**2. Plasticity and learning of the synapse**

of certain animals with comparable speed and complexity, the energy consumptions increase exponentially as the animal hierarchy becomes higher with a very huge volume. Conversely, the biological brain is a compact dense system which can offer parallel processing, self-learning, and adaptivity with a combination of storage and computation in very low power consumption [3]. In these decades, the implementation of Von Neumann architecture computers to mimic biological systems has been in the form of software but such simulations are not comparable to biological systems in terms of efficiency and speed due to the physical limitation of those digital computers. Even the artificial neural networks based on CMOS-integrated circuits are far inadequate for constructing bionic systems. The truly reason for this drawback is the need to transfer data between a memory(storing data) and a processor(computing based on the data). This requirement of data transfer generates an intrinsic delay and inefficiency, which is a bottleneck for all CMOS-based neural networks [4]. In the past decades, the semi-conductive technology has led to great progress under the aid of the rapid development of the electronic industry, which has promoted the steps forward to develop artificial neural networks. In 2011, the supercomputer Watson, with 2880 computing cores [5], won the human-machine contest which proved that supercomputers have their advantages in some aspects [6]. But the important point that has been ignored in this comparison is the energy consumption and the physical volume of the computers. Watson has thousands of cores and requires about 80 kW of power and 20 tons of air-conditioned cooling capacity [7], while

4 Advances in Memristor Neural Networks – Modeling and Applications

the human brain occupies space like a soda bottle and consumes power of 10 W.

which will lead to effective, high-performance neuromorphic computing hardware.

elaborate more on these oxide-based memristors (TiOx

cover the literature on neuromorphic circuits.

In this chapter, we will discuss synaptic devices and summarize the recent progress in neuromorphic hardware, which is based on memristors. In particular, we will focus on a few typical devices based on metal oxides and their key properties served as synapses. We will start with a brief description of memory and the learning of synapses in Section 2. In Section 3, we will

emphasis on resistive switching (RS) characteristics, which is followed by neuromorphic computing applications and the underlying physical mechanism. We limit this review to metal oxide-based memristive devices for the emulation of synaptic functionalities and will not

, WOx

, HfOx, TaOx, NiOx, etc.) with an

Therefore, an alternative approach to building a brain-like or neuromorphic computational system with distributed computing and localized storage in networks becomes an attractive option [1, 8–11]. The brain-like computational system can outperform conventional computers with good performance in handing the real-time processing of unstructured sensory data, such as image, video or voice recognition, navigation, etc. [12–17]. Also, the brain-like computational system has the advantages of architecture and function compared to conventional computers, offering massive parallelism, small area, scalability, power efficiency, the combination of memory and computation, self-learning and adaptivity [3]. Many researches have helped us understand how neurons and synapses function and revealed how essential synapses are to biological computations, especially in memorizing and learning [18–21]. However, building compact neuromorphic computing systems remains as a challenge, especially for the lack of electronic elements which could mimic the biological synapses. In recent decades, the research of neuromorphic systems is renewed by the understanding of biological neural networks and the emergence of new nanodevices. Particularly, the emergence of the fourth electronic element, memristor [22–28], makes it feasible to construct bionic hardware In the nervous system, neurons and synapses are the basic units for transit information to the whole biological body. In the human brain, it consists of ~1011 neurons and an extremely large number of synapses, ~10<sup>15</sup>, which act as a highly complex interconnection network among the neurons [29]. Neurons consist of three main parts: a soma, dendrites, and an axon. Neurons generate action potentials (spikes), with amplitudes of approximately 100 mV and durations in the range of 0.1–1 ms in their soma. The spikes propagate through the axon and are transmitted to the next neuron through the synapses. A synapse [30] is a 20–40 nm junction between the axon and the dendrites (shown in **Figure 1**) that permits a neuron (or nerve cell) to pass an electrical or chemical signal to another neuron or to the target efferent cell. Each neuron connects with other neurons through 10<sup>3</sup> –10<sup>4</sup> synapses to form a complex network. The information transmission between neurons with the synapses is very complicated which

**Figure 1.** A schematic illustration of synapse.

is excited by the surroundings. At the synapse, the plasma membrane of the signal-passing neuron (the presynaptic neuron) comes into close apposition with the membrane of the target (postsynaptic) cell. Both the presynaptic and postsynaptic sites contain extensive arrays of molecular machinery that links the two membranes together and carries out the signaling process. The presynaptic neuron will open the voltage-gated calcium channels as the action potentials arrive, and then the diffusion of Ca2+ ions will make the synaptic vesicle release neurotransmitters to the synaptic junction. Released neurotransmitters bind with their receptor sites of the Na+ gated ion channels at postsynaptic neurons, which lead them to open and allow Na+ ions to diffuse inside the cell. When the aggregated membrane potential reaches a certain threshold, the neuron generates a spiking. The activation either potentiates or inhibits the postsynaptic neuron. The action potentials propagation, the neurotransmitters release and diffusion, and the neurons spiking activity constitute the ways whereby neurons communicate and transmit information to one another and to nonneuronal tissues [31].

∆*wi* = ∑

W(x) <sup>=</sup> {

and *A*<sup>−</sup>

very critical for biological neuron computation.

