Nano Resistive Memory (Re-RAM) Devices and their Applications

Abstract Use of solid state ionic conductors the so-called Solid Electrolytes has brought new impetus to the field of solid state memories namely resistive random access memory (Re-RAM). In this review article, to begin we present the detailed understanding on the basics of solid electrolytes. Later, the same has been reviewed focusing on its application in novel solid state memory applications. Few examples of solid electrolytes are considered and their impact on the state-of-art research in this domain is discussed in detail. An in-depth analysis on the fundamentals of Resistive switching mechanism involved in various classes of Memristive devices viz., Electrochemical Metallization Memories (ECM) and Valence change Memories (VCM). A few important applications of Memristors such as Neuristor and artificial synapse in neuromorphic computing are reviewed as well. Finally, the most anticipated energy efficient battery-like cells as artificial synapse in brain-inspired computing is also covered.


Introduction
The key parameters that determine the performance of the memory element is reproducibility, endurance, density, cost, read time, write time, Read/Write Energy. Although loads of memory technologies are present in the market but they have almost reached their lithographic limit and they cannot be scaled beyond certain limit, moreover they are power hunger and occupy more die area [1][2][3][4]. The silicon based memories have dominated the market but they suffer from shortcomings such as high power consumption, poor endurance and Read/Write access speed. For instance, the emerging non-volatile memory technologies that are explored recently are Magneto resistive Random access memories (MRAM) and Phase change random access memory (PCRAM) [5][6][7]. In MRAM resistive switching is caused by magnetic field while in PCRAM the joule heating plays a crucial role which thermodynamically transits the phase of the switching material such as GeSbTe(GST) from high resistance amorphous state to low resistance crystalline state and vice versa [5][6][7][8]. The only issues pertaining with the above class of memory technologies is that they cannot be scaled below certain nanometer i.e. the density attained with MRAM and PCRAM is almost equivalent to the existing flash today. Although many nonvolatile memory technologies are explored, most importantly NVM's based on the change in resistance state of the Metal-Insulator-Metal (MIM) under the influence of an external electric field proposed by Hickmott et al. [9]. This class of memory is generally placed under the umbrella of Resistive Switching Random access Memories commonly termed as ReRAM. The term 'M' stands for metal which can be any good electron conductor and it serves as top and bottom electrode. Both the top and bottom electrode can be made up of similar metal layers or asymmetric metallic layers. I is an active layer having electron insulating characteristics yet it is the modest ion conducting material for instance, metal Oxides, selenides, tellurides, nitrides, iodides etc. Leon chua in the year 1971 coined the name "Memristor" which is the fourth missing electronic passive circuit element linking between charge (q) and magnetic flux [10][11][12]. The research in this area fade away with the advent of silicon integrated circuit technology and its rapid development [13]. About 37 Years later HP lab came out with the memristor device in the year 2008 [14,15]. It is a Metal-Insulator-Metal (Pt/MOx/Pt) [MO = Metal oxide] stacked structure that exhibits functional features as memory element constituted by ionic charge transport in solid state by controlled flux variations. The intrinsic bulk resistivity is altered due to the movement of the ions under the effect of an external electric field. Upon removal of the electric field the ion motion ceases and the migrated ions occupies the defect sites where it is migrated and this is supposed as memory tuned exclusively by the resistivity changes the so called non-volatile memory. The fingerprint of memristor is a hysteresis loop pinched at origin elucidates the word write and erase in a cyclic manner. This lies under the umbrella of ReRAM [12].
This fundamental passive element has been regarded recently as an element of surprise for electronic computation of different levels. The typical computing application for such class of device is resistive switching random access memories (ReRAM). The dynamic non linearity in current voltage characteristics encouraged researchers around the globe to develop alternate memory architecture. The existing digital computer is extremely capable to emulate the brain functionality of the biological creatures such as spider, mouse, and cat. The configurations of brain of biological creatures are completely unlike to the existing Von Neumann architecture [16]. The biological systems are more efficient because of complex connection between the neurons that aid in parallel processing. The synaptic weight between the post and pre neuron can be adjusted by controlling the ionic flow through them and it is widely accepted that adaptation of synaptic weight enables the biological system to learn. If the conductance of memristor is considered as synaptic weight it functions similarly to the nonlinear transmission characteristics of synapse mimicking the brain functionalities for developing artificial intelligence (AI) [16,17]. Recently memristor is being used to fabricate neuristor which is considered to be the electrical equivalent of the biological neuron [18].
The only impediment that has restricted the memristor from being commercialized is the lack of extrapolative and robust understanding of the underlying switching mechanism [13]. During the last decade memristor have been fabricated utilizing a wide variety of materials and intuitive characterization techniques are used to investigate the switching mechanism involved in memristor. In this paper first basics of solid electrolytes is presented and its application in novel memory applications is studied in detail in the subsequent section. An in-depth analysis on fundamentals of Resistive switching mechanism involved in ReRAM devices is done with aid of advanced characterization and their impact on state of art of research in this domain is discussed in detail. A few important applications of Memristors such as Neuristor and artificial synapse in neuromorphic computing are reviewed as well. For the first time an attempt is made to compare the working of the artificial synapse and neuristor to the biological synapse and neuron respectively. Finally, the energy efficient battery-like cells as artificial synapse in braininspired computing are also covered.

Why fast ion conductors?
