Thermal Compact Modeling and Resistive Switching Analysis in Titanium Oxide-Based Memristors.

Resistive switching devices based on the Au/Ti/TiO2/Au stack were developed. In addition to standard electrical characterization by means of I-V curves, scanning thermal microscopy was employed to localize the hot spots on the top device surface (linked to conductive nanofilaments, CNFs) and perform in-operando tracking of temperature in such spots. In this way, electrical and thermal responses can be simultaneously recorded and related to each other. In a complementary way, a model for device simulation (based on COMSOL Multiphysics) was implemented in order to link the measured temperature to simulated device temperature maps. The data obtained were employed to calculate the thermal resistance to be used in compact models, such as the Stanford model, for circuit simulation. The thermal resistance extraction technique presented in this work is based on electrical and thermal measurements instead of being indirectly supported by a single fitting of the electrical response (using just I-V curves), as usual. Besides, the set and reset voltages were calculated from the complete I-V curve resistive switching series through different automatic numerical methods to assess the device variability. The series resistance was also obtained from experimental measurements, whose value is also incorporated into a compact model enhanced version.

Spatially-Resolved Thermometry of Filamentary Nanoscale Hot Spots in TiO2 Resistive Random Access Memories to Address Device Variability.

Resistive random access memories (RRAM), based on the formation and rupture of conductive nanoscale filaments, have attracted increased attention for application in neuromorphic and in-memory computing. However, this technology is, in part, limited by its variability, which originates from the stochastic formation and extreme heating of its nanoscale filaments. In this study, we used scanning thermal microscopy (SThM) to assess the effect of filament-induced heat spreading on the surface of metal oxide RRAMs with different device designs. We evaluate the variability of TiO2 RRAM devices with area sizes of 2 × 2 and 5 × 5 µm2. Electrical characterization shows that the variability indicated by the standard deviation of the forming voltage is ∼2 times larger for 5 × 5 µm2 devices than for the 2 × 2 µm2 ones. Further knowledge on the reason for this variability is gained through the SThM thermal maps. These maps show that for 2 × 2 µm2 devices the formation of one filament, i.e., hot spot at the device surface, happens reliably at the same location, while the filament location varies for the 5 × 5 µm2 devices. The thermal information, combined with the electrical, interfacial, and geometric characteristics of the device, provides additional insights into the operation and variability of RRAMs. This work suggests thermal engineering and characterization routes to optimize the efficiency and reliability of these devices.

Inkjet-printed h-BN memristors for hardware security.

Inkjet printing electronics is a growing market that reached 7.8 billion USD in 2020 and that is expected to grow to ∼23 billion USD by 2026, driven by applications like displays, photovoltaics, lighting, and radiofrequency identification. Incorporating two-dimensional (2D) materials into this technology could further enhance the properties of the existing devices and/or circuits, as well as enable the development of new concept applications. Along these lines, here we report an easy and cheap process to synthesize inks made of multilayer hexagonal boron nitride (h-BN)-an insulating 2D layered material-by the liquid-phase exfoliation method and use them to fabricate memristors. The devices exhibit multiple stochastic phenomena that are very attractive for use as entropy sources in electronic circuits for data encryption (physical unclonable functions [PUFs], true random number generators [TRNGs]), such as: (i) a very disperse initial resistance and dielectric breakdown voltage, (ii) volatile unipolar and non-volatile bipolar resistive switching (RS) with a high cycle-to-cycle variability of the state resistances, and (iii) random telegraph noise (RTN) current fluctuations. The clue for the observation of these stochastic phenomena resides on the unpredictable nature of the device structure derived from the inkjet printing process (i.e., thickness fluctuations, random flake orientations), which allows fabricating electronic devices with different electronic properties. The easy-to-make and cheap memristors here developed are ideal to encrypt the information produced by multiple types of objects and/or products, and the versatility of the inkjet printing method, which allows effortless deposition on any substrate, makes our devices especially attractive for flexible and wearable devices within the internet-of-things.

