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Nano-Scale Conductive Filament with Alternating Rectification as an Artificial Synapse Building Block Dan Berco, Yu Zhou, Sankara Rao Gollu, Pranav Sairam Kalaga, Abhisek Kole, Mohamed Hassan, and Diing Shenp Ang ACS Nano, Just Accepted Manuscript • DOI: 10.1021/acsnano.8b02193 • Publication Date (Web): 24 May 2018 Downloaded from http://pubs.acs.org on May 24, 2018

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Nano-Scale Conductive Filament with Alternating Rectification as an Artificial Synapse Building Block Dan Berco1 Yu Zhou, Sankara Rao Gollu, Pranav Sairam Kalaga, Abhisek Kole, Mohamed Hassan and Diing Shenp Ang2 Nanyang Technological University, School of Electrical and Electronic Engineering, 50 Nanyang Avenue, Singapore 639798 ABSTRACT A popular approach for resistive memory (RRAM) based hardware implementation of neural networks utilizes one (or two) device that functions as an analog synapse in a crossbar structure of perpendicular pre- and post-synaptic neurons. An ideal fully automated, large scale artificial neural network, that matches a biologic counterpart (in terms of density and energy consumption), thus requires nano sized, extremely low power devices with a wide dynamic range and multi level functionality. Unfortunately the tradeoff between these traits proves to be a serious obstacle in the realization of brain inspired computing platforms yet to be overcome. This study demonstrates an alternative manner for the implementation of artificial synapses in which the local stoichiometry of metal oxide materials is delicately manipulated to form a single nano-scale conductive filament that may be used as a synaptic gap building block in an equivalent manner to the functionality of a single connexon (a signaling pore between synapses) with dynamic rectification direction. The structure, of a few

1

Corresponding Author: Dr. D. Berco, Email: [email protected]

2

Corresponding Author: Prof. D. S. Ang, Email: [email protected]

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nanometers in size, is based on the formation of defect states and shows current rectification properties which can be consecutively flipped to a forward or reverse direction to create either an excitatory or inhibitory (positive or negative) weight parameter. Alternatively, a plurality of these artificial connexons may be used to create a synthetic rectifying synaptic gap junction. In addition, the junction plasticity may be altered in a differential digital scheme (opposed to conventional analog RRAM conductivity manipulation) by changing the ratio of forward to reverse rectifying connexons.

Keywords: synaptic gap junctions, electrical synapses, connexons, nano-scale stoichiometry manipulation, artificial synapses, memristors

Electrical synapses are fast conductive links between neurons capable of transmitting and receiving electrical signals.1,2 The links contain numerous ion channels (connexons) scattered along plasma membranes forming the connection between the pre- and post-synaptic neurons.3,4 The trans-membrane interface has a separation of ~3.8 nm, bridged by two adjacent connexons from opposing sides that together form a construction known as a “gap junction”.1 Signals between synapses are conducted by ionic motion through these channels. The channels have a diameter of ~2.0 nm and are mostly bidirectional,5 meaning that ions may transverse in any direction while experiencing the same resistance. Some of these junctions demonstrate a rectifying behavior while being stimulated by electric pulses resulting in a preferred direction for ion flow.3,5 The connection ‘plasticity’ (resistivity to ion movement modulated by signaling activity) was measured by Hass et al.6 to be less than 15% in addition to


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having an asymmetric behavior (i.e. depending on signal direction).7 This asymmetry could imply that at least one connexon located across the gap junction has a designated directionality (gap junctions usually contain hundreds of channels). Memristors,8,9,10 on the other hand, have long been considered as suitable candidates for the hardware implementation of brain inspired computing platforms which dictate the use of artificial synaptic devices and where a single device represents a synaptic connection between crossbar array neurons.11 One requirement from an artificial synaptic device is having nano scale dimensions12,13 to allow integration levels to reach the ones found in the human cerebral cortex, potentially achievable using a 3D stack crossbar array architecture.14 The importance of this requirement is emphasized by the inverse correlation between size and power consumption. Other key features are having a large dynamic range (on/off ratio) and supporting multi level states to match the analog nature of the synaptic weight in biological synapses. These features translate to high accuracy, more degrees of freedom for synaptic weight adjustment during training and network robustness. Unfortunately a tradeoff exists between device dimension and the number of multilevel states it can support.15 The long-term potentiation (LTP) and long-term depression (LTD) processes observed in biologic synapses correspond to the incremental conductivity increase and decrease required from the artificial counterpart. The desirable change that would best simplify the design of an automated controller should be both symmetric (direction of change) and linear (differential magnitude). However, memristors show both nonlinear and asymmetric conductivity changes in response to successive set and reset pulses,16 a feature which highly complicates the task of designing peripheral circuitry and affects the achievable network accuracy. In addition, the relatively abrupt set process


