Overview of amorphous carbon memristor device, modeling, and applications for neuromorphic computing

1 Introduction

Carbon-based materials have been considered as one of the most prospective contenders for conventional silicon (Si)-based semiconductors [1,2]. This can be ascribed to its abundant sources, superior performances and good environmental compatibility. In addition to the well-known diamond and graphite, several attractive derivatives of carbon-based materials, such as fullerenes, carbon nanotube (CNT), single-layer graphene, and amorphous carbon (a-C), have been discovered in the past [3,4,5,6], as revealed from Figure 1. Such versatility endows carbon-based materials with excellent mechanical, electrical, and optical properties, thus making them suitable for various electronic components that include transistors [7], sensors, field emission device [8], and anti-radiative devices [9].

Figure 1

Appearances of the most studied carbon allotropes today.

In addition to the above applications, carbon-based materials have recently been adopted as a promising candidate for emerging memristor technologies. According to the classic definition [10], memristor, usually nominated as the fourth fundamental element of the circuit, is a two-terminal device whose resistance can be switched between high resistive state (HRS) and low resistive state (LRS) via external stimulus [10]. Most importantly, such resistance modulation process is usually accompanied with several physical superiorities such as high switching speed, long endurance, good retention, and low power consumption [11]. Additionally, its fairly simple architecture considerably shrinks the occupied area, and consequently booms resulting density [12]. These remarkable merits make memristor completely resemble synapses and neurons of biological brain, and open a new path towards neuromorphic applications [13]. As illustrated in Figure 2, the mainstream memristive materials today include transition metal oxides (TMOs) [14,15], chalcogenides [16,17], ferroelectric materials [18,19], and magnetic materials [20,21]. In comparison with these well studied materials, aforementioned carbon derivatives also exhibited resistive switching (RS) behaviors when subjected to stimulus. More excitingly, their inherent physical properties assigned carbon-based memristors with some fascinating traits such as low toxicity, chemical stability, and flexibility over conventional memristive materials [22]. Within various carbon derivatives, a-C-based memristor has been receiving consistent attention during the last decade, owing to their flexibility on RS and mature fabrication techniques. This led to the birth of multiple a-C-based device prototypes and modeling algorithms. Nevertheless, a comprehensive review on the state-of-the-art a-C-based memristor technologies is still missing from the perspective of either device physics or theoretical simulations. It is therefore necessary to provide a comprehensive overview of different types of a-C-based memristors, including their material composition, operating principles and performance characteristics, whereby researchers can better understand the diversity and potential application areas of a-C-based memristors through such systematic summarization. To address this drawback, here we first reviewed the classification of a-C-based materials associated with their respective electrical and thermal properties. Subsequently, several a-C-based memristors with different architectures were presented, followed by their respective memristive principles. We also elucidated the state-of-the-art modeling strategies of a-C memristors, and their practical applications on neuromorphic fields were also described. The possible scenarios to further mitigate the physical performances of a-C memristors were eventually discussed, and their future prospect to rival with other memristors was also envisioned. The aim of the article is to provide a comprehensive overview of different types of a-C-based memristors, including their material composition, operating principles, and performance characteristics. Through the systematic summarization, readers can better understand the diversity and potential application areas of a-C-based memristors.

Figure 2

Common memristive materials and their corresponding memristor devices. The inner most ring exhibits the typical I–V characteristic of memristor, described visually as a pinched hysteresis loop. The middle ring presents common memristive materials that can be represented clockwise as MgO, BiFeO, GeSbTe, and TiO₂, respectively. The outer most ring in clockwise shows their corresponding memristors, classified into magnetic random access memory (MRAM), Ferroelectric RAM (FeRAM), phase-change RAM (PCRAM), and resistive RAM (ReRAM).

2 a-C classification

a-C families can be physically discriminated via the following critical features: (1) the sp³ content, (2) the clustering of the sp² phase, (3) the orientation of the sp² phase, (4) the cross-sectional nanostructure, and (5) the hydrogen (H) or nitrogen (N) content [23], as clearly illustrated in Figure 3 in the form of ternary phase diagram. Note that the structure versatility of carbon materials mainly arises from their different bonding hybridizations, i.e., sp³, sp², and sp¹. sp³ hybridization indicates a carbon atom σ bonded to four other atoms, resulting in a mixture of one s orbital and three p orbitals in the same shell of an atom to form four new equivalent orbitals. sp² hybridization corresponds to a formation of two single σ bonds and one double σ bond among three atoms, revealing a mixture of one s orbital and two p orbitals in the same shell of an atom to form three equivalent orbitals. Carbon having sp hybridization is bounded to two other atoms through a combination of either two double bonds or one single and two triple bonds, making a mixture of one s orbital and one p orbital in the same shell of an atom to form two new equivalent orbitals. Three corners of the triangle in Figure 3 correspond to graphite, diamond, and hydrocarbons, respectively. Carbon ordering along the graphite-diamond line can be classified into graphite, nanocrystalline graphite, sp²-dominated a-C, sp³-dominated a-C, and diamond [23,24,25]. Such ordering variations, involving sp² clustering evolution and sp³ content evolution, can result from different deposition techniques. Note that one of the most important carbon ordering phases along the graphite-diamond line is tetrahedral a-C (i.e., ta-C) with maximum sp³ content. The key technique to deposit ta-C film is ion bombardment, which can be realized by pulsed laser deposition, filtered cathodic vacuum arc, and mass-selected ion beam deposition [26,27,28,29]. High proportion of sp³ hybridization endows ta-C with various attractive properties such as high elastic modulus, chemical inertness, high hardness, high electrical resistivity, and optical transparency, thus attaining considerable attention for electro-optical applications [30,31,32].

