Thermal Reliability Issues in ReRAM Memory Arrays

Abstract

A localized buildup of Joules heat occurs in a memory cell as a result of the switching of resistive memory (resistive random access memory, (ReRAM)) cells. In ReRAM memory crossbar architecture, heat accumulated in one cell transfers to nearby cells via shared electrode metal lines and impacts adversely the performance of the devices. The cell-to-cell heat transfer leads to reduced number of switching cycles (SWC) and, in specific circumstances, to a loss of a bit in the cell brought about by a rupturing of the nanofilament. This chapter identifies the main causes for the thermal ReRAM reliability issues, offers a detailed analysis of the intercell heat transfer, characterizes its effects on the electric behavior of cells, and describes the thermal cross-talk in terms of three key material properties: specific heat capacity, the mass given by the geometry of the conductor material, and thermal conductivity of the electrode. By depositing several distinct composite inert electrodes, multiple ReRAM arrays have been manufactured to alter deliberately the thermal conductivity, specific heat capacity, and the electrode geometry. The proposed thermal analysis, based on those electrode properties, accurately anticipates the experimentally discovered variations in the degradation of electric output characteristics of the ReRAM devices operated under the same conditions.

1. Introduction

Since scaling limitations have been reached for conventional nonvolatile memory (NVM) that relies on metal-oxide-semiconductor field-effect transistors (MOSFETs) with a floating gate, it is essential to design substitute memory cells. Owing to its simple structure, strong miniaturization capacity, low power usage, high switching frequency, large ON/OFF resistance ratio, remarkable endurance, and retention features, resistive random access memory (ReRAM) is one of the leading contenders to supplant the existing NVM technology [1, 2, 3]. For neuromorphic applications, resistive memory cells are also very promising building elements [4, 5]. An authoritative review of the memristor technologies has been given recently by YF Chang [6]. The suitability of several types of nonvolatile and volatile memristive switches for neuromorphic applications has also been thoroughly reviewed [7]. The two-terminal resistive switching device, such as Cu/TaO_x/Pt, consists of two metal electrodes and a solid electrolyte insulating layer (in this case, TaO_x). In response to an appropriate applied electric field, the solid electrolyte film exhibits a transition between low and high states of resistance. In ReRAM devices called bipolar resistive devices, the switchover between a high resistance state (HRS), denoted by the resistance R_off, and a low resistance state (LRS), denoted by the resistance R_on, takes place at a polarity opposite to that at which the transition between HRS and LRS occurs. The establishment and dissolution of conductive filaments (CFs) in the matrix of the insulating dielectric as a result of metal ions and charged defect electromigration as well as heat impacts account for the resistance switching effect [8]. Metallic cations of the so-called active electrode (in our case, Cu) migrate in the electric field toward the second electrode, known as the inert electrode (such as Pt, Rh, Ru, and Co), where they are reduced to neutral atoms [9]. A metal nanofilament is created between the two electrodes as a result of the Cu metal atoms gradually accumulating at the interface of Pt and TaO_x. This mechanism is known as the “SET operation.” The filament ruptures at a definite current I_res when an opposite bias is applied to the copper electrode. A relatively large current of a few milliamperes (mA) is flowing through the filament at that point, dissipating Joules heat, and thus triggering the copper atoms’ outdiffusion from the body of the nanofilament. The RESET operation is the term used to describe the filament rupturing. Joule heating is essential during the RESET processes. The dominance of Joule heating in the RESET process has been thoroughly proven in several investigations [10, 11, 12, 13, 14, 15]. The R_off/R_on ratio degrades due to the self-heating effects of switching the cell, decreasing as the ambient temperature increases [16]. The computational reliability of neuromorphic computing systems based on ReRAM cells suffers noticeably from such variations in R_on and R_off of ReRAM cells [5]. In particular, a cell at higher temperature is more likely to produce an inaccurate output. ReRAM’s heat stability is a separate issue for embedded memories used in automotive applications [17].

The temperature of the filament during the RESET procedure will rise, rendering the cell more unstable under the same operating conditions if the bottom electrode is thinner because less Joules heat generated in the nanofilament can be dissipated. Reference [18] provides a thorough overview of resistive switching processes. Repeated switching of a cell causes the device to accumulate more Joules heat. It has been discovered [19, 20] that the Joules heat generated in a particular cell is preferably transferred along the copper and platinum electrodes, impacting the next cell positioned along the same electrode lines and impairing its electrical characteristics. Furthermore, it has been demonstrated [21, 22] that in case of a fragile nanofilament and enough heat delivered to it from a heated cell (HC), the nanofilament can be ruptured due to the cell-to-cell heat transfer, leading to an erasure of a programmed neighboring cell. In some other cases, a combination of the strength of the Cu nanofilament and of the amount of heat transfer leads only to a temporary erasure of the bit, i.e., the ruptured filament recovers spontaneously after a few seconds of a cooling-off period [21, 22]. The objective of this research is to present a thermal methodology that explains the manifold occurrences of electric deterioration induced by thermal transport with reference to the composition, properties of the electrode material, and geometry of the electrodes.

The organization of the chapter is as follows. In Section 2, the fabrication process of our ReRAM devices is described. Various different composite inert electrodes have been fabricated to test the impact of thermal material properties on the thermally induced electrical degradation of the ReRAM cells. The thermal properties of the materials employed in the construction of the inert electrodes are listed in Table 1 and effective thermal conductivities are calculated in Table 2. The fundamental forming, setting, and resetting I–V characteristics are also presented and explained. In Section 3, we introduce the concept of a “marginal” device as a means to measure the amount of electrical degradation suffered by inactive cells subjected to remote heat transfer from the heated cell. In Section 4, we present thermal analysis based on material properties of the electrode material and its dimensions to predict the amount of degradation of cells subjected to thermal cross-talk. In this section, we show that approximate temperature of the heated cell and of the probed cells can be determined using our thermal analysis based on fundamental thermodynamic mechanisms. We use selected cases of the manufactured composite inert electrodes to verify predictions of our thermal analysis. In Section 5, we summarize the main results of the chapter.

Conductor	ρm [g/cm^3]	μth [W/(mK)]	cs [J/(gK)]	kth [cm^2/s]	ρel [Ω cm]
Co	8.9	69	0.419	0.19	$6.2\times$10^−6
Cr	7.2	94	0.460	0.28	12.5
Cu	9.0	396	0.395	1.11	1.7$\times$10^−6
Pt	21.7	69	0.134	0.24	10.6$\times$10^−6
Rh	12.4	150	0.242	0.5	4.3$\times$10^−6
Ru	12.4	116	0.239	0.39	$7.1\times$10^−6
Ti	4.5	18	0.544	0.07	42.0

Table 1.

Material properties of the metal conductors used in the construction of the inert electrodes: mass density, ρ_m, thermal conductivity μ_th, specific heat capacity c_s, thermal diffusivity k_th, and electric resistivity ρ_el.

Co50; Ti30	Cu150	Pt50; Ti30	Pt50; Cu100	Pt50; Cu200	Rh50; Cr30	Ru50; Ti30	Ru50; Cr30
50	389	50	282	325	129	81	110

Table 2.