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common to filament formation in oxide based RRAMs make it difficult to implement weight change algorithms. Furthermore, although neural networks have inherent immunity for non-uniformity associated with memristive devices when online continuous training schemes are used, that may not be the case when networks are operated in offline training modes. A sub class of devices called ‘Neuristors’17 were also demonstrated in this context for sharing the threshold switching feature with the biologic synapse. Unfortunately, parametric variation and uniformity are some key issues that render the task of designing a fully automated, self learning machine to be extremely challenging. Additional previously published papers presented micrometer sized non-volatile resistive oxide memory devices that have rectifying unidirectional properties and few state levels (multilevel).18,19 Kim et al.20 recently demonstrated a ‘Nociceptive’ micrometer device which showed a transient (time dependent volatile state) current voltage dependence, modulated by electron trapping and de-trapping. This capture and release mechanism resulted in a time dependent switching threshold that was restored to its original state after a relaxation period. However, both size and functionality may turn out to have a key role in accurate artificial implementation of biologic synapses. For example, the long-term depression measured by Hass et al.6 was distinctively non-volatile and persisted for at least 30 min. In addition, currently demonstrated self rectifying devices have a fixed rectification direction which cannot be changed dynamically. Manipulation of device conductivity as the parametric synaptic weight during the learning phase of artificial neural networks thus becomes very challenging due to inter device parametric variation. In this work, the authors present the possibility of using a single conductive filament


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(CF)21 in a metal oxide material (Hafnium-Oxide, HfOx) based nano-scale artificial rectifying connexon (ARC) having both a switchable rectification direction and a non-volatile conductivity state. The dimensions of the ARC, with a diameter of about ~2.5 nm and ~3.5 nm in length, match those of synaptic gap channel.22 The ARC may be consecutively set to conduct current either in a forward direction, corresponding to a positive voltage polarity (PR – positive rectifying), or in a reverse direction, corresponding to a negative voltage polarity (NR – negative rectifying). This polarity dependent rectification may be exploited by combining a plurality of ARCs to form a synthetic rectifying synaptic gap junction with an incrementally adjustable plasticity. A bidirectional gap junction can be created as well by using an equal number of PR and NR ARCs. The measured electrical characteristics are presented along with a supporting analytical model and corresponding numerical simulations (supporting information). Statistical data are provided as well to support the robustness of the said implementation and show that parametric distribution associated with nano-scale implementations may be successfully handled. A group of ARC used in conjunction to form an artificial synapse thus has an inherent robustness that may overcome some of the drawbacks associated with memristor devices.

RESULTS AND DISCUSSION Electrical Characterization Electrical measurements, performed at 300 °K using a parameter analyzer and a conductive atomic force microscope (C-AFM) in ultra-high vacuum, are used to determine the ARC electrical properties. Modulation of the hafnia switching layer (HSL) current-voltage (I-V) dependence was accomplished by a current compliance