In general ionic conductors are broadly categorized into two categories namely normal ion conductors and fast ion conductors. The family of materials that exhibit high electronic conduction and low ionic conductivity named normal ion conductors. Fast ion conductor exhibits high ionic conductivity and low electronic conduction. The application of external bias causes migration of randomly oriented ions in bulk material in the direction of electric flux thereby initiating ionic conduction. The ionic conduction in solids is closely related to its atomic structure as the presence of defects and imperfections aid in enhancing it. The ionic conductivity in normal ion conductors is temperature dependent as at an elevated temperature defects are generated thermally [19]. The process of activation involves two steps namely energy required for the formation of defects (h f ) and energy due to migration of ion (hm).The total ionic conductivity in normal ion conductor is given by (1) Where σ 0 = e 2 ϑ0fλ 2 Nx kT e = Charge of mobile ions ϑ 0 = Jump Frequency N = charge carrier density x = Fraction of Mobile charge carriers T = absolute temperature k = Boltzmann's Constant h f = Energy of defect formation hm = Energy of defect Migration Schotky and Frenkel defects are predominantly found in this class of ionic conductors, where ionic conductivity is in the order of 10 −14 to 10 −12 scm −1 . While in fast ion conductors the population of carrier ion concentration is very high at room temperature as well as at higher temperature and even the enthalpy of formation (h f ) is zero. The total ionic conductivity in it is given by (2) Furthermore, fast ion conductors can be classified on the basis of presence of mobile charge carriers that take part in charge transport viz. anionic and cationic conductors. The mobile charge carriers in anionic conductors are mainly oxide and fluoride ions, whereas cationic conductors are predominantly Ag + , Cu + , Li + , Na + etc [19]. The proper understanding of kinetics of ionic conductors is extremely critical to identify suitable materials to develop efficient ReRAM. For instance, the use of fast ion conductors will not only enhance the Write/Read access time, but also lowers the overall power consumption. We will discuss about this in detail in subsequent sections. The basic 3D stack structure of memristor is shown in Figure 1. The memristor is basically a MIM cross layer structure in which a metal oxide or metal oxides layers is sandwiched between top and bottom perfect ion blocking electrode (Pt, Au, Pd etc.) [13,14]. To achieve memristive effect a typical amount of ion vacancy is intentionally created within the host sub-lattice of metal oxide. The resulting stack structure upon creation of vacancy is Pt/MOx−y/MOx/Pt, which comprises of low resistant, defect abundant (MOx−y) layer, in series with high resistant defect free metal oxide. To achieve memristive effect a typical amount of ion deficiency is created within the host sub-lattice of metal oxide. For instance a rutile phase of titanium oxide (TiO 2 ) is partially created with oxygen deficiencies making it to be TiO 2−y . Indirectly a large number of defects and void sites are created within the sub-lattice metal oxides so that oxygen ions can hop freely from one position to another. The resulting structure after creation of vacancy is Pt/MOx−y/MOx/Pt, which comprises of a nonstoichiometric layer of metal oxide (low resistance state The potential applied to write into or erase the content of the memory cell. A ReRAM which exhibits bipolar switching, typically a positive/negative bias is required to write in to the memory cell (Write '1') and negative /positive potential is necessary to erase the content of the cell (Write '0').Its amplitude lie in the order of few hundred mV to Volts. *Read Voltage: The potential required to fetch the content of the memory cell. In memristor basically the read voltage is much lower than the write voltage as it should not cause any significant change in the internal resistance state of the ReRAM. In general the polarity of the read and SET voltage is same.
MOx−y) in series with a high resistance defect free metal oxide.
When a moderate potential is applied to the top metal electrode, an enormous E-Field is developed as thickness of the stack is in nano regime. This bias potential provides energy to break M-O bond in the buffer layer resulting in the hopping of oxygen ions from the buffer layer (MOx) to the non-stoichiometric (MOx−y). As a result of this vacancies are spread over a larger area of the metal oxide thus reducing the overall resistance of the device. This movement of oxygen vacancies results in a conduction modulation that makes device to transfer from high Resistance State (HRS) to low resistance State (LRS) causing the device to SET. Similarly, upon reversal of polarity of applied bias, it alters from low resistance State (LRS) to high resistance State (HRS) causing it to RESET. Thus, the movement of oxygen ions under the influence of external electric field help transform the transition of metal oxide from insulator to conduction phase and vice versa. The defect concentration (n d ) of the order of 10 21 cm −3 makes the metal oxide to behave like a fast ion conductor [19][20][21][22][23][24][25][26][27]. Thus, it is construed that each of such carrier ions (q i ) possesses the memory content [18].

General switching mechanism of ReRAM
Prior to getting into the switching mechanism associated with resistive switching it is important to understand the performance metrics which are need to be achieved by the proposed ReRAM technology to replace the existing NAND flash and SRAM which are widely employed for memory storage applications. Table 1 describes the various memory parameters with their corresponding required desired result and the best reported results till date.

Electrochemical Metallization Memories (ECM)
The switching in ReRAM is mainly determined by the factors like electrical, ionic and thermal. It is basically of two kinds namely unipolar and bipolar. If the polarity of the SET and RESET voltage is identical then it is said to be unipolar switching otherwise bipolar switching. The process of transit of device from high resistance state to low resistance state is termed as SET and RESET when vice versa. The bipolar switching in ReRAM is mainly due to the movement of randomly oriented ions in the direction of electrical flux and electrochemical redox reactions at the electrode and switching material interface [2]. Although, there are ample reports on switching mechanism of memristor, but till date none of the mechanisms are elucidated, rather they are suggested on the basis of theoretical understanding or with aid of advanced physical and electrical characterization techniques [28]. Among all suggested mechanism for resistive switching filamentary conduction is widely accepted by researchers around the globe. In order to explain filamentary conduction here we consider three examples one from anion and two from cation conducting ReRAM. The general memristive structure using Ag as an active electrode can be in any of the following structures such as Ag This causes the Ag + ions to hop across the ionic conductor towards the cathode and get reduced, which is an ion blocking electrode viz. Pt, Au and W. Beside due to the effect of external field an electrocrystallization process takes place that causes the development of metal nanofilaments towards the active electrode (Ag). The top electrode being electrochemically active, an unceasing oxidation take place on it and silver metal cations dissolves into the switching layer supporting in the process of growth of metal filaments. When the metal nanofilaments join the top and bottom electrode, the ReRAM turns ON, i.e. the device is in LRS. The device retains its resistance state until the polarity of the applied E-field is not inverted. The inversion of polarity of applied bias causes electrochemical annihilation of metal nanofilaments causing the transit of resistance state of the device from LRS to HRS. These kind of devices are sometimes called as ECM memories.