Figure 3

A ternary phase diagram for a-C.

In addition to hydrogen-free a-C, hydrogenated a-C alloy (a-C:H) is also one of the most researched materials owing to its novel optical, mechanical, and electrical properties and its similarities to diamond. It was reportedly classified into four groups. The first group is the a-C:H having 40–60% H content with up to 70% sp³. The materials inside this group are soft and has low density [6], usually referring to polymer-like a-C:H (PLCH). The second a-C:H group is defined to have 20–40% H content. Such group exhibits more excellent mechanical properties because of more C–C sp³ bonds [6]. These films are usually called diamond-like a-C:H (DLCH). Increasing the sp³ content (∼70%) of DLCH resulted in ta-C:H with larger optical gap and higher density [33]. The last group a-C:H has low H content (≤20%), corresponding to higher sp² content and sp² clustering. These films are usually named as graphite-like a-C:H (GLCH). Plasma enhanced chemical vapor deposition (PECVD) has been considered as the most common approach to deposit a-C:H films such as PLCH [34,35], DLCH [35,36], and GLCH [35,36], while ta-C:H films can be deposited by electron cyclotron wave resonance [37] and plasma beam source techniques [38].

Another important type of a-C is carbon nitrides that can also be categorized into four classes. The first class of carbon nitrides is a-C:N with a high sp² bonds content, which is required to be deposited above 200°C and allows for better mechanical hardness and large elastic recovery [39,40]. ta-C:N is usually defined to be the second class of carbon nitrides, which presents smaller resistivity and optical gap than pure ta-C films [41]. Note that ta-C:N exhibits high sp³ content (80–90%) up to about 10% N, after which its sp³ content and density decrease sharply [41]. Such trend was ascribed to the high deposition pressure [42]. Implementing PECVD using a mixture of a hydrocarbon gas enables the deposition of a-C:H:N [43,44], regarded as the third class of carbon nitrides. Increasing N content can however reduce the hardness of a-C:H:N films, and a more graphite-like material can be obtained by decreasing the N and H contents [41]. ta-C:H:N, the last class of carbon nitrides, is usually secured by introducing N into ta-C:H, which gives rise to sp² clustering and maintains an inappreciable sp³ to sp² conversion within ∼ 20% N content. Increasing N contents can result in lower sp³ fraction and softer films [45].

3 Modeling of a-C-based memristor

The concept of the a-C-based memristor originated from the finding of RS phenomenon on a so-called “insulation” carbon film sandwiched between a bottom tungsten (W) electrode and a top metal electrode. It was postulated that the initial form of the carbon material is a diamond structure dominated by sp³ with low conductivity. After applying voltage to the metal electrodes at both ends, part of sp³ is transformed into a graphite structure dominated by sp² with high conductivity under the action of high current density, forming a conductive filament connecting the upper and lower electrodes. Under the influence of the high current density, the thin metal electrode melts, and the fine carbon filaments are oxidized and evaporated, thus forming the fine filamentous crater [46], as illustrated in Figure 4(a).

Figure 4

(a) Two spots formed inside the melted metal where sp² filaments were oxidized and vaporized, leaving two craters (left) and their zoom-in image (right), (b) simulated and measured I–V curves of a TiN/a-C/PtSi conductive tip stack, resulting from the modified Poole–Frenkel model, (c) experimental data of the device in its three states. Included are theoretical fits for a barrier (direct tunnelling and Schottky emission) model and a modified P-F model, (d) simulated electrical conductivity of a-C sandwiched between TiN and PtSi conductive tip, based on different physical assumptions, and (e) comparison between measured and calculated electric field-dependent electrical conductivities of an a-C-based device (Pt/ta-C/W). (a), (b), (c), and (d) are reprinted with permission from [46,47,48,49], respectively.

Following such hypothesis, majority of a-C memristor models were devoted to the imitation of sp²-to-sp³ conversion and vice versa [47,48,49,50,51]. One reported work defined the resistance switching behavior as the well-known “threshold switching,” which can be described by a modified Poole–Frenkel (P-F) type conduction [47]:

where K ′ is a constant and Φ_B, k _B, T, q, and t are the energy barrier at zero field, Boltzmann constant, temperature, elementary charge, and thickness of the film, respectively. dz is the average inter-trap distance. LRS according to the P-F model occurs by the field assisted thermionic emission of electrons from donor traps lying just below the conduction band edge, while HRS was dominated by the hopping conduction via states near the Fermi level within the mobility gap [52]. It was further speculated that the induced electric field increased the sp² clusters in size and caused reversible bond rearrangements [53]. This subsequently reduced the inter-trap distance, and lowered the effective barrier height from HRS to LRS, thus contributing to the remarkable reduction in electrical resistance. The experimental current–voltage (I–V) curve and the corresponding fit agreed well, as reflected in Figure 4(b). Another hypothesis ascribed RS behaviors to the gradual decrease in the height of formed potential barrier within the device [53]. As illustrated in Figure 4(c), it was observed that HRS and LRS I–V characteristics were consistent with current transport by direct tunneling through a barrier at low voltages, followed by Schottky emission over a barrier at high voltages. The barrier heights, depending on the structural rearrangements, gradually decreased, thus giving rise to different resistance states. Instead of directly deriving the sub-threshold current, an alternative strategy was to define the electrical conductivities of the a-C at subthreshold (σ _LE) and threshold switching (σ _HE) regimes, respectively, given by [48]:

