Moisture effect on the diffusion of Cu ions in Cu/Ta2O5/Pt and Cu/SiO2/Pt resistance switches: a first-principles study

ABSTRACT Cu/Ta2O5/Pt and Cu/SiO2/Pt are two of the most promising resistance switches. From experimental observations, it is speculated that the presence of H2O in the amorphous Ta2O5 and SiO2 (a-Ta2O5 and a-SiO2) facilitates the rate-limiting step during the switching process. This rate-limiting step is essentially the diffusion of Cu ions along the nanopores of the amorphous. To better understand this behavior and obtain a detailed examination of the atomic structures, a first-principles simulation was conducted. In addition, we investigate the diffusion behaviors of Cu ions in bare a-Ta2O5 nanopore and in the one covered with H2O–together with those in a-SiO2 nanopore. Our work reveals that Ta and Si atoms on the sidewalls of bare a-Ta2O5 and a-SiO2 nanopores are in the unsaturated (TaO5) and saturated (SiO4) forms, respectively. Consequently, H2O molecules are adsorbed on the nanopore sidewall strongly in the case of a-Ta2O5, and weakly in a-SiO2, by forming O-Ta and H∙∙∙O bonds, respectively. This can explain the experimental observation that the desorption of H2O occurs only at high temperatures for a-Ta2O5 films, while it is observed for a-SiO2 even when the temperature is low. The calculated diffusion barrier of Cu ions in a-Ta2O5 nanopores covered with H2O is about 0.43 eV, which is much lower than that without H2O (~1.40 eV). In view of the similar chemical environments of O and the adsorbed Cu ions in a-SiO2 and a-Ta2O5 nanopores, it is expected that the diffusion of Cu ions in a-SiO2 nanopore without H2O is much more difficult than with H2O. This could be attributed to the strong and weak adsorption of Cu ions on the sidewall in the absence and presence of H2O, respectively, for both, a-Ta2O5 and a-SiO2. Our investigation provides a full atomic picture to understand the moisture effect on the diffusion of Cu ions in Cu/a-Ta2O5/Pt and Cu/a-SiO2/Pt resistance switches.


Introduction
Cation-based resistance switches or electrochemical metallization memories (ECM) have attracted significant attention due to their high scalability, low power consumption and potential application in memory cells [1,2]. In general, such devices consist of an insulator (such as, HfO x [3], SiO x [4], TaO x [5], etc.) layer sandwiched between an inert electrode (Pt or Au) and an oxidizable electrode (Cu or Ag). Their switching processes (from high resistance state to low resistance state) could be realized by changing the polarity of the applied voltage between the electrodes.
Among the ECM devices, amorphous Ta 2 O 5 and SiO 2 (a-Ta 2 O 5 and a-SiO 2 )-based devices (i.e. Cu/a-Ta 2 O 5 /Pt and Cu/a-SiO 2 /Pt) have been extensively studied considering their high performances [5,6]. Composition analyses of a-Ta 2 O 5 and a-SiO 2 films before and after applying a voltage reveal that the switching phenomenon is mainly due to the formation/rupture of Cu filaments [7,8]. Recently, the moisture effects on the performance of a-Ta 2 O 5and a-SiO 2 -based ECM devices have been studied experimentally [6,9]. The following are the key outcomes: (i) none of the devices could be formed without the presence of H 2 O, (ii) the forming voltage drops dramatically with increase in the content of H 2 O in a-Ta 2 O 5 and a-SiO 2 films, (iii) the operation voltage of a-Ta 2 O 5 (a-SiO 2 )-based ECM device rarely (strongly) depends on the ambient H 2 O pressure.