As illustrated in Figure 2 at point "1" of the hysteresis loop indicates the beginning of process of SET, there is the initiation of the process of growth of metal nanofilaments towards the top electrode. At point "2" a complete filament is formed joining the top and bottom electrode indicating that the device is in LRS. Upon reversal of applied bias at point "3" initiation of rupture of filament occurs and finally at "4" metal nanofilaments are completely obliterated.
Contrasting to above study Yang et al. studied the geometry of filaments in Ag/SiO 2 /Pt stack structure, where they reported the observation of thinnest region of the filaments near the inert electrode/dielectric interface. As thinnest zone of the filament plays a critical role in controlling the dissolution and reformation of filament, thus it directly impacts the process of write/erase in the memory cell. Same kind of mechanism is also elucidated by Ag/Al 2 O 3 /Pt and Ag/a-Si/Pt structure [29,30]. The typical shape of the filaments observed with aid of HRTEM is shown in Figure 3.
Xu et al. observed the direct formation and rupture of conducting pathway in superionic (Ag 2 S) Ag/Ag 2 S/W memory cell in inside HRTEM (High-Resolution-Transmission electron Microscope) comprising of STM unit inside it. Reproducible switching characteristics were observed in this class of device as shown Figure 4. By using in tandem spatially resolved energy-dispersive X-ray spectroscopy (EDS) and HRTEM lattice imaging the crystal structure of the device during the HRS and LRS is studied. In the off state the switching layer Ag 2 S is in acanthite phase which is basically HRS, upon the effect of an external electric field its phase transits to high conducting argentite Ag 2 S phase. Hence, the conduction pathway grown out of the original surface of the electrolyte, comprises of mixture of Ag and the argentite phase [31].
In 2007 Liang et al. for the first time observed resistive switching in thin film RbAg 4 I 5 which is reported to be a room temperature super ion conductor [32]. It exhibited reversible switching characteristics in Ag/RbAg 4 I 5 /Pt ReRAM structure and further Valov et al. confirmed phenomenon of filamentary conduction, by demonstrating the electrochemical Ag phase formation on the surface of the RbAg 4 I 5 [33].
Let us consider a basic Cu/MO/Pt structure, where {MO = metal oxide} switching layer. The lack of Cu ions in the host lattice of switching layer restricts it from exhibiting repeatable switching characteristics. The application of external bias causes the Cu ions to migrate through the amorphous metal oxide layer, there by incorporating themselves into matrix of switching layer. This causes an irreversible nano morphological change in the ion conducting switching layer by forming low conducting incomplete filaments [34,35]. This process is termed as electroforming which is extremely essential to enable the device to exhibit reproducible switching characteristics. Celano and Hubbard et al. investigated the restive switching in Cu/Al 2 O 3 /TiN based ReRAM, using atomic force microscopy based tomography which assists in spotting 3D conducting filaments. They observed the direction of growth of conducting filament from the active (Cu) to the inert (TiN) electrode which is completely contradictory to the previous studies. Under the effect of external bias copper atoms gets ionized and migrate into switching layer causing an enhancement of oxygen vacancies within the Al 2 O 3 sublattice. These vacant sites assist in migration of Cu ions through the oxygen sites of Al-O bonding in the amorphous matrix. Owing to the low mobility of cation (Cu + ) in switching layer, they travel short distance and get reduced by capturing electrons that are unceasingly introduced into the Al 2 O 3 layer due to the presence of external E-field. As a result Cu + ions reduced to Cu and turn out to be an extension of top Cu electrode, and this process continues until it forms a contact with the bottom inert electrode. These assumptions explain the cause for growth of conducting filament from non -blocking (Cu) electrode to blocking electrode. In order to visualize the shape of the conducting filament at various resistance state of the ReRAM Conductive-Atomic force microscopy based tomography is used. The Figure 5 shows the image of conducting filament joining top and bottom electrode i.e. in LRS. The conducting diamond tip is utilized as a scalpel for controlled removal of material layers as shown in Figure 5.
The 2D image of the conducting filaments is recorded at each stage and joined together to produce 3D image (tomogram) of the conducting filament [34].The same technique is employed to observe the shape of filaments when the device is in LRS and HRS. The complexity in understanding the switching mechanism of the device surges up when the device fabricated with same material exhibit dissimilar switching characteristics during the RESET operation as shown in Figure 6 [36]. For the same structure during RESET there is an abrupt and progressive decline in the level of current at V reset (−0.5V) is observed, where both broken and non-broken filaments were spotted while carrying out C-AFM tomography. The abrupt decline in the level of current at V reset is made fit to a direct conduction model explaining the rupture of conducting filament which is further confirmed by 3D tomogram confirming the presence of broken filament with a gap of 0.4nm whereas for the case of progressive decline in the current at V reset , it follows a quantum point contact. The filament is not completely broken while low conducting filaments observed throughout the switching layer. Undeniably 3D tomogram exhibit the shape of the conducting filament but the material composition of the filament is still under debate. Hence, future scope lies with development of advanced characterization technique to determine the material composition of the conducting filaments.

