2D MoS2 monolayers integration with metal oxide-based artificial synapses

In this study, we report on a memristive device structure wherein monolayers of two-dimensional (2D) molybdenum disulfide (MoS₂) are integrated with an ultrathin yttrium oxide (Y₂O₃) layer to simulate artificial synapses functionality. The proposed physical simulation methodology is implemented in COMSOL Multiphysics tool and is based on the minimization of free energy of the used materials at the applied input voltage. The simulated device exhibits a stable bipolar resistive switching and the switching voltages is significantly reduced by increasing the number of MoS₂ layers, which is key to conventional low-power computing and neuromorphic applications. The device is shown to perform synaptic functionalities under various applied bias conditions. The resulting synaptic weight decreases almost linearly with the increasing number of MoS₂ layers due to the increase in the device thickness. The simulation outcomes pave the way for the development of optimised metal oxide-based memristive devices through their integration with semiconducting 2D materials. Also, the 2D MoS₂ integration can enable the optoelectronic operation of this memory device.

1 Introduction

Emerging non-volatile memories such as memristive devices that can act as artificial synapses, have attracted huge interest recently in the field of neuromorphic computing, due to their unique capabilities, including high-density integration, fast write and read speed, and compatibility with the existing complementary metal oxide semiconductor process (Yang et al., 2013; Wang et al., 2017; Zidan et al., 2018; Xia and Yang, 2019). In memristive devices data can be written, processed, and erased by changing resistance states between one or multiple low resistance (LRS) and high resistance states (HRS), while the original resistance state, usually, remains unchanged (Raffone, 2017; Sato et al., 2021; Alshaya et al., 2022).

Several material systems, including transition metal oxides (TMOs), such as HfO₂ (Maldonado et al., 2023), Y₂O₃ (Kumar et al., 2022a; Kumar et al., 2022b; Kumar et al., 2022c; Gautam et al., 2023; Kumar et al., 2023; Kumbhar et al., 2024), Ta₂O₅ (Kim et al., 2022), and TiO₂ (Strukov et al., 2008)), and 2D transition metal dichalcogenides (TMDs), like MoS₂ (Naqi et al., 2022), WS₂ (Cao et al., 2022), and MoSe₂ (Duan et al., 2023), have been extensively employed to develop memristive devices for numerous applications (Cao et al., 2022; Naqi et al., 2022; Duan et al., 2023).

Notably, 2D TMD materials offer outstanding electronic, optical, and mechanical properties (Ge et al., 2018; Kim et al., 2018), as compared to conventional TMO materials, which further enables significant advantages (Marseglia, 1983; Yin et al., 2019; Luo et al., 2020), including low-power switching (Feng et al., 2019; Yan et al., 2019; Ranganathan et al., 2020; Lu et al., 2021; Li et al., 2022), device thermal stability (Tong and Liu, 2023), electrostatic tunability (Sangwan et al., 2015), and mechanical flexibility (Ge et al., 2018). Therefore, the integration of layered 2D TMD materials with TMO materials in memristive devices can further enhance thermal stability, induce switching at lower voltages, and enable low power/energy operation (Pickett et al., 2009; Wang et al., 2021; Li et al., 2023; Lin et al., 2024). Moreover, such memristive structures can be utilized to emulate artificial synapses by mimicking basic synaptic functions, such as potentiation, depression and voltage-dependent synaptic responses.

Several successful attempts have been demonstrated to physically model the metal oxide-based memristive devices. For example, Kim et al (Kim et al., 2013a) have reported a physical electro-thermal model of Ta₂O₅ bilayer-based resistive memory by utilizing COMSOL Multiphysics. Bocquet et al (Bocquet et al., 2014) and Traore et al (Traore et al., 2016) have presented the physics-based compact numerical models and density function theory (DFT)-based calculation by adopting generalized gradient approximation (GGA) and Perdew–Burke–Ernzerhof functional (PBE) for HfO₂-based RRAM (Traore et al., 2016), respectively. Kumar et al (Kumar et al., 2022d) have implemented an Y₂O₃-based nanoscale memristor emulating synaptic functionality. However, the aforementioned metal oxide-only based memristive devices have several disadvantages, including thermal instability (Korotcenkov and Cho, 2012), high switching voltage (Ielmini, 2016), and limited tunability of the device conductance.