where K _LE and K _HE are prefactors for σ _LE and σ _HE, respectively, E is the electric field, E _a is the low-field temperature dependent activation energy, s is the distance between two coulombic centers, β is the Pool–Frenkel constant. Accordingly, the electrical conductivity of the a-C was assumed to be σ _LE when the electric field was smaller than a pre-defined threshold value, while it was considered as σ _HE when resulting electric field exceeded the threshold value. Resulting electrical conductivities from above definitions also matched the experimentally measured case well, as shown in Figure 4(c). Differing from the above two methods, another scenario to mimic the RS of a-C was to define the electrical conductivities of sp² and sp³ contents, respectively. The electrical conductivity of sp² content was regarded as a constant of 1.2 × 10⁵ Ω⁻¹ m⁻¹, while that of sp³ content was interpreted as [49]:

The electrical conductivities of the a-C-based carbon memory device for different bias voltages were therefore calculated and found to show a good agreement with the measured values, as demonstrated in Figure 4(d).

It should be kept in mind that for the above models, physical conversions between sp² and sp³ contents were only described in terms of device resistances. This implied that aforementioned models were unable to predict the exact proportions of sp² and sp³ contents. To address this issue, mass action law was combined with the electro-thermal model to determine the concentrations of sp² and sp³ contents, constructed by [50]:

where r sp 2 is the concentration of sp² content, t is the time, k _f and k _r correspond to the reaction rates for the transition from sp² to sp³ and sp³ to sp², respectively. The reaction rate k _r , governing “SET” operation (i.e., sp³ to sp²), was attributed to the outcome of the electric field intensity, defined by

where | E 0 | and k r 0 are the fitting parameters in describing the threshold of the electrical field intensity and reaction rate constant from sp³ to sp², respectively. In contrast, the reaction rate k _f , responsible for “RESET” operation (i.e., sp² to sp³), was liable to be dominated by non-uniform temperature distribution, calculated by

where | ∇ T | 0 and k f 0 are the fitting parameters in describing the threshold of the temperature gradient intensity and reaction rate constant from sp² to sp³, respectively. By simultaneously solving above mass diffusion model with electro-thermal model, it was possible to dynamically reproduce the formation and rupture of the conductive filaments (CFs) inside the a-C layer, and thus to determine the volume fractions of the sp² and sp³ contents, as demonstrated in Figure 5(a). As can be seen from Figure 5(a), the a-C precursor film consisted of numerous breakers that were adopted to describe the path between two neighboring spots, which can be defined as either sp² (red) or sp³ (grey) clusters. It was clearly observed that during the “RESET” process, the red breakers inside the green box were missing, corresponding to the rupture of the CFs. In contrast, previous gaps between different spots were re-connected by red breakers, implying the formation of new CFs. One severe drawback of the above model arose from the fact that it did not take into account the complex electrical transport mechanism of a-C films. As a result, another model that included both electrical transport behaviors of a-C films with the reaction rates of sp² to sp³ and sp³ to sp² conversions has recently been proposed [51,54]. The electrical transport behaviors of a-C films were elaborated based on equations (2) and (3), while reaction rates slightly differed from equations (6) and (7), resulting in

where c ₁ and c ₂ denote different prefactors for sp² to sp³ and sp³ to sp² conversions, respectively, and E _b represents the activation energy for sp² to sp³ conversion. By means of this comprehensive model, the “SET” current was calculated and promisingly coincided with the experimental counterpart. More importantly, such approach allowed for the visualization of the conductive filament formation and erasure in three-dimension (3D), as illustrated in Figure 5(b), which can be employed to predict the threshold switching voltages for a variety of preliminary sp² fractions. Note that few researchers [50,51,54] considered the transition from LRS to HRS as the sole temperature-dependent rehybridization of sp² atoms to sp³ atoms, which generated separations in the conductive bridge through the a-C layer or the contact regions. However, as the sp² phases of carbon are thermodynamically favored at atmospheric pressure, the speculation that the transition from LRS to HRS only relied on temperature remained doubtful. Qin et al. [50] also proposed that resulting pressures from temperature gradient may facilitate the presence of HRS by driving sp² atoms to sp³ atoms owing to thermal expansion, whereas experimental evidences that pressures were required to form sp³ phase were still missing.

Figure 5

(a) Formation and breakage of conductive a-C filaments inside an a-C-based device for two successive cycles. Green rectangles indicate the locations where the breakage of a-C filaments occurred. (b) Measured and calculated “SET” (left) and “RESET” (middle) current for different a-C thicknesses, and simulated current density (right) inside the a-C layer. (a) and (b) are reprinted with permission from [50,51], respectively.

Table 1 summarizes the working mechanisms of various a-C-based memristor models reported so far.

4 Design principles of a-C-based memristors

According to the reported modeling results, one viable approach to achieve its memristive character is to change the ratio of sp² to sp³ bond either electrically or thermally. Besides, the electrochemical metallization of the CFs for conventional ReRAMs using TMOs also applies to a-C-based memristor by appropriately choosing the capping metal electrode. Moreover, doping a-C with other reactive elements can also tailor the electrical properties of a-C effectively. For above reasons, a-C-based memristor here is simply classified into undoped a-C-based memristor and doped a-C-based memristor.