Holistic Variability Analysis in Resistive Switching Memories Using a Two-Dimensional Variability Coefficient.

We present a new methodology to quantify the variability of resistive switching memories. Instead of statistically analyzing few data points extracted from current versus voltage (I-V) plots, such as switching voltages or state resistances, we take into account the whole I-V curve measured in each RS cycle. This means going from a one-dimensional data set to a two-dimensional data set, in which every point of each I-V curve measured is included in the variability calculation. We introduce a new coefficient (named two-dimensional variability coefficient, 2DVC) that reveals additional variability information to which traditional one-dimensional analytical methods (such as the coefficient of variation) are blind. This novel approach provides a holistic variability metric for a better understanding of the functioning of resistive switching memories.

Hybrid 2D-CMOS microchips for memristive applications.

Exploiting the excellent electronic properties of two-dimensional (2D) materials to fabricate advanced electronic circuits is a major goal for the semiconductor industry1,2. However, most studies in this field have been limited to the fabrication and characterization of isolated large (more than 1 µm2) devices on unfunctional SiO2-Si substrates. Some studies have integrated monolayer graphene on silicon microchips as a large-area (more than 500 µm2) interconnection3 and as a channel of large transistors (roughly 16.5 µm2) (refs. 4,5), but in all cases the integration density was low, no computation was demonstrated and manipulating monolayer 2D materials was challenging because native pinholes and cracks during transfer increase variability and reduce yield. Here, we present the fabrication of high-integration-density 2D-CMOS hybrid microchips for memristive applications-CMOS stands for complementary metal-oxide-semiconductor. We transfer a sheet of multilayer hexagonal boron nitride onto the back-end-of-line interconnections of silicon microchips containing CMOS transistors of the 180 nm node, and finalize the circuits by patterning the top electrodes and interconnections. The CMOS transistors provide outstanding control over the currents across the hexagonal boron nitride memristors, which allows us to achieve endurances of roughly 5 million cycles in memristors as small as 0.053 µm2. We demonstrate in-memory computation by constructing logic gates, and measure spike-timing dependent plasticity signals that are suitable for the implementation of spiking neural networks. The high performance and the relatively-high technology readiness level achieved represent a notable advance towards the integration of 2D materials in microelectronic products and memristive applications.

Hardware implementation of a true random number generator integrating a hexagonal boron nitride memristor with a commercial microcontroller.

The development of the internet-of-things requires cheap, light, small and reliable true random number generator (TRNG) circuits to encrypt the data-generated by objects or humans-before transmitting them. However, all current solutions consume too much power and require a relatively large battery, hindering the integration of TRNG circuits on most objects. Here we fabricated a TRNG circuit by exploiting stable random telegraph noise (RTN) current signals produced by memristors made of two-dimensional (2D) multi-layered hexagonal boron nitride (h-BN) grown by chemical vapor deposition and coupled with inkjet-printed Ag electrodes. When biased at small constant voltages (≤70 mV), the Ag/h-BN/Ag memristors exhibit RTN signals with very low power consumption (∼5.25 nW) and a relatively high current on/off ratio (∼2) for long periods (>1 hour). We constructed TRNG circuits connecting an h-BN memristor to a small, light and cheap commercial microcontroller, producing a highly-stochastic, high-throughput signal (up to 7.8 Mbit s-1) even if the RTN at the input gets interrupted for long times up to 20 s, and if the stochasticity of the RTN signal is reduced. Our study presents the first full hardware implementation of 2D-material-based TRNGs, enabled by the unique stability and figures of merit of the RTN signals in h-BN based memristors.

Defect-Free Metal Deposition on 2D Materials via Inkjet Printing Technology.