In this work, we propose an integration of a number of 2D MoS₂ layers with ultrathin Y₂O₃ in a memristive device structure that is operated as artificial synapse. Here, it should be noted that the integration of 2D MoS₂ with metal oxide memristive structure can be implemented in optoelectronic memories and may also act as optoelectronic synapse for bionic visual applications. The proposed physical model is based on the quantitative thermodynamic numerical modelling of the memristive devices, while COMSOL Multiphysics is used to model the memristive device operation. COMSOL Multiphysics (Kim et al., 2013b) helps to solve the partial differential equations by utilizing Finite Element Method (FEM). The heat transfer and electrodynamic equations have been resolved by utilizing physical parameters of 2D MoS₂ and Y₂O₃.

2 Modelling work

2.1 Memristive device structure and adopted numerical methodology

In this physical modelling process, an Al (top electrode, TE, 30 nm)/MoS₂ (1-3 layers)/Y₂O₃ (5 nm)/Al (bottom electrode, BE, 50 nm) memristive structure is analysed having a cross-sectional area of 314 nm². Figures 1A–C shows the simulated device structure wherein the 2D MoS₂ layers are varied from 1 to 3 with corresponding film thickness. As can be seen in Figures 1A–C, a layer of SiO₂ (with a width of 500 nm) is also utilised as a heat shield layer surrounding the memristive device. The thickness of Al top and bottom electrodes is 30 and 50 nm, respectively, while a thin Y₂O₃ (5 nm) layer is used as the primary resistive switching (RS) layer. We introduce in this structure the 2D MoS₂ monolayer(s), which are known to offer higher thermal conductivity, as compared to transition metal oxide materials (Peng et al., 2016; Wang et al., 2018; Wu et al., 2019; Jin et al., 2021). Therefore, this structure is expected to contribute to improved thermal stability of the device and to enable low-power in-memory computation by reducing the device switching voltage. Furthermore, this device structure also enables the concept of the optoelectronic memories (as 2D materials have more attractive optical properties, as compared to metal oxides) that can be used in various applications, including optical in-memory computing sensors, and bionic visual systems.

Figure 1

Figure 1. 3D structure of 2D MoS₂ integrated thin Y₂O₃-based memristive device integrated with (A) single layer MoS₂, (B) double layer MoS₂, and (C) triple layer MoS₂. Insets of each section show the SET and RESET operations wherein the dominant resistive switching mechanism is the formation and rupture of the CFs.

The thermodynamic numerical analysis model that was used relies on the principle of minimizing free energy (FE) within a memristive device, as FE varies under the influence of an external voltage. Simultaneously, the device reduces its free energy by utilizing phase transitions in the oxide material, involving the breaking of chemical bonds. This free energy within a memristive device is expressed as follows (Niraula and Karpov, 2017):

$F=\int \rho C_{\mathrm{P}}\delta T{dx}^3+\frac{1}{2}\int \epsilon {\left|E\right|}^2{dx}^3+2\pi rh{\sigma }_{\mathrm{S}}+\pi r^{2}h\delta \mu (1)$

Herein, ρ: mass density of materials used in memristive structure, C_p: specific heat capacity of materials used in memristive structure at constant pressure, δT: change in temperature due to variations in thermal gradient inside the device, ε: permittivity of the active materials utilized in the memristive device, E: electric field, r: radius of conductive filament (CF), h: CF height in SET process, l: gap length in the case of RESET process, σ_s: interfacial energy, and δμ: difference in chemical potential between unstable conductive phase and insulating phase in SET process (δμ₁) and between unstable conductive phase and metastable conductive phase in RESET process (δμ₂) (Niraula and Karpov, 2017; Niraula and Karpov, 2018).

Eq. 1 delineates thermal and electrostatic energies in its first and second terms, respectively. The latter two terms correspond to phase transformation energy. Notably, the electrostatic energy stemming from the conductive elements (electrodes and filament) is marginal compared to the insulating layer, which possesses higher capacitance. Consequently, the insulator layer predominantly influences the overall free energy. Conversely, the thermal contribution is primarily driven by the conducting filament facilitating current flow between the top and bottom electrodes.

This work utilizes the following algorithmic steps to determine the device’s minimum free energy configuration and its corresponding current-voltage (I-V) characteristics: (a) Construct the device. (b) Apply a source voltage and compute the device’s free energy for varying filament radii. (c) Determine the change in free energy (∂F/∂r) corresponding to filament radius and gap length (∂F/∂l) for a constant source voltage. (d) Repeat steps (b) and (c) for different source voltages. (e) Record the device voltage, current, filament radius, filament gap length, and their respective minimum free energies for all source voltages. (f) Finally, obtain two sets of current-voltage (I-V) characteristics in step (e) pertaining to the SET and RESET processes.

