Symposium S.EL07—Fundamental Mechanisms and Materials Discovery for Brain-Inspired Computing—Theory and Experiment

Vanadium dioxide, a strongly correlated electronic material, is known for its metal-insulator transition (MIT) accompanied by a structural phase transition. While the controversy in the phase transition mechanism makes VO₂ one of the most challenging subjects, recent years have witnessed a great effort in studying the MIT mechanism and modulation, and the potential of VO₂ in device applications, owing to the MIT temperature close to room temperature. Element doping is an effective approach to regulate MIT in VO₂. For example, W and Mo doping reduce MIT temperature of VO₂, while Ge doping has opposite effect. Here we present our first-principles study of VO₂ upon element doping. We will reveal the effect of the doping on atomistic and electronic structure of VO₂ as well as the corresponding defect chemistry in both insulating monoclinic phase and metallic tetragonal phase. Finally, we will discuss the implications of first-principles simulation results on the phase transition and future improvement of VO₂ based neuromorphic materials.

The mechanistic origins of memristive behaviour strongly depend on the chemical composition and morphology of materials comprising memristive devices and their interfaces. We use symmetric TiN/SiO₂/TiN and asymmetric Au/Ti/a-SiO_1.95/Mo stacks described in [1] and HfO₂ based stacks [2] as model systems to discuss the mechanisms of electroforming and reset in resistive random access memory devices (ReRAM) using density functional theory (DFT) and atomistic modelling. The bulk system (far from the interface) is approximated as stoichiometric polycrystalline HfO₂ or amorphous (a)-SiO₂ and HfO₂, whereas the oxide/TiN interface is considered explicitly and constructed using DFT simulations assuming different degrees of hydroxylation of oxide surface. Grain boundaries in polycrystalline HfO₂ are shown to attract O vacancies and facilitate electroforming [2]. Structural degradation of amorphous oxide films is facilitated by electron injection and bias application. In particular, trapping of two extra electrons at intrinsic sites inside a-SiO₂ film results in weakening of Si-O bonds and emergence of efficient bond breaking pathways for producing neutral O vacancies and interstitial O_i^2- ions with low activation barriers (≈ 0.2 eV) [3]. These barriers are further reduced at the TiN/SiO₂ interface and by the electric field, facilitating diffusion of O_i^2- from the bulk towards the interface coupled to a lowering of the formation energies for the O_i^2- as a function of the distance from the interface. The charge transition level for the O_i (0/2-) moves towards that of the TiN Fermi level as the O_i approaches the interface resulting in a transfer of the electrons to the TiN electrode at the interface. Once the interstitials arrive at the interface, there is an initial ‘oxidation’ of the interface via the formation of a TiO layer, preferably at Ti-interface sites [4]. The Ti-O bonds are strong with high barriers (> 1.2 eV) for dissociation and O migration along the surface. Once the interface Ti-sites are occupied, O_i are incorporated at or in the layers directly below the interface or diffuse inside TiN via grain boundaries. A significant amount of oxygen is emitted into gas [1,4]. Reset happens as a result of O trapped at the interface and inside the grain boundaries diffusing back into the oxide and recombining with O vacancies. Retention is facilitated by the high barrier to Ti-O bonds dissociation at the interface, which is reduced as the reset bias is applied. We discuss the role of interface structure in the mechanisms of oxygen trapping and release at the metal/oxide interfaces in resistive switching/reset processes.

[1] A. Mehonic, et al., Adv. Materials, 28(34), 7486-7493 (2016)
[2] G. Bersuker et al. J. Appl. Phys. 110, 124518 (2011)
[2] D. Z. Gao, et al., Nanotechnology, 27(50), 505207 (2017)
[4] J. Cottom et al. ACS Appl. Mater. Interfaces 11, 36232 (2019)

