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TiO$_2$-based Memristors and ReRAM: Materials, Mechanisms and Models (a Review)
Ella Gale
TL;DR
The review addresses how closely related memristor and ReRAM research can be understood across TiO2 materials, switching mechanisms, and models. It synthesizes these areas and finds convergence between the fields, while noting that device behavior and modelling remain subject to important distinctions and limitations.
Problem
Memristor and ReRAM research spans related but differing definitions, materials, mechanisms, measurements, and models, motivating a focused synthesis of TiO2-based systems.
Method
The review surveys TiO2-based memristors and ReRAM through their material properties, switching mechanisms, historical development, and modelling approaches.
Results
The review identifies convergence between memristor and ReRAM research, with ReRAM using and extending memristor theory and memristor research drawing on ReRAM device properties.
Takeaways & Limitations
TiO2-based devices provide a shared archetypal system, but interpreting them across the two fields requires attention to device definitions, mechanisms, and modelling assumptions.
Takeaways & Limitations
No single mechanism is expected to explain all published TiO2 devices because materials are treated and measured differently.
Abstract
from arXiv · showhide
The memristor is the fundamental non-linear circuit element, with uses in computing and computer memory. ReRAM (Resistive Random Access Memory) is a resistive switching memory proposed as a non-volatile memory. In this review we shall summarise the state of the art for these closely-related fields, concentrating on titanium dioxide, the well-utilised and archetypal material for both. We shall cover material properties, switching mechanisms and models to demonstrate what ReRAM and memristor scientists can learn from each other and examine the outlook for these technologies.
1 Introduction
Memristors and ReRAM are candidate technologies for extending semiconductor scaling beyond CMOS, with TiO2 serving as a central material for both fields. The review surveys their history, properties, mechanisms, and models to clarify their closely related state of the art.
- Memristors and ReRAM are among the technologies proposed to combine continued miniaturisation with functional diversification beyond CMOS.
- The review focuses on TiO2-based devices because TiO2 has received extensive memristor research and is an archetypal, well-studied ReRAM system.
- The review covers material properties, elucidated mechanisms, and current models across these closely related fields.
- Memristors were proposed as a fourth fundamental circuit element relating charge to magnetic flux and introducing a nonlinear circuit element.
- ReRAM generally uses a metal-insulator-metal structure with transition-metal-oxide insulators and provides high- and low-resistance states.
2 Materials
Memristors and ReRAM overlap in TiO2 devices but are distinguished by different naming conventions, measurement practices, and application scopes. TiO2 devices provide an important historical link between the fields.
- ReRAM names a proposed memory use for materials, whereas memristors are named after a property and support applications beyond RAM.Memristor applications include neuromorphic hardware, chaotic circuits, processors, vision processors, and robot control.
- Memristor measurements tend to use a.c. signals at varying frequencies, contributing to confusion with ReRAM measurements.
- The first device called a memristor used a TiO2 thin film, while a 1963 TiO2 device exhibited hysteretic memristor curves during repeated testing.The curves progressed from pinched open curves to BPS curves and eventually a single line as the device degraded.
3 Mechanisms
TiO2 resistance switching has been explained through ionic, thermal, and other mechanisms, but device fabrication and measurement differences prevent a single explanation for all devices. Magnéli conducting filaments are currently the most generally accepted mechanism.
- Suggested switching mechanisms divide broadly into ionic and thermal groups, with TiO2 devices providing examples of both.
- Ionic mechanisms: Ionic switching involves oxygen-vacancy migration that creates auto-doped, metallically conducting TiO(2−x) phases for x > 1.5.Suggestions involving migrating OH− ions have also been made, and oxygen evolution has been observed in several device types.
- Thermal mechanisms: Thermal switching can use Joule heating to form conducting filaments along grain boundaries, with excess heat breaking paths that can later reform.Related crystalline systems suggest electroforming and poly-filamentary conduction channels.
- Other mechanisms: TiO2 devices have also been associated with Magnéli phases, metal–semiconductor transitions, phase transitions, Schottky-barrier changes, and filament transport.A Pt-TiO2-Pt device showed a roughly 10-20 nm Magnéli-phase filament with metallic conduction.