Calculated effective thermal conductivity in W/(mK) of the inert composite and active electrodes investigated in this study. The thickness t_i of a material i is given in nanometers (nm). The effective thermal conductivity of two respective materials 1 and 2 is calculated as follows: μ_eff = (μ₁$\times$t₁ + μ₂$\times$t₂)/(t₁ + t₂).

2. ReRAM device fabrication

Resistive random access memory devices are typically arrayed in a crossbar architecture at the junction of two parallel metal electrode lines, as shown in Figure 1(b). The cross-sections of our reference memory cell Cu/TaO_x/Pt and of the ReRAM devices derived from the base line device are illustrated in Figure 2. The devices have been manufactured on silicon wafer [3] covered with a silicon dioxide (SiO₂) layer that was 730 nm thick. One observes from Figure 2 that the inert electrode’s design is the only difference between the seven various devices investigated here. Cu(100 nm, 150 nm, and 200 nm), Co(50 nm), Cr(30 nm), Pt(51 nm), Rh(51 nm), and Ti(28 nm) layers have been deposited by physical vapor deposition (PVD) using a Kurt Lesker electron-beam physical vapor deposition (EBPVD) equipment, and have been patterned using lift-off technology using photoresist with a thickness of 2 μm. Between Pt, Ru, Rh, Co, and SiO₂, a thin Cr or Ti glue film of 30 nm was utilized to increase the adherence of the inert electrode proper layer and to also modify the thermal characteristics of the inert electrode composed of several materials (composite electrode). TaO_x dielectric has a thickness of 25 nm. To deposit TaO_x film, Ta₂O₅ pellets have been evaporated by electron beam in the evaporation chamber with oxygen-deficient atmosphere, resulting in oxygen-deficient TaO_x (x ∼ 1.9). The rectangular device regions of the device are between (5 and 35) × (5 and 35) μm², depending on the metal line width, which ranges between 5 and 35 μm. The square dimension of the contact pads is 100 μm on the side, and the neighboring line pitch is 150 μm, as indicated in Figure 1(b).

Figure 1.

(a) An example of a SET and RESET operation of the Cu/TaOx/Pt device with I_cc = 10 μA. (b) Photomicrograph of the crossline arrangement of the Cu/TaO_x/Pt, Cu/TaO_x/Ru, and Cu/TaO_x/Co devices.

Figure 2.

Resistive random access memory (ReRAM) arrays with different composite inert (bottom) electrodes that have been assembled, characterized, and analyzed in this work. All devices have the same TaO_x switching film and the same active (top) Cu electrode, 150 nm thick. (a) The figure shows our baseline ReRAM device Cu/TaO_x/Pt/Ti, (b) composite inert Pt/Ti electrode of the baseline device, and (c)–(h) various composite inert electrodes designed to modulate thermal properties of the electrode materials listed in Table 2. The thicknesses of the respective layers are also indicated.

The memory cells employed in this study are thoroughly detailed in [21, 23, 24]. At room temperature, the I–V characteristics were carried out on a probe station with a Keithley 4200-SCS Semiconductor Parameter Analyzer. Keithley equipment lets one select the voltage step height to define the ramp rate, and it chooses the appropriate time step automatically. A ramp rate of 0.276 V/s is a result of a ratio of step height of 0.025 V and a time step of 91 ms, which is internally set by the Keithley analyzer.

Cu⁺ ions are produced when a positive bias is provided to the top copper electrode in accordance with the redox reaction, Cu ↔ e⁻ + Cu⁺, and move into the body of TaO_x dielectric in the electric field to be reduced electrochemically at the surface of the Co, Pt, Rh, or Ru counter-electrode, which serves, at the same time, as a reliable diffusion barrier for copper atoms. The copper atom dendrites on the inert electrode expand toward the Cu electrode as more and more Cu atoms gather, and a conductive filament (CF) made of copper atoms acting as building elements creates an electrically conductive channel from the inert Pt to the active Cu electrode. At a threshold voltage V_set, when the growing Cu CF makes contact with the Cu electrode, conductance abruptly starts to increase. During the RESET procedure, by applying a negative voltage to the copper electrode while grounding Pt electrode, the filament can be disrupted and the cell’s resistance reverts to the HRS. At a threshold voltage, V_reset, the filament ruptures abruptly causing an abrupt drop of current in the I–V characteristic.

Figure 1(a) displays common I-V characteristics for RESET and SET operations. To ensure that the cell capacitor is completely depleted, the two grounded probe needles are put on the cell contacts for tens of seconds before any measurement is performed. The voltage of the Cu electrode is then ramped for the SET operation at a ramp rate (RR) in the interval [0.005 V/s to 3.00 V/s]. To prevent damage to the device, a limiting current, the so-called compliance current (I_cc) between 5 μA and 1 mA, is applied during the SET operation.

Table 1 lists the key physical properties of the electrode metals used during the manufacture of the devices and their inert electrodes are illustrated in Figure 2. In case of composite electrodes, such as the Pt/Cu electrode, the effective thermal conductivity is determined as an average of the weighted respective layer thicknesses that have been deposited. The resistance R_on of the LRS can be determined by the application of I_cc via equation [2]:

$$R_{\mathit{on}}=C/I_{\mathit{cc}}^n$$E1

where C comes to a value of C = 0.29 V for n ≅ 1 as extracted from experiments on the Cu/TaO_x/Pt devices. When n is unity, the constant C signifies the lowest voltage possible under which the device can be switched to the ON state, as demonstrated in [2]. This has been verified by delivering a constant bias to a cell to reset it while observing the time dependence of the current [2]. The cell may be switched to a conductive or ON-state for any voltage exceeding 0.286 V, but for voltages less than 0.286 V, the cell remains in the nonconductive state, i.e., OFF-state, even when the constant voltage is maintained for an extended time period. The relationship between R_on and I_cc enables the formation of both strong, low resistive, R_on = 500 Ω, at I_cc = 0.2 mA, and weak, highly resistive, R_on = 50kΩ, Cu filaments at I_cc = 5 μA. The excellent retention and endurance of the Cu/TaO_x/Pt-type devices have been extensively discussed in [25].

The filament either does not develop at all for compliance current values below 5 μA or it becomes volatile and ruptures spontaneously without being stressed. Contrarily, cells with strong low-resistance Cu filaments are more likely to become inoperable when I_cc > 0.25 mA, indicating that the device has been permanently damaged and became nonresettable.

In this study, we are interested in the study of cells that, as shown in Figure 3, are connected to the heated device by a thermal conductance channel and have been placed into a LRS condition under predetermined levels of compliance current, I_cc, before the transfer of heat from the heated cell (HC) to the probed cell is being applied.

Figure 3.

A schematic resistive random access memory (ReRAM) crossbar array shown for the baseline device. The cell marked by the red dot represents the heated cell (HC). The neighboring devices impacted by the heated cell are positioned alongside the Pt and Cu metal lines and marked by blue crosses. The neighboring probed cells are set prior to heating by the cell HC to an ON-state. Immediately after the heating by the HC cell comes to an end, the neighboring cells are checked to determine the corresponding maximum switching cycle (SWC).