4.1 Undoped a-C-based memristor

Various architectures of undoped a-C-based memristors have previously been proposed by several groups [55,56,57,58,59,60,61,62,63,64]. Despite these architecture variations, majority of these memristors shared one common configuration, i.e., top metal electrode/a-C/bottom metal electrode structure. The top electrode in fact plays a more important role in determining the RS mechanism of the undoped a-C-based memristor than the bottom electrode. The a-C-based memristor whose top electrode is made of active metal, such as silver (Ag), copper (Cu), and gold (Au), usually exhibits a bipolar switching characteristic such that modulation of resistive states is realized by alternating the polarity of the applied bias, as reflected in Figure 6(a).

Figure 6

(a) Unipolar (left) and bipolar (right) switching I–V curves, (b) SET/RESET voltages (top) and HRS/LRS (bottom) distributions for different compliance currents (CCs), (c) schematic of a-C memristor embedded with graphite microislands (GMs) (top) and its resulting I–V curves (bottom), (d) the cumulative probability of HRS/LRS (left) and operation voltage (bottom) with and without single-layered graphite (SLG), (e) fabrication process of the metal/a-C/CNT/metal memory (left), and SET/RESET voltages distribution during different programming cycles and statistical distribution of SET/RESET voltages for different metal electrodes (i.e., Au and Ag). (b), (c), (d), and (e) were reprinted with permission from [55,56,57,64], respectively.

Similar to the widely studied TMO memristors, such bipolar switching commonly results from the formation and rupture of conductive bridges via the diffusion of dissolved metal cations from the interface of the electro-chemically active electrode into the a-C region and vice versa [65,66]. The metal cations, stemming from the oxidization of the electrochemically active metals, can migrate into the a-C layer to form conductive channels, driven by the positive electric field. Since a-C films reportedly exhibited low ion mobility and redox rates [67], metal cations were able to accumulate and reach the critical nucleation conditions inside the a-C layer under high field bias. Moreover, the local electric field near the conductive sp² sites can be significantly enhanced due to the dielectric mismatch between the sp² and sp³ sites [68], thus making these sp² atoms as nucleation sites. The advent of enhanced electrical field undoubtedly increased the nucleation probability of metal cations and improved nucleation process. In contrast, a negative voltage applied to active electrode can induce oxidation and potential Joule heating effect, which facilitates the dissolution of previously formed conductive channels. According to the above mechanism, both non-volatile and volatile RS behaviors were found on one memristor configuration based on Cu/a-C/Pt design [59]. It was reported that changing CCs can vary the size of CFs, thus giving rise to different RS types. One simple method to further mitigate the RS performance of the Cu/a-C/Pt structure was implemented to adjust the degree of sp² clustering by changing CCs, as shown in Figure 6(b) [56]. The small sp² clusters can gather to become larger clusters along with increasing CCs, and conductive channels can be produced along the pre-formed sp² clusters, thus improving the memristor performance. This method has recently been improved by producing uniform GMs inside the Cu/a-C/nickel (Ni) memristor [64], as illustrated in Figure 6(c). The conductive filaments were apt to grow along the GMs, and the enhanced local electric field around the GMs not only reduced the energy consumption, but also suppressed the relative fluctuation of HRS/LRS resistance. In addition to the optimization of a-C film itself, physical performances of undoped a-C-based memristor can also be alleviated by utilizing different electrode materials. One paradigm is to insert an additional SLG between top Au electrode and ta-C film to form Au/SLG/ta-C/Pt structure [55], as shown in Figure 6(d). This novel configuration allowed for both bipolar switching and unipolar switching, while inducing ten times higher ON/OFF ratio than the sole metal electrode. This was likely caused by a suppressed tunneling current due to the low density of states of graphene near the Dirac point [55]. Another device that adopted Au/a-C/CNT architecture was also studied (Figure 6(e)), substantially reducing the size of the active device area [57].

Another type of undoped a-C-based memristor is accompanied with top inert electrode such as platinum (Pt), tungsten (W), and chromium (Cr). Unipolar switching was reportedly the main RS behavior of the a-C memristor with top inert electrode [57]. This is because the generated CF inside the a-C film that governs its RS behavior is only made of sp² carbon bond. As bipolar switching is more controllable than unipolar switching [57], undoped a-C-based memristor with inert top electrode has received less attention than that with active electrode. One typical architecture was Pt/a-C/W memristor [60], as shown in Figure 7(a). Such memristive characteristic, arising from the formation and rupture of conductive graphitic filaments, exhibited several merits such as high ON/OFF resistance ratio, high switching speed, low operation voltage, low power consumption, and good reliability. Similar results were also observed on the same Pt/a-C/W memristor configuration by different groups, leading to good scaling-down properties (Figure 7(b)) [58]. To further improve the memristor performances, it was possible to sputter the a-C target with argon and ammonia (NH₃) gas [62], resulting in Pt/C(NH₃)/TiN memristor (Figure 7(c)). Compared to conventional fabrication technology, such memristor induced ten times larger ON/OFF resistance ratio and much smaller leakage current during “forming” process. These advantageous features were ascribed to the replacement of some C-H bonds by C-NH₂ bonds in C(NH₃) film. Therefore, the proportion of insulated sp³ carbon in Pt/C(NH₃)/TiN memristor was larger than that in Pt/a-C/TiN, giving rise to lower current at high-resistance level and larger memory window.

Figure 7

(a) Cross-sectional HRSEM image of an a-C memristor with W/a-C/Pt structure (left) and its HRS/LRS variation during endurance test (middle) and retention test (right), (b) cross-sectional HRSEM image of W/diamond-like carbon/Pt memristor (left) and its corresponding quasi-static I–V curves under different carbon thicknesses and CCs (right), (c) comparison of 100 cycles current between sputtering a-C with and without NH₃. (a), (b), and (c) were reprinted with permission from [58,60,62], respectively.