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(CC) limit setting in a parameter analyzer. Figure 1a depicts the experimentally measured I-V sweeps for a PR-ARC over a random location ‘A’ on the HSL. Four consecutive I-V sweeps are marked 1-4 where ‘1’ demonstrates initial aligned defect states creation in the HSL (O-OV creation, defect like oxygen vacancies marked as OV and mobile oxygen species marked as O) at the high end of a positive voltage sweep; ‘2’ is a post forming sweep showing the overall higher conductivity through the originally insulating HSL; ‘3’ is a negative voltage sweep showing the conductive behavior in the reversed voltage polarity, followed by annihilation of some of the defects (O-OV recombination) as evident by a sharp current drop at the negative end and ‘4’ is a following negative voltage sweep showing a reduced conductivity verifying the partial annihilation of defects. The indication for whether the ARC has a rectifying nature or not is done through a comparison of the I-V behavior in the positive and negative conductive regimes (thin dashed lines in Figure 1a, curves ‘2’ and ‘3’). For a given voltage V1, an overall symmetric behavior where I(V1) ≅ I(-V1) is regarded a non-rectifying state while an asymmetric one where I(V1) >> I(-V1) (and vice versa) is considered as rectifying. The non-trivial nature of ARC implementation is also highlighted in Figure 1. A state where current rectification was successfully achieved for an intermediate CC of 30 nA with a rectification ratio (RR) of I(V1)/I(-V1) ≅ 10 for V1 = 0.5 V is presented in Figure 1a. The use of either too low CC = 10 nA (Figure 1b) or too high CC = 90 nA (Figure 1c) yielded a symmetric or non-rectifying state for this specific location. Figure 1d shows a NR-ARC with RR ≅ 102 for 0.25 V on a different location ‘B’ while using a CC of 50 nA. The optimal CC is believed to be directly related to the localized structure, thickness and composition of the HSL. Different locations may thus require different CC conditions. However the overall potential to successfully


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produce an ARC is quite robust as will be demonstrated further by statistical data. The concept of rectification flipping may be utilized in the formation of artificial synapses by using a plurality of ARCs. Figure 1e and Figure 1f depict the consecutive flipping of the rectification direction from PR to NR in yet another location ‘C’ using CC = 100 nA. Figure 1e shows PR-ARC with RR ≅ 103 for 1.0 V and Figure 1f NR-ARC with RR ≅ 102 for 2.0 V. Based on the simulation results (supplementary information – simulation progress movie), it can be seen that during formation, defects states migrate and align themselves starting from the cathode (charge injecting electrode) to form a conductive path towards the anode (opposite electrode). If this buildup process is arrested, by preventing the current from rising beyond a preset compliance, a partial conductive path separated by a “gap” (region of unbroken oxide) from the anode would be formed. This structure has a current rectifying property with the gap region presenting a higher injecting barrier after the electrode polarity is interchanged. In this sense, the formation of an ARC requires the careful manipulation of local oxide stoichiometry through an electrically driven defect formation process. A large CC will result in the formation of a continuous conductive path with symmetric I-V behavior as shown in Figure 1c. As for a low CC, defect formation is terminated at an early stage. The conductive path is sparsely populated and contains only one or two defected spots which results in a relatively symmetric tunneling barrier for current injected by both electrode and a symmetric current behavior. In the case of high CC, the defected formation process is allowed to continue until a well defined, defect rich and continuous (no gaps) conductive filament is formed which has an inherent symmetric current voltage dependence regardless of the injecting electrode. The symmetric I-V behavior common to previously reported RRAM devices is most


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likely due to relatively large areas (on the order of micrometer2) which necessitated the use of a high current compliance in order to either differentiate the conductive path induced current from background tunneling or soft-breaking the thick oxides. As shown in this work, a large current compliance would also result in a symmetric I-V. Moreover, devices which are sized in the micrometer regime are likely to yield randomly distributed multiple CFs where precise control of individual path formation cannot be achieved and the asymmetric behavior of rectifying filaments will be obscured by the more dominant (higher conductance) symmetric ones. The time constant for ionic motion in hafnia is on the order of 10-12 s. It was shown by Lee et al. that the entire switching process may occur within less than a pico-second.23 Electron trapping and de-trapping in hafnia is a widely studied subject in the field of high-k gate dielectric. Electron motion is believed to occur through a two-step process. Lee et al.24 used a 3 nm thick HfO2 gate stack and demonstrated that the motion begins with resonant tunneling of the injected electron into existing defect states followed by thermally activated migration of the trapped electrons to unoccupied states. The time scales for these processes were measured to take few µs. Therefore, it may be safe to assume that the measured currents represent a steady state electron flow since defect creation, annihilation and migration occurs almost instantly in comparison. Functional Mechanism The HSL material-hafnia belongs to the group of transition metal oxides which are compounds made of oxygen atoms bound to transition metals. Current understanding of resistive switching in HfO2 RRAM is based on O-Frenkel pairs interactions. Williams at al. identified the formation of a localized oxygen-deficiency conductive filament surrounded by a low-conductivity ring of excess oxygen as a low resistance