A repeated switching of a device results in the dissipation of Joules heat in that device, which can disperse to nearby devices placed along one of the metal lines common with the heated device, as further explained in [8, 20]. As long as the other array cells are switched to the conductive state, where the Cu nanofilament acts as a conductor for the heat transfer, even those devices that do not share any of the two electrode lines with the heated device may be impacted by the cell-to-cell heat transfer as well. Depending on the heat generated in the heated device, the kind of common electrode selected (Cu or Pt), and the distance between the probed and the heated device, this phenomenon permits to heat a neighboring cell in a controlled gradual way (see Figure 3).

The maximum temperature of the filament, according to Sun et al. [26], lies between 600°C and 900°C. The majority of the models published in the literature consider the mesoscopic electrodes to be a constant heat sink condition fixed at ambient temperature. Our findings completely disprove this presumption. Heat transfer between the array’s cells is made possible by the electrode lines’ significant heating. Joules heat in metallic nanofilaments with various wire cross-sections has been investigated by Fangohr et al. [27] who discovered that the temperature at the constriction can reach the high temperature of 1336 K. By using infrared (IR) detection, Uenuma et al. [28] observed a hot spot on the surface of the top electrode indicating the position of the nanofilament and estimated the temperature of the spot to lie well above 900°C. Sato et al. [29] calculated that the temperature of filaments with radii ranging between 10 nm and 40 nm will result in a 1000–1200°C temperature interval, depending on the filament’s resistance. There exists, therefore, broad agreement that when the device is switched back and forth at a high frequency of SET-RESET cycles, the maximum temperature of the filament can readily surpass 900°C. In Ref. [30], it has been experimentally observed that frequent switching of a ReRAM cell leads to the incipient melting of the Cu electrodes including Cu pads. This gives a definite reference point for the local temperature of 1085°C, which is the melting temperature of copper. In Figure 4(a), it can be seen that the entire segment of the Cu electrode of a 6 μm wide device has been removed after three RESET cycles performed under the same bias conditions. Figure 4(b) shows the result of an irretrievably damaged cell after six identical RESET cycles as before for a 10 μm Cu and Pt line. We will discuss the impact of the line width on the cell temperature and severity of melting in Section 4 in more detail. Here, we wish to point out that from Figure 4(b) it can be seen that the location of local melting is visible on the perimeter of the cell along the Pt electrode’s edge, a preferable location of the nanofilament, where the TaO_x coverage is slightly less than on the planar surfaces, which is an intrinsic property of limited conformality of the EBPVD deposition. The Cu electrode above the cell is damaged by electromigration, which is triggered by current crowding at the nm-sized region where the Cu nanofilament makes contact with the Cu electrode. As a result, electromigration depletes the Cu atoms at this interface. The extremely high current densities and Joule heating that raise temperatures to the melting point of copper exacerbate this phenomenon, which is similar to the effects of electromigration in vias and contact holes.

Figure 4.

Damage to the Cu/TaO_x/Pt cells due to excessive heating. Both cells have been set and reset under the same conditions (i.e., the same voltage ramp rate and the same I_cc during the SET operation). (a) The cell on 6 μm Cu and Pt lines shows complete melting of Cu over the cell after three RESET-SET cycles. (b) The cell on 10 μm Cu and Pt lines shows local melting of Cu along the Pt lines after six RESET-SET cycles. After the damage is shown, both cells became inoperable.

3. Effects of thermal cell-to-cell cross-talk in ReRAM arrays

N RESET-SET cycles were applied to heat the cell incrementally, in well-defined quanta of heat. It should be observed that compared to the RESET cycle, the heat dissipation during a SET cycle is extremely low and negligible. At the beginning of the voltage ramp, the current is less than 1 nA during the SET operation until V_set is reached, and then does not exceed the I_cc limit of less than 100 μA when threshold voltage V_set is surpassed. However, the current flowing through the device, when it is reset, is in the range of a few milliamperes (mA), i.e., at least more than two orders of magnitude higher. As a result, heating primarily occurs during RESET operations, and, therefore, resembles a triangular-shaped heat pulse with a pulse duration of several seconds given by t_res = V_res/RR and pulse periods of 40–60 s, which correspond to the time needed to reposition the probe needles of the probe station between the application of changing bias conditions from RESET to SET. This indicates that when the cell gets heated up during the RESET operation, there follows a relatively lengthy cool-off period of about 40 s. As a result, the heating’s duty cycle is less than about 0.05. The cell and the entire cell array will partially cool during the off-pulse period as a result of attending Newtonian heat losses. Only a portion of the heat deposited is kept in the cell, and this portion is described by the factor f_loss. As a consequence, it takes several cycles for the device to build up enough heat to achieve a target temperature in the cell. The number (N) of RESET-SET cycles, the magnitude of the voltage ramp rate (RR) applied, and the ON-resistance, R_on resistance of the nanofilament, can all be employed to modulate the amount of Joule heating generated at the heated memory device.

The electrical characteristics of a virgin cell have been found to be impaired when a neighboring device has been heated by the application of multiple RESET-SET cycles. This was found when all memory devices joined by a thermal path to the heated device were electrically characterized later. It has been observed that the electrical reliability of the neighboring device degrades significantly when subjected to this kind of remote heating. However, when the affected probed neighboring cell was examined again after 3–5 min or a longer cool-off time, this deterioration of electrical characteristics disappeared. We assume that after a period of time in the order of 2–5 min, the thermally induced degradation abates gradually. During the electric testing of the neighboring cells, we made sure beforehand that there exist no sneak pathways [31].

To measure the impact of the cell-to-cell heat transfer talk [19, 20] on neighboring cells, we have established the concept of a “marginal” memory cell as a convenient metric. Cell’s property of displaying only a very small number of RESET-SET cycles is what we mean when we say that a cell is “marginal”: We have configured a neighboring cell with an I_cc of just 10 μA and a voltage ramp rate of RR = 1.1 V/s to form a weak filament in the cell.

After specific number of consecutive RESET-SET switching cycles, such cell set at I_cc = 10 μA turns volatile. RESET events that occur on their own, i.e., without any external bias, are one example of cell’s volatility. When the cell’s on-resistance R_on is adjusted at higher and lower I_cc, the nature of marginality of the memory cell is further elucidated. The device cannot hold the LRS when I_cc = 7 μA is imposed on the SET operation. A nanofilament set at such low I_cc ruptures spontaneously. The ON-state remains stable when the device is placed at higher level of I_cc, such as 10 μA, but even here only for a very limited number of consecutive SWC, usually 11–13, depending on the specific cell. When this number of SWC is reached, the cell’s electrical performance turns erratic. To firm up this metric, 100 cells with an I_cc of 10 μA were tested, and the maximum number, M_x, of consecutive switching RESET-SET cycles was registered. We find that average maximum number of SWC is M_x = 12.7 cycles, with a standard deviation of =1.3 for such “marginal” cells.

To allow for a lengthy heating period during the RESET procedure, a low RR = 0.1 V/s has been selected. Because at low RR, the high reset current persists for a prolonged period of time, low RR allows for large deposition of heat in the cell. It has been demonstrated in [32] that the reset voltage V_res decreases as the voltage ramp rate, RR, decreases, according to V_res$\sim \sqrt[3]{\mathit{RR}}$. When the maximum number of SWC, (M_x), for the cell has been reached, the cell’s performance becomes extremely unstable.