Valence change Memories (VCM)
In order to explain resistive switching in anion conducting ReRAM, the resistive switching in Pt/ TiO 2 /Pt based Note, the average space between each slice is~0.5 nm. (d) The data set for the 3D interpolation is constituted by collection of 2D slices, and the CF is observed near the center of the active electrode upon removal of top electrode. The top-left and bottom right region exhibited highly conductive features corresponding to exposed region of the TiN BE, which is gradually exposed during the process of Al  memristor is considered. On application of external bias at anode positively charged oxygen vacancies migrate towards the cathode-oxide interface with an improved mobility due to the presence of vacancies and grain boundaries. These Ti 4 O +2 5 ion hop towards the host lattice and react with oxygen ions forming high conducting Ti 2 O 3 nanofilaments (HCNF).The process of formation of conducting filaments involves two steps viz. nucleation and growth, nucleation site is determined by the localization of E-field owing to thinning of switching layer or localization of current due to presence of defects in abundance. With the end of process of nucleation, filament growth occurs by ion migration and reduction on the surface of the conducting filament. The above process ends when conducting filament forms a galvanic contact with the top electrode. Subsequently, on reversal of the applied bias vacancies retraces back to the anode-oxide interface, resulting in thinning of conducting filament and finally initiation of depleted gap from the anode [27]. Furthermore Chen et al. reported the thermal effects on the filamentary conduction in Pt/ZnO/Pt ReRAM structure with aid of in situ TEM observations. The shapes of the filament at various stages of switching were observed. Finally with the help of electron energy loss spectroscopy (EELS) they observed, it is the zinc conducting filament joining the top and bottom electrode. The switching is predominantly due to the migration of oxygen ions under the effect of an external E-Field causing toggling between low resistance ZnO 1−X and high resistance ZnO. The Figure 7 depicts the shapes of the conducting filament, during various resistance states of the ReRAM [37]. Undeniably high speed Read/Write access, low power consumption is achievable in ECM memory cells, yet their compatibility with existing CMOS technology is questionable. As the write voltage is in the order of mV and is not enough to bias the existing CMOS transistors which are mainly employed as peripherals. In anion conducting ReRAM a reservoir of ions is highly essential just be-neath the positive electrode, while in cationic conductors the role of reservoir is played by the active electrode [38]. For example the MIBM (Metal-Insulator-Base-Metal) structure Pt/Ta 2 O 5−x /TaO 2−x /Pt, here the switching takes place by formation and dissolution of filaments in the insulating Ta 2 O 5−x layer. The filament comprises of positively charged oxygen vacancies (TaOx conducting sub oxide phase) which is conducting in nature. As the base layer (TaO 2−x ) layer serves as a reservoir (abundance of TaOx), under the application of negative bias the TaOx ions move towards the top Pt electrode resulting in forming a filament across theTa 2 O 5−x layer and dissolution takes place under the effect of an external positive bias. Thus the presence of vacancies ensures an improved endurance performance and enhanced stability in switching.
As discussed above filamentary conduction is dominant in ECM and VCM memories, an attempt is made here supporting the view of Goux et al., to summarize the mechanism of growth of filaments by considering the cumulative effect of electrodes and nature of ion conducting insulating layer [39].
a When the redox process is homogenous and ion mobility is high, the dissolved ions can reach the counter inert electrode causing the growth of conically shaped filament within a tip pointing to the active electrode from the bottom inert electrode. This phenomenon is widely observed in ECM cells. b When redox reaction rate is low and ion mobility is high, this leads to growth of branched filaments towards the active electrode from the counter electrode. Nucleation occurs near the counter electrode and reduction mainly at edges. c When both ion mobility and redox reaction rate is high, in this case ions gather within the solid electrolyte and when it attains the critical nucleation state, and bipolar electrode effect filament can proceed by cluster displacement from the active electrode towards the inert counter electrode. d The ion mobility is low but the electrode reaction rates are high. Nucleation can now occur inside the dielectric while large amounts of atoms can be deposited onto the cathode sides of the nuclei, leading to gap filling. After a connection between the nuclei and the active electrode is achieved, the process is repeated leading to an effective forward growth towards the inert electrode.

Carrier Transport in ReRAM
The phenomenon of ionic transport is identical in both anion and cation conducting ReRAM. Microscopic resistive switching in this class of device can be explained through solution of partial differential equations. The migration of oxygen ions and subsequent ordering of vacancies in the oxide layer under the effect of an external field is the cause for resistive switching, where presence of V O (va-cancies) assists in formation of low resistive channels for ionic transport. The migration of defects is defined by a flux and it consist of two components namely drift and diffusion. The process of migration of defects involves a series of jumps amid neighboring sites, considering a hopping distance 'a' and uniform energy barrier (Ea). The energy barrier is lowered by a factor of qaE due to the effect of external field (E) which accounts for enhancing the hopping rate and directional movement of ions which is extremely essential to achieve bipolar switching. The defect transport equation is given by (4)  ) where a, f and Ea are hopping distance, escape-attempt frequency, activation energy for ion migration respectively. As size of device is in nano regime even a small applied bias may produce extremely high electric field and current density within device there by concluding the significant role of joule heating in the process of resistive switching. In addition to that the expression for ionic diffusivity (D) suggests that it is temperature dependent process following Arrhenius law. The Soret diffusion coefficient (S) is given by S = −Ea kT 2 and velocity of migration of defects is given by .sinh( qaE kT ). The current continuity equation for electronic conduction (5) is coupled with (4), given as To solve the above (5) the electrical conductivity (σ) of the oxide layer and the conducting filament is required and φ is the electrostatic potential related to the E-field (E) by the ∇φ = −E. The conducting filament in case of ECM is assumed to be metallic, while in anion conducting device conducting filament is presumed to comprise of suboxide (oxygen deficient metal oxide with enhanced defects (n d )) [40,41]. The ion migration within the switching layer is thermally driven due to the dependency of electrical, thermal conductance on density of defects and it follows Arrhenius equation given by (6) In another study Larentis et al. observed rise in conductivity (σ 0 ), with increment of defects (n d ) thereby lowering the overall resistance of the device causing a transit of resistance state from HRS to LRS. In this state the activation energy (Ea) is reported to be almost zero as conducting filament is joining top and bottom electrode. With decrease in defects (n d ) a semiconductor like conduction observed corresponding to conduction in low conducting broken filaments [42,43]. In addition to (5), a steady state Fourier equation for joule heating is required to solve (4) i.e. (7) −∇.k th ∇T = σ |∇φ(r, z)| 2 (7) where RHS denotes the local dissipated power density computed by the product of electric field by current density and LHS corresponds to the space variation of heat flow because of heat conduction. The thermal conductivity k th is high for higher value of n d , while low for lower value of n d inferring to availability of free carriers thermal conduction [41][42][43][44].