Table 2 summarizes the physical performances of various undoped a-C-based memristors.

Table 2

Performance comparison among different un-doped a-C memristors

Structure	V set/V reset (V)	Endurance (cycles)	Retention (s)	Power density (W/μm2)	R On/R Off	Switching time (ns)	Ref.
Au/SLG/ta-C/Pt	—	>104	—	1.4 × 10−5	105	4–50	[55]
Cu/a-C/Pt	1.5/−0.4	>1,000	>104	3 × 10−5	102	—	[56]
Pt/DLC/W	0.7/2.3	—	—	—	∼8,000	—	[58]
Cu/a-C/Pt	—	—	—	—	100	—	[59]
W/DLC/Pt	—	>103	>6 × 103	—	>300	<50	[60]
Ag/TiOxNy/a-C/Pt	0.33/	>3 × 104	>104	—	30	—	[61]
Pt/C(NH3)/TiN	1/−1.4	>107	>104	—	1,000	—	[62]
Cu/a-C/Pt	0.1/−0.15	>104@300℃	108	10−7	100	—	[63]
Cu/a-C/GMs/Ni	0.13–0.3/−0.13	>103	>104@85℃	—	100	—	[64]
Ag/a-C/CNT	5.4–7.5/−(5.4–7.5)	31	>106	0.48	40–200	—	[57]

4.2 Doped a-C-based memristor

Doped a-C-based memristor can be classified into metal-doped a-C memristor [69,70,71,72,73], hydrogenated a-C (i.e., a-C:H) memristor [74,75,76,77], oxygenated a-C (i.e., a-C:O or a-CO _x ) memristor [78,79,80,81,82,83], and nitrogen-doped a-C (i.e., a-C:N) memristor [84,85,86]. The common metal dopants are Cobalt (Co) and Cu, and the doped a-C films can be prepared by either radio frequency reactive magnetron sputtering or direct current magnetron sputtering techniques [87]. One prototype was based on aluminum (Al)/a-C:Co/Fluorine-doped tin oxide (FTO) architecture that led to an ON/OFF ratio of 25 and retention time >10⁵ s, as shown in Figure 8(a). Ohmic conduction and space charge limited current conduction were assumed to be responsible for threshold and sub-threshold regimes, respectively. The RS effect can be attributed to the formation/rupture of Co filaments in the film [69]. In contrast to inert electrodes, a-C:Co film combined with active electrodes also exhibited memristive characteristics, resulting in Au/a-C:Co/Au configuration [72], as illustrated in Figure 8(b). Such design enabled an ON/OFF ratio of >4, endurance of >200 cycles, and retention of >10⁵ s. In addition to Co dopant, Cu element was another common dopant that incorporated with a-C to secure CuC film. Accordingly, a Pt/CuC/Cu-based memristor was proposed, which exhibited bipolar switching behavior [70], as reflected in Figure 8(c). Differing from previous work, its RS mechanism was regarded as a tunneling between Cu filamentary channel and electrode through the solid electrolyte other than conduction through fully connected Cu filamentary channel. Table 3 summarizes the performance metrics of different metal-doped a-C memristors. As can be seen from Table 3, Co-doped a-C memristors have good time retention, so this material is able to maintain stable performance under different resistance states, which is suitable for long-term data storage. In addition, Co-doped a-C-based memristors usually have a fast switching speed, which is important for some high-performance applications. However, the preparation of Co-doped a-C-based amnesia may require complex processes that increase the manufacturing cost. Cu-doped a-C-based memristors typically exhibit a bistable resistance mechanism, allowing flexibility in non-volatile and volatile switching. However, their preparation, like Co-doping, requires more complex engineering treatments.

Figure 8

(a) Schematic of FTO/a-C:Co/Al memristor (left) and its HRS/LRS variation with respect to programming cycles (middle) and retention time (right), (b) typical I–V curve of Au/a-C:Co/Au memristor and its structural diagram, (c) measured I–V curve of Pt/CuC/Cu memristor (left) and its HRS/LRS distribution with respect to programming cycles (right). (d) Cross-sectional structure of a-C:H/Pt/Ti/SiO₂/Si memristor (left) and its HRS/LRS states along with retention time, (e) measured I–V curves of TiN/a-C:H/Pt memristor for the “pristine,” “SET” and “RESET” operations, (f) cross-sectional TEM image of the CN_0.15 thin film, (g) measured I–V curves for unimplanted and N₂-implanted ta-C films at a thickness of 15 nm, (h) “RESET” current as a function of pore size (left), and corresponding I–V curves for pore diameter of 60 nm (top right) and 120 nm (bottom right). (a), (b), (c), (d), (e), (f), (g), and (h) were reprinted with permissions from [69,70,72,75,77,84,85,86], respectively.