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state.25 The resetting process to high resistive state was shown to occur via thermal annealing driven by Joule heating and recombination of these meta-stable Frenkel pair defects. O-OV creation is driven by current induced heating and high electric fields in the HSL that in turn lead to the generation of O-Frenkel pairs. The theoretical model proposed by Berco et al.[26] demonstrates that random variations in the pristine HSL give rise to “hot spots” (oxide sections with a higher defect density that initially present a preferable current path resulting in localized Joule heating and trap build up) out of which a CF can evolve. The ARC is based on careful alignment of defect states in HfOx while using different electrode materials on both ends to electrically manipulate the local stoichiometry. One of the electrodes is oxygen impervious while the other is oxygen reactive. Current conduction through the HSL is understood to occur due to the formation of a percolation path consisting of defect like oxygen vacancies (marked OV with a spatial density Nov) and mobile oxygen species (marked O with a spatial density No).26,27 Both the analytical and experimental results indicate that initial charge injection changes the local stoichiometry, particularly near the injecting electrode to a non-uniform, high concentration of conductive defect states along with an insulating gap near the opposite electrode. This distribution results in the formation of a barrier based on the energy band difference between the electrodes (either TE or BE) and the HSL. A schematic description representing the internal structure and processes believed to occur during the formation and operation of positive and negative rectification in the proposed ARC is presented in Figure 2. PR-ARC formation with a positive bias is depicted in Figure 2a. O-OV generation in the HSL occurs due to temperature buildup and high electric field. The O species are negatively charged and attracted to


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the TE (red arrow) while the positively charged OV are driven to the BE (blue arrows). The buildup of OV near the BE creates a ‘stepping stone’ like path, made up of trap states, for electron hopping (thin black lines) across the HSL with an insulating tunneling barrier (marked by a double-sided arrow placed between two dashed lines) at the edge. The inert nature of the TE leads to accumulation of readily available O in the top of the HSL. Charge transfer under lower positive bias conditions is based on hopping and tunneling through the barrier. The tunneling current depends on both the barrier width and the energy difference between the traps and the TE. Figure 2b shows the reverse processes occurring as the TE potential polarity is flipped to a magnitude that annihilates the PR state. Readily available oxygen species migrate back into the HSL to recombine with OV. The barrier width increases and electron current drops exponentially. NR-ARC formation with a negative bias is depicted in Figure 2c. In this case, OV builds up near the TE (charge injecting source) while the interaction between the reactive TiN and O results in the creation of interfacial TiOxNy (oxygen scavenging) near the BE.28,29 The tunneling current through the insulating barrier during low voltage operation, in this case, depends on the energy difference between the traps and the BE as well as the barrier width. Figure 2d shows the elimination (resetting) of the NR-ARC using a reverse bias. Annihilation of OV leads to the widening of the insulating gap and a drop in current. However, oxygen migration back into the HSL requires a high negative potential to overcome the activation energy associated with O release from the TiOxNy layer (opposed to available O in Figure 2b). Numerical Analysis In light on these results, it is suggested that the underlying mechanisms of rectification are based on asymmetric trap distributions, mainly a large density near


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the BE in PR-ARC and near the TE in NR-ARC (i.e. near the charge injecting electrode). In addition, the non-identical work functions of the two electrodes determine the characteristics of the I-V exponential dependence. Oxygen scavenging capabilities of the BE along with the inert TE lead to different potential magnitudes needed to reverse the rectification polarity from NR to PR (compared with PR to NR) and provide an additional degree of freedom in designing threshold switching behavior. The main current mechanisms involved in ARC operations are illustrated in Figure 3. The figure shows the energy band diagram and resulting current for electrons and holes (e- and h+) for PR-ARC and NR-ARC with different voltage polarities (ecurrent marked red and h+ current blue). The BE Fermi energy (Ef), HfOx energy gap and TE valence band maximum (VBM) are shown as well. The TE material is degenerately boron-doped-diamond (BDD). The VBM is located ~0.4 eV below the boron doping level and the electron affinity equals to -1.0 eV, resulting in a work function of 3.9 eV.30 Charge transfer in BDD is based on semi-metallic conduction (~1021 cm-3 in a degenerate state).31 Trap like states are depicted as hollow circles (Figure 3) and are located 0.7 eV below the HfOx conduction band.32 The band structure of a PR-ARC formed with a positive voltage polarity is given in Figure 3a. A high density of traps located directly at the BE-HSL interface makes it relatively easy for e- to occupy them by means of thermal excitation and wave-function overlap. Once trapped, e- may ‘hop’ through the HSL on stepping stone path down the potential gradient to reach the gap (trap deficient section). The gap width (marked WB) is relatively small and e- can tunnel through it to recombine with h+ supplied by the TE. The reverse case of a PR-ARC reset while operated using a negative voltage polarity is given in Figure 3b. Since the TE is of negative polarity, e-


