective way to reduce both transition time and energy consumption in RRAM. To achieve such large CF resistances, however, one should ensure a sufficiently high resistance in the reset state, too. In this perspective, having a large resistance window available in the RRAM device is a key requirement, since it allows writing extremely small CFs by taking advantage of the improved programming speed and reduced energy consumption.

The reduction of the CF size has another important impact on the scaling of memory arrays with crossbar architecture. In fact, one of the most attractive features of RRAM is the ability to organize the memory array in a crossbar circuit, where each memory cell occupies an area of only 4F2 [4, 50, 54]. However, such architecture is prone to interference during program and read. For instance, application of a voltage across a cell during read results in a sneak-through current through cell belonging to the same row or column: this may result in a major misinterpretation of the bit status, when the cell to be read is in the high resistance state [44, 49, 50]. To solve this issue, each memory cell must be accompanied by a nonlinear selector, e.g., a rectifier diode [49–51]. Several types of select devices have been proposed so far, including monocrystalline silicon diodes [47], polycrystalline silicon diodes [48], oxide unipolar heterostructure diodes [49–52], Schottky diodes [53], mixed ionic–electronic conduction diodes [55, 56], and VO2 threshold switches [51, 57]. For the purpose of diode screening for selector applications, three critical requirements should be considered: First, the diode should be available in the back-end of the line, to allow the stacking of several memory layers. Si-based selectors may hardly be compatible with such requirement due to the high temperatures needed for deposition and doping diffusion/activation. The second key requirement is a sufficient ON/OFF current ratio of the selector, to allow for sufficient blocking of the current through unselected devices during read. Finally, an important requirement is the capability to supply sufficient current during program, to allow for the set/reset of the memory element. Such a requirement seems the most hard to be met: Fig. 6.20 shows the current density at about 2 V of reported select elements, compared to the reset current density as a function of the device size F [37]. Note that the required current density increases for decreasing F, and thus with the down scaling of the memory cell. Therefore, to meet the reset current requirement in future technology nodes, one should ensure (1) satisfactory current density in the select element and (2) sufficiently small reset current I reset = V reset/R, and thus sufficiently small CFs. From this standpoint, the size reduction of filaments in oxide RRAM is essential.

Fig. 6.20
figure 20

Reset current density as a function of the technology node F, assuming a constant reset current I reset = 1 and 10 μA. The reset current increases for decreasing F according to I reset ∝ F −2. The current density reported in literature for Si and non-Si diodes is also shown for comparison [47–53, 55, 56]. Reprinted with permission from [37] (© 2011 Elsevier, Ltd.)

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In view of CF scaling, it should also be mentioned that CF size reduction might conflict with reliability requirements, namely data retention and noise issues. Data retention at elevated temperature was in fact shown to strongly depend on the CF resistance, since smaller filaments with higher resistances were found to display shorter retention time according to the formula [80, 81]:

$$ {t_{\rm{ret}}} = \frac{{\phi_{\rm{set}}^2}}{{{D_0}}}{{\text{e}}^{{\frac{{{E_{\rm{A}}}}}{{kT}}}}} $$
(6.17)

where D 0 is a diffusivity factor. Equation (6.17) is based on a diffusion model, where the diffusion of conductive atoms from a CF is driven by the concentration gradient, and thus critically depends on CF size [77]. Figure 6.21a shows the Arrhenius plot of retention times for a failure rate of 10 %, i.e., the retention time of one device out of 10 devices on the average was shorter than t ret in the figure. Data are reported for a cell initially programmed within three different resistance ranges, namely below 200 Ω, between 200 Ω and 1 kΩ, and above 1 kΩ. Data retention time decreases for increasing resistance, and thus decreasing size of the CF. Figure 6.21b shows the retention temperature corresponding to t ret = 103 s as a function of initial resistance, from Fig. 6.21a [82] and from MoO-Gd RRAM devices [80]. The retention temperature T ret decreases with R according to the formula:

Fig. 6.21
figure 21

Measured retention times at 10 % percentile [81] (a) and measured/calculated retention temperatures as a function of initial resistance [80, 81] (b). Three different initial resistances were used in (a), namely less than 200 Ω, between 200 and 1,000 Ω, and above 1,000 Ω. The retention times obey the Arrhenius law, however t ret decreases for increasing R, as a result of size-dependent oxidation [81]. The retention temperature change at 1,000 s can be reproduced by the analytical reset model of Eq. (6.18). Reprinted with permission from [81] and [82] (© 2011 IEEE and ECS)

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$$ {T_{\rm{ret}}} = \frac{{{E_{\rm{A}}}}}{{k\log \frac{{{D_0}{t_{\rm{ret}}}}}{{\phi_{\rm{set}}^2}}}} \approx \frac{{{E_{\rm{A}}}}}{{k\log \frac{{\pi R{D_0}{t_{\rm{ret}}}}}{{4\rho L}}}}, $$
(6.18)

where the ohmic approximation for R was used. Calculations based on Eq. (6.17) are also shown in the figure, supporting the size-dependent retention model.

Another potential concern for small CFs is the fluctuation of the current during read, which might be induced by surface charging/discharging effects due to surface rearrangement [83]. The relative amplitude of random telegraph noise (RTN) has been shown to increase for decreasing CF size, as a result of the stronger impact of surface conduction [83]. From this viewpoint, the trade-off between reset time/energy reduction and reliability must be carefully assessed.

6.10 Conclusions and Outlook

RRAM is the strongest candidate for high-density nonvolatile memory technologies below the 10 nm node. The RRAM technology offers several key advantages, such as switching speed, low voltage operation, good retention and endurance reliability, and low cost. However, the scalability of RRAM is still under debate, due to the lack of understanding and physically based models for the switching mechanisms. This review provides an overview of the recent progress on the physical interpretation and modeling of the oxide-based bipolar switching RRAM. The switching mechanism has been discussed based on experimental results regarding the time evolution of resistance and voltage across the cell, revealing the key role of voltage as the controlling parameter for the switching characteristic. The voltage dependence of switching times has provided evidence for an Arrhenius law, revealing the temperature-activated nature of the switching process and the key role of voltage-driven Joule heating at the localized filament. It has been thus concluded that set/reset processes of bipolar switching RRAM rely on thermally activated ion migration driven by the electric field. Based on this physical interpretation, a model has been developed to describe the filament growth and dissolution during set and reset, respectively. The filament grows/dissolves through ion migration in the direction of the field, and such process is strongly accelerated by the local temperature, which largely increases through Joule heating. The model was tested against the time dependence of set dynamics, the set/reset parameters as a function of current compliance, and the set/reset times. Finally, the consequences of this new understanding and modeling in terms of scaling have been discussed. In particular, RRAM technology will face a severe challenge in matching, on the one hand the requirement of reducing time, energy, and space within the chip (i.e., cost), and, on the other hand, the current density limits of select devices and size-dependent reliability issues of the RRAM device.