Table 3

Performance comparison among different metal-doped a-C memristors

Structure	V set/V reset (V)	Endurance (cycles)	Retention (s)	Power density (W/μm2)	R On/R Off	Switching time (ns)	Ref.
Cu-CuC/Pt	1.0/−1.1	>103	104@85℃	—	>102	—	[70]
Pt/CuC/Pt	1.31–2.29/−2.38 to −1.32	—	—	—	—	—	[71]
Au/a-C:Co/Au	−4/−1.2	>200	>105	—	∼4	—	[72]
Al/a-C:Co/FTO	—	—	>105	—	—	—	[69]
Pt/CuC/Pt	1.5/−1	—	—	—	102	—	[73]

RS phenomenon was also observed on various nanoscale devices using a-C:H films. One representative structure, proposed by Zhuge et al. [75], was Cu/a-C:H/Pt memristor where a-C:H film was deposited by the linear ion beam deposition technique using C₂H₂ as the precursor of hydrocarbon ions. Such RS behavior, as shown in Figure 8(d), resulted from the diffusion of the metal ions from active electrode, exhibiting ON/OFF ratio of >100 and retention time >10⁵ s. The device, devised by Chen et al. [76], was analogous to Zhuge et al. [75], while replacing Cu electrode with inert Pt electrode. An intriguing finding was that in spite of the inert electrode, this device presented the bipolar switching characteristic. It was speculated that the negative bias can push hydrogen atoms away from the Pt electrode, which were absorbed by double bonds of sp² carbon. Such hydrogenation process transformed the sp² CF into insulated sp³ CF, inducing “RESET.” Another design also adopted Cu/a-C:H/TiN configuration, while the polarity of the programming pulses was chosen such that the Cu did not diffuse into carbon, as reflected in Figure 8(e). A high ON/OFF resistance ratio (>1,000), high switching speed (<30 ns), and non-destructive readout were observed [77].

In addition to a-C:H films, a-C:N films have also received considerable attention. A nanoporous nitrogen-doped a-C was deposited and a Pt/a-C:N/Cu architecture was subsequently fabricated [84], as illustrated in Figure 8(f). Switching voltage was reduced along with decreasing the nitrogen amount, and endurance of >1,000 cycles and retention of >80 days were attained. Unipolar switching trait was also found on a ta-C:N/Pt/Ti/SiO₂/Si structure when using doped diamond conductive tip as the top electrode [86], as illustrated in Figure 8(g). Unimplanted a-C films exhibited switching voltages between 7 and 10 V for ta-C films of thickness 15–40 nm, whereas nitrogen implanted films reduced the switching voltage by 60%. This was ascribed to the nitrogen implantation that benefited the size and number of sp² clusters. The memristor performances can be further improved on a Cu/nanoporous a-C:N/Pt configuration [85], resulting in Figure 8(h). Nanopore structure can facilitate Cu atoms to easily migrate into the films along the nanopores, leading to preformed CFs inside the film. Resulting preformed CFs can enhance the local electric field around CFs and mitigate the switching uniformity. In spite of this, the size and microgeometry of the preformed CFs were strongly affected by N₂ partial pressure, thus impacting the switching fluctuation. Table 4 summarizes the various results on both a-C:H and a-C:N films.

Table 4

Performance comparison among different a-C:H and a-C:N memristors

Structure	V set/V reset (V)	Endurance (cycles)	Retention (s)	Power density (W/μm2)	R On/R Off	Switching time (ns)	Ref.
Metal/a-C:Pt	−1.2 to −0.8/0.6–2.2	>110	105	—	103	—	[75]
Pt/a-C:H/TiN	1.5/–	>107	104@85℃	9.4 × 10−4∼0.42	100	—	[76]
TiN/a-C:H/Cu	—	—	>5.76 × 104	—	2,500	<30	[77]
CrN/a-C:H/Au	—	—	—	—	>100	—	[74]
Cu/DPCC/Pt	0.25/−1	>105	>105@85°C	7.96 × 10−7	102	<50	[85]
Cu/a-C:N/Pt	0.6/−0.5	1,000	>106	7.64 × 10−6	102	—	[84]
Conductive probe/a-C:N/Pt	—	—	—	—	—	5	[86]

As a-CO _x can be prepared by a simple physical vapor deposition (PVD) technique at room temperature [87], a-CO _x -based memristor has recently been under intensive research. One representative work was to produce a-CO _x by PVD of a graphitic carbon target in oxygen [78], and the physical properties of a-CO _x can be well tailored by controlling the oxygen content. Accordingly, the deposited a-COx film was sandwiched between Pt top electrode and W bottom electrode to form metal-insulator-metal structure, as shown in Figure 9(a). Such design allowed for a switching speed of 10 ns, an endurance of >10⁴, and retention time of >10⁴ s at 85°C. The “SET” operation was still dominated by conductive filaments mainly consisting of highly reduced a-CO _x , while the “RESET” operation was governed by partial dissolution of the CF with the help of the release of oxygen ions trapped in bottom electrode. Instead of inert electrode, an electrochemical metallization cell with Pt/a-CO _x /Ag structure was fabricated. Such design provided both non-volatile and volatile switching characteristics [79], as illustrated in Figure 9(b). Non-volatile switching was readily ascribed to the formation and rupture of Ag ion filaments inside a-CO _x film, whereas volatile switching was pertinent to the passivation of oxygen vacancies by thermally activated migration of oxygen ions. One promising strategy to improve a-CO _x -based memristor was to stack an additional Cu layer on the original Pt/a-CO _x /W frame [83], as shown in Figure 9(c). This interfacial layer gave rise to more Cu-O bonds and thus increased the sp² bond CFs. The advent of these Cu–O bonds can therefore suppress the random formation and rupture of sp² bond CFs, which can benefit the device reliability. Jin et al. [82] studied the bi-stable resistance mechanism of Pt/a-CO _x /W memristor. The bi-stable resistance was likely to result from the O²⁻ distribution near the bottom W electrode, as demonstrated in Figure 9(d). Accordingly, the proportion of conductive C–C sp² covalent bond played a critical role in determining forming voltage and endurance. Performance comparison among different a-CO _x memristors are detailed in Table 5.