During the switching processes of Cu/a-Ta 2 O 5 /Pt and Cu/a-SiO 2 /Pt ECM devices, three rate-limiting steps have been proposed in the literature. These are (i) ionization of Cu electrode at the Cu/a-Ta 2 O 5 and Cu/a-SiO 2 interfaces, (ii) diffusion of Cu ions in the a-Ta 2 O 5 and a-SiO 2 , and (iii) nucleation of Cu ions at the Pt electrode. These key factors determine the performance of ECM devices (such as, the forming and operation voltages, endurance and switching rates). Accordingly, the 'moisture effect' on the performance of ECM devices can be attributed to the influence of the above-mentioned rate-liming steps due to the presence of H 2 O [6,[9][10][11]. In particular, moisture has been found to be important in the processes of diffusion and resistive switching (e.g. the counter electrode reaction) [10,11]. Studies on moisture effect in such processes remain to be done. In the present work, we pay due attention on the 'moisture effect' on the diffusion of Cu ions in ECM devices. The following hypothesis is proposed on the basis of experimental observations: the nanoporous structures of the deposited a-Ta 2 O 5 and a-SiO 2 films have strong and weak moisture adsorption characteristics during ambient exposure [12,13], respectively. The Cu diffusion along the sidewalls of a-Ta 2 O 5 and a-SiO 2 nanopores becomes smoother when the nanopores are covered with H 2 O. The strong dependence of the operation voltage on the ambient H 2 O pressure in the case of a-SiO 2 can be understood from weaker adsorption of H 2 O on the sidewall of a-SiO 2 . However, several issues need to be addressed: (i) what is the atomic structures of a-Ta 2 O 5 and a-SiO 2 nanopores, (ii) why is the adsorption behavior of H 2 O in a-Ta 2 O 5 and a-SiO 2 nanopores significantly different, (iii) how the Cu ions diffuse along the a-Ta 2 O 5 and a-SiO 2 nanopores with and without the presence of H 2 O. Accordingly, the atomic-scale simulations on the structures of a-Ta 2 O 5 and a-SiO 2 nanopores, and the Cu diffusion behaviors in these nanopores would be very helpful not only to understand the switching process of ECM devices, but also to design the devices for high performance.
In this work, by using the first-principles simulation, we examine the atomic structures and Cu ions diffusion behaviors in a-Ta 2 O 5 and a-SiO 2 nanopores with and without the presence of H 2 O. Our work shows that the different adsorption behaviors of H 2 O in a-Ta 2 O 5 and a-SiO 2 nanopores can be ascribed to the different features of the sidewalls of their nanopores. That is, the existence of unsaturated and saturated cations on a-Ta 2 O 5 and a-SiO 2 , respectively. On the other hand, the presence of H 2 O is found to enhance the diffusion of Cu ions along the nanopores in both cases of a-Ta 2 O 5 and a-SiO 2 . This can be attributed to the drastic weakening of the interaction between Cu ions and a-Ta 2 O 5 /a-SiO 2 nanopores after H 2 O adsorption.

Theoretical method
All calculations are performed using the Vienna ab initio simulation package (VASP) [14,15]. A plane wave basis set with a cutoff energy of 400 eV is used. A projector augmented-wave (PAW) [16] method and a generalized gradient approximation (PW91) [17] are adopted to describe the electronion and electron-electron interactions, respectively. To construct the surface structures of amorphous Ta 2 O 5 , molecular dynamics (MD) simulations are carried out at room temperature using the NVT ensemble (constant number, volume, and temperature). The time steps are set at 3 fs and 1 fs for the systems without and with H 2 O, respectively. The structure is sampled up to 9 ps to obtain a sufficiently equilibrated structure. Considering the large cell size, only the Г point is used during the MD simulation for the Brillouin-zone integration. The structure optimization is performed with 2 × 2 × 1 k-points. The convergence criteria adopted here assumes that the maximum force acting on each atom is smaller than 0.05 eV/Å.