In contrast to the “marginal” cell, a cell set into the ON-state at high I_cc = 40–100 μA is very stable and may be switched very frequently (hundreds of times and more). In summary, a “marginal” memory cell marks the boundary line between the cell’s volatile and stable switching performance. As a result, our “marginal’ device with a filament formed at I_cc value of 10 μA, and allowing for at most M_x, of RESET-SET SWC, serves as the indicator for determining the severity of the cell-to-cell heat transfer.

It has been found consistently that such a marginal cell is very sensitive to the amount of heat being transferred between the cells. Any significant heat transfer is bound to reduce the maximum number M_x = 13 to a lower value, which serves then as the indicator of the degradation of electrical performance. As a result, the onset of the device’s instability in response to its local temperature is mirrored in the metric M_x. As a consequence of the heating by the neighboring cell, the heat dissipated locally by the cell’s intrinsic switching is building on the heat provided by a remote source. The time it takes to change the contact needles on the probe station is approximately 50 s in our experimental setup between the point at which the heat cell’s heating is stopped and the probed cell’s characterization begins.

The M_x for a remotely preheated cell is compared to the M_x of the same cell in the absence of remote heating, i.e., unstressed cell, to establish then the degradation metric defined as follows:

$$\mathit{DEG}=\frac{M_x\left(\mathit{\text{unstressed cell}}\right)-M_x\left(\mathit{\text{preheated cell}}\right)}{M_x\left(\mathit{\text{unstressed cell}}\right)}$$E2

As previously indicated, it has been discovered that the average M_x for a cell without remote heating (unstressed cell) is about 13 RESET-SET cycles. Based on 125 devices evaluated, the results of cell’s deterioration of switching ability for devices positioned along the Cu and Pt electrode lines are displayed in Table 3 for four different devices with different inert electrodes. The maximum SWC are then used to determine the degree of degradation suffered by the cells due to the remote heating.

1. Cu(150 nm)/TaOx/Pt(50 nm)/Ti(30 nm); Next neighbors to the heat cell along Cu(150 nm) 10 μm wide line					1. Cu(150 nm)/TaOx/Pt(50 nm)/Ti(30 nm); Next neighbors to the heat cell along Pt(50 nm) 10 μm wide line
prob. Cell #	I	II	III	IV	I	II	III	IV
Mx	2.6	3.3	3.9	4.3	4.8	6.1	7.8	11.3
DEG [%]	80	75	70	67	67	53	40	13
2. Cu(150 nm)/TaOx/Pt(50 nm)/Cu(100 nm); Next neighbors to the heat cell along Cu(150 nm) 10 μm wide line					2. Cu(150 nm)/TaOx/Pt(50 nm)/Cu(100 nm); Next neighbors to the heat cell along Pt(50 nm)/Cu(100 nm) 10 μm wide line
prob. Cell #	I	II	III	IV	I	II	III	IV
DEG [%]	57	41	0	0	23	1	0	0
3. Cu(150 nm)/TaOx/Pt(50 nm)/Cu(200 nm); Next neighbors to the heat cell along Cu(150 nm) 10 μm wide line					3. Cu(150 nm)/TaOx/Pt(50 nm)/Cu(200 nm); Next neighbors to the heat cell along Pt(50 nm)/Cu(200 nm) 10 μm wide line
prob. Cell #	I	II	III	IV	I	II	III	IV
DEG [%]	11	0	0	0	0	0	0	0
4. Cu(150 nm)/TaOx/Pt(50 nm)/Ti(30 nm); Next neighbors to the heat cell along Cu(150 nm) 35 μm wide line					4. Cu(150 nm)/TaOx/Pt(50 nm)/Ti(30 nm); Next neighbors to the heat cell along Pt(50 nm) 35 μm wide line
prob. cell	I	II	III	IV	I	II	III	IV
DEG [%]	65	52	40	33	43	31	19	0

Table 3.

The average maximum number of RESET-SET switching cycles (SWC) and the amount of electrical degradation of neighboring devices alongside Cu and Pt electrode lines exposed to the remote heating by the heated cell for four different devices with different inert composite electrodes: 1. Pt(50 nm)/Ti(30 nm), 10 μm wide line, 2. Pt(50 nm)/Cu(100 nm), 10 μm wide line, 3. Pt(50 nm)/Cu(200 nm), 10 μm wide line, and 4. Pt(50 nm)/Ti(30 nm), 35 μm wide line.

As seen in Table 3, for the device 1 (our baseline and reference device), Cu(150 nm)/TaO_x/Pt(50 nm)/Ti(30 nm), 10 μm wide line, the deterioration of SWC for the first neighbor along the Pt line is approximately DEG = 67%. The fourth device, also attached to the Pt electrode, has a substantially reduced rate of degradation (DEG = 13%). The amount of thermal cross-talk depends on the distance in units of 150 μm between the heated and probed cells, or n × 150 μm, where n = 1, 2, 3, and 4 stand for the first, second, third, and fourth adjacent cells, respectively, as shown in Figure 3.

As seen from Table 3, for the device 1, the degradation of the adjoining cells positioned alongside the Pt electrode is far less severe than that of the corresponding cells disposed alongside the Cu metal line, as extensively detailed in [20]. For example, the first neighbor along the Cu line to the heated cell suffers a degradation of 80% compared to 67% for first neighbor alongside the Pt line. At first, this result was unexpected to learn that the deterioration along the platinum metal line is less severe than that along the copper metal line [20], as one could anticipate that the geometry of the filament, due to its genesis, should have a larger contact footprint with the Pt electrode and a small contact footprint of the top part of the Cu CF with the copper electrode. Because of the above observation, one is forced to revise the hypothesized configuration of the filament from a truncated cone to a something resembling more an hour glass silhouette, which would exhibit similar size contact areas with Cu and Pt metal lines as shown in Figure 5. Given that it now has a larger contact area with the Cu electrode, the hourglass-shaped filament would more accurately represent our data. Consequently, it would be easier to understand why there is such a significant heat transfer from the filament along the Cu electrode line to the nearby cells along the Cu electrode. Apparently, the substantially higher cell-to-cell heat transport along the copper electrode than alongside the platinum metal line is the root cause for the more severe deterioration in electrical performance of the cells positioned along the copper metal line.

Figure 5.

Hypothesized geometrical shapes of the Cu conductive nanofilament. (a) A truncated cone conventionally assumed with a small contact area with the Cu electrode. (b) An hour glass silhouette providing larger contact area with the Cu electrode.

From the heat conduction transport mechanisms, it is known that the product of the electrode’s cross-section and its thermal conductivity determines the rate of heat transmission. The rectangular cross-section of the Pt/Ti electrode is two-and-one-half times smaller than that of the copper electrode, and the thermal resistivity of copper is about eight times smaller than that of weighted thermal resistivity of the composite Pt/Ti (see Table 2). As a result, Cu electrode’s rate of heat transmission is in excess of 20 times that for the heat transfer rate for the platinum electrode. Hence, the adjacent cells positioned on the Cu electrode reach higher temperatures than the corresponding cells disposed along the platinum metal line.