Solid-state materials that exhibit electronic instabilities can be leveraged to emulate the spiking behavior characteristic of neuronal function; however, beyond VO₂ and NbO₂, the palette of materials that exhibit sharp electronic phase transitions above room temperature is sparse. The rational design of such materials is complicated by the complexity of neuronal dynamics which further requires independent control over the onset threshold and the conductance switching magnitude of their electronic transitions. Thereby, synthetic approaches that enable precise control over the extent and strength of electron correlation within a given system are greatly desirable. Given the complexity of the problem, the chosen chemical system should exhibit electronic behavior spanning extremes between highly-correlated and itinerant domains. Ternary vanadium oxides (M_xV₂O₅) represent such a system due to the availability of multiple accessible redox states and a variety of low-dimensional structural motifs that can accommodate the intercalation of a variety of ions spanning the breadth of the periodic table, offering vast compositional tunability. We have reported a number of electronic phase transitions in this mixed-valence (xd¹/d⁰) M_xV₂O₅ system, including voltage-driven lone pair-mediated metal-insulator transitions in the quasi-1D β-Pb_0.33V₂O₅, temperature-driven metal-insulator transitions in the layered δ-K_0.5V₂O₅, and pronounced semiconductor-semiconductor transitions in δ-Ag_0.88V₂O₅. More recently, we have observed colossal (six orders of magnitude) metal-insulator transitions in β′-Cu_xV₂O₅ and have shown these electronic transitions to be driven by polaron oscillations that are mediated by copper diffusion between two adjacent crystallographic sites. However, moving beyond elucidation of the mechanisms underpinning these observed transitions into intuitive materials design requires a robust and modular synthetic approach. We have recently pioneered the use of topochemistry to synthesize metastable polymorphs of V₂O₅. These polymorphs exhibit distinctive vanadium-oxygen bonding motifs that in turn give rise to varying extents of d-band dispersion. We have used these metastable V₂O₅ materials as inorganic equivalents of ‘synthons’ in subsequent intercalation reactions to independently control the intercalated ion (‘M’), its stoichiometry (‘x’), and how it is situated within the desired V₂O₅ framework (layered or quasi-1D tunnel structure). Using this approach we have targeted and synthesized metastable binary and ternary vanadium oxide materials that have found use as photocatalysts, multivalent ion cathode materials, and as materials for neuromorphic computing. Ultimately, we have demonstrated a chemical system, denoted as [M(H₂O)_n]_xV₂O₅, where M, its degree of hydration, its stoichiometry, and the vanadium-oxygen connectivity are each independently tunable, establishing ternary vanadium oxides a promising system for the rational engineering of electronic instabilities.

Exploration of new computing architectures is underway in order to meet the challenge of advancing computing past the limitation of the impending end to the further downsizing of transistors. Neuromorphic computing architectures are being developed in order to push the constraints of conventional computing by mimicking certain behaviors of the brain. However, using conventional materials, many different elements are needed in order to simulate the most basic of functions. Consequently, the development of novel functional materials to replace materials used in conventional networks is necessary to enable efficiency. Vanadium dioxide is of interest for neuromorphic applications due to its temperature-controlled metal-insulator transition (MIT) from an insulating monoclinic phase to a metallic rutile phase. It has been shown that vanadium dioxide devices are well-suited to applications in neuromorphic computing because of their ability to mimic neuronal behavior. In order to control various aspects of the phase transition, such as transition temperature, hysteresis, and change in resistivity, it is common practice to dope the VO₂. However, this also can introduce intrinsic defects into the material that can result in a length-scale dependent variability in properties. Consequently, a comprehensive study of the behavior of doped VO₂ on a device level is critical for moving forward in the development of neuromorphic devices.
In this study, it is demonstrated that doping VO₂ with interstitial boron results in the formation of multiple domains. Temperature-controlled optical microscopy confirms their presence, which causes the MIT in a single particle to occur in discrete steps over a small range of temperatures. Within that temperature range, there exist stable phase fractions of fully transitioned material. This behavior is not immediately evident through the characterization of a B-VO₂ device, in which the phase transition is triggered by Joule heating due to application of current or voltage across the material. When the device is switched by application of a voltage sweep, the decreasing resistance from M1 to R results in sudden, self-propagating heating to above the T_MIT, accelerating the transition of the material. In this case, the phase transition appears to occur suddenly and abruptly as in undoped VO₂. However, when the MIT is triggered by application of a current sweep, the decreasing resistance results in a self-limiting heating. This slows down heating of the device, allowing an indirect observation of the more gradual transition of the material as seen in optical microscopy. Analysis of the current sweeps shows small discrete changes in the measured resistance, corresponding to the discrete transition of a domain. This study provides insight into the number of domains present in the material, as well as information on the relationship between the dopant concentration and the number of domains formed. Through the different electrical characterization methods, it illustrates a history-dependent coexistence of the two phases of B-VO₂.