Brief history of resistive switching
In 1960, Bruyere et al. for the first time observed bipolar resistive switching in NiO [45]. Although the conceptual thought was put forth by Leon Chua in 1971 [12], but practical device was developed by HP labs in the year 2008 by sandwiching a Titanium dioxide layer between top and bottom platinum electrode [14]. The serendipitous find of memristor by HP labs have invigorated researchers around the globe to investigate the possibility of resistive switching in other metal oxides [46]. However, prior to HP labs claim, the materials like

Effect of Doping on Resistive switching
The metal oxides like HfO 2 , ZrO 2 , Yb 2 O 3 and tantalum oxide have been doped with metallic impurities like Gd, Al, La, Ti and Si in order to expedite the migration of oxygen vacancies under the effect of an E-field by altering the atomic structure to create preferential transport channels for vacancies thus allowing in tuning the resistive switching performance at atomic level by lowering the hopping distance and velocity of migration of oxygen vacancies [65][66][67][68]. Furthermore, Kim et al.   [69,70]. Though a single layer exhibits resistive switching behavior, in order to enhance the speed of Write/Read access multilayer oxide are placed which acts as reservoir of oxygen vacancies. However, complexity linked with process of fabrication increases as the number of oxide layer increases [71][72][73][74]

Electrochemical Impedance Spectroscopy in ReRAM
The properties of grain and grain boundaries play a pivotal role in determining the ionic conductivity of polycrystalline materials. Grain boundary is the region in a polycrystalline material isolating identical phase crystals. This region is abundant of defects, consequently facilitates ionic conduction. AC impedance spectroscopy is widely used in order to study the electrical property of polycrystalline material at its bulk and grain boundaries [79]. EIS can be used to study the intrinsic switching mechanism of memristor and to calculate ionic conductivity. When a pristine device is stimulated with an AC signal of magnitude 10mV scan rate varying from 1mHz to 1MHz, effects the existing ionic state and initiates the motion of oxygen vacancies. This makes the device capable to exhibit reproducible switching characteristics by causing a permanent nano morphological change from where it cannot recover. Alternatively, EIS can be used for electroforming the virgin device, in addition to that EIS can be used determine various resistance states of device like LRS,HRS, and the intrinsic switching mechanism can be studied by observing the variation of grain boundary resistance and bulk resistance with varying external electric field. To begin with Lee et al. for the first time studied EIS on Pt/TiO 2 /Pt Memristor and studied the electrical conduction at HRS [80].
Qingjiang et al. performed EIS to explain the filamentary conduction in Pt/TiO 2+x /TiO 2 /Pt ReRAM structure by perturbing the device with an AC signal of magnitude 10mV, scan rate varying from 10KHz to 10 MHz, at DC biasing point of 0 V. Impedance spectrum active cell is taken at HRS and LRS. During the process of toggling between HRS and LRS a conducting filament is formed and broken as shown in Figure 9(a) [81]. Mehonic et al. performed EIS in silicon rich silica based memristor to find the nature of conducting paths. In OFF state a single arc is observed which, conveyed that HRS is mainly controlled by the bulk properties of SiOx switching layer, while in On state two different arcs are observed corresponding to destruction and formation of conducting pathways respectively [82]. Koza et al. reported repeatable unipolar resistive switching in Au/Mn 3 O 4 /AuPd based ReRAM and explained the SET and RESET operation with aid of electrochemical impedance spectroscopy [83]. The equivalent circuit used to define LRS contains an inductance (I wire is the inductance due to connecting wire) in series with resistance (R lament corresponds to the resistance of filament joining top and bottom electrode) of 14.8 Ω. Upon transit of resistance state of the device from LRS to HRS a parallel combination of R and CPE (constant phase element usually used to model non perfect capacitances) and value R increased from 14.8Ω to 30MΩ. The shape of the obtained impedance spectrum is identical to the impedance spectra of virgin device as shown in Figure 9(b). Greenlee et al. studied the analog resistive switching in LiNbO 2 based memristor and found that switching is due to the electric field induced migration and distribution of Li ions. Further they performed PDEIS in order to observe instances of meminductive and memcapacitance effect at certain frequency [84,85].

