Switching mechanisms of CMOS-compatible ECRAM transistors—Electrolyte charging and ion plating

With the advance of big data and neuromorphic computing, analog solutions are being sought to enable efficient and low-power computing. To realize the biological synapse that stores analog data in electronic devices, non-volatile resistive memories based on various physical mechanisms have been extensively studied.^1–6 Electrochemical random-access memory (ECRAM) is emerging as a promising building block for non-von Neumann computing using neuromorphic systems.^2,6–15 Initially, the devices developed were mainly based on Li-ion, but the requirement for CMOS compatibility leads to schemes relying on protons (H⁺) or copper ions (Cu⁺). While the CMOS-compatible ECRAM transistors have a structure similar to those based on lithium ions, the materials and length scale are very different. Namely, the operation principles of CMOS-compatible ECRAM devices must be studied independently. This contribution aims at combining detailed simulations with experimental data to provide a theoretical framework for such studies. We also show that detailed modeling allows shedding light on internal chemical physics.

Unlike conventional transistors, a solid-state electrolyte that enables ion movements has been used instead of gate oxide in ECRAMs. An ion reservoir¹⁶ or gate electrode with ionizable material (e.g., Cu)⁷ was introduced to provide ions to the electrolyte. Part of the attraction of this device configuration relates to the decoupling between the “write” and “read” operations using a “gate” electrode to tune the conductance state of the semiconductor layer. Typically, the gate electrode is connected to an ion reservoir such that a gate bias (voltage and/or current) would release an atom to the solid electrolyte. From there, it may transport to the semiconducting layer. Suppose one follows the chemical physics picture established in the field of batteries. In that case, the atom that enters the electrolyte is charged; hence, the electric field between the gate and the semiconductor drives and activates its motion. In most publications, the next significant event is when the ion enters the semiconductor layer. For positively charged ions such as Cu⁺ or H⁺, the drive for charge neutrality attracts electrons from the contacts to form an ion–electron pair that functions as N-type doping. As a result, the current in the channel increases, corresponding to potentiation. Recently, it has been suggested that the ions could affect the channel's conductance before intercalating into the semiconducting layer.¹³ Namely, the known effect of charged defects in the oxide¹⁷ could be responsible for the channel's potentiation. Another effect we wish to explore is the one known in the battery world as lithium plating.¹⁸ Although Li⁺ is not supposed to accept electrons from the electrode material in well-designed batteries, under certain operation conditions, it would plate as Li⁰. For the ECRAM field, one considers a variety of metallic ions, making it more probable for the ion neutralization reaction to occur.

Regarding semiconductor device model based simulations, we found only 1D device models as in Ref. 19. Unfortunately, the device geometry and the physical implementation of the electric field activation¹⁹ are too different to allow for a direct comparison to our model results. In the following, we use a 2D device simulation model to study and visualize the abovementioned mechanisms. Comparing simulations to the measured ECRAM device, we find that the effect of charged defects in the oxide is sufficient to explain potentiation in the CuO_x/HfO_x/WO_x stack.¹³ We also find that inducing high ion flux leads to ion-plating, which serves as an ion-loss mechanism explaining the sub-linear response reported for some devices.¹² 

The device parameters were derived from Ref. 13 and are collated in Table I.

The simulations were performed using Sentaurus Device (Synopsys^®), and the dynamics of the atomic species were implemented using the hydrogen diffusion module.

Here, E is the electric field and fE is the activation energy lowering by the electric field (for Cu⁰ f = 0). Note that we use the linear field dependence (β = 1) and not the $E$ one (β = 0.5). Historically, the E dependence is due to Onsager, and $E$ is due to Frenkel, who considered slightly different experimental scenarios.²² To clearly distinguish between the two, one must cover a wide range of electric fields,²³ which is beyond the scope of this paper.

Here, K_c and K_e are the capture and emission coefficients, respectively. $N C u +$ is the density of Cu⁺ ions (“traps”), $N e$ is the electron density in the WO_x conduction band, $N C u 0$ is the density of neutral copper atoms or the density of “trapped” electrons, and $N e 0$ is the electron density at the WO_x conduction band if the electron quasi-Fermi level coincides with the Cu⁺ (“trap”) energy and $( N e 0 − N e)$ is the density of available states. If the densities are low and the material is non-degenerate, then $( N e 0 − N e)≅ N e 0$⁠. The generated Cu⁰ atom may diffuse within the structure; however, since it is a neutral specie, its diffusion is not field-activated, making it effectively static. We should also note that the level of plating considered here is relatively low such that it may be in the nucleation stage and not in a continuous film form (i.e., it does not form an electric short).