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should either direct tunnel to the BE or gain thermal energy and then tunnel through a larger barrier (due to O-OV recombination) into the remaining traps near the BE. Both these processes have much lower quantum probabilities compared to the positive bias case (Figure 3a) and the resulting current is thus much lower. A NR-ARC with a negative voltage polarity is shown in Figure 3c. Trap states are located near the TE so e- are able to occupy them through thermal excitation. Once trapped, e- move down the potential gradient and tunnel into the BE through the small barrier. However, this current will be small when compared to Figure 3a due to h+ based conduction in the BDD TE (OV traps are positively charged). At even more negative potentials, direct tunneling of e- from the VBM into the traps can occur resulting in larger currents. This model may explain the differences seen in curve ‘2’ between Figure 1e,f. Figure 1e-‘2’ shows stronger exponential growth with virtually no threshold while Figure 1f-‘2’ has a switching threshold level of about -0.25 V. The reverse bias case is depicted in Figure 3d where a NR-ARC is reset while operated with a positive voltage polarity. The BE supplied e- must either direct tunnel through the entire HSL or gain enough thermal energy and tunnel though a large barrier (WB) to the TE (again due to O-OV recombination). However, they are low probability processes and the resulting currents are thus much lower. The difference in electrode work function when operating in the reverse mode (Figure 3b,d) can account for the higher RR seen in Figure 1f compared to Figure 1e as well. Numerical simulations based on an analytic model (supplementary information) were carried out to confirm the hypothesis concerning the underlying physical mechanisms associated with ARC operation. Figure 4 shows the simulation results for OV trap and O species densities (NOV and NO) in the HSL formation at a CC condition of 100 nA. Figure 4a,e show the NOV distributions after forming a PR-ARC and a NR-ARC


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using a potential of +4.25 V and -4.25 V respectively, thus simulating curve ‘1’ in Figure 1e,f. In both cases, NOV indicates the existence of a hopping path through the HSL having a gap WB ≅ 0.5 nm at the edge near the positively charged electrode. These gaps correspond to the tunneling barriers depicted in Figure 3a,c. The corresponding NO density profiles, shown in Figure 4b,f respectively, are higher near the positive electrode as well since the negatively charged O species are driven toward it by the electric field. Figure 4c,g depicts NOV for resetting the PR-ARC and NR-ARC under reverse bias conditions that simulates curves ‘4’ in Figure 1e,f. It is evident that some of the traps were annihilated due to O-OV recombination resulting in much larger gaps (wider e- tunneling barriers). The matching NO density profiles given in Figure 4d,h also indicate that recombination took place in the HSL by showing reduced O levels in section previously occupied with OV when compared to the profiles in Figure 4b,f. The simulation reveals that once defect states are generated due to local high temperatures and electric fields they migrate away from the positive charged electrode and accumulate near the opposite one. The positively charged OVs columbic interaction imposes an upper limit on the possible local concentration and a hopping path emerges at that region.26 This behavior may explain the symmetric currents observed in Figure 1b,c for curves ‘2’ and ‘3’. In the case of a low CC (Figure 1b), defect formation is terminated at early stages and the hopping path is sparsely populated (e.g. an ‘island’ of defects located in the midpoint of the HSL). This will result in a relatively symmetric tunneling barrier from both directions and a symmetric current behavior. As for a high CC (Figure 1c), the defects accumulate up to a well formed continuous conductive path26 between both electrodes which has an inherent symmetric current voltage dependence.