4. Prediction and verification of ReRAM devices’ electric degradation

The amount of I_cc, the number of consecutive RESET-SET SWC, N, and the rate at which the voltage ramps up during the RESET cycles, RR, can all affect how hot the heated cell (HC) (see Figure 3) becomes. For the RESET operation, a low RR = 0.1 V/s and/or a high I_cc that results in a strong low resistance Cu CF may be chosen to enhance heating by allowing for a lengthy heating period before the threshold voltage V_res is reached. Low ramp rate maximizes the cell heating because the current persists for a long time during the RESET operation until it reaches the critical value I_res. Eq. (3) [32, 33] can be used to compute the Joules heat (JH) dissipated in a device when an increasing voltage bias with a constant voltage ramp rate is applied, and where the relationship between R_on vs. I_cc given in Eq. (1) is used to derive the final expression for JH.

$$\mathit{JH}={\int }_0^{t_{\mathit{res}}}\frac{V^2\left(t\right)}{R_{\mathit{on}}}\mathit{dt}={\int }_0^{V_{\mathit{res}}/\mathit{RR}}\frac{{\mathit{RR}}^2\times t^2}{R_{\mathit{on}}}\mathit{dt}=\frac{V_{\mathit{res}}^3\times I_{\mathit{cc}}}{3\times \mathit{RR}\times C}$$E3

Here, t_res = V_res/RR [32, 33] determines the time of voltage ramp rate application to effect the rupture. JH can range from 3 to 60 μJ depending on the I_cc and RR parameters that are used. The experimental values for R_on and V_res, and the applied voltage ramp rate, RR, solely determine the amount of JH, which is the energy that is being dissipated in the memory cell during the RESET action. The nanofilament, which is characterized by the ON-resistance R_on, and completely embedded in the dielectric, is the main source of heat generation. How the generated heat is being stored is a concern to which we advert now. Material’s temperature as a result of the heat transfer rises according to Eq. (4):

$$Q=\mathrm{\Delta }T\times c_s\times m$$E4

where the total mass $m=V\times {\rho }_m.$ The energy that was dissipated within the memory array, JH, is determined by the experimental values for R_on and V_res and by the applied voltage ramp rate (RR). Eq. (4) shows, among other things, that the volume of the electrode affects how much the temperature difference ΔT increases. To calculate ΔT, one must determine the total mass of the electrode, which is determined by the product of the mass density ${\rho }_m$ of the electrode material and by the electrode’s total volume V $\left(V=\mathit{\text{width}}\times \mathit{\text{length}}\times \mathit{\text{thickness}}\right)$ including also the contact pads’ volume at both ends of the electrode. Evidently, the electrode’s temperature increase $\mathrm{\Delta }T$ is inversely correlated with both the thickness and the width of the electrode. As a result, the geometry, or the electrode’s volume, controls how much the temperature may rise by ΔT. For the time being, let us suppose that the entire amount of heat JH produced by the filament is held in the Cu conductive filament. The question of what temperature difference $\mathrm{\Delta }T$ would be required to hold a heat of 10 μJ in a Cu CF then arises. It requires estimation of the mass density, specific heat, and volume of the Cu NF in order to be answered. The volume of the nanofilament equals 4.6 $\times$ 10⁻¹⁸ cm³ if we assume that the nanofilament has the shape of a truncated cone with a radius of 9 nm at the base, 4.5 nm at the top, and 25 nm height (a calculation for an hourglass-shaped CF would be similar), which is limited by the thickness of TaO_x [34]. If the electrical resistivity of the Cu CF is assumed to be ρ_el = 5$\times$10⁻⁴ Ω cm, which is around 20 times greater than that of bulk Cu, then this volume results in a R_on resistance of about 1000 Ω. At I_cc = 10 μA, such a R_on value is in fact experimentally observed. Here, the resistivity of the Cu filament has to be larger than that of bulk copper, since CF consists of Cu atoms embedded in the matrix of TaO_x. Given that Ta₂O₅ has a mass density of 8.2 g/cm³ and that of Cu is 9.0 g/cm³, the filament’s mass density must fall between the two values. If it does, then the total mass of Cu CF is about 4$\times$10⁻¹⁷ g. Furthermore, the specific heat capacity of copper filament must fall between that of Ta₂O₅ of about 750 J/(gK) and Cu’s 0.385 J/(gK). One may determine the temperature differential ΔT required to store such energy within the nanofilament alone using Eq. (4) and the extreme case of 750 J/(gK). Under these circumstances, the temperature differential from the ambient temperature is at least 3 $\times$ 10⁸ K, which is 20-fold higher than the core temperature of the sun of 1.5 $\times$ 10⁷ K. The temperature would be even higher (3 $\times$ 10¹¹ K) if the specific heat capacity was at its other extreme, c_s (Cu-CF) = 0.385 J/(gK). This is obviously impossible, and given the filament’s incredibly small volume, it is evident that this amount of energy cannot be accommodated by the filament. Instead, the heat must be partially dissipated and partially stored, through the primary conductive heat transfer mechanism, at least in the two electrodes (Cu and Pt), and in the body of the nanofilament with its negligible contribution to the overall volume. Additionally, a significant portion of the energy conductively transferred to the electrodes will be lost owing to Newtonian heat losses, such as buoyancy-driven convection and radiation, all the more as the metal lines display a relatively large surface-to-volume ratio [35]. Therefore, it is reasonable to suppose that only a small portion of JH will be accommodated in the body of the electrode over the course of a more or less continuous heating session during the reset procedure, or Q_st = JH $\times$ f_loss, where f_loss signifies a portion of the heat still present in the material after the losses of heat to the environment. The relationship between the coefficient f_loss and the ambient temperature is f_loss$\approx$ exp.(−rt_diss), where r denotes the coefficient of heat transfer and t_diss the dissipation time [36]. The remnant heat, Q_Nst, after considering the losses to the environment (f_loss) and amount of cooling off (f_diss) between the switching operations stored in the electrodes when a memory cell is quickly switched to and from N times is given then by Eq. (5).

$$Q_{\mathit{Nst}}=N\times Q_{\mathit{st}}\times f_{\mathit{\text{diss}}}=N\times Q_{\mathit{JH}}\times f_{\mathit{\text{loss}}}\times f_{\mathit{\text{diss}}}=c_s\times m\times \mathrm{\Delta }T$$E5

where f_diss is a coefficient smaller than unity and reflects the heat dissipation time between SWC and accounts for both the heat loss that occurs when heat is transferred between heated and probed neighboring cells during the set operation as well as the cooling period between the set operation when no substantial current flows until V_set is reached or very little current flows when the bias exceeds V_set but is still limited by I_cc. The mass of the two electrodes joined by the filament is now reflected in the mass parameter in Eqs. (4) and (5). To make practical use of Eq. (5), we avail ourselves of a valuable experimental reference [30] that can be used to calibrate Eq. (5). When a cell is repeatedly switched on and off under specific switching conditions for moderately large R_on and low value for RR, which were purposefully designed to increase the amount of heating, we witness melting of the copper electrode at the heated device that extends to the metal line pads [30]. It has also been noticed that the contact pads for the Pt electrodes are free of any visible distortion of their square shape on account of much higher melting temperature of Pt (1768°C) than that of Cu (1085°C). The reflowing of the Cu electrode has been observed after 25 SWC for a cell whose heat dissipation according to Eq. (3) is JH = 40 μJ based on the values utilized for RR, as well as experimental values for R_on and V_res. Using c_s = 0.385 J/(gK), for Cu and c_s = 0.13 J/(g°K) for Pt, respectively, we can compute the product f_loss$\times$ f_diss from Eq. (5) and arrive at f_loss$\times$ f_diss = 0.063.