A way of considering the potentiation mechanism is to recall some of the basics of thin film transistors (TFTs, Fig. 2). The gate electrode can induce conductivity between the source and drain. Applying a positive bias to the gate would charge it positively and induce electrons in the semiconductor (left scenario). Charged defects in the insulator (central scenario) would also induce electrons in the semiconductor. Finally, N-type doping is effectively adding a positive atom that is accompanied by a free electron (right scenario). By using a gate that is also an ion source, one can control the density of charged defects and eventually also the doping density. Part of the motivation here is deciphering which mechanism is dominant in the measured devices we study.

Figure 3 shows the simulation's results of the Cu⁺ ions’ distribution during a potentiation sequence. Here, we assume that CuO_x defines, at the interface with HfO_x, a Cu⁺ density of 10¹⁹ cm⁻³ and that the WO_x doping is N_D= 10¹⁹ cm⁻³. Figure 3(a) is after the first pulse, Fig. 3(b) is after 15 pulses, and Fig. 3(c) is after 30 pulses. Figure 3(d) shows the Cu⁺ density distribution along a cut made in the middle between the source and the drain. Figure 3 shows that the Cu⁺ ions’ distribution has a front that gradually propagates across the HfO_x layer, and only toward the end of the potentiation do we see some Cu⁺ entering the channel region. Since the WO_x doping used is 10¹⁹ cm⁻³, the Cu⁺-induced doping has a negligible effect on the potentiation. Namely, the main effect is of the Cu⁺ density front propagating across the HfO_x layer, in good agreement with the mechanism suggested in Ref. 13. Note that the shape of the red curve in Fig. 3(d) is indicative of space charge limited current where the charge density beyond the first few nanometers is independent of the density imposed by the contact.²⁷ 

Developing the simulations described above, we relied on the data provided for the devices described in Ref. 13. Common to all experimental data is the background current associated with WO_x doping that existed before potentiation. This nonintentional doping could be due to oxygen vacancies at the WO_x layer or to the diffusion of Cu⁺ ions from the top gate stack. To this end, we measured the WO_x layer's conductivity as fabricated and after the gate stack's deposition. The differences were non-significant. Using the parameters listed in Table I, we compare the measured data of Ref. 13 to simulated responses where we vary the values of those listed at fitting parameters (Fig. 4).

For Fig. 4, we used three values for the WO_x nonintentional doping of N_D= 1.5 × 10¹⁸ cm⁻³ [(a) and (d)], N_D= 10¹⁹ cm⁻³ [(b) and (e)], and N_D= 10²⁰ cm⁻³ [(c) and (f)]. The measured data in (a)–(c) are shown using red empty symbols. The simulated data are shown using full symbols, where in (a)–(c), we varied the Cu⁺ density at the CuO_x interface with HfO_x between 10¹⁹ cm⁻³ (cyan), 10²⁰ cm⁻³ (green), and 10²¹ cm⁻³ (orange). E_a and f in Table I were chosen such that during potentiation (V_G= + 6 V, high field), the ion diffusion in the HfO_x layer is D = D₀ and that at V_G= 0 V, $D≪ D 0$⁠. This leaves only three fitting parameters: μ_e, D₀, and N_D.

Figure 4 examines three sets of μ_e, D₀, and N_D values chosen using the following logic. The background current is due to μ_eN_D; hence, choosing one determines the other. The increase in the electron density in the channel due to potentiation is dictated by the amount of Cu⁺ ions injected into the HfO_x per pulse, which is determined by D₀. Thus, the change in the electron current is determined by μ_eD₀. Table II shows the parameters used for the simulations presented in Fig. 4. The simulation responses showed a slight (<15%) shift in the background current and the potentiation response relative to the experimental data. Thus, we aligned the baseline and normalized the potentiation response for easy comparison.

Examining the potentiation responses in Fig. 4, we note that all the parameters used provide a reasonably good fit for the measured potentiation. However, the situation with the depression is very different. We take this opportunity to thank the anonymous reviewer for suggesting that reproducing the depression is important. Figures 4(a)–4(c) suggest that for a depression to take place, there must be a minimal level of unintentional doping present in the WO_x layer. We also note that the depression shown in Fig. 4(b) is closest to the experimental data but still not exact. The common theme is that the current response does not fully recover such that the next potentiation–depression cycle would start from a higher baseline. In Figs. 4(d)–4(f), we examine the effect of repeated cycles of potentiation–depression. For Figs. 4(e) and 4(f), the response reaches a steady state after the 4th cycle, and for the low WO_x doping [Fig. 4(d)], the response is still increasing after the 8th cycle. The significant increase in the current in Fig. 4(d), and the fact that in Fig. 4(f), the response remains highly asymmetric leads us to conclude that the parameter set used for Figs. 4(b) and 4(d) is closest to the actual material parameters. Moreover, the steady state response that evolves within five cycles assumes the shape that matches perfectly the measured one [inset to Fig. 4(b)].