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Statistical Analysis The robustness of the proposed ARC is statistically analyzed to demonstrate that parametric distribution associated with nano-scale implementations may be overcome. A histogram plot of the CC condition required to produce a rectifying ARC for 42 different locations (i.e. curve ‘1’) is given in Figure 5. A state is considered as rectifying by observing an asymmetric I-V for opposite voltage polarities (i.e. curves ‘2’ and ‘3’). A successful condition was thus determined for each location by an increase of the CC and inspection of the resulting I-V curves at each step. In this manner, the histogram shows the number of locations for a given CC which resulted in asymmetric curves. The calculated mean value and standard deviation are 48.6 nA and 32.3 nA respectively. One consideration in ARC formation is the setting of current compliance as detailed previously. The CC condition effectively manifests itself as an upper limit on the amount of stress (charge injection) put over the HSL during forming. Both the theoretical model and the simulation results show that the appropriate condition for yielding an ARC depends on the local “quality” of the pristine HSL. For example, local thickness variations, defect density and distribution (disorder) may require different compliances or “forming stress”. The statistical data provided in Figure 5 supports the robustness of obtaining a rectifying state by showing that a CC condition should exist for virtually any local non-uniformity or disorder state. The data was collected using the exact same C-AFM measurement setup in each location for consistency. The only varying parameter (CC) was stepped in increments of 20 nA starting from 10 nA. Once a rectifying structure was identified through an I-V measurement, the CC level was recorded. These results


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imply the possibility of engineering the HSL to a more uniform, consistent and predicable manner that would narrow down the CC distribution. The ARC physical dimensions (3-D spatial defect distribution) matched those of its biological counterpart. The length corresponds to the thickness of the HSL while the lateral cross section was determined by a current map measurement. Figure 5 inset depicts a 2-D map of the current measured by the C-AFM during surface scanning over the top of the ARC as a function of tip location. The current is directed from the tip into the HSL in a normal direction, thus giving an indication for the width of the ARC. The average current is ~72 pA and the maximal width of the bright spot, corresponding to the location where an ARC was formed, is ~2.5 nm. The data in Figure 5 indicate that the current rectifying behavior is neither sporadic nor random and is in fact possible by careful defect manipulation regardless of the location. The inset image was acquired using a surface current map scanning performed immediately after ARC formation. The bright regions show the top view cross section of the ARC and provide a measure for its width and number of conductive paths (spots where current flows into the HSL). It can be seen that it is constructed mainly out of a single dominant CF, which is common to all ARCs. Synaptic Weight Model Implementation The proposed arrangement of defect giving rise to an asymmetric rectifying behavior was further verified by comparing the measured data with the hopping-tunneling simulation results as shown in Figure 6. The simulated I-V curves were obtained by using the same initial state for density distributions (NO and NOV) and the same number of simulation steps for each potential. Parametric fitting was used to match the low bias simulation output to the measured value and set a common benchmark.


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The HSL temperature was set to 300 °K in each case as well. The measured I-V curved for a PR-ARC and NR-ARC under forward bias conditions are presented with the simulation data. Figure 6a displays PR-ARC with positive bias and Figure 6b NR-ARC with negative bias. The experimental curves show rectifying threshold switching with an exponential current growth in both cases. The measured thresholds (40 mV for PR-ARC and -225 mV for NR-ARC) are within the same operating range of the thalamic reticular nucleus neurons characterized by Haas et al.6 which were maintained at a baseline of –65 mV and demonstrated a spiking threshold of ~40 mV. The operating range of the ARC may thus be tuned to match that of the biological counterparts.