With this knowledge, it is now possible to determine the average temperature rise in the CF-electrode system utilized in the tests described in Table 1 after a single switching cycle, where one reset cycle has JH = 10 μJ. Since the contact pads are square in shape with 100 nm on the side, we can repeat the calculation using Eq. (4) and determine the T for the specific heat capacities of the Cu and Pt electrodes, c_s = 0.385 K/J/(gK) and c_s = 0.13 J/(gK), respectively. Using the heat released in one switching (reset) cycle of JH = 10 μJ and assuming tentatively f_loss = 0.1, one can infer the temperature increase is ΔT = 27°C. Obviously, the temperature at first is not uniform along the electrode lines when the heated device begins to heat up, but as was already mentioned, due to the high thermal diffusivity, it quickly reaches the steady state. The highest temperature of the heated device will be transmitted to the adjacent cells resulting in lower temperature of the neighboring cells. For an isolated metal rod, the 1-D heat equation’s solution can be used to accurately predict f_diss [37]:

$$\frac{\partial T}{\partial t}=k_{\mathit{th}}\frac{{\partial }^{2}T}{{\partial }^{2}x}+\frac{g}{c_s{\rho }_m}$$E6

where g is the heat produced, k_th is the thermal diffusivity, c_s represents the specific heat capacity, T denotes temperature, and ρ_m stands for the mass density. The explicit solution to Eq. (6) for the metallic rod with a heated end can be found in [37]. It should be observed that TaO_x has a thermal diffusivity of k_th = 0.02 cm²/s, while the thermal diffusivities of Pt and Cu are much larger (see Table 1), thus approximating well the isolated rod model. The time defined by t_ts = L²/k_th provides the typical time scale for Eq. (6). With a cell-to-cell distance L of 150 μm and a thermal diffusivity of Cu k_th = 1.11 cm²/s, one can calculate t_ts to be ∼200 μs. In view of this, one is justified to evaluate Eq. (6) under steady-state conditions because the period of the pulse of the SET-RESET cycles is about 60 s, which is 3 $\times$ 10⁵ times larger than t_ts. Under steady state, the temperature becomes a linear function of the spatial coordinate alongside the electrode. Surely, during the 60 s of idle time, the electrode will cool down as a result of Newtonian heat losses, and the amount of heat still stored in the electrode can be approximated using the parameter f_loss as previously explained. Thus, if a corner array cell is heated up, the temperature will be a linear function of a distance along both of the electrodes.

One can calculate the transit time, t_tr, needed for a given temperature value to travel the distance of D = 850 nm, from the heat device to the pad on the far end of the metal line using the equation D = $\sqrt{{\mathit{k}}_{\mathit{th}}\times {\mathit{t}}_{\mathit{tr}}}$. This duration is less than 10 μs for the copper electrode and 2.23 times larger for the platinum metal line on account of the latter’s fivefold lower thermal diffusivity (see Table 1) as well as the smaller cross-section of the Pt metal line than the Cu line. This makes it plain that, for the neighboring devices being studied after the heated cell’s heating has been terminated for 45–65 s, the temperature distribution is well approximated by a steady state. The result is a linear dependence of the temperature on the spatial coordinate designating the location of the neighboring cells. Considering that the first cell positioned on the Cu or Pt electrode is heated up to temperature T_c while the electrode’s farthest end is kept at temperature T_o < T_c, the temperature decrease from device to device is given by (T_c − T_o) $\mathit{\times }$ 150/(100 + 5 $\mathit{\times }$ 150) = (T_c − T_o) $\mathit{\times }$ 0.18, where 150 μm is the distance between two immediate neighboring cells and 100 + 5 $\mathit{\times }$ 150 = 850 μm is the total length between the heated device and the contact pad at the far end of the line. T_o at the very beginning of the heating will be still 27°C but it will rise as the heating keeps persisting. When the heat loss from the neighboring cells that are the farthest away is taken into account, a reasonable estimate of f_diss is between 0.6 and 0.7. The estimate of f_diss enables us to estimate f_loss to be between 0.11 and 0.09, which renders our aforementioned choice of f_loss = 0.1 self-consistent. This determination is based on the experimentally extracted value f_loss$\mathit{\times }$ f_diss = 0.063. As a result, heated cell’s threshold temperature T_c decreases as heat is transmitted to the adjacent cells via one of the common electrodes. The robustness of the Cu CF determines the threshold temperature, T_c for the specific cell, at which the cell’s instability sets in, and as a result, T_c is bound to increase with the increasing strength of the filament or its decreasing R_on resistance. The critical cell temperature for a weak filament with a R_on resistance value of several tens of kiloohms (kΩ) has been determined to be around 350°C.

The number of SWC precipitating a rupturing of a Cu filament of a specific strength can be used to estimate the temperature increase ΔT for a single RESET operation. We found previously that it took 25 cycles of heating of a heated cell with a robust Cu filament of R_on = 5kΩ set at I_cc = 100 μA to see the beginning of the reflowing of the contours of the Cu electrode pads, indicating an incipient melting of the copper metal. As a result, we may estimate ΔT for a single cycle using the formula ΔT = (1085°C − 27°C)/25 = 42°C. The experiment was then performed with the same probed and heated cells, except that the probed cell was initially set with a thin filament of high resistance R_on = 20 kΩ formed at I_cc = 20 μA, and we found that 7–8 heating cycles have been enough to cause the device to rupture. The temperature is raised by 42°C in one cycle, hence 42°C $\mathit{\times }$ 8 + 25°C = 361°C. Thus, a value of around 350°C represents a crucial temperature for rupturing the weaker Cu filament. However, a robust copper nanofilament with low resistance of a few hundred Ohms is likely to display a critical temperature needed to rupture it near the Cu melting temperature, i.e., 1085°C. The threshold temperatures T_i for a weak filament for each of the five cells arranged along the Pt line are plotted in Figure 6, with the first cell serving as the heated device and the other four serving as remotely heated neighboring cells. The heated device stressed with 13 maximum RESET-SET cycles reaches the instability threshold of T_c = 350°C. The nearby cells will exhibit lower temperatures, T_c$\mathit{\times }$ f_diss, T_c$\mathit{\times }$ f_diss², T_c$\mathit{\times }$ f_diss³, and T_c$\mathit{\times }$ f_diss⁴, for the first, second, third, and fourth neighbors, respectively, as explained above.

In Figure 6, the temperature difference ΔT = T_c − T_i between each neighboring cell and T_c is shown. This temperature margin ΔT limits how many inherent heating cycles the cell can withstand before the cells becomes unstable. For the first neighboring cell, this difference is 130°C. Since each heating cycle increases the temperature effectively by 27°C, the cell can switch maximally for 130°C/27°C = 4.8 or 5 cycles, while the fourth neighboring cell has a temperature margin of (350 – 50°C) = 300°C, which allows for maximum 300°C/27°C = 11.1 $\mathit{\approx }$ 11 cycles. Using our definition of degradation given in Eq. (2), these two cases would correspond to degradation of the first cell of (13 – 5)/13 = 62% for the first neighboring cell and (13 – 11)/13 = 15%, respectively, in perfect agreement with the experimentally measured values shown in Table 3.