Neuristor -An Electrical Equivalent of neuron
Neuromorphic engineering, also known as neuromorphic computing started as a concept developed by Carver Mead in the late 1980s, describing the use of very-large-scale integration (VLSI) systems containing electronic analogue circuits to mimic neurobiological architectures present in the nervous system especially the brain [86]. The mammalian brain is basically a neural network comprising of neurons and synapses which are considered as unit cell to develop hardware based artificial neural networks (ANN) to emulate brain-like computing. The presence of complex neural networks in brain comprising of 10 11 neurons communicating with 10 15 synapses makes it capable of performing tasks like recognition of objects, abstract reasoning, and linguistic comprehension makes the human brain to outperform existing digital computers. The neuron models which are employed in ANNs are leaky integrate-andfre (LIF) neuron, Hodgkin-Huxley neuron, and Izhikevich neuron models. There are reports on the hardware implementation of Hodgkin-Huxley neuron using memristor, while leaky integrate-and-fire (LIF) neuron using memristor is successfully simulated [87][88][89][90][91]. The Hodgkin-Huxley proposed a model that defines how action potential is generated in biological axons, which is critical to analyze the computational ability of nervous system. Signal transduction in neurons is facilitated by sodium and potassium ion channels, which dynamically allow or obstruct the flow of polarizing currents, through which the cell membrane is charged or discharged. When the cell body is sufficiently polarized because of its dendritic inputs, a remarkable change in conductance of the system occurs with the application of voltage spike /ac- tion potential. The Neuristor which is an electronic equivalent of biological neuron proposed by Hewitt Crane in the year 1960, which generate a spike upon sufficient excitation [92]. The proposed prototype is equivalent to the size of shoe box as it is made up of large inductors. The original intent was to develop logic gates using it. Chua et al. proposed the revised memristive Hodgkin -Huxley model by modeling the sodium and potassium ion channels using memristor [93]. In the year 2013 Pickett and Williams came out with the prototype using NbO 2 Mott memristor, shown in Figure 10 [18,94].
For proper understanding of working of neuristor an analogy between neuristor and biological neuron is discussed. Neurons are the basic building block of the central nervous system (CNS) that process information in the form of electrical signals (action potential) which are responsible for inter neuron communication. A typical biological neuron is shown in Figure 11.
It consists of two regions namely extracellular and intracellular, demarcated by lipid membrane. The cell body causes discrete distribution of Na + , K + , Cl − and Ca 2+ ions in the extracellular and intracellular region. The extracellular region comprises of Na + and Cl − ions while intracellular region predominantly contains Ca 2+ and K + ions [95,96]. This uneven distribution is established by Na + -K + AT-Pase. The uneven distribution of ions results an electromotive force that is defined as Nernst potential across the membrane or concentration gradient. When the cell is at rest (in the absence of external bias) the membrane potential is around −70mV (close to equilibrium potential of K + ions) and this is commonly defined as Resting Membrane potential [95][96][97]. For the existence of potential difference across a lipid membrane, two conditions must be met (i) unequal distribution of ions across the lipid membrane.
(ii) Presence of ion channels which is permeable to above mentioned ionic species.
At rest as more number of K + channels are open than Na + channels, therefore membrane permeability to K + ions is high. Hence, resting membrane potential is nearly equal to the equilibrium potential of K + . Pickett Neuristor comprises of two Mott memristor (M 1 , M 2 ), three capacitors (C 1 , C 2 , C out ) and three resistors. Each memristor is fed with an external positive/Negative DC bias and in combination with shunt capacitor, acts as switchable dynamic conduction channel which can provide power to the core from the power lines [18]. This setup is identical to the potassium and sodium ions channel of Hodgkin-Huxley model and R L2 is the common load resistance which helps in stabilizing the circuit when it is inactive. It consists of an input resistance (R L1 ) and while output consists of parallel RC stage which is mainly responsible for coupling signal between Neuristors. The nerve cell membrane comprises of ion channels namely ligand and voltage gated and mostly Na + and K + channels are liable for the process of generation of axon potential.
Under the effect of a depolarizing stimulus, voltage gated Na + channel opens and the membrane potential during this phase shoots up to the equilibrium potential of Na + (60mV) but does not reach as rise in conductance due Na + ions is transient i.e. Na + ions are fast to open and fast to close. This process is known as depolarization. In the absence of bias voltage the input and output node are fixed at ±V dc . Upon excitation at the input, capacitor (C 1 ) charges further and if the excitation is above a sharp threshold voltage memristor turns ON, resulting in transferring the device from HRS to LRS. This phenomenon relates to the process of opening of Hodgkin-Huxley ion channel. The coupling resistance R L2 must be chosen in such way that the depolarization caused by the capacitor (C 1 ) is sufficient enough to charge capacitor (C 2 ). During the process of charging of capacitor (C 2 ), the memristor (M 1 ) correlating to the closing of sodium ion channel. Upon completion next, the process of repolarization is initiated by opening of voltage-gated K + channels, which are slow to open and close in comparison with Na + channels. This causes net movement of positive charge out of the cell due to K + e ux at this time helps complete the process of repolarization. As these channels are slow to close, further there will outflow of K + ions resulting in decrease of cell membrane potential and this phenomenon is known as hyperpolarization followed by a coming back to resting membrane potential. When capacitor (C 2 ) is fully charged this will transfer the resistance state of the memristor (M 2 ) from HRS to LRS correlating to the opening of K + ion channels, which hyperpolarizes the core towards +V dc. Finally, spike is produced over the output stage. The biomimetic properties of the Neuristor such as all or nothing spiking, refractory period, threshold is verified by providing both sub-threshold (0.2 V 10µs) and super threshold voltage (0.3 V 10µs). The Figure 12 illustrates the biomimetic properties such as threshold and signal gain. The sub-threshold pulse is attenuated while a signal gain is observed in case of super-threshold pulse and is compatible with traditional CMOS technologies. The intrinsic switching mechanism involved in Mott Memristor is yet to be addressed. Although metal to insulator transition is reported previously, still a group of new materials need to be predicted where metal to insulator transfer occurs at temperature around~200 ∘ C. This recent utilization of memristor based neuristor paved the way for transistor-free logic in thin film circuits and as these are compatible with existing CMOS technology, hence neuristor can be integrated with CMOS circuits to develop hybrid silicon-nanodevice architectures [18].