The

experimental

results

show

good

agreement

with

the

hopping-tunneling model in the low voltage operating range (~1 V). One aspect of the idea in the present work lies in the demonstration of a nano-scale conductive path with switchable rectification direction. Another aspect is in the use of different electrode materials where one is oxygen reactive (BE) and the other is inert (TE). The simulation reveals that a resultant interfacial layer near the BE after forming a NR-ARC (supporting information) degrades the material by affecting the switching properties and may account for the different thresholds observed in the experimental data (40 mV and -225 mV in Figure 6a,b). Furthermore, the matched simulations in Figure 6 show a weaker current voltage dependence (a lower current for a given absolute voltage value) in the presence of this layer (Figure 6b) when compared to the opposite case (Figure 6a). This feature provides an additional degree of freedom in the design of different synaptic activation functions for a PR-ARC and a NR-ARC. An estimated operational power consumption of the ARC can be done using the read voltage and related current given in Figure 6. Defining the read current threshold at 1


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pA per ARC can provide enough margins to mask any noise related issues while keeping power consumption in the pW regime. The associated read voltages are therefore about 200 mV for a PR-ARC (Figure 6a) and 650 mV for a NR-ARC (Figure 6b). The expected power dissipation is thus ~0.25 pW for a PR-ARC and ~0.65 pW for a NR-ARC. The proposed ARC based implementation of a weighted sum operation (dot product in neural networks) generic matrix, compared with the conventional approach is schematically depicted in Figure 7. The conventional matrix implementation33,34 using analog memristors is shown in Figure 7a. Two memristors are used to determine a single synaptic weight in a differential manner thus allowing for both positive and negative parametric values. Based on the current work, one proposed ARC based implementation is given in Figure 7b. The ARC operation principal allows for dynamically switching the rectification direction thus resulting in either an excitatory or inhibitory weight parameter at each junction. In addition, the dynamic nature of ARCs may be utilized for real time modulation (online training) of the junction plasticity using a plurality of ARCs (grouped together) by changing the ratio of the number of PR to NR-ARCs as shown in Figure 7c. Individual ARCs in the group may be dynamically flipped during training to determine the overall conductivity according to a differential digital scheme. However, the combined weight contribution of the entire group may be summed by turning ‘on’ all the multiplexer outputs during evaluation. This implementation clearly requires added supporting multiplexing circuitry (trapezoid representation) and bit-lines to support individual control for each ARC. However this drawback may be compensated by the functional simplification since analog RRAM operation (conductivity adjustment) usually requires complicated pulsing schemes to account for its nonlinear nature.35,36


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The proposed implementation was verified with spice simulations using a behavioral model based on the experimental data given in Figure 6. The circuit under simulation is composed of 20 ARCs connected in parallel to a single DC voltage source representing the input vector value (Figure 7c). The simulation progresses by consecutive flipping an additional NR-ARC to a PR-ARC starting from n=1 to n=19 and calculating the overall conductance under positive (0.25 V) and negative (-1 V) voltage polarities. Figure 7d displays the simulation results for the conductance dependence on the ratio of PR-ARC number (n) to NR-ARC number (20-n) under opposite bias polarities. The results show a linear dependence in both cases. The positive slope for PR may be used to design an excitatory synaptic weight (increased current flow to the post synaptic circuitry for a positive input vector) while the negative slope for NR may be used for an inhibitory synaptic weight design (increased current flow from the post synaptic circuitry for a negative input vector).

CONCLUSIONS In summary, the authors presented a metal-oxide based nano-scale artificial rectifying connexon (ARC) which may be utilized to mimic biological connexons found in synaptic gap junctions. The structure is based on changing the local stoichiometry of a metal oxide thin film by manipulation of defect states to having high density at one end and an insulating gap at the other. Experimental measurements show that the structure has a current rectification property of up to 3 orders of magnitude which may be consecutively flipped to either forward or reverse direction to create either an excitatory or inhibitory (positive or negative) synaptic weight. Numerical analysis reveals that the rectification mechanism is based on electron tunneling which depends on both the trap profile and electron work function of the two electrodes. A plurality of ARCs may thus be used to create a rectifying synaptic gap junction. In addition, the


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plasticity of each junction may be altered by changing the ratio of the number of forward to reverse ARCs.

EXPERIMENTAL METHODS ARCs were demonstrated over a sample of ~3.5 nm uncapped hafnia (HfOx) thin film fabricated on a TiN/Ti/p-Si substrate. A 10 nm thick Ti layer was sputter-deposited at room temperature followed by 90 nm thick TiN using the same process. The hafnia was formed by atomic layer deposition using tetrakis (dimethylamino) hafnium as the metal precursor and H2O vapor as the oxidizer. The growth temperature and pressure were 250 °C and 0.1 Torr, respectively without post-deposition annealing.