With the near saturation of Moore’s scaling of transistors, there has been a recent explosion in activity and creativity to find new modes of computation that will continue to advance exponentially with time even though transistor circuits only improve modestly. Much of the inspiration for new ways of computing comes from what little we understand about the brain. We actually don’t know how the brain computes, but many different possibilities have been proposed, e.g. multinary logic, Neural Networks of all kinds, extensions of Hebbian learning via spike-timing dependent plasticity, Boltzmann/Ising machines, Hopfield networks, Bayesian inference and Markov chains, to name a few. These possibilities are not necessarily mutually exclusive – the brain may use some combination of several of them or even use a higher order generalization that contains all of them, since many share mathematical similarities. How to express these computational approaches in an electronic circuit is a significant challenge. Since the brain itself is a highly nonlinear dynamical system, an appropriate area to investigate is nonlinear dynamical circuit theory. This is the realm of the Principle of Local Activity, which provides a basis for inventing and building new generations of two-terminal oscillators and amplifiers that emulate the integrate and fire dynamics of neurons to produce action potentials for signal processing and axon-like active transmission lines. Combining such devices will enable the design of circuits that are biased at the Edge of Chaos, where the emergence of complex patterns and behavior in a homogeneous medium are found. What new types of devices will be used to construct these circuits? Can we emulate neural computation using new electronic-ionic-thermal devices that exhibit dynamical behavior? These could be based on properties such as negative differential resistance and/or capacitance that arise from thermally activated transport, Mott transitions, molecular redox chemistry, electro-mechanical response in soft matter, and/or multi-ferroelectric characteristics. Finally, how do we find the materials that we will use to build these new devices and measure their properties? There are known materials that have the right type of electronic properties, but they often have disadvantages such requiring exotic elements or a phase transition temperature that is too low or too high compared to normal operating conditions. Can we intentionally design materials that will operate in the Goldilocks zone for a brain-inspired computing machine – or must we test everything that we can fabricate combinatorially? What properties should we try to optimize, e.g. transition temperatures, hysteresis loop widths, conductance and capacitance changes, or magnitude of negative differential resistance? What are the ways of using the properties we do understand to invent the new materials we need? This is a rapidly growing research field that requires coordinated efforts across a broad range of materials expertise from fundamental chemistry to circuit design and fabrication.

In-memory computing using crossbar arrays of non-volatile memory has the potential to significantly decrease the energy consumption of both inference and training. While crossbar arrays for inference, or dot-product engines, using two-terminal memristors and three-terminal flash memory have been demonstrated to be more efficient than their digital counterparts, crossbar arrays for training have been much more challenging due to difficulties in matching materials properties with training algorithms. In particular, energy-efficient training arrays necessitate the ability to conduct an outer product update, where all the synaptic weights are simultaneously updated, a feat which has not been accomplished in two-terminal devices. We recently developed the three-terminal organic redox transistor based on PEDOT:PSS which is able to conduct binary outer product updates between neighboring conductance states, a crucial step towards energy-efficient training [1]. However, no training algorithm has been implemented.

In this work, we demonstrate for the first time how three-terminal redox transistors are able to train a perceptron network that is adapted to multiple tasks in parallel. We use a small crossbar array of nine synapses to simultaneously train an AND gate, an OR gate, and a NAND gate. We conduct nonbinary and continuous analogue weight updates by controlling the programming time along a given row and column, at micro-second time scales. We use crossbar simulation software (CrossSim) to replicate this training in simulation, and show strong agreement between simulation and experiment. Simulations further show that the ability to train small perceptron networks is enabled by linear and predictable weight updates as well as the low device-to-device variation of the redox transistors, and that two-terminal TaO_X memristors will not be able to train this small network to complete accuracy. By showing experimental evidence of training, this work further validates the ability of CrossSim to predict how accurately and quickly analogue non-volatile memory are able to train an artificial neural network.

Reference:
[1] Fuller, et al. Parallel programming of an ionic floating gate memory array for scalable neuromorphic computing. Science, 364, 570-574 (2019)

The Preisach model describes the hystersesis response of a ferroelectric material as being a composite of an ensemble of hysterons. The irreversible hysteron distribution can thus be used to estimate the stability of various states as a function of prior field history. This paper will describe the first order reversal curve distributions for lead zirconate titanate thin films as a function of a number of variables, including the levels of donor and acceptor doping, the level of imprint, and temperature from 10 – 300 K. Ultimately, data of this type are required to fully describe the number of discriminable states in a neuromorphic computing system.