To shed light on the importance of the WO_x doping density, we plot in Figs. 5(a)–5(c), the electron density distribution within the WO_x channel during a depression pulse of V_G= −6 V during the first potentiation–depression cycle. The motivation is that for a voltage to drop between the gate and the WO_x layer (i.e., across HfO_x), the WO_x layer must function as an electrode or a transistor channel. Examining Figs. 5(a)–5(c), we note that in the device with the nonintentional doping of N_D= 1.5 × 10¹⁸ cm⁻³ [Fig. 5(a)], the WO_x layer is fully depleted (the blue color indicates an electron density below 10¹¹ cm⁻³). Namely, for this device, WO_x is like a charged dielectric that can support only minimal voltage drop across it. For the device with N_D= 10¹⁹ cm⁻³ [Fig. 5(b)], the depletion extends only into half the film thickness leaving the other half fully conducting. The device with N_D= 10²⁰ cm⁻³ [Fig. 5(c)] shows that the depletion is only at the HfO_x/WO_x interface.

To show the relation between the WO_x doping and the effective depression pulse value, we extracted the simulated voltage drop across a vertical cutline shown in the subfigures. Figure 5(d) shows the extracted voltage drop for the three devices. If the WO_x would act as a transistor channel, then the potential at the WO_x would be positive and between the voltage on the source (V_S= 0) and drain (V_D= 0.5 V) electrodes. For the nonintentional doping of N_D= 1.5 × 10¹⁸ cm⁻³ (cyan line), this is clearly not the case, and the voltage drop across the HfO_x layer is only about 1 V. We define this as an effective depression pulse of 1 V. For N_D= 10¹⁹ cm⁻³ (purple), the voltage drop across the entire structure is ∼6 V, and across HfO_x, it is ∼5 V. For N_D= 10²⁰ cm⁻³, the 6 V drops directly on the HfO_x layer. Namely, within the scope of the current model, the effective depression pulse depends on the WO_x doping level up to about N_D= 10¹⁹ cm⁻³.

To facilitate establishing the connection between WO_x doping, the electric field across HfO_x, and the depression response, we simulated the N_D= 1.5 × 10¹⁸ cm⁻³ [Fig. 5(a) and Table II] structure implementing the ion diffusion parameter of N_D= 10¹⁹ cm⁻³ [Fig. 5(b)]. This way we ensure that the only difference the Cu⁺ ions experience is the WO_x doping (N_D). Figure 6 shows the Cu⁺ and electric field distribution of the devices with N_D= 1.5 × 10¹⁸ cm⁻³ [Fig. 6(a)] and N_D= 10¹⁹ cm⁻³ [Fig. 6(b)]. The green line shows the Cu⁺ density distribution after potentiation (30 pulses) and before the depression starts (1st cycle). This distribution is identical between the two structures since, during potentiation, a high-density electron channel forms making the doping density irrelevant. The cyan line shows the electric field distribution during the V_G= −6 V depression pulse. For the low doping density case [Fig. 6(a)], the magnitude of the electric field is smaller (note the right y axis scale), and it decreases significantly toward the HfO_x/WO_x interface. The red line shows the Cu⁺ density distribution after 30 depression pulses (1st cycle). Figure 6(b) shows that the depression pulses pulled the Cu⁺ distribution back toward the CuO_x layer. However, Fig. 6(a) shows that part of the distribution remains fixed and unaffected by the depression pulses. As the electric field (Fig. 6, cyan line) decreases, it reaches a point where it can no longer sufficiently activate the Cu⁺ diffusion [see Eq. (1)]. This is why beyond the 0.025 μm point, the Cu⁺ distribution is fixed, and the depression pulses have a minimal effect [Fig. 4(a)].

To test the generality of our model, we also attempted to fit a different batch of devices. In particular, we chose a device relevant to the potentiation results shown in Ref. 12. The main differences are that the potentiation response is stronger and sub-linear. To fit the response of the measured sub-linear response device, we used the same parameters and approach as before.

