Multi-scale simulation and modeling of memristors based on bidimensional materials

Abstract

Nanoelectronics is crucial for the development of modern societies. However, despite advances in software, progress in hardware has slowed down due to the physical limits of transistor miniaturization. Although two-dimensional materials such as graphene or MoS2 offer certain advantages, transistors based on these materials have yet to surpass silicon technology. As an alternative, the implementation of artificial neural networks is proposed. This novel computing architecture, inspired by the brain, combines memory and logic in the same location, increasing energy efficiency. The constituent units must replicate the synaptic behavior of biological neurons, with memristors, emerging as the most promising candidates. Experimental development must be supported by theoretical models to guide progress. However, the literature on this subject remains scarce. Therefore, this Thesis aims to contribute to the numerical state of the art, thereby fostering the development of this technology. The main objective of this Thesis is to develop a numerical simulation tool capable of predicting the behavior of memristive devices based on a wide variety of structures and materials. To achieve this, the focus is on modeling the phenomena of electron capture/emission by interface traps, and ion migration in amorphous oxides, two physical mechanisms responsible for the appearance of hysteresis in devices with FET structures. With this tool, it will be possible to analyze the devices’ responses and the evolution of various physical magnitudes over time, studying the most relevant performance metrics in each case. This work begins with a review of the theoretical foundations necessary for studying memristive devices based on 2D materials, organized in increasing levels of abstraction. First, essential concepts from solid-state physics are revisited, such as the band structure of a material and Fermi-Dirac statistics. Next, the behavior of junctions between different materials is analyzed, both in equilibrium and under bias, as well as their role in the operation of FET-like devices. Finally, a qualitative analysis of memristor responses under various modes of operation is introduced, with a focus on trap-assisted memristive devices and those based on ion migration in amorphous gate insulators. Special attention is given to conductivity variations in the channel induced by changes in the charge concentration at the oxide-semiconductor interface. To model these types of devices, a numerical simulation tool has been developed that solves the electrostatics and charge transport within the device. The relevant equations are: i) the Poisson equation, which determines the electrostatic potential profile; ii) the electron and hole continuity equations based on the quasi-Fermi energy level, which describe charge flow; and iii) the ion continuity equation based on a drift-diffusion model that uses the Scharfetter-Gummel scheme to obtain the ion concentration. Additionally, the calculation of electron and hole densities, as well as donor and acceptor interface traps, involves defining the density of states and energy distribution profiles for traps. Essential details are provided on time-dependent modeling and the boundary conditions defined for each case. The program workflow required to ensure the self-consistent resolution of the aforementioned equations is also described. Finally, the simulator’s flexibility in defining a wide range of structures is highlighted, as well as its versatility in working with externally calculated densities of states using ab-initio techniques, enabling multiscale studies of memristive devices. The modeling of memristors begins with a two-terminal device based on laserinduced graphene. Experimental measurements reveal the hysteresis behavior of these devices, transitioning between low and high resistance states due to the application of triangular voltage pulses. Based on these results, the simulation tool is used to propose a model that explains this behavior through the migration of defects within the induced graphene channel, which shield the external field. After validating this model, the results are expanded with theoretical simulations showing the variation in the memristors’ response to changes in material parameters, the frequency of the applied signal, or the length of the device. Additionally, conditions are theorized that would allow for scaling down the memristors without compromising their performance. Regarding three-terminal memristive devices, the analysis begins with a FETlike structure, known as a ferroelectric-like memristor, where the gate oxide is amorphous, meaning it contains a significant concentration of defects (ions and oxygen vacancies) capable of migrating in response to a variable gate signal. After fitting the experimental current curve of a device based on amorphous HfO2 and a germanium channel, a theoretical study is conducted to analyze the dependence of two key performance metrics, namely the memory window and retention time, on the characteristics of the applied signal. Additionally, the impact of ion-related parameters on these metrics is examined, concluding with a demonstration of the device’s ability to emulate the synaptic plasticity of biological neurons, specifically potentiation and depression. Regarding the use of 2D materials in three-terminal memristive devices, a backgated FET structure is selected, combining a MoS2 channel with an amorphous Al2O3 layer acting as the gate oxide. Initially, a theoretical study is conducted on modeling the dynamics of interfacial traps located at the MoS2-Al2O3 interface, without considering ion migration within the oxide. In this first case, the dependence of the threshold voltage and memory window in the I-V curves, which exhibit clockwise hysteresis, is evaluated based on the parameters used to model the trap concentration, such as their energy distribution or the electron capture and emission rates. Subsequently, trap and ion modeling is combined, and a frequency analysis is carried out. By examining the synchronized/delayed evolution of charge concentrations relative to time-dependent voltage stimuli, different operating regimes of the device are established, depending on whether hysteresis is present. Finally, a collaborative project with Professor Daniele Ielmini’s group at Politecnico di Milano is presented, stemming from an international research internship at their institution. After fabricating and characterizing memristors based on MoS2 and amorphous Al2O3 in a top-gated FET structure, counter-clockwise hysteresis curves were obtained, contrary to other devices previously studied by their group. Consequently, the simulation tool developed in this thesis was employed to propose and validate a model based on ion migration within the Al2O3 layer, which not only explained the origin of the hysteresis but also addressed an observed asymmetry in the frequency dependence of the threshold voltage. This collaboration is ongoing, currently focusing on studying the potentiation of these memristors in response to pulse trains, and all results obtained since the beginning of this project are presented in this Thesis. In conclusion, this thesis makes a significant contribution to the numerical state of the art in the modeling of memristors based on 2D materials. The simulator developed not only allows the study of device responses, but also tracks the temporal evolution of physical variables such as charge densities and the electric field. This paves the way for the design and optimization of memristors with potential applications in the practical implementation of artificial neural networks.