Figure 9

(a) HAADF-STEM image of an a-COx memristor (top) and its HRS/LRS states along with cycles under different oxygen pressure (bottom), (b) graphic interpretation of the non-volatile switching mechanism (top), the second forming process (middle), and the threshold switching mechanism (bottom) of Pt/a-CO _x /Ag memristor, (c) schematic of W/Cu/a-CO _x /Pt memristor, (d) typical I–V curves of a-COx memristor during forming, SET and RESET operations (left), and its cross-sectional TEM image (right). (a), (b), (c), and (d) are reprinted with permissions from [78,79,80,82], respectively.

Table 5

Performance comparison among different a-C:H and a-C:N memristors

Structure	V set/V reset (V)	Endurance (cycles)	Retention (s)	Power density (W/μm2)	R On/R Off	Switching time (ns)	Ref.
Ag/a-COx/Pt	1/−1.65	>103	>105	—	5	<1.5 × 104	[79]
Pt/ta-C/a-Cox/Ag	0.2–0.7/−0.9	—	—	3.18 × 10−12	—	<50 × 106	[80]
Pt/a-COx/W	3.2/−2.5	—	—	—	—	—	[81]
Pt/a-COx/Cu/W	0.4/−0.6	>103	HRS:5 × 104 LRS:4 × 104	5 × 10−4	<102	30 (set) 20 (reset)	[83]
Pt/a-COx/SiO2/W	−1.10/1.6	>106	8.6 years	3.1 × 10−8	∼103	85 (set) 75 (reset)	[82]
Pt/a-COx/SiO2/W	0.6/1.0	>104	>104@85°C	0.024	>102	10	[78]

5 a-C -based memristors for neuromorphic applications

It is well known that the most charming feature of memristor stems from its suitability for neuromorphic computing [88,89,90,91,92]. Neuromorphic computing is aiming to design both hardware and software computing elements that can operate in a manner similar to human brain. Today software computing elements require considerable computing source, usually accompanied with ultra-high energy consumption and relatively low computing efficiency. Hardware realization of neuromorphic computing is mainly based on complementary-metal-oxide-semiconductor transistors. Nevertheless, the integration density of the transistor-based device is approaching the limits of Moore’s law [93], which can be hardly enhanced. Besides, the transistor-based devices still adopt the well-known von Neumann computational mode that data storage and processing functions are executed by memory and central processing unit, respectively. This mode is obviously against the biological mechanism of human brain where computation and storage are simultaneously processed in the same location. Under this circumstance, memristor that enables ultra-low power consumption, super-fast processing speed, and integration of data processing and computation presents the closest similarity to the key component of human brain, i.e., biological synapse, as demonstrated in Figure 10. For the above reasons, the feasibility of using a-C-based memristor to mimic the biological response of human synapse has recently been under intensive research.

Figure 10

Illustration of the strategy of building memristor-based neural networks to imitate the biological neural networks.

One promising design was to combine an additional aluminum oxide (AlO _x ) layer with a-CO _x memristor to form Cu/AlO _x /a-CO _x /TiN _x O _y /TiN configuration [94], as illustrated in Figure 11(a). The introduction of thin AlO _x layer can effectively control Cu migration, and enabled stable switching of >2,000 DC cycles, endurance of >1.5 × 10⁹ cycles, and switching speed of 100 ns. The device conductance experienced gradual increase when subjected to consecutive positive voltage, while continuously decreasing when undergoing consecutive negative voltage. Accordingly, a variety of conductance states, indicating the weight of the artificial synapse, can be obtained by varying the number of the applied pulses, demonstrating its long-term potentiation (LTP) and long-term depression (LTD) functionalities. Meanwhile, Murdoch et al. [95] proposed a novel design based on amorphous zinc tin oxide (ZTO)/a-CO _x /ta-C/Pt architecture. Such a transparent conducting ZTO electrode allowed the proposed device to effectively respond to both optical and electrical stimulations, thus triggering its optoelectronic function. As illustrated in Figure 11(b), paired-pulse facilitation (PPF), defined as an increased output current from two consecutive input stimuli, was induced on the proposed device using light pulses. The conductivity decay time, also called “forgetting” time, was also measured with respect to pulse intervals. The detected mapping presented an analogous trend to Ebbinghaus forgetting curves, accounting for the probability of short-term memory recall along with time [96]. Differing from previous work based on a-C films, a novel a-C memristor with carbon CFs based on carbon quantum dots (CQDs) was recently proposed [97], as illustrated in Figure 11(c). The designed memristor, i.e., palladium (Pa)/CQDs/gallium oxide (Ga₂O₃)/Pt, exhibited smaller programming power, longer retention, and better performance uniformity than the counterpart without CQDs. The fitting I–V curves indicated that the conduction behavior at HRS was governed by trap-assisted tunneling mechanism, whereas it was switched to ohmic contact at LRS due to the formation of carbon CFs. The proposed device can not only mimic the well-known LTP and LTD behaviors but also reproduce the important spike-timing-dependent plasticity (STDP) of the biological synapse such that the synaptic connection strength is determined by the relative timing of a particular neuron’s output and input action potentials. Additionally, such devices also exhibited its ability for associative learning. To reproduce the associative learning behavior (i.e., Pavlovian conditioning), the “bell” and the “food” in the top and middle rows of Figure 11(d), respectively, were defined as a neutral signal and an unconditioned stimulus, respectively, while “salivation” in the bottom row corresponded to the resulting reaction. When paired “bell” and “food” signals were applied to CMD, the initial resistance of CMD remained as HRS. Under such circumstance, only “food” signal led to unconditioned response, whereas only “bell” signal induced no reaction. The device was switched to LRS when both ”bell” and “food” pulses were imposed on CMD simultaneously. During this process, these two signals were associated, indicating that only the “bell” signal allowed for the conditioned response. Most excitingly, hand written digit recognition was achieved via a single-layer perceptron model comprised of the designed memristor, resulting in a recognition accuracy of 92.63%.