Recently, Pickett et al. have designed logic circuits using neuristor by adapting Wilamowski's scheme for neuristor logic [98][99][100]. Since neuristors are dynamic threshold spiking devices, the logic design is based on the existence, interpreted as logical '1', or absence, logical '0', of a spike at the input of a gate within a specific time window [96]. The four important properties of neuristor like threshold, pulse shaping during transmission, constant velocity of pulse transmission make it ideal candidate for its application in transmission lines [18]. The above sur-vey suggests that all the blocks of the neural system can be implemented utilizing all passive elements thus it pave a roadmap for world without power hunger CMOS transistors. It does not claim to completely replace the existing CMOS technology; rather it would complement the existing technology.

Artificial Synapse
Memristor have been widely used for data storage and logical applications. The intrinsic non-linear ionic switching in this class of device has prompted researchers around the globe to utilize memristor to emulate various synaptic learning functions by correlating synaptic weight to the conductivity of memristor as shown in Figure 13 [16,101,102]. The synaptic learning rule Spike timing dependent plasticity (STDP) have been successfully validated using memristor. In biological synapse, synaptic plasticity is attained through non-overlapping spikes and controlled by the activity of synapse [103]. The synaptic weight is determined by receptor level which is modulated by post synaptic Ca 2+ ion concentration that acts as secondary state variable beside spikes. The incessant variation in the level Ca 2+ concentration offers an internal timing mechanism to encode the activity information on the spikes. As the value of the Ca 2+ concentration throughout the spike is determined by the cumulative effect from the current spike and remainder value from the previous activity [103]. This model have been predominantly employed in order to illustrate synaptic plasticity properties viz. LTP (long -term plasticity), STDP (Spike timing dependent plasticity) [103]. The Synaptic weight can be modulated by continuous spiking from post, pre synaptic neuron and by utilizing the nonvolatile nature the memory device, the synaptic weight can be stored for a longer duration of time. This feature aid memristor to emulate the memory and learning capability of biological synapse. In order to enable learning in synapse, it is stimulated with pre and post synaptic spikes by following a specific order known as temporal order. An increase in conductance of memristor is observed when it is stimulated by a pre synaptic spike followed by a post synaptic spike termed as long-term potentiation, while fall in conductance observed upon reversal of the temporal order called as long-term depression. Large change in conductivity of the device is seen when it is stimulated with input spikes frequently, thus change in synaptic weight. An efficient synaptic learning can be achieved maintaining proper pulse width or amplitude such that overlapping of the spikes leads to proper programming pulse to encode the information on relative timing of spikes from pre-and postsynaptic neurons and to attain desirable conductance change [104].
Kim et al. noticed that above synaptic structures could not emulate synapse in a bio-realistic manner [104]. They considered memristor as dynamic device controlled by internal processes rather than mere programmable memory devices. In second order memristor there are two state variables which would control the total conductance of the memristor. A typical memristor is modeled using one state variable 'w' (size of the switching layer) which directly modulated by the external stimuli (8) The second order memristor is comprised of an additional state variable 'T', where two variables (w, T) jointly regulate the total conductance of memristor. By adapting second order memristor it is feasible to implement complex biorealistic dynamic effects. The second order memristor can be mathematically stated as (9) dw The role of Ca 2+ like internal dynamics is believed to be played by the second order variable 'T' by providing an internal timing mechanism and assists in activitydependent modulation of the conductance state variable 'w'. As mentioned in the previous section, filamentary conduction is dominant in most of the metal oxide based memristor. The resistive switching in this class of memristor is presumed to be due to migration of oxygen vacancies under the effect of an external bias. A low resistive channels or conducting filament is formed in the region comprising of more number of oxygen vacancies. The memristor conductance is determined by size of the filament which corresponds to the first order state variable (w). The drift and diffusion of oxygen vacancies under the effect of an external field and local temperature of the device causes formation of conducting filament. Under the effect of an external bias local temperature (T) of the device increases because of joule heating which play a vital role in the process of formation and annihilation of conducting filaments. Temperature (T) rises when the device is stimulated with voltage spikes and falls impulsively on the abstraction of stimulation. If the voltage pulse is applied prior to the completion of activity of the previous pulses then state variable 'w' may be affected by 'T' as T has not reached to steady-state value for previous pulses. Hence, relative timing between stimuli plays a pivotal role in determining the extent to which input voltage will get affected. Thus, T is not weight state variable but it plays a significant role in regulating synaptic weight [104]. There are basically two kinds of plasticity namely short term and long term plasticity (STP, LTP) on the basis memory retention characteristics; which corresponds to short term and long term memory behavior described in psychology. STP causes temporary potentiation while LTP causes permanent potentiation of neuronal connections. Repeated rehearsals are essential for converting STP to LTP which results in causing a physical change in the structure of neuron. This phenomenon is achieved in InGaZnO memristor reported by Wang et al. [105]. Previously Chang et al. in Pd/WOx/W based memristor reported the process of transfer of memories of importance from short term to long term memory. The existence of few oxygen vacancies results in rupture of conductive channels which causes the device to transit from LRS to HRS. This process is considered as loss of retention for LRS, [105][106][107] which bears striking resemblance to the memory loss in  biological synapse, where this effect can be modeled by a stretched exponential function which is also known as Kohlrausch law. Mathematically, this can be stated as (10) Where, φ(t) = relaxation function, τ = characteristic relaxation time which is used to compute the forgetting rate, I 0 is the prefactor, and β is the stretch index ranging between 0 and 1. When t < τ the rate of decay will be high while oth-erwise slower rate of decay [106]. Further Wang et al. proposed a mathematical model in order to define the process of relaxation of STP stated as (11).