- Current view: Magnéli conducting filaments are currently the most generally accepted mechanism, but no single explanation is expected to cover all published TiO2 devices.The diversity of material treatments and measurement conditions contributes to this scope boundary.
4 Models
ReRAM models commonly emphasize device materials and chemistry, while memristor models often emphasize physics and mathematics. The field is moving toward models that are more general, experimentally informed, and easy to simulate despite unresolved issues in influential formulations.
- ReRAM modeling generally focuses on materials science and chemistry, whereas memristor modeling more often uses physics- and mathematics-based approaches.
- Memristor foundations: Chua’s formulation derives the memristor as the sixth relationship between charge and magnetic flux after defining the resistor, capacitor, and inductor relations.The proposed relation is ϕ = Mq.
- Strukov model: The Strukov model’s omission of magnetic flux and interpretations of a uniform field raised questions about whether the device model matched Chua’s definition.A field discontinuity associated with the state variable w also creates electrochemical concerns.
- Strukov model: Despite these issues, the Strukov model remains widely adopted for test-circuit simulation and SPICE comparisons.
- Material-based models: Material-based models can fit experimental data more closely, but models using tunnelling-barrier descriptions may be difficult to simulate.
- Modeling direction: Current model development favors approaches that are general, experimentally informed, and easy to simulate.
- Memristive systems: The memristive-system concept extends the memristor idea to systems with two state variables and has been applied to thermistors and neuron ion channels.
5 Memristors and ReRAM - one field or two?
Memristors and ReRAM have increasingly converged, with ReRAM researchers extending memristor theory and memristor researchers using ReRAM to explain device properties. Their relationship remains unsettled because conductive-filament behavior and differing memristor definitions require theoretical extensions.
- The two communities initially developed separately, but their work has increasingly converged through reciprocal use of theory and device evidence.Some researchers now use the terms interchangeably or treat memristors as a ReRAM technology.
- The field boundary remains unsettled because some ReRAM phenomena preceded or remain disconnected from memristor work despite the broader convergence.The review notes that some ReRAM papers still fail to reference memristor research.
- Memristor theory requires extensions to represent conductive filaments, non-zero crossings, active devices, and memory read/write operations.These extensions help relate ideal memristor theory to real device behavior.
- BPS ReRAM is described as a real-world memristor, whereas UPS ReRAM’s classification depends on the adopted memristor definition.UPS ReRAM does not satisfy the 1971 definition in its ohmic regime but can fit the 1976 memristive-system definition using filament state as a second state variable.
6 The Future
Memristor and ReRAM research is expanding from storage toward commercial memory, neuromorphic computing, and biological applications, while their shared phenomena are increasingly recognized.
- Future directions: Memristor theory has broadened ReRAM’s outlook beyond novel storage, while ReRAM materials research has accelerated memristors toward practical devices.The review expects the two fields to be increasingly viewed as describing the same phenomena.
- Future directions: Commercial development is targeting computer RAM, flash drives, and other storage, with ongoing work to stabilize device properties and identify manufacturing materials.Panasonic announced the first computer containing TaOx-based ReRAM in 2013.
- Memory: Memristor memory still faces state-change-on-read effects, sneak-path errors, undefined states, and fabrication faults requiring theoretical, algorithmic, and experimental remedies.Proposed responses include threshold-limited reads, read-and-rewrite algorithms, improved testing, and sneak-path-based fault detection.
- Memory: Adoption of memristor-based memory requires further experimental testing of proposed approaches, including designs involving additional column lines and three-terminal devices.
- Neuromorphic computing: Neuromorphic computers require novel hardware approaches, including IMPLY-based logic, CMOS-compatible crossbar arrays, transistor-memristor encoders and decoders, and parallel vector operations.Researchers are also examining hysteresis and other engineering figures of merit.
- Biological systems: Memristive mechanisms have been identified in leaves, skin, blood, and eukaryotic mould, and used to study synaptic learning and update neuron models.The review suggests electrophysiology and bio-inspired computers as potential directions for future memristor research.