Figure 6.

The red dots show the temperature of the heated cell when it reached a threshold temperature T_c of 350°C as well as of the four neighboring cells. The yellow double arrows indicate the temperature difference to the threshold temperature, which determines the amount of the cell’s intrinsic heating to reach the threshold temperature at which the cell becomes unstable. Since one heating cycle increases the cell temperature by 27°C, the ratio of (T_c – T_{i N})/27 (where i = 1, 2, 3, 4) determines how many heating cycles the cell can tolerate before becoming unstable. For example, the fourth cell can tolerate 11 cycles before it becomes unstable, in very good agreement with the experimental degradation data.

The maximum SWC M_x can be computed in the same way for all other cells. The corresponding M_x numbers are also indicated in Figure 6. Thus, there is a striking match between the expected number of the extra permissible RESET-SET cycles and the respective experimental figures M_x(ave) provided in Table 3. It should be noted that the temperatures shown in Figure 6 represent a snapshot of a transient phenomenon when the peak temperatures have been reached just after the heating of the heat cell has been stopped. If the cells are then probed just afterwards, they display degraded switching properties in terms of reduced number of switching cycles, as evidenced in Table 3. The transient nature of this phenomenon precludes, however, the determination of the endurance and retention properties.

We have tested the predictions based on the methodology described above by building ReRAM arrays with modified thermal properties of the electrodes. To accomplish it, we have manufactured, in addition to the Pt(50 nm) inert electrode, two composite Pt(50 nm)/Cu(100 nm) and Pt(50 nm)/Cu(200 nm) electrodes, as well as Rh(50 nm). It should be noted that for composite Pt/Cu electrodes, the intrinsic layers defining the memory cell are the same as for the Pt cell. The additional Cu layers present just two different embedment scenarios external to the cell proper, but are of crucial importance for the heat conduction properties. The key material characteristics of Cu, Pt, and Rh are listed in Table 1 and the effective thermal conductivities are calculated in Table 2. For the addition of Cu layers of 200 nm and 100 nm, respectively, the thermal conductivity of the bottom inert electrode increases 4 times, and the product V $\mathit{\times }$ c_s = m increases 1.95 and 1.47 times, respectively.

We now apply this methodology and compute the temperature for a single heating cycle by repeating the similar I–V measurements of the deteriorated cells applying the same RESET parameters used for calculating JH in Eq. (3). A temperature increment of 26.5°C for the Pt(50 nm) array, 18.1°C for Pt(50 nm)/Cu(100 nm), and 13.5°C for Pt(50 nm)/Cu(200 nm) has been measured, respectively, for one SWC. It is intuitively obvious that with the bottom electrode’s increased ability to store and conduct heat, it will take more heating cycles to reach the same threshold temperature T_c upon reaching which the device is rendered unstable. Because of the bottom electrode’s substantially better thermal conductivity, which causes a much faster transport of the heat pulse across the length of electrode, the maximum number of SWC is bound to increase.

The thermal diffusivity increased fivefold as a result of the composite inert electrode’s enhanced thermal conductivity (Pt(50 nm)/Cu(200 nm), and the coefficient f_diss for the Pt(50 nm) should have been at least three to four times smaller. This would suggest that the maximum number of switching steps for the ReRAM array with modified inert electrode with the same switching parameters should be 6–8 times greater, or 75–100 maximum SWC. The corresponding metrics (ΔT and M_x) for an array with Pt(50 nm)/Cu(100 nm) are ΔT = 18.0°C and a maximum RESET-SET cycle of approximately M_x = 25. Table 4 displays the information on the maximum RESET-SET cycles for the Rh electrode, the Pt/Cu(100 nm), and Pt/Cu(200 nm) inert electrodes.

Inert electr.	Pt(50 nm)/Cu(200 nm)	Pt(50 nm)/Cu(100 nm)	Rh(50 nm)	Pt(50 nm)
Mx	75	25	26	13
μeff [W/mK]	325	282	79	50

Table 4.

The measured maximum M_x of RESET-SET SWC for a fragile filament set at the same value of I_cc for four different inert electrodes. The last column in the table shows our baseline device with the Pt(50 nm)/Ti(30 nm) with the maximum mx of 13, as described already in Section 3. The effective thermal conductivity of the inert electrodes is also displayed to demonstrate palpably the clear correlation of maximum SW with the effective thermal conductivity of the inert electrode.

The results of similar electrical degradation tests executed on the Pt(50 nm)/Cu(100 nm) and Pt(50 nm)/Cu(200 nm) ReRAM memory crossbar arrays in the same way as tests performed on Pt(50 nm) arrays are shown in Table 3 for devices #2 and #3, respectively. It is seen that the cells positioned along the Pt electrode do not degrade at all in the case of the Pt(50 nm)/Cu(200 nm) (device #3) inert electrode, while the first neighboring device positioned alongside the Cu electrode degrades only by 11% while the subsequent neighbors do not degrade at all. In contrast to the Pt(50 nm)/Ti(30 nm) ReRAM array (device #1), the local temperature for Pt(50 nm)/Cu(200 nm) is clearly considerably lower due to the better thermal conductivity and specific heat capacity of the Pt(50 nm)/Cu(200 nm) electrode. Since fresh cells fail for a Pt(50 nm) electrode after just 13 times, but now for 72–90 times for a Pt(50 nm)/Cu(200 nm), this type of experimental testing undertaken for this study is rather laborious, but has been undertaken to demonstrate the accuracy of the predictions of our thermal analysis. As one would expect, the degradation data shown in Table 3 for the inert electrode Pt(50 nm)/Cu(100 nm) (device #2) lie between those of the Pt(50 nm) (device #1) and Pt(50 nm/Cu(200 nm) (device #3).

The suggested thermal study can be expanded to include the relationship between cell degradation and the width of the electrode lines. According to Eq. (4), the volume of the electrode grows proportionally with the width, causing the temperature difference ΔT to decrease with wider widths of the electrode lines. Pt and Cu lines (10 μm) have served as the standard for all of our tests thus far. We have gone over the analogous study for the 35 μm wide Pt line in the Pt(50 nm) ReRAM array. The mass of the platinum 35 μm metal line has risen, obviously, 3.5-fold compared with the 10 μm Pt line and the same applies to the respective product m $\mathit{\times }$ c_s. However, because the Pt substance did not change, the thermal conductivity remained constant. According to Table 3 degradation for the device #4 (Pt(50 nm) 35 μm wide inert electrode), electrical probing of the Pt(50 nm) line with a width of 35 μm, the surrounding cells’ degradation is less severe than that of the Pt(50 nm) arrays’ 10 μm Pt lines but slightly worse than that of the Pt(50 nm)/Cu(100 nm) 10 μm wide lines. At this point, it is instructive to revisit Figure 4 where it is shown that excessive heating leads to damaged (burned) cells. Both cells were operated under identical RESET-SET conditions featuring a Cu filament of the same resistance. The cell at the cross-section of 6 μm Cu and 6 μm Pt line shows severe damage just after three switching cycles. It is seen that the section of Cu electrode covering the cell has completely melted away. The cell at the cross-section of 10 μm Cu and 10 μm Pt line becomes inoperable after six of identical RESET-SET heating cycles and shows only a local melting of Cu along the ridge of the Pt line. The observation provided in Figure 4 confirms our thermal analysis: the wider Cu line provides not only more thermal mass to accommodate the temperature and therefore the maximum temperature decreases by 40%, but also larger heat loss to the heated cell because of larger heat transfer along the Cu electrode line. Therefore, more heating cycles are needed to cause localized Cu melting on a 10 μm wide electrode lines than on 6 μm wide lines.