The SET process comprises two key sub-processes: the rapid shunting of electrodes and the radial expansion of conductive filaments (CFs). Within the shunting phase, there are distinct stages: nucleation and longitudinal growth of CFs, both characterized by their stochastic behaviour (Gaba et al., 2013). Likewise, the RESET process consists of two fundamental sub-processes: the initiation of a gap through CF rupturing, followed by the stochastic growth of this gap.

2.2 COMSOL multiphysics modules

Figures 1A–C depicts the 3D schematic of the memristive devices used to build the 2D axisymmetric model in COMSOL for the SET and RESET processes. Leveraging a 2D geometry in COMSOL facilitates the reduction of volume integrals in Equation 1 to area integrals. The area integrals directly corresponding to the SET and RESET processes in COMSOL are expressed as (Niraula and Karpov, 2017; Niraula and Karpov, 2018):

$F_{\text{SET}}=\iint \rho C_P\delta Tdrdz+\frac{1}{2}\iint \epsilon {\left|E\right|}^{2}drdz+2\pi rh{\sigma }_S+\pi r^{2}h\delta {\mathrm{\mu }}_1(2)$

$F_{\text{RESET}}=\iint \rho C_P\delta Tdrdz+\frac{1}{2}\iint \epsilon {\left|E\right|}^{2}drdz+2\pi rh{\sigma }_S+\pi r^{2}l\delta {\mathrm{\mu }}_2(3)$

In COMSOL modelling, the values of electric field (E) and temperature (T) can be determined by solving a set of partial differential equations, as presented below:

[i] Electric current module:

$\nabla .J=0(4.1)$

$J=\sigma E(4.2)$

$E=-\nabla V(4.3)$

[ii] Heat transfer module (in solid):

$-\kappa {\nabla }^{2}T=Q_{\mathrm{S}}(5)$

[iii] Multiphysics module:

$Q_{\mathrm{S}}=J.E(6)$

Herein, J: current density, σ: electric conductivity, κ: thermal conductivity and Q_s: heat source. These equations are typically integrated into their corresponding COMSOL modules and extended for numerical modelling purposes.

Equations (4.1-4.3) establish the current conservation law, Ohm’s law, and the relationship between electric field and electric potential derived from Maxwell’s law, respectively. Eq. 5 represents the Fourier heat law, with the Joule heat term from Equation 6 providing the heat source. Detailed descriptions of the boundary conditions and electrical configurations employed during modelling are provided elsewhere (Kumar et al., 2024).

In this modelling approach, internal Joule heating and non-uniform electric field distribution within the memristive device are taken into account. Additionally, the study distinctly illustrates how the number of MoS₂ layers impacts the device’s switching voltage and synaptic weight, characterized by potentiation (P) and depression (D), which constitutes the core concept of the research. The coefficients of the differential equations, including (4.1) to (4.3), (5), and (6), as well as the free energy equations 2 and (3) employed in this physical electro-thermal modelling, are provided in Table 1. Herein, the phonon assisted hopping mechanism is used through the optimum hopping chains. Additionally, the material non-crystallinity is one of the most common features of filamentary RRAM structures. In a non-crystalline material, some atoms or groups of atoms retain a certain mobility being able to move between two equilibrium positions which is described in terms of double well potential (DWP) as discussed in our previous report (Kumar et al., 2024).

Table 1

Table 1. Values of the coefficients of the differential equations and FE used in this physical electro-thermal modelling.

3 Results and discussion

Figure 2A illustrates the simulated RS behaviour of the 2D MoS₂ integrated thin Y₂O₃-based memristive device subjected to a voltage pulsing scheme in the range −1.5 V to +1 V in forward and reverse bias, delivered to the top electrode through a load resistance. The RS response is segmented into four phases: positive forming voltage (+V_F), positive SET voltage (V_SET), negative rupture voltage (-V_R), and negative RESET voltage (V_RESET).

Figure 2

Figure 2. I-V characteristics depicting resistive switching response of the 2D MoS₂ integrated thin Y₂O₃-based memristive device for (A) single layer MoS₂, (B) double layer MoS₂, (C) triple layer MoS₂, and (D) comparative analysis of resistive switching response with number of MoS₂ layers.