To investigate the diffusion behaviors of Cu ion on a-Ta 2 O 5 surface, again MD simulation can be employed as have done in a recent study of the moisture effect on the diffusion of ions in a novel CO 2 sorbent [18]. In the present study, however, the climbing-image nudged elastic band (CI-NEB) method [19] is employed using 2 × 2 × 1 k-points because realistic atomic structures of nanopores are difficult to obtain as mentioned in the next section. To examine the interaction strength between Cu or H 2 O and a-Ta 2 O 5 /a-SiO 2 surface, the adsorption energy is defined as following:

Atomic structure of a-Ta 2 O 5 nanopore without water
To examine the diffusion behaviors of Cu ions in a-Ta 2 O 5 -based ECM device, first a structure model of a-Ta 2 O 5 nanopore is constructed. Experimental studies suggest that the diameters of the nanopore structures in a-Ta 2 O 5 are about several nm [6,20,21], which are too large to be treated using first-principles simulation directly. Accordingly, we need to construct an approximate a-Ta 2 O 5 nanopore model that can reproduce the actual Cu ion diffusion behaviors within available computational resources. Since the interaction between the two sidewalls several nm apart from each other can be negligible, the diffusion of Cu ions along the sidewall of a-Ta 2 O 5 nanopore could be viewed as the diffusion on the surface of a-Ta 2 O 5 as schematically shown in Figure 1(a). Therefore, we adopt a-Ta 2 O 5 surface model to investigate the diffusion behavior of Cu ions in Cu/ a-Ta 2 O 5 /Pt, instead of the a-Ta 2 O 5 nanopore structure.
In our previous work, we constructed the a-Ta 2 O 5 bulk model by using molecular dynamics (MD) simulation [22]. The structural features of as-generated a-Ta 2 O 5 is consistent with the experimental data. To construct the a-Ta 2 O 5 surface model, the a-Ta 2 O 5 bulk model is cleaved with O-termination, which has been proven to be more stable than the Ta-terminated one [23]. Subsequently, structure optimization and MD simulation are performed at the room temperature. As shown in Figure 1(b), the as-generated a-Ta 2 O 5 surface model (with the chemical composition of Ta 40 O 100 ) possesses a relatively large surface area (14.64 × 14.86 Å 2 ) with a slab thickness about 11.20 Å in average.
As discussed in our previous study [22], most of the Ta atoms in the bulk a-Ta 2 O 5 are saturated by bonding with six O atoms. In the case of the surface region, on the other hand, most of Ta atoms are in the unsaturated forms, for example, Ta 2 O 5 (see Figure 1(b)). This point is discussed in more detail below.
In the a-Ta 2 O 5 bulk structure, most of the O atoms bond with two Ta atoms [22]. As a result, in the freshly cleaved a-Ta 2 O 5 surface, most of the O atoms are coordinated with only one Ta atom. During the structure relaxation, we have observed the following trends of structural change on the a-Ta 2 O 5 surface: (i) two adjacent O atoms with single coordination tends to bond together to form O 2 , and leave away from the system; (ii) TaO 6 components tend to change into TaO 5 by breaking one Ta-O bond in the subsurface region. As a result, TaO 5 components become predominant on the a-Ta 2 O 5 surface. In the case of a-SiO 2 , on the other hand, the surface structure has been successfully constructed in a previous theoretical study [24] as shown in Figure 1(c), where all the O atoms on the a-SiO 2 surface are coordinated with more than one Si atoms. The Si atoms on the surface and in the bulk region are all in their saturated form (SiO 4 ). In the present study, we adopt this model in our calculations.

The atomic structure of a-Ta 2 O 5 surface covered with water
The experimental work suggests that a small amount of H 2 O molecules tend to adhere to the sidewalls of a-Ta 2 O 5 and a-SiO 2 nanopores. The desorption of H 2 O takes place only at high temperature (~350°C) on a-Ta 2 O 5 surface, but at room temperature on a-SiO 2 surface [12,13]. To understand this point better, we have examined the adsorption of a single H 2 O molecule on the surface of a-Ta 2 O 5 and a-SiO 2 . In doing so, all the possible adsorption sites have been considered because various chemical environments must appear on the surface of amorphous material (for details, see Figures S1 and S2 in Supporting Information). Our calculations show that a H 2 O molecule prefers to adsorb on an unsaturated Ta atom on the surface of a-Ta 2 O 5 , and it forms an O-Ta bond as seen in Figure 2(a) and Figure S1. The calculated averaged adsorption energy for such adsorption structures is about −0.94 eV, which means that the interaction between H 2 O and a-Ta 2 O 5 surface is strong. Thus, the desorption process can only occur at high temperatures. On the other hand, in the case of a-SiO 2 , we have found that a H 2 O molecule weakly adsorbs on the a-SiO 2 surface by forming hydrogen bonds (H•••O) as shown in Figure 2(b) and Figure S2. The calculated adsorption energy for such adsorption structures is about −0.35 eV in average. As a result, facile desorption of H 2 O from a-SiO 2 surface is expected.