We present in Fig. 7(a) the measured response using a 100 ms pulse (red symbols). In our simulations, we tried to best fit the response to 100 ms wide pulses. Using the electron mobility of Figs. 4(b) and 4(e) (1.8 cm² V⁻¹ s⁻¹), the required background doping of the WO_x layer was 9 × 10¹⁹ cm⁻³. To arrive at the measured higher-level potentiation response, the ion diffusion had to be increased to D₀ = 10⁻¹³ cm² s⁻¹. Similar to Fig. 4, the orange and cyan lines were computed using the boundary conditions for Cu⁺ at the CuO_x interface of 10²¹ and 10¹⁹ cm⁻³, respectively.

For the relatively low and linear potentiation studied in Figs. 4(b) and 4(e), the Cu⁺ ions hardly reached the WO_x; hence, there was no effect of adding plating reaction (2) (not shown). The much higher D₀ value used for Fig. 7 leads to a more significant density of Cu⁺ ions reaching the WO_x layer and for reaction (2) becoming relevant. The relatively high doping density (N_D) implies that in reaction (2), we can use the approximation $( N e 0 − N e)≅( N e 0 − N D)≡ N e 0 ∗$⁠.

In reaction (2), the ratio between the capture (K_c) and emission (K_e, $N e 0 ∗$⁠) parameters dictates the relative densities at a steady state or the fraction of Cu⁺ ions plating at the WO_x layer. The absolute value of the parameters dictates how quickly the steady state is reached (i.e., the reaction's timescale).

The capture and emission parameters that provided the best fit were $K c= K e=7× 10 − 21 c m 3 s − 1$ and $N e 0 ∗=4.2× 10 19 c m − 3$⁠. This dictates a time scale for deplating the Cu⁰ is $( K e N e 0 ∗ ) − 1=3.33 s$⁠. The rate of plating Cu⁺ is $( K c N e)$⁠, and since during potentiation, the electron density at the channel is in the 10²⁰s, the timescale is about 1 s.

As before, the first depression [Fig. 7(a)] is not precisely reproduced, indicating that not all the injected Cu⁺ ions were pulled back. The inset of Fig. 7(a) shows the simulation result after repeating the potentiation–depression cycle several times. The baseline rose a bit during the first few cycles, and the baseline of the plotted simulation was adjusted to match that of the experimental result. As before, the excellent fit suggests that potentiation–suppression cycles serve as the annealing process driving the baseline Cu⁺ distribution toward its steady state profile. Figure 7(b) shows the result of the plating reaction in the form of the average density of plated Cu⁰ at the WO_x during potentiation and depression. The cyan and orange lines are for the 1st potentiation–depression cycle, and the black line is for the steady state that was reached on the 5th cycle. For the 1st cycle, the density of plated Cu⁰ becomes notable only at the 6th pulse after which it grows linearly. The deplating starts linearly, and it slows down as the depression proceeds, leaving a significant plated Cu⁰ density as the potentiation ends. As in Fig. 4, the inability to fully extract Cu by the end of the first cycle results in the baseline rising above zero. The black round symbols show the steady state Cu⁰ potentiation–depression response.

Figures 7(c) and 7(d) are to show that the shape of the response is sensitive to the parameters of the plating reaction. Figure 7(c) examines the effect of the energy level of the Cu⁺ trap. A higher $N e 0 ∗$ implies an energy level closer to the vacuum level. In these simulations, we kept the deplating rate $( K e N e 0 ∗)$ constant and, indeed, it is mainly the shape of the potentiation that changes. In Fig. 7(d), we fix the Cu⁺ (trap) energy by keeping $N e 0 ∗$ constant and we vary the rate of both sides of the reaction (i.e., K_c and K_e). Note that changing the overall rate does not change the absolute magnitude of the potentiation as much as varying the trap energy $( N e 0 ∗)$⁠. However, the depression's shape is highly affected.

Finally, we show the distribution of copper as obtained after the 1st 50 potentiation pulses (V_G= +6 V). Figure 8(a) shows the distribution of Cu⁺ ions where by the end of the 50 pulses, a significant density has been injected into the WO_x layer. Since the pulse that injects the Cu⁺ ions (V_G= +6 V) also generates an electron channel at the WO_x/HfO_x interface, the electric field beyond the channel is negligible. Hence, the Cu⁺ diffusion drops sharply, and they are confined to the top WO_x surface. Figure 8(b) shows the corresponding distribution of plated Cu⁰ atoms. Since their diffusion is not field-activated, they stay at the same place where they were generated.