During the formation process, all CFs are created within the MoS₂ and Y₂O₃ layer of the RS device, causing it to transition into the SET state when subjected to a voltage amplitude equal to or less than V_F (as illustrated in Figure 2A). For the single layer MoS₂ integrated Y₂O₃-based memristive device, V_F and V_SET are modelled to be +0.81 V and +0.91 V, respectively. Conversely, during the rupturing process, all previously formed CFs are disrupted, leading the memristive device to switch into the RESET state when exposed to a voltage amplitude equal to or less than -V_R. The modelled values for -V_R and V_RESET are −1.5 V and −0.89 V, respectively, while in the case of double layer MoS₂ with thin Y₂O₃ (shown in Figure 2B), the V_F is +0.83 V, V_SET is 0.62 V, -V_R is −1.18 V and V_RESET is −0.61 V. Subsequently, in triple layer MoS₂ (shown in Figure 2C), the V_F is +0.88 V, V_SET is 0.15 V, -V_R is −0.81 V and V_RESET is −0.34 V. From Figures 3A,B it is concluded that the SET and RESET voltage values decrease as the number of 2D MoS₂ monolayers increases. This proves that the presence of 2D MOS₂ plays a pivotal role in the switching process, as compared to primary metal oxide layer. It is well known that the 2D MoS₂ layer requires lower bias potential to switch the device in SET and RESET region, because it shows quantum confinement effect and high carrier mobility (Ling et al., 2023). Therefore, charge carriers can move more easily within the material under the influence of a lower electric field, facilitating faster switching at lower bias potentials. This attribute further enhances the low power computation capability of the presented memristive device structure (Xu et al., 2019).

Figure 3

Figure 3. Impact of the number of 2D MoS₂ layers in thin Y₂O₃-based memristive device over the switching voltages (A) V_SET and V_RESET, and (B) V_F and V_R. The lines are guide to the eye.

Additionally, to demonstrate the synaptic plasticity characteristics of the memristive device, such as potentiation and depression, a series of positive and negative voltage pulses with an amplitude of ±1 V and a voltage rise rate (V_RR) of 100 V/s are administered to the device. Figure 4 shows the potentiation and depression functionality of single layer MoS₂ (Figure 4A), double layer MoS₂ (Figure 4B) and triple layer MoS₂ (Figure 4C). As depicted in Figure 4A, when subjected to positive voltage pulses, the synaptic weight or normalized conductance of the memristive device undergoes a continuous reinforcement. Conversely, in response to negative electrical stimuli the synaptic weight diminishes. This ongoing modulation of the device’s conductance closely mimics the synaptic plasticity mechanisms observed in the brain (Jo et al., 2010; Das et al., 2018).

Figure 4

Figure 4. Impact of the number of 2D MoS₂ layers in thin Y₂O₃-based memristive device over the device conductance (i.e., synaptic weight) for (A) single layer MoS₂, (B) double layer MoS₂, (C) triple layer MoS₂, and (D) comparative analysis in the change of device conductance with number of MoS₂ layers.

As evident from Figure 4D, the synaptic weight (or device conductance) of the memristive device is linearly decreased with an increment in the number of MoS₂ layers within the device structure. It should be noted that in monolayer (∼0.65 nm thickness) MoS2, quantum confinement effects are more pronounced due to the atomic layer thickness of the material, resulting in enhanced carrier mobility (Ling et al., 2023). However, as the number of layers increases, these effects diminish, leading to reduced carrier mobility as well as conductivity. Additionally, this trend may be attributed to alterations in the lateral dimensions of the device. Moreover, in configurations with a higher number of MoS₂ layers, the role of the thin metal oxide layer in the switching process diminishes, with primary switching being predominantly influenced by the MoS₂ layers rather than the Y₂O₃ layer, which basically constitutes combination of interfacial and filamentary switching mechanism (Wang et al., 2016; Li et al., 2018; Ginnaram and Maikap, 2021; Pam et al., 2022). This shift in dominance significantly impacts the overall conductance of the device. In this study, a series of 100 identical pulses (comprising 50 positive and 50 negative pulses) with an amplitude of ±1 V and a pulse width of 10 ms are employed to analyse the synaptic characteristics. Consistent with findings in existing literature (Zhang et al., 2013; Jang et al., 2014; Liu et al., 2018; Kim et al., 2020), the metal/metal oxide interfaces demonstrate a gradual potentiation process and an abrupt depression process, as illustrated in Figure 4D. The sudden shift observed during the depression process is attributed to variations in the free energy at metal/metal oxide interfaces (Yu, 2017). Additionally, accounting for the metal/metal oxide free energy and induced oxide layer, non-identical spike pulses featuring varying pulse amplitudes or durations offer a potential solution to mitigate the high asymmetry ratio observed in potentiation and depression processes (Yu, 2017). However, employing non-identical spikes may introduce complexity to peripheral circuits and neuro-inspired computing systems (Yu, 2017).