Additionally, further support for our thermal analysis comes from earlier research [19], where it has been discovered that a ReRAM using Rh(50 nm)/Cr(30 nm) electrodes in place of Pt(50 nm)/Ti(30 nm) electrodes has nearly identical electric properties to a Cu/TaO_x/Pt/Ti memory cell. But, in contrast, for Pt/Ti devices, a cell set at I_cc = 10 μA with M_x of 15 grows to M_x = 26 for Rh/Cr devices. Because of higher thermal conductivity, the device Rh/Cr needs more of the identical SWC to reach the same T_c at which the device becomes inoperable. This is in line with our explanation of the thermal effects. In this particular case, we recall that the only purpose of Cr and Ti layers of 30 nm was to act as suitable adhesion layers. But the two inert electrodes have different thermal conductivities of 150 W/mK and 94 W/mK for Rh/Cr, compared to 69 W/mK and 18 W/mK for the Pt/Ti bilayer combination. According to our thermal investigation, the m $\mathit{\times }$ c_s of the Rh and Pt electrodes are comparable, with the Rh electrode’s product and being only marginally greater than the corresponding product for the Pt metal line (see Table 1). The product is about the same because Pt has 1.75 times higher mass density but 1.80 times lower specific heat capacity. As, however, Rh’s thermal conductivity is 2 times greater than Pt’s, we anticipate that using Rh as the electrode will result in cooler surrounding cells than using Pt as an inert electrode. The discovered boost of 26/15 = 1.73 is within a reasonable interval of the estimates provided by our thermal investigation set forth in this work. In a way, the case of the narrower (10 μm wide) Rh(50 nm) electrode is the opposite of the case of the wider Pt(35 μm) electrode. The product m $\mathit{\times }$ c_s grew by a factor of 3.5 when the Pt line was wider, but the thermal conductivity remained constant when compared to a Pt line of 10 μm width. For the Rh 10 μm electrode, the product m $\mathit{\times }$ c_s is the same, but the thermal conductivity value has doubled.

In addition, different adhesive layers Ti and Cr have been added to two identical devices (Cu/TaO_x/Ru) in Figure 2 (compare inert electrodes (e) and (g)). As opposed to Ti, which has a thermal conductivity of 18 W/mK, Cr has a thermal conductivity of 94 W/mK, i.e., about five times higher. One discovers that the type of adhesive layer sensitively affects the electric performance of apparently equivalent devices. We discover that the Ru/Cr device’s V_res = −3.8 V is 0.4 V higher than the Ru/Ti device’s (V_res(Ru/Ti) = −3.4 V). According to our analysis, this outcome should have been readily anticipated. Compared to the Ru/Ti device, the Ru/Cr device sees a substantially higher rate of heat conduction from the Cu CF when the device is being heated during the RESET procedure. When using the Ru/Ti electrode, the heat produced in the Cu CF is not released quickly and remains in the area near the hot point for a while because of Ru/Ti’s low thermal conductivity. As a result, inert electrodes with lower thermal conductivities require less heating SWC than those with higher thermal conductivities because heat accumulates in the nanofilament at a faster rate with lower thermal conductivities, resulting in lower V_res voltage. A comparison of V_res values of the other devices is also useful. We discover that the V_res for the Co/Ti and Pt/Ti devices are, respectively, V_res(Pt/Ti) = −0.9 V and V_res(Co/Ti) = −1.0 V, i.e., statistically the same, which, once more, matches extremely well with the identical thermal conductivities of the two metals of 69 W/mK for both Pt and Co. Last but not least, there is a significant variance in V_res of around 2.5 V between Pt and Co devices and Ru devices, which is perfectly consistent with Ru’s significantly higher heat conductivity than that of cobalt.

As a result, the impact of cell-to-cell heat transfer on the electrical performance of the device is shown to be influenced almost in equal parts by three mechanisms: (i) the electrode materials’ specific heat capacity, (ii) thermal conductivity, and (iii) the product of volume and mass density of the electrodes, i.e., its total mass. Our thermal guidelines are able to predict quantitatively the amount of improvement or deterioration of the electrical degradation effects with reference to thermal material properties and geometrical shape of the electrodes, once our thermal methodology has been calibrated to a baseline array (here Cu/TaO_x/Pt/Ti device). Finally, we would like to address the issue of maximum SWC for different devices. Cu/TaO_x/Ru and Cu/TaO_x/Pt devices exhibit identical behavior at first, despite having differing V_form, V_set, and V_res threshold voltages, as demonstrated in Ref. [26]. The basic distinction between the two devices is the severely reduced cycling capability of the Ru devices. The Pt device may cycle through up to 100 SWC under optimal switching conditions, compared to the Ru device’s mere 13 cycles. It was discovered that the Ru electrode’s decreased inertness qualities were responsible for the reduced switching cycling ability. Similar to this, it was demonstrated in [38] that Cu/TaO_x/Ti and Cu/TaO_x/Ta devices had much lower switching capabilities than Cu/TaO_x/Pt devices.

5. Conclusion

We have provided a wealth of experimental data showing how the material properties and geometrical dimensions of the ReRAM electrodes affect the amount of cell-to-cell heat transfer, and, in turn, how the heat transfer affects the several appearances of degradation of the electrical performance of the resistive memory cells. The degree of device degradation has been quantified using a thorough thermal methodology of the heat transfer that takes into account the electrode materials’ thermal conductivity, thermal diffusivity, specific heat capacity, and mass density. Although our memory arrays manufactured in a university laboratory match commercial ReRAM architecture only in terms of the vertical dimension, i.e., the thicknesses of the constitutive layers but exceed commercial products significantly in lateral dimensions, they still provide a great starting point for a reliable source of the essential physics and methodology true also for commercial ReRAM because the thermal reliability issues are driven by the same physical mechanisms and the same fundamental material properties. Actually, the heat density dissipated in state-of-the-art memory arrays is far worse than in our memory arrays, as demonstrated in [20], being about two orders of magnitude greater. The reliability problems and ReRAM degradation brought on by heat-cross-talk may thus be lessened with the help of the thermal analysis put forward here, which can act as a reliable road map for a suitable choice of materials or material combinations. There is currently no satisfactory answer to the question of what might be the best options for the inert electrode as far as their thermal properties are concerned. Low conductivity materials result in lower V_res value, which is obviously advantageous for the reduction of the heat dissipated in the arrays, and distant devices are mostly unaffected by the reduced thermal cross-talk alongside the metallization lines. However, for low thermal conductivity electrodes, the Joules heat dissipated in a device lingers longer within the electrode materials and cell. In contrast, the rapid heat transport in the case of a high thermal conductivity electrode impacts by dint of the thermal cross-talk even the cells farthest from the heated cell. ReRAM arrays must be optimally designed and operated taking into account how the memory is being used in terms of programming and erasure cycles to minimize adverse thermal cross-talk effects.