We have presented detailed 2D device simulation model results, including mobile Cu⁺ ions. We found no evidence for the ions experiencing any energy barrier crossing the interfaces; hence, we assumed it to be zero. The only memory mechanism included in the simulations was the electric field-activated diffusion of the Cu⁺ ions. Inspired by the field of batteries, we also allowed for Cu plating through the reaction $C u ++ e −⇌ C u 0$⁠. Using our model, we started by showing fitted results to measurements of linear potentiation and depression. We found that the (linear) potentiation is associated with charging the HfO_x dielectric with Cu⁺ ions. This is somewhat similar to a floating gate electrode, where the charging is done through electron injection. The other important effect we noticed is associated with the depression pulses. It is known that attaching a single electrode to a dielectric would not support a voltage drop across the insulator, and a second electrode has to be provided on the opposite side of the dielectric. During potentiation pulses, the transistor is switched to the ON state, and the channel that forms assumes the second electrode's role. During the depression pulses, the negative bias negates the formation of the electron channel. In such a case, the N-doping of the WO_x channel plays a crucial role where the electron depletion provides the required opposite (positive) charge. We found that to create the field required to pull the Cu⁺ ions back to CuO_x, the N-type doping density has to be ∼10¹⁹ cm⁻³ or above (Figs. 4–6). Knowing the conductivity of the WO_x, we were able to determine that μ_Wox= 1.8 cm² V⁻¹ s⁻¹ and N_D= 10¹⁹ cm⁻³.

We then turned to fitting experimental data of devices having very different response characteristics.¹² Our simulation results suggest that the Cu⁺ diffusion is much higher for these devices (probably due to differences in the HfO_x crystallinity). This pushes a higher density of Cu⁺ ions through HfO_x and into the WO_x layer. This leads to two significant differences in the device's operation. First, while the charging of HfO_x still plays a role, the potentiation response is largely dominated by Cu⁺ induced doping. Second, filling WO_x with a high density of Cu⁺ ions initiates the Cu plating reaction, suppressing the potentiation and creating the sub-linear response. The ratio of D₀ in Fig. 7 to those in Fig. 4(b) is 59. This implies that for the simulations of Fig. 4(b), the plating would have become noticeable only after 360 pulses. The ability to reproduce both linear and non-linear potentiation responses suggests that our model captures important parts of the chemical physics of the CuO_x/HfO_x/WO_x ECRAM transistor.

The issue of ion neutralization or “plating” is an issue to watch out for in the context of ECRAM. The computed densities of Cu⁰ atoms correspond to an average spacing of 10 Å, which is about five times larger than the atomic spacing in copper metal. Namely, our assumption that the plating reaction is only at the nucleation stage and no continuous film forms is self-consistent. To have an estimate for the energy of the Cu⁺ trap level or the energy required for plating, we need to translate N_e0 to an energy level. To do that we need to recall that the formalism developed by Shockley and Read²⁶ assumed that the semiconductor is not degenerate. However, in our case, the semiconductor is degenerate and the shape of the DOS becomes important in determining the relation between the position of the Fermi level and the charge density. If, for simplicity, we assume a parabolic DOS and an effective DOS at the band edge of 10¹⁹ cm⁻³, then the corresponding Cu⁺ level resides ∼0.2 eV above the WO_x conduction band edge. This also leads us to the conclusion that the reversibility of the plating reaction (electron emission from Cu⁰) between potentiation pulses is limited by the high doping density of WO_x that results in smaller $N e 0 ∗$ (N_e0–N_D).

Other CMOS-compatible schemes use H⁺ as the mobile ion. It is tempting to assume that since the energy of the hydrogen reaction is well above the WO_x conduction band, such an ion neutralization process would not take place for H⁺ based ECRAM. However, borrowing again from the field of batteries, it is known that at high charging rates, the system is not governed by equilibrium considerations, and the high ion flux induces plating. This may prove a long-term degradation pathway for H⁺ based devices currently showing impressive short-term stability.² 

The authors have no conflicts to disclose

Nir Tessler: Conceptualization (equal); Investigation (equal); Writing – original draft (equal); Writing – review & editing (equal). Nayeon Kim: Validation (equal); Writing – review & editing (equal). Heebum Kang: Validation (equal); Writing – review & editing (equal). Jiyong Woo: Validation (equal); Writing – original draft (equal); Writing – review & editing (equal).

The data that support the findings of this study are available from the corresponding author upon reasonable request.