@misc{10481/102527,
year = {2025},
url = {https://hdl.handle.net/10481/102527},
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.},
organization = {Tesis Univ. Granada.},
publisher = {Universidad de Granada},
title = {Multi-scale simulation and modeling of memristors based on bidimensional materials},
author = {Cuesta-Lopez, Juan},
}