M(t), Mo are the measure of memory level at time t and t=0, while Me corresponds to memory level at steady state after long time. The above expression can be used to deduce forgetting rate. With increase in the number stimulations, the relaxation time (τ) increased from several seconds to tens of seconds, thereby lowering the forgetting rate which is analogous to human memory tendency i.e. a fast initial decay followed by an extended, slow decay. This phenomenon closely correlates to the STM to LTM transition in biological synapse [105][106][107]. As described in previous section filamentary conduction is predominantly responsible for switching in ReRAM, STP corresponds to the state prior to the formation of complete filament connecting the top and bottom electrode. The decay in conductance corresponds to the deformation of incomplete conducting filament. LTP corresponds to the LRS when a complete conducting filament is formed and persists for a longer time period.
When memristor is stimulated with large number of spikes to perform STM to LTM transition, on removal of bias a fall in synaptic weight is observed but interestingly its original conductance is attained with fewer number of external spike stimulation. This closely correlates to the learning function of biological synapse. The above mentioned phenomenon is clearly observed in Memristor. The biological process like pulse-paired facilitation (PPF) and post-tetanic potentiation (PTP) are positively tested by stimulating a chain of pulses and it is observed that with an increased rate of stimulation of pulse, there is an enhancement in retention time of memristor.

Electrochemical nonvolatile memories
Recently Moradpour et al. observed spectacular bipolar resistive switching in Au/LixCoO 2 /(p ++ )silicon (Si) nanobattery [108]. When a negative bias voltage applied to bottom Si electrode, Li+ ions migrates towards the (p++) silicon electrode where they are reduced to form LixSi complex thus generating an electromotive force (EMF). The SiO 2 interface layer grown thermally prior to the deposition of LixCoO 2 solid electrolyte layer serves as a solid electrolyte, which facilitates Li + ion diffusion and prevents the possibility of electrical short circuits between the top and bottom electrode. With the decrease of x from 0.95 to 0.75 in LixCoO 2 layer, there is a transition from high resistance insulating phase to a low resistance metal conducting phase and vice versa upon the reversal of polarity of the applied bias. The bipolar switching behavior is definitely not due to local filamentary conduction as in ECM and VCM, while it involves a bulk "homogeneous" process as conductivity is widely studied as battery cathode material. Further Mai et al. successfully realized synaptic learning rule STDP in the LixCoO 2 based nanobattery structure making it a promising candidate for the field of neuromorphic computing [109]. Borrowing the principle of working of battery van de Burgt et al. fabricated a three terminal organic switch on a flexible polyethylene terephthalate (PET) substrate [110,111]. The proposed device is extremely power efficient and it can be employed as an artificial synapse in neuromorphic computing.
Three terminal organic device is named as electrochemical neuromorphic organic device (ENODe). The working of ENODe is similar to a concentration battery. The device is fabricated on the PET substrate by sandwiching a proton conducting nafion layer between poly (3,4-ethylenedioxythiophene):polystyrene sulfonate (PEDOT:PSS) and PEDOT:PSS film partially reduced with polyethylenimine (PEI) which serves as presynaptic and postsynaptic electrode respectively. When the presynaptic electrode is applied with an presynaptic potential (Vpre), cations to flow from the presynaptic electrode to the post synaptic electrode causing protonation of the PEI, while electrons flow through the external circuit. This results in removal of holes from the PEDOT backbone in the postsynaptic electrode, thereby lowering its electronic conductivity while maintaining electroneutrality in the electrode. A reverse reaction is observed upon reversal of polarity of Vpre. The neutral form of the PEDOT:PSS/PEI electrode is stabilized by PEI, confirming the oxidation state of the postsynaptic electrode is maintained. In order to monitor the conductance states of the postsynaptic electrode a postsynaptic potential V post is applied. This conductance (PEDOT:PSS/PEI channel) signifies the synaptic weight of the connection among two neurons, which is the required characteristics of an artificial synapse. The charge in the electrode is manipulated while performing Write operation. While performing 'read' operation the cell is disconnected thereby not altering the electronic charge of the electrodes by virtue of an ion conducting/electron blocking electrolyte. This enhances the retention capability of ENODe devices as during read operation the charge associated with the electrodes is unaltered [110,111]. As the open circuit potential between presynaptic and postsynaptic electrode is low it allows extremely lower switching voltage and moreover they are nonvolatile. More studies are required to be performed in order to fabricate high density crossbar memory array utilizing ENODe devices.

Summary and outlook
Memristive devices are fabricated by employing a wide variety of solid electrolytic (fast ion conductors) materials over a decade or so owing to the renewed efforts imposed by the researchers and engineers around the globe, which threw much light into the state-of-art of non-volatile memory technologies. Recently different switching mechanisms have been suggested by various research groups for the same memory stack fabricated with identical materials. The lack of understanding of underlying switching mechanism has impeded its commercialization. Therefore, it is imperative that conductance behavior of such materials must be well understood so as to correlate the underlying switching mechanism when fabricated as memristive device. To expedite the process of memory access and lowering the power consumption, new materials need to be identified in order to have switching at very low voltage. As far as the bio-computation is concerned, these memory devices are widely being adopted to mimic the characteristics of biological synapse to further develop into neuristor. Extremely low switching energy and long retention time demonstrated by electrochemical neuromorphic organic device thanks to its organic nature which helps consider a significant step towards developing brain-inspired computing hardware. Further research in integration of ENODe devices in the form of massive crossbar arrays need to be investigated and steps needed to be taken in order to enhance device scalability. Moreover, it is required that circuit designers must go hand in hand to developing accurate SPICE models and search for new applications employing this device.