2D materials have many outstanding properties that make them attractive for the fabrication of electronic devices, such as high conductivity, flexibility, and transparency. However, integrating 2D materials in commercial devices and circuits is challenging because their structure and properties can be damaged during the fabrication process. Recent studies have demonstrated that standard metal deposition techniques (like electron beam evaporation and sputtering) significantly damage the atomic structure of 2D materials. Here it is shown that the deposition of metal via inkjet printing technology does not produce any observable damage in the atomic structure of ultrathin 2D materials, and it can keep a sharp interface. These conclusions are supported by abundant data obtained via atomistic simulations, transmission electron microscopy, nanochemical metrology, and device characterization in a probe station. The results are important for the understanding of inkjet printing technology applied to 2D materials, and they could contribute to the better design and optimization of electronic devices and circuits.

Standards for the Characterization of Endurance in Resistive Switching Devices.

Resistive switching (RS) devices are emerging electronic components that could have applications in multiple types of integrated circuits, including electronic memories, true random number generators, radiofrequency switches, neuromorphic vision sensors, and artificial neural networks. The main factor hindering the massive employment of RS devices in commercial circuits is related to variability and reliability issues, which are usually evaluated through switching endurance tests. However, we note that most studies that claimed high endurances >106 cycles were based on resistance versus cycle plots that contain very few data points (in many cases even <20), and which are collected in only one device. We recommend not to use such a characterization method because it is highly inaccurate and unreliable (i.e., it cannot reliably demonstrate that the device effectively switches in every cycle and it ignores cycle-to-cycle and device-to-device variability). This has created a blurry vision of the real performance of RS devices and in many cases has exaggerated their potential. This article proposes and describes a method for the correct characterization of switching endurance in RS devices; this method aims to construct endurance plots showing one data point per cycle and resistive state and combine data from multiple devices. Adopting this recommended method should result in more reliable literature in the field of RS technologies, which should accelerate their integration in commercial products.

Variability and Yield in h-BN-Based Memristive Circuits: The Role of Each Type of Defect.

In the race of fabricating solid-state nano/microelectronic devices using 2D layered materials (LMs), achieving high yield and low device-to-device variability are the two main challenges. Electronic devices that drive currents in-plane and homogeneously along the 2D-LMs (i.e., transistors, memtransistors) are strongly affected by local defects (i.e., grain boundaries, wrinkles, thickness fluctuations, polymer residues), as they create inhomogeneities and increase the device-to-device variability, resulting in a poor performance at the circuit level. Here, it is shown that memristors are insensitive to most types of defects in 2D-LMs, even when fabricated in academic laboratories that do not meet industrial standards. The reason is that the currents produced in these devices, which flow out-of-plane across the 2D-LM, are always driven locally by the most conductive locations. Consequently, it is concluded that it is much easier to fabricate 2D-LMs-based solid-state nano/microelectronic circuits using memristors than using transistors or memtransistors, not only due to the inherent simpler fabrication process (i.e., less lithography steps) but also because the local defects do not degrade the yield and variability of memristors considerably.

Advanced Data Encryption ​using 2D Materials.

Advanced data encryption requires the use of true random number generators (TRNGs) to produce unpredictable sequences of bits. TRNG circuits with high degree of randomness and low power consumption may be fabricated by using the random telegraph noise (RTN) current signals produced by polarized metal/insulator/metal (MIM) devices as entropy source. However, the RTN signals produced by MIM devices made of traditional insulators, i.e., transition metal oxides like HfO2 and Al2 O3 , are not stable enough due to the formation and lateral expansion of defect clusters, resulting in undesired current fluctuations and the disappearance of the RTN effect. Here, the fabrication of highly stable TRNG circuits with low power consumption, high degree of randomness (even for a long string of 224  - 1 bits), and high throughput of 1 Mbit s-1 by using MIM devices made of multilayer hexagonal boron nitride (h-BN) is shown. Their application is also demonstrated to produce one-time passwords, which is ideal for the internet-of-everything. The superior stability of the h-BN-based TRNG is related to the presence of few-atoms-wide defects embedded within the layered and crystalline structure of the h-BN stack, which produces a confinement effect that avoids their lateral expansion and results in stable operation.

