**5. Switching mechanisms in 2D-based memristors**

To further elucidate the mechanism of NVRS phenomenon in 2D monolayers, a Dissociation-Diffusion-Adsorption (DDA) model has been proposed, (**Figure 7a**). In the vertical MIM structure, the symmetric electrodes choice (in most cases both TE and BE are gold) enables the formation of "conductive points" from either the top or bottom electrode. The first step is "Dissociation", which is based on the metal atom/ ion dissociating from a cluster of metal atoms at the electrode-2D material interface. It is straightforward that this process depends on the choice of metal electrode. As discussed above, Au electrodes, as a noble metal, were selected to rule out potential effects from interfacial metal oxidation. It is also worth noting that Au has relatively low atomization enthalpy among various transition metals, thus can serve as an appropriate electrode [44]. First-principle calculation results have been performed and show that the dissociation energy required to move a Au atom sufficiently far from the bulk Au surface is 3.80 eV. For conventional conductive-bridge memory, the dissociation step is a common prerequisite that relies on the formation of metal ions to create a conductive filament and has been extensively investigated in previous reports, so the subsequent diffusion and adsorption steps will be the focus [45].

After Au atom/ion dissociates from the electrode, two scenarios may happen, with either directly adsorbing (chemical bonding) into a vacancy when they are close (Case 1), or it first weakly bonds to the pristine region and subsequently diffuses across the surface and finally finds a vacancy to fill and bond (Case 2). The two scenarios are illustrated in **Figure 7a**. Case 1 is a simpler scenario with only two steps "Dissociation" and "Adsorption" courtesy of the initial close position to a vacancy. On the other hand, Case 2 consists of all three steps and is expected to be more common since the adsorbed neutral Au atom (Au) or positively charged Au ion (Au+1) in the pristine region are energetically favorable compared to their isolated states. Benefitting from the simplicity of Case 1, first-principle calculations for a collection of 12 materials were conducted, which have all been demonstrated to show NVRS behavior. In contrast, for the more probable Case 2, owing to the system complexity, only MoS2 is analyzed as a prototypical monolayer in the TMD family.

In the simpler scenario Case 1, the dissociated Au is at first in an isolated state and tends to directly get adsorbed into the defect, resulting in the formation of conductive point that causes switching from HRS to LRS. It has been reported that the most common defects for 2D materials are vacancies, for example, S vacancy in MoS2, Se vacancy in MoSe2, B vacancy in BN, etc. The first-principle calculations

#### **Figure 7.**

*(a-d) Calculated energy results and (e-g) STM observations for dissociation-diffusion-adsorption (DDA) model.*

indicate that there is no barrier energy for Au to move in and bind with the defect site. This is straightforward to understand since isolated Au is unstable and the system energy tends to decrease as Au moves towards a defect site. In **Figure 7b**, the adsorption energy of Au atom/ion into a vacancy site has been calculated for various 2D materials. The negative adsorption energy (the energy difference between final state and initial state) means that adsorption is energetically favorable and releases energy, while a positive value means that the adsorption requires extra energy. Based on the calculations on diverse 2D materials, a common trend can be observed that both Au+1 and Au are energetically favorable to be adsorbed into defects, resulting in a SET process. To be more specific, Au+1 is the most favorable candidate, then neutral Au, and finally, negatively charged Au ion (Au−1). A major reason for such a trend is that Au+1 is the most energetically unstable in its isolated vacuum state, thus releasing the most energy when covalently binding to a vacancy site, followed by the neutral Au atom and then Au−1.

For the "Diffusion" step in Case 2, **Figure 7c** shows the calculated diffusion pathway and barrier energies (the energy difference between transition state and initial state) with Au moving along MoS2 surface from the top of one S atom to the top of a neighboring S atom in the pristine region (without defects). Based on the first-principle calculations, the energy barrier for the Au atom/ion moving from one S atom site to another is quite low (< 0.1 eV), indicating that Au atom/ion can easily migrate around the pristine region at room temperature. This can be easily understood because the adsorption of Au atom/ion in the pristine region is weak, making them very mobile on the surface.

### *Memristors Based on 2D Monolayer Materials DOI: http://dx.doi.org/10.5772/intechopen.98331*

With regard to the final "Adsorption" step in Case 2, Au will diffuse to the atom close to the defect site, and eventually bind to it, since Au can easily move around the surface. **Figure 7d** shows the calculated energies for the transition and final states in the adsorption step. The low energy barrier (≤ 0.18 eV) indicates that Au/Au+1 can adsorb from the pristine region to the defect site, especially at high temperatures due to the Joule heating from the increased electrical current. In addition, this process can release a large amount of energy (≥ 1.72 eV). The low energy barrier and high energy released suggest that the adsorption of Au/Au+1 from the pristine region to the defect site is preferable both kinetically and energetically. However, the reversed process, for instance, the Au/Au+1 moving out from the vacancy site to the pristine region, has a much higher energy barrier (1.89 eV). Thus, it is much more difficult for Au/Au+1 to desorb from the vacancy site. As a result, Au/Au+1 can stably bind to the vacancy site, acting as a conducting point at LRS. During the RESET process, a high current usually passes through the conductive point, providing enough energy to overcome the barrier and driving Au/Au+1 away from the vacancy site. On the other hand, the Au−1 ion has the highest energy barrier and the smallest binding energy. As a result, the Au−1 ion is the least favorable to participate in the NVRS from both the kinetic and energetic viewpoints and it is not likely to play an essential role in resistive switching for both the scenarios discussed.

To provide experimental evidence to support the Dissociation-Diffusion-Adsorption model discussed above, STM measurement fitted with a gold tip was performed. STM was at first used for atomic resolution imaging of the MoS2 surface to locate and identify the sulfur vacancies (**Figure 7e**). It was followed by a controlled physical contact of gold STM tip with the MoS2 surface and voltage sweepings to emulate NVRS operation in a vertical MIM memory device. The STM image of the same location after SET shows a bright protrusion on the surface (**Figure 7f**). Stability of the site indicates it is not a diffusing atom. Instead, it is strongly bonded to the surface and identified as a gold atom absorbed into the sulfur vacancy [26]. RESET is realized by an opposite voltage sweeping where the gold atom is removed from the defect site (**Figure 7g**). The differences in sharpness and contrast of the STM images before and after the switching indicate that the tip apex has been changed due to the dissociation of a gold atom from the STM tip. In an extensive STM measurement, the STM tip was not only placed on top of the sulfur vacancy, but also in a pristine (defect-free) region. Compared with the I-V curves which resemble NVRS observed at the defect locations, electrical measurements on pristine regions reveal a tunneling-like I-V behavior with no switching phenomenon, suggesting the important role of defects (e.g. S vacancy) in a switching event [26].