Acknowledgements The authors acknowledge the partial funding support by Singapore Ministry of Education under grants MOE2016-T2-1-102 and MOE2016-T2-2-102.

Supporting Information Available The Supporting Information is available free of charge on the ACS Publications website. Thin film structural analysis and theoretical methods (PDF), Numerical simulation progress movie file (MP4).


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Figure 1. (a) PR-ARC in location ‘A’ with CC=30 nA (b) non-rectifying with CC=10 nA (c) non-rectifying with CC=90 nA (d) NR-ARC in location ‘B’ with CC=50 nA; consecutive dynamic flipping in location ‘C’ using CC=100 nA: (e) PR-ARC with (f) NR-ARC.


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Figure 2. Schematic description for positive and negative rectification with the associated defect lateral distribution (local stoichiometry) in the HSL cross section (O species direction of motion marked by red arrows, OV by blue arrows, electrons by thin black lines and the width of the insulating barrier by a double sided arrow placed between two dashed lines); (a) PR-ARC formed with positive bias (b) PR-ARC reset with negative bias (c) NR-ARC formed with negative bias (d) NR-ARC reset with positive bias.


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Figure 3. ARC energy band diagram during positive and negative rectification states with different voltage polarities (electron current marked red and hole current marked blue): (a) PR-ARC with a positive voltage polarity – high current (b) PR-ARC with a negative voltage polarity – low current (c) NR-ARC with a negative voltage polarity – high current (d) NR-ARC with a positive voltage polarity – low current.


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Figure 4. Simulated trap densities and O species (NOV and NO) in the HSL for positive and negative rectification forming for a current compliance condition of 100 nA. The plots show the 2D densities throughout the HSL indicated by the x- and y- axes with cyclic boundary conditions in the x-direction. The boundary conditions along the top and bottom are determined by the TE and BE materials respectively. The simulation starts from an initial randomly generated disordered state and progresses up to a final CC matching condition of 100 nA using a Metropolis Monte Carlo algorithm.26 PR-ARC formed with positive bias: (a) NOV (b) NO; PR-ARC reset with negative bias: (c) NOV (d) NO; NR-ARC formed with negative bias: (e) NOV (f) NO; NR-ARC reset with positive bias: (g) NOV (h) NO.


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Figure 5. Histogram plot of the minimal CC condition required to produce a rectifying ARC for 42 different locations (inset: 2-D current map measured by C-AFM touch mode scanning over the top of the ARC showing a conductive filament from top view).


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Figure 6. Measured I-V curved for PR-ARC and NR-ARC under forward bias conditions compared with the fitted hopping model simulation. (a) PR-ARC with positive bias showing a threshold switching of 40 mV (b) NR-ARC with negative bias showing a threshold switching of -225 mV.


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Figure 7. (a) conventional crossbar implementation of a weight matrix with analog memristors; two memristors are used to determine a single synaptic weight in a differential manner thus allowing for both positive and negative values (b) proposed ARC based implementation; by dynamically switching the rectification direction, either an excitatory or inhibitory (positive or negative) weight parameter may be implemented at each junction (c) proposed multi level operation using multiple ARCs for each synapse; each ARC may be dynamically flipped during online or offline training to determine the conductivity according to a differential digital scheme (d) behavioral model based spice simulation showing the conductance dependence on the ratio of PR number (n) to NR number (20-n) in a group of 20 ARCs with opposite bias polarities.


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Graphical TOC Entry:

The authors demonstrate the concept and feasibility of nano-scale defect manipulation in metal-oxide thin films to produce an artificial rectifying connexon (ARC). This localized asymmetric defect arrangement results in a structure that may be used to construct artificial gap junctions in a similar manner to biological connexons found in electrical synaptic gap junctions. The structure is based on changing the oxide local stoichiometry to having conductive defects at one side and an insulating gap at the other. Experimental measurements demonstrate that the structure has current rectification properties of up to 3 orders of magnitude which may be consecutively flipped to either forward or reverse direction to create either an excitatory or inhibitory weight. A plurality of ARCs may be used to create a rectifying synaptic gap junction. In addition, the plasticity of each junction may be altered by changing the ratio of the number of forward to reverse ARCs.


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Nanoscale Conductive Filament with Alternating ... - ACS Publications

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