In the experiments, the sidewall of a-Ta 2 O 5 nanopore is covered with a thin layer of H 2 O molecules [6]. To model such a situation, 10 H 2 O molecules are initially placed on a surface of a-Ta 2 O 5 so as to form O-Ta bonds. Then the system is relaxed (with the other surface fixed) by MD simulation for 6 ps at the room temperature, and structure optimization is done subsequently. It is found that the H 2 O molecules on a-Ta 2 O 5 surface tend to split into OH groups and H atoms during the structure relaxation. The OH group tends to adsorb on the undercoordinated Ta atom, and the H atom tends to bond with the adjacent O atom by forming another OH group. This is consistent with the fact that a large amount of OH groups was detected in the previous experimental study [6]. To achieve a full OH termination on a-Ta 2 O 5 surface, another 8 H atoms are added to the isolated O atoms to form the OH groups. The structure relaxations (including MD simulation for 3 ps and optimization) are carried out subsequently. As shown in Figure 2(c), the as-generated a- Ta

The diffusion of cu ions on a-Ta 2 O 5 surface without and with water
Using the above a-Ta 2 O 5 surface models, next we examine the diffusion behavior of Cu ion on the a- Ta 2 O 5 surface. To do this, we first consider all the possible adsorption sites of a single Cu ion on the a-Ta 2 O 5 surface without and with the presence of H 2 O. The possible diffusion pathways between the adjacent Cu adsorption sites are then calculated.
In the case of bare a-Ta 2 O 5 surface, total 14 Cu adsorption sites have been identified as shown in Figure 3(a). We have found that a single Cu ion prefers to locate itself between the two O atoms in the void spaces of pure a-Ta 2 O 5 surface (for details, see the supporting information ( Figure S3)). The calculated average adsorption energy of Cu ion on the bare a-Ta 2 O 5 surface is −1.88 eV, which indicates a strong interaction between the Cu and the surface. Then, we calculate the possible diffusion pathways between two adjacent Cu adsorption sites, and four paths across the whole a-Ta 2 O 5 surface as identified in Figure 3(b). In each path, at least one of the diffusion steps between two adjacent Cu adsorption sites has the energy barrier higher than 1.40 eV, with the maximum value of about 2.20 eV. It is to be noted that one of the authors of this work and his collaborators recently examined the diffusion barriers of Cu ion in the bulk a-Ta 2 O 5 (with the volume of 1447.46 Å 3 ) using a neural network interatomic potential fitted to density functional theory calculation data. That work reported barrier values ranging from 0.68 eV to 1.79 eV [25] for paths connecting a site in a supercell, and an equivalent one in the adjacent supercell. From calculations presented in [25] and in this work, we conclude that the diffusion of Cu ions in pure a-Ta 2 O 5 (both the bulk region and the nanopore of a-Ta 2 O 5 ) is quite difficult. In fact, experimental study in [26] has shown that the a-Ta 2 O 5 could act as the barrier layer for the Cu ions diffusion within the temperature range of 450-600°C. It should be noted that this temperature range is higher than the desorption temperature of H 2 O from a-Ta 2 O 5 (~350°C) [6]. Thus, the barrier property in that experiment must be ascribed to that of the pure a-Ta 2 O 5 , which further confirms our findings. Another experimental study [27] showed that the coordination number of a diffusing Cu with O atoms in a-Ta 2 O 5 at 350°C is about 1.8~2.0. This is consistent with our theoretical result that the Cu ion prefers to bond with two O atoms on the bare surface of a-Ta 2 O 5 .