Soild-solid phase transitions are often accompanied by massive changes in fundamental materials properties such as resistivity and optical transmittance. The relative stabilities of the phases involved in these transitions can be modulated through several means one of which being through doping or alloying which has been shown to create an immutable alteration of the transformation barriers. Reversible post synthetic modulation of a phase transition continues to be a challenge that, if allowed, would enable distinct potential for useful for neuromorphic computing, chronometry, and sensing. Metal—insulator transition materials are excellent candidates for neuromorphic computing of which VO₂ is a canonical example. We demonstrate in VO₂ mobile dopants that are weakly coupled to the lattice provide a means of imbuing an entirely reversible and dynamical modulation of the metal-insulator transition of VO₂. Specifically, we demonstrate the remarkable time-dependent evolution of the relative phase stabilities of insulating monoclinic (M₁) and metallic rutile (R) phases of VO₂ in a completely reversible “hourglass” fashion as interstitial boron species relax from high-energy sites where they are situated upon a thermally induced phase transition. The relaxation process corresponds to a 50°C range of the transition temperature achieved within the same sample as a function of residence time and temperature. The diffusive boron dopant atoms provide a means of attaining a reconfigurable and readable time- and thermal history dependent response that derives from intrinsic material properties.

This talk will present the latest research progress on the atomic-level details of non-volatile resistance switching (NVRS) in 2D memory devices. In particular, we will focus on our scanning tunneling microscopy (STM) based imaging and transport studies, together with the first principle calculations on the common point defects of 2D materials. For this investigation, we employ the STM tip as the top electrode of vertical metal-insulator-metal (MIM) memory device and examine the defect sites in atomic resolution before and after resistive switching events. These studies provide one to one correlation between the structural and electronic properties of the heterogeneities and their role in the resistance switching mechanism. Through these studies, we seek to deduce which particular defect structures are most desirable for NVRS and utilize this information for emerging applications.

Chemical control of the coupled electronic-structural transformation in correlated oxide systems is a vigorously investigated area, due to fundamental interest in the role chemical dopants play in stabilizing different crystal structures and altering electronic band structure, as well as practical interest in being able to tune the critical transformation temperature and the degree of volatility of the transformation. Such an approach holds promise for tuning the properties of adaptive oxide phases to demonstrate novel functionality and emulate neuromorphic behaviors. While chemical doping has shown dramatic effects in changing the thermodynamic stability of different doped VO₂ phases, including increasing or depressing phase transformations by up to ~20 ^oC, and stabilizing phases that are not typically observed in undoped VO₂ upon simple heating and cooling, very little is known regarding the impact of chemical doping on transformation behavior in this system. Doping could potentially modify the behavior of the electronic-structural phase transformation by at least three mechanisms: 1) by altering the energy landscape of the system, including the magnitude of energy barriers limiting forward and reverse transformation, 2) by stabilizing intermediate phases, which may introduce alternative transformation paths, or 3) by introducing localized regions of strain surrounding chemical dopants, which could affect local thermodynamic equilibria heterogeneously throughout a sample. Importantly, all three of these effects could potentially impact either the energy barriers limiting incipient nucleation of a new daughter phase within a parent phase, or the mobility of heterophase boundaries, impacting the rate of growth of domains of a daughter phase. Clarifying changes in phase transformation mechanisms requires microscopic investigation of domain nucleation and growth in both undoped and doped systems. Resolving these questions can expose important underlying clues in understanding transformation mechanisms in both undoped and chemically doped systems, and can reveal new approaches to engineering metal-insulator transitions (MIT) with desired transformation behavior.
Here, we present representative illustrations of the effect of chemical dopants on altering phase transformation mechanisms and progression, drawn from select interstitial and substitutional doping schemes. We will illustrate 1) the use of dopants to simultaneously alter transformation equilibrium temperature and hysteresis, 2) the use of dopants to extend the width of the phase transformation, introducing extended regions of phase coexistence, as well as 3) the use of dopants to introduce relaxation effects, which can be used to dynamically tune the equilibrium transformation temperature of the system.

Neuromorphic computing has recently emerged as a non-Von Neuman computing method. Because its analog switching ability to represent multiple synaptic weights by varying conductance in the vertical filaments formed in the switching medium, a resistive memory has been considered as an artificial synapse for suitable neuromorphic hardware platform. Conventional resistive memories typically utilize a defective amorphous solid as a switching medium for defect-mediated formation of conducting filaments. However, the imperfection of the switching medium also causes stochastic filament formation leading to spatial and temporal variation of the devices. Such variation of artificial synapses prevented community from obtaining large-scale artificial neural networks. In this talk, I will present new type of resistive memory that can more precisely confine the conducting paths so that uniform artificial synapses have been obtained leading to 100% yield 32x32 arrays with a great programmability. In this talk, I will discuss about our strategies to control the ionic conduction paths: one is to utilize threading dislocations as confinement paths of ionic conduction in SiGe epitaxally grown on a Si wafer and another is to alloy Ag active metal with silicidable metals to have additional controls in conduction channels. These result in low temporal/spatial variation, linear synaptic weight update, great endurance, and long retention time. Actual crossbar arrays were fabricated and I will present properties and programmability of our ANN arrays.