Electroforming in Metal-Oxide Memristive Synapses.

Memristors have shown an extraordinary potential to emulate the plastic and dynamic electrical behaviors of biological synapses and have been already used to construct neuromorphic systems with in-memory computing and unsupervised learning capabilities; moreover, the small size and simple fabrication process of memristors make them ideal candidates for ultradense configurations. So far, the properties of memristive electronic synapses (i.e., potentiation/depression, relaxation, linearity) have been extensively analyzed by several groups. However, the dynamics of electroforming in memristive devices, which defines the position, size, shape, and chemical composition of the conductive nanofilaments across the device, has not been analyzed in depth. By applying ramped voltage stress (RVS), constant voltage stress (CVS), and pulsed voltage stress (PVS), we found that electroforming is highly affected by the biasing methods applied. We also found that the technique used to deposit the oxide, the chemical composition of the adjacent metal electrodes, and the polarity of the electrical stimuli applied have important effects on the dynamics of the electroforming process and in subsequent post-electroforming bipolar resistive switching. This work should be of interest to designers of memristive neuromorphic systems and could open the door for the implementation of new bioinspired functionalities into memristive neuromorphic systems.

On the Limits of Scanning Thermal Microscopy of Ultrathin Films.

Heat transfer processes in micro- and nanoscale devices have become more and more important during the last decades. Scanning thermal microscopy (SThM) is an atomic force microscopy (AFM) based method for analyzing local thermal conductivities of layers with thicknesses in the range of several nm to µm. In this work, we investigate ultrathin films of hexagonal boron nitride (h-BN), copper iodide in zincblende structure (γ-CuI) and some test sample structures fabricated of silicon (Si) and silicon dioxide (SiO2) using SThM. Specifically, we analyze and discuss the influence of the sample topography, the touching angle between probe tip and sample, and the probe tip temperature on the acquired results. In essence, our findings indicate that SThM measurements include artefacts that are not associated with the thermal properties of the film under investigation. We discuss possible ways of influence, as well as the magnitudes involved. Furthermore, we suggest necessary measuring conditions that make qualitative SThM measurements of ultrathin films of h-BN with thicknesses at or below 23 nm possible.

Graphene-Boron Nitride-Graphene Cross-Point Memristors with Three Stable Resistive States.

Two-dimensional (2D) material-based memristors have shown several properties that are not shown by traditional ones, such as high transparency, robust mechanical strength and flexibility, superb chemical stability, enhanced thermal heat dissipation, ultralow power consumption, coexistence of bipolar and threshold resistive switching, and ultrastable relaxation when used as electronic synapse (among others). However, several electrical performances often required in memristive applications, such as the generation of multiple stable resistive states for high-density information storage, still have never been demonstrated. Here, we present the first 2D material-based memristors that exhibit three stable and well-distinguishable resistive states. By using a multilayer hexagonal boron nitride (h-BN) stack sandwiched by multilayer graphene (G) electrodes, we fabricate 5 µm × 5 µm cross-point Au/Ti/G/h-BN/G/Au memristors that can switch between each two or three resistive states, depending on the current limitation (CL) and reset voltage used. The use of graphene electrodes plus a small cross-point structure are key elements to observe the tristate operation, which has not been observed in larger (100 µm × 100 µm) devices with an identical Au/Ti/G/h-BN/G/Au structure nor in similar small (5 µm × 5 µm) devices without graphene interfacial layers (i.e., Au/Ti/h-BN/Au). Basically, we generate an intermediate state between the high resistive state and the low resistive state (LRS), named soft-LRS (S-LRS), which may be related to the formation of a narrower conductive nanofilament across the h-BN because of the ability of graphene to limit metal penetration (at low CLs). All the 2D materials have been fabricated using the scalable chemical vapor deposition approach, which is an immediate advantage compared to other works using mechanical exfoliated 2D materials.