In the case of a-Ta 2 O 5 surface covered with H 2 O molecules, 14 Cu adsorption sites have been identified as shown in Figure 4(a) and Figure S4. The calculated average adsorption energy is −0.69 eV, which is obviously lower than that of pure a-Ta 2 O 5 surface (−1.88 eV). Four diffusion paths have been considered as shown in Figure 4(b). Here, the lowest diffusion barrier is estimated to be 0.43 eV, which agrees excellently with the value estimated in a recent experimental study (0.40 eV) [27]. In addition, the estimated diffusion barrier (0.43 eV) of Cu ions on a-Ta 2 O 5 surface covered with H 2 O is much lower than that in the case of bare a-Ta 2 O 5 surface (>1.40 eV), which further confirms the experimental result that H 2 O molecules in a-Ta 2 O 5 matrix could enhance Cu ion diffusion in Cu/a-Ta 2 O 5 /Pt device [6]. Accordingly, the simulation results based on our constructed models can reproduce the experimental results well. Now, let us discuss the atomic details of the diffusion of Cu ion on a- Ta [6,9] have shown that the operation voltages of the Cu/Ta 2 O 5 /Pt device, which are strongly related to the diffusion behaviors of Cu ions, are not changed by increasing the ambient H 2 O pressure. In addition, the diffusion of Cu and H and/or O atoms may coexists. This possibility would be worth considering. This would need significantly more computations, as there are variety of possible cases. This is left as a future task. It is also left as a future task to build a mathematical model to describe the vapor pressure dependence of diffusion behaviors, such as the one constructed for an anion exchange absorbent for CO 2 capture [28].

The diffusion of Cu ions on a-SiO 2 surface without and with water
Finally, we would like to discuss the diffusion behaviors of Cu ions on a-SiO 2 surface. As seen in Figure 1  a-SiO 2 surface due to the low atomic density of this material. Our results show that Cu ion prefers to locate itself in such a void space of a-SiO 2 surface while forming two Cu-O bonds. The calculated adsorption energies for the cases of such spaces are lower than −3.16 eV. It is to be noted that, in spite of different characters of Ta and Si atoms on bare a-SiO 2 and a-Ta 2 O 5 surfaces, the chemical environments of O and the adsorbed Cu ion are similar on the two amorphous surfaces in the sense that the Cu has two Cu-O bonds. Thus, an irreversible trapping of Cu ion on the bare a-SiO 2 surface is expected. With the presence of H 2 O, the void space of a-SiO 2 surface will be filled with the H 2 O, and Cu ion will diffuse along such H 2 O layer. Similar to the case of a-Ta 2 O 5 , it is expected that the diffusion of Cu ion on a-SiO 2 surface covered with H 2 O will be much easier than that of bare a-SiO 2 surface.

Conclusions
In this work, the atomic structures and the diffusion behaviors of Cu ion on a-Ta 2 O 5 and a-SiO 2 nanopores with and without H 2 O are discussed by using the first-principles simulations. Our results reveal that the Ta and Si atoms on the sidewalls of a-Ta 2 O 5 and a-SiO 2 nanopores are in under-and full-coordination with O atoms, respectively. As a result, the H 2 O molecules tend to strongly adsorb in the a-Ta 2 O 5 nanopore with forming O-Ta bonds, while the interaction is weak between H 2 O and a-SiO 2 nanopore with the formation of H•••O hydrogen bonds. This result could well explain the experimental observation that the desorption of H 2 O from a-Ta 2 O 5 could occur only at high temperatures, while such process could easily take place at lower temperatures in the case of a-SiO 2 . Without the presence of H 2 O, the Cu ions tend to get irreversibly trapped in the void spaces on the sidewalls of a-Ta 2 O 5 and a-SiO 2 nanopores by forming two Cu-O bonds. With the presence of H 2 O, the adsorption strength of Cu ions in a-Ta 2 O 5 and a-SiO 2 nanopores dramatically weaken, since the H 2 O fills in the void spaces in a-Ta 2 O 5 and a-SiO 2 nanopores. As a consequence, the diffusion of Cu ions could be enhanced by the presence of H 2 O in a-Ta 2 O 5 and a-SiO 2 nanopores. Our results would be helpful to understand the switching mechanisms of Cu/Ta 2 O 5 /Pt and Cu/SiO 2 /Pt resistance switches.