**4. Parameter-dependent studies in 2D-based memristors**

To gain more insights into the underlying mechanism(s), electrical measurements with the dependence of temperature, area scaling, compliance current, voltage sweep rate and layer thickness were performed with MoS2 as the active layer owing to its greater material growth and characterization maturity. The low-voltage I-V characteristics at different temperatures are analyzed to explain the electron transport mechanisms at LRS and HRS. Metallic ohmic conduction can be deduced at LRS (**Figure 6a**) since the current decreases as the temperature increases, and the normalized conductance

$$\mathbf{G}\_{\mathbf{u}} = (d\mathbf{I} / d\mathbf{V}) / (\mathbf{I} / \mathbf{V}) \tag{1}$$

is approximately one, a signature of linear transport that can be attributed to direct tunneling

$$J \ll KV \exp\left(\frac{-4\pi d\sqrt{2m^\circ \mathfrak{p}}}{h}\right) \tag{2}$$

Where J is the current density, m\* is the effective mass, φ is the tunnel barrier height, h is Planck's constant, and K is proportional to the lateral area (A) and dependent on the barrier parameters (m, φ, d) [40]. d is the 2D barrier thickness. The direct tunneling model exhibits linear transport characteristics and is illustrated with an MIM band diagram (**Figure 6a**). Non-linear I-V characteristics are observed at HRS (**Figure 6b**), showing the current increasing as the temperature increases. The HRS data can be best fitted by the Schottky emission model with good agreement (**Figure 6c**) [40].

$$\mathbf{J} \ \mathbf{c} \ A^\prime T^2 \exp\left[\frac{-q\left(\oint\_{\mathbf{b}} -\sqrt{\frac{qE}{4\pi \mathbf{s}\_r \mathbf{s}\_o}}\right)}{kT}\right] \tag{3}$$

*Memristor - An Emerging Device for Post-Moore's Computing and Applications*

$$A^\* = \frac{\mathbf{120m^\*}}{m\_0} \tag{4}$$

where A\* is the effective Richardson constant, m0 is the free electron mass, T is the absolute temperature, q is the electronic charge, ϕB is the Schottky barrier height, E is the electric field across the dielectric, k is Boltzmann's constant, ε0 is the permittivity in vacuum, and εr is the optical dielectric constant. For estimation, the effective thickness of ~1 nm is used and m\* /m0 is ~1. The extracted barrier height is ~0.47 eV at 300 K, and the refractive index n is 6.84.

Area scaling studies have also been conducted and clearly show distinct profiles with the LRS relatively flat while the HRS has a more complicated relationship (**Figure 6d**). The LRS profile is consistent with the theory of a single (or few) localized filament(s) for TMO-based RRAM [10, 41]. With the area below 100 μm<sup>2</sup> , the HRS resistance scales inversely with area owing to uniform conduction. For larger sizes, the resistance is relatively area-invariant, which can be attributed to the presence of localized grain boundaries. Note that the average domain size of typical CVD MoS2 monolayer is ~102 –103 μm<sup>2</sup> . The current and resistance dependence on compliance current (see **Figure 6e** and **f**) reveal a linear relation that can be explained by an increase in the cross-sectional area of a single filament or to the formation of multiple filaments [41]. From the results of the temperature-dependent conduction experiments, the existence of Schottky barrier through TMD-metal interface from literatures [42, 43], and area-dependent studies, the NVRS behavior in MoS2 devices can be explained by the proposed model

#### **Figure 6.**

*Dependence of (a-c) temperature, (d) area scaling, (e, f) compliance current, (g) sweep rate, and (h, i) layer thickness of MoS2 memristors.*

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

that, during SET process, the electrons are transported through a filamentary-like 1D conductive link (or a virtual "conductive point"), and during RESET process, the conductive link is broken, resulting in a Schottky barrier at the device interfaces. Atomic level elucidation of the mechanisms(s) through advanced microscopy imaging and theoretical modeling is of great importance and is the focus of further research.

As to applications, the programmable resistance states are ideal for multilevel memory and neuromorphic computing. Moreover, the intrinsic low-resistance values ~5 Ω (**Figure 6f**), inspires a new application for low-power non-volatile RF switches. The dependence of the SET/RESET voltages on sweep rate (**Figure 6g**) suggests that more time is needed for ionic diffusion, which results in lower switching voltages. Layer dependent studies up to four layers demonstrate that the switching phenomena can be observed in few-layer 2D films (**Figure 6h**), with a distinction that the LRS resistance increases with layer number (**Figure 6i**).