Figure 11

(a) HAADF image of the Cu/AlO _x /a-CO _x /TiN _X O _y /TiN structure (left) and its LTP and LTD characteristics (right), (b) imitations of PPF (top) and STDP (bottom) mechanisms using the proposed light-gated a-C memristor, (c) schematic of CQD memristor device, and (d) experimental results of associative learning and forget relation (top) and designed neural network for hand-written digit recognition (bottom), realized by the CQD memristor device. (a) and (b) are reprinted with permissions from [94,95], respectively, while (c) and (d) are reprinted with permissions from [97].

6 Technological challenges and future prospect

In principle, the memristive characteristic of a-C-based device strongly depends on its resistance switching between LRS and HRS, whereby a-C-based device falls into the category of ReRAMs. Accordingly, the performance metrics of a-C-based memristor are partly analogous to ReRAMs, as demonstrated in Table 6. When compared to its compatriots, the most attractive feature of a-C-based memristor perhaps arises from its excellent retention even at 250°C [98], thus rendering it practicable for automotive and harsh conditions [98]. Besides, a-C-based devices can be readily disposed and recycled, while independent of rare mineral extraction with low total energy production [99].

In spite of the above merits, it should be noted that a-C-based memristors are also facing some stringent challenges. In comparison with classic TMOs-based memristors, a-C-based memristor technologies are still at their youth stage. In contrast, TMOs-based technologies have been subjected to intensive research for more than 60 years, for which TMOs-based memristors have been consistently advanced since the debut of TiO₂-based memristor in 2008 [100,101]. To date, the energy consumption, switching speed, endurance, and retention time of TMOs-based memristor have been incredibly improved, which obviously outpaces the state-of-the-art a-C-based technologies. According to Table 6, ON/OFF resistance ratio seems to lag far behind that of TMOs-based memristor. As presented above, this can be attractively mitigated by introducing an additional SLG layer between top electrode and a-C layer, which can reportedly circumvent the leakage currents owing to the low SLG density of states near the Dirac point [55]. This advanced technology brought ON/OFF resistance ratio to 4 × 10⁵ at 0.2 V. Endurance is another critical property over which TMOs-based memristor prevails a-C-based memristor. It can be however improved by using a-CO _x film sandwiched by W top electrode and Pt bottom electrode [102]. This remarkably boomed the endurance to ∼ 4 × 10⁴ cycles. Additionally, using a-CO _x allowed for “SET” and “RESET” speed of 40 and 4 ns, corresponding to programming energy of 2 and 1 pJ, respectively [102].

In terms of practical applications, it should be kept in mind that the systematic circuits in fact comprise a myriad of cells with inconsistent area and thickness, originating from current immature fabrication technologies. This caused the so-called device-to-device variation [117,118]. Moreover, temporal stochasticity induced by the randomness in CF formations unwantedly gives rise to the cycle-to-cycle variations [119,120]. Other reasons to cause cycle-to-cycle variation may include the shape of the conductive filament, the oxygen vacancy distribution at and around the filament, and the changing location of the active filament between one cycle to the next. It was astonishing that both device-to-device and cycle-to-cycle variations of a-C-based memristors were rarely investigated at the time of writing. One viable scenario was to artificially form some more conductive dots or clusters inside a-C films [62], which can facilitate the growth of CFs along these pre-defined locations and thus overcome the randomness. Besides, depositing 2D materials such as graphene and MXene, on top of a-C films is likely to improve the cycle-to-cycle variations due to the fact that the CF can preferably grow along honeycombs of the 2D materials [121,122]. For potential applications of a-C-based memristors, multiple resistance states between HRS and LRS can be obtained by sophisticatedly tuning the size of the formed CFs. As a result, a-C-based memristor is capable of providing multilevel function, which can not only enhance the storage density but also provide synaptic and neuron-like mimics. This implied that a-C-based memristor can operate at the non-von-Neumann mode in which processing and storage are executed simultaneously [123,124]. In spite of its promising prospect for non-von-Neumann applications, a-C-based memristor was mainly devoted to the achievement of artificial synapse, while other attractive non-von-Neumann applications such as logic implementation and matrix computing are yet to be studied in detail. These two areas are very likely to become the future hotspots of a-C-based memristors.

7 Conclusion

As one of the most important allotropes of carbon materials, a-C families exhibit distinct optoelectronic properties according to different dopants and proportion of bonding hybridization. Thanks to this, a-C families have been considered as one of the most promising memristive materials beyond Moore’s law. However, a comprehensive review regarding the physical principles of different a-C-based memristors and their potential applications in the era of “non-von-Neumann” still remains vague. To address the above concerns, we here reviewed different types of a-C families whose memristive principles, architectures, modeling methods, as well as merits and weakness, were elucidated in detail. Their promising applications for non-von-Neuman computing and storage, in association with some technical challenges were eventually discussed.