The brain-inspired computing schemes are expected to reduce the time, energy and area required to propose solutions for a number of Artificial Intelligence-related applications.
Brain-inspired computing architectures can be implemented by analog or digital circuits using innovative materials and CMOS or beyond CMOS nanodevices, such as small slope switches, to potentially improve energy efficiency thanks to their steep subthreshold slope and low operating voltage.
The exploitation of the subthreshold FET characteristics, which naturally exhibit exponential relationships in their transfer functions, also allow to directly emulate the biophysics of neural systems.
On the other hand, the ability to alter the conductance levels in a controllable way makes Phase Change Memory devices particularly well-suited for synaptic realizations. The two key synaptic attributes of efficacy and plasticity can be efficiently realized using a unit comprising PCM devices and FETs.
In this presentation, we will show the disruptive properties of advanced NanoFETs for ultimate integration , reduction of energy consumption and enhanced performance, such as Nanowire FETs, Carbon NanoTube FETs, Tunnel FETs, Negative capacitance FETs, Hybrid Devices, combined with novel materials such as III-V, Ge, 2D/TMDs, Heterostructures, Phase Change, Nanofilament, Ferroelectric, Semimetal.
These innovative materials could be used for boosting NanoFETs electrical properties and/or developping new generation of memory devices, for instance Storage Class Memories, for near-memory computing where FET processing units are placed in close proximity to the memory unit for increased system performance. They can also be used for In-Memory Computing, for which the computation is performed in place by exploiting the physical attributes of memory devices organized as a computational memory unit [1-5].

[1] F. Balestra, Challenges for high performance and very low power operation at the end of the Roadmap, Solid-State Electronics, Volume 155, May 2019, pp. 27-31
[2] F. Balestra, Tunnel FETs for ultra low Power Nanoscale Devices, ISTE Open Science, Nanoelectronic Devices, Volume 18- 1, DOI : 10.21494/ISTE.OP.2018.0219
[3] F. Balestra, Challenges to Nano-scale Device World, ECS Transactions 66(5): 211-222, 2015
[4] F. Balestra, Beyond CMOS Nanodevices, Book (tome 1&2) edited by Francis Balestra, ISTE-Wiley, 2014
[5] F. Balestra, Advanced technologies for future materials and devices, Chapter in Springer Handbook of Semiconductor Devices, to be published, 2020

Silicon circuitry has been the mainstay of the semiconductor industry for several decades but is fundamentally constrained by the Fermi-Dirac electron distribution of electron energies, which establishes an immutable limit to the steepness of switching characteristics that can be achieved within a device. As such, electrostatically-modulated transistors inevitably give rise to much wasteful power consumption, requiring large swathes of logic circuitry on a chip to be left inoperative at any given time. Much attention has therefore focused on the design of materials exhibiting a pronounced switching of electrical conductance with minimal energy dissipation in response to small external stimuli. Electron-correlated transition metal oxides exhibiting pronounced metal-to-insulator transitions are excellent candidates for energy efficient computation and further provide a means of emulating the spiking behavior of biological neural circuitry. Amongst the rare palette of materials exhibiting pronounced metal—insulator transitions, β′-Cu_xV₂O₅ stands out for its tunability of the transformation temperature and, as we demonstrate here, a pronounced nonlinear response to applied temperature, voltage, and current in relation to Cu stoichiometry. We have shown that polaron oscillation, underpinned by the real-space shuttling of Cu-ions between two adjoining split-site positions within a 1D tunnel defined by VO₅ square pyramids and VO₆ octahedra underpins the metal-insulator transition of this material. Our work combines high-resolution structure refinement from variable-temperature single-crystal and powder X-ray diffraction; variable-temperature extended X-ray absorption fine structure spectroscopy (EXAFS) studies of local structure; angle-integrated photoemission spectroscopy, resonant inelastic X-ray scattering (RIXS), and hard X-ray photoemission spectroscopy (HAXPES) studies of electronic structure; density functional theory (DFT) modeling of electronic structure; and single-nanowire measurements of transport phenomena. The results provide unprecedented mechanistic insight into the close interplay between crystal structure distortions and emergence of electron correlation which gives rise to the metal—insulator transition of a strongly correlated system. The utilization of cation diffusion and polaron shuttling demonstrates a means of using ionic vectors in conjunction with subtle structural distortions to obtain highly nonlinear and memristive conductance switching as required for neuromorphic computing and sensing.