Figure 5 depicts the impact of pulse amplitude on synaptic plasticity, delineating both potentiation and depression processes. The graphs illustrate how altering the pulse amplitude effectively modulates the device conductance for single (Figure 5A), double (Figure 5B) and triple layer MoS₂ (Figure 5A), akin to the way spikes in neural communication influence synaptic strength. Notably, successive potentiation spikes elevate memristive conductance, while subsequent depression spikes induce a cycle of conductance reduction. The different pulsing scheme (non-identical pulses) is utilized during the computation of Figure 5. Maldonado et al (Maldonado et al., 2023) have observed similar behaviour experimentally in HfO₂-based memristive devices. Therefore, considering the aforementioned analysis, it can be concluded that control over the MoS₂ number of layers affects the conductance but not the synaptic response of the Yttria-based memristive device.

Figure 5

Figure 5. Synaptic plasticity, potentiation, and depression events in the memristive device under the application of varying pulsing scheme (non-volatile states) for (A) single layer MoS₂, (B) double layer MoS₂, and (C) triple layer MoS₂.

4 Conclusion

We presented a physical model detailing the integration of a number of nanoscales 2D MoS₂ layers with a thin metal oxide-based memristive device, aimed at emulating artificial synapse functionalities. The simulations demonstrate a bipolar RS response across all different number of MoS₂ layers, with device switching voltages decreasing as the number of MoS₂ layers increases. This phenomenon enhances the feasibility of 2D materials combined with transition metal oxide-based memristive devices in low-power computing applications. Moreover, the MoS₂-modified memristive device structure successfully demonstrated synaptic plasticity in terms of potentiation and depression, while the device conductance can also be varied by tuning the amplitude of the input pulsing scheme. Notably, in monolayer MoS₂, quantum confinement effects are more dominant due to the atomic layer thickness of the material, resulting in enhanced carrier mobility and corresponding increment in the device conductance. Conversely, in double and triple-layer MoS₂, these effects are minimized, which further affects the synaptic response of the device. However, in double and tri-layer device structures, the bulk materials conductivity may play a more important role, affecting thus the device switching voltages more significantly, as compared to the overall effect on device conductance. Moreover, the modified memristive device structure with the integration of 2D MoS₂ can pave the way for optoelectronic memories development that may also act as optoelectronic synapses in bionic visual applications. Hence, the profound advantage of the herein presented physical model lies in its ability to inform researchers about the potential functionalities of MoS₂ integrated Y₂O₃-based memristive devices and guide them in developing novel low computing power 2D-TMD/TMO-based artificial synapses for tuneable neuromorphic computing applications.

Data availability statement

The original contributions presented in the study are included in the article/Supplementary material, further inquiries can be directed to the corresponding authors.

Author contributions

MG: Conceptualization, Data curation, Formal Analysis, Methodology, Software, Validation, Writing–review and editing. SR: Formal Analysis, Investigation, Visualization, Writing–review and editing. IZ: Funding acquisition, Investigation, Project administration, Resources, Software, Supervision, Visualization, Writing–review and editing. DG: Formal Analysis, Funding acquisition, Investigation, Project administration, Resources, Supervision, Validation, Visualization, Writing–review and editing. SK: Conceptualization, Data curation, Formal Analysis, Investigation, Methodology, Supervision, Validation, Visualization, Writing–original draft, Writing–review and editing.

Funding

The author(s) declare that no financial support was received for the research, authorship, and/or publication of this article.

Acknowledgments

The authors would like to thank the Indian Science Technology and Engineering Facilities Map (I-STEM), IISc, Bengaluru, India, and the University of Southampton, United Kingdom, for providing license for COMSOL^® Multiphysics. SK would like to thank Department of Science and Technology (DST), New Delhi for research grant via IFA23-ENG-375. The support of the UK’s Engineering and Physical Science Research Centre is gratefully acknowledged, through EP/N00762X/1 and EP/X016730/1. MKG would like to thank National Overseas Scholarship (File No.: K-11015/100/2023-SCD-V-(NOS)). DGG acknowledges support from the UKRI Future Leaders Fellowship Grant (MR/V024442/1).

Conflict of interest

The authors declare that the research was conducted in the absence of any commercial or financial relationships that could be construed as a potential conflict of interest.

The author(s) declared that they were an editorial board member of Frontiers, at the time of submission. This had no impact on the peer review process and the final decision.

Publisher’s note

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