**3. Synaptic devices based on metal oxide memristors**

materials and devices that have memristive effects, such as NiO, WO<sup>3</sup>

, SrTiO3

/NiOx

of the recent work of oxide-based memristors including memristive properties.

, ZnSO3

[44–50] binary oxides, BiFeO3

/TiO2, and TaOx

*W(x)* is given as

The parameters *A*<sup>+</sup>

and *τ*<sup>−</sup>

and TiO2

and CuO/ZnO, HfO2

*f*=1 *N* ∑ *n*=1 *N W*(*t j <sup>n</sup>* − *t i f*

where *W(x)* denotes the STDP function, *i,j* are the notes of the pre- and postsynapses, and *t*

labels the firing times of the pre(post)synaptic neuron. An acceptable form of STDP function

*A*<sup>+</sup> exp(−*x*/*τ*+), x > 0 <sup>−</sup>*A*<sup>−</sup> exp(*x*/*τ*<sup>−</sup>

 are the time constants in the order of 10 *ms for* biological synapses [36]. Several recent reports have shown the STDP dependencies on rate, higher-order spiking motifs, and dendritic location [39]. This timing-centric view of plasticity is not meant to imply that spike rate is irrelevant. However, this timing-centric view of plasticity is not the only form responsible for synaptic learning in the biological brain. The learning rules may vary with different factors, such as the type, location of a synapse, firing rate, and spiking orders. Several other fundamental learning rules including rate-dependent synaptic plasticity, frequency-dependent synaptic plasticity, and cooperativity have also been studied extensively and believed to be

To imitate the learning and memorization of the biological system, new materials as well as architectures exhibiting memristive behavior fit the need well. Memristor, an abbreviation of memory and resistor, is the fourth fundamental passive circuit elements, the others being the resistor, the capacitor, and the inductor, which were proposed theoretically by Professor Leon Chua [22]. It is a kind of a nonlinear, two-terminal element that cannot be replicated with any combination of other fundamental electrical elements. Memristors behaves like a resistor with resistance depending on the history of the current passing through. In fact, it maintains a relationship between the time integrals of current and voltage across a two-terminal element, and the resistance remains in the value as it had earlier when the current stopped. In other words, the memristor has a memory of the current that was last turned on. In 2008, HP Labs realized memristors physically in nanoscale titanium dioxide cross-point resistive switches [24]. In this operation, the device exhibits pinched current-voltage(I-V) hysteresis indicating a resistive memory effect, and the conductive area is adjusted by the concentration of oxygen vacancies, which determine the whole conductive states (resistive switching state), that is, high resistance state (HRS) and low resistance state (LRS). This work invoked a renewable research of new

depend on the current value of the synaptic weight *wi*

) (1)

Synaptic Behavior in Metal Oxide-Based Memristors http://dx.doi.org/10.5772/intechopen.78408

), <sup>x</sup> <sup>&</sup>lt; <sup>0</sup> (2)

ZrO2

[55–57] heterostructures. **Table 1** gives a summary

, and LiNbO<sup>3</sup>

, ZnO, HfO2

[51–54] ternary oxides,

, TaO2,

*i f* (*t j n* ) 7

where *τ*<sup>+</sup>

In the biological brain, neurons and synapses are the two basic computational elements connected to each other. To perform different functions including visual, auditory, olfactory, gustatory and tactile means, as well as modulating and regulating a multitude of other physiological processes, the neuron system operates computation by integrating the inputs coming from other neurons and generating spikes across the synapses. In neuron computation, the synapses change their connection strength as a result of neuronal activity, which is known as synaptic plasticity. It is widely accepted that synaptic plasticity is the key mechanism of learning and memorizing for the biological brain [32]. In Hebbian's theory, both pre- and postsynaptic cells are activated coincidently, which results in modifications of synaptic strength between the two cells, thereby creating associative links between them [33]. In other words, the synapse plasticity is triggered by release of neurotransmitters of the presynaptic neurons and by diffusion of calcium ions into postsynaptic neurons, through excitatory amino-acid receptors and possibly voltage-gated calcium channels (VGCCs).

How the brain can achieve learning and memory is a critical question in neuroscience. In 1949 [34], Hebbian postulated a concept of spike-timing-dependent plasticity (STDP), firstly, as a synaptic learning rule which has been demonstrated in various neural circuits over a wide spectrum including insects, animals, and humans, even plants [35–37]. It has attracted considerable interest in neuroscience from experiment to computation [38–41]. According to the asymmetric window of STDP, the synaptic plasticity depends on the order of pre- and postsynaptic spiking within a window of tens of milliseconds. Over the past decades, much progress has been made in understanding the mechanism of STDP. In general, the synapse will be excited (increases in synaptic strength or weight) if repeated presynaptic spikes arrive a few milliseconds before postsynaptic spikes, whereas the synapse will be inhibited (decreases in synaptic strength or weight) if repeated spikes arrive after postsynaptic spikes. In [35], Bi and Poo have plotted a figure of the synaptic weight change as a function of relative timing of pre- and postsynaptic spikes which is called the STDP function or learning window and varies in synapse types. The change of synaptic weight ∆*wi* depends on the relative timing between presynaptic spike and postsynaptic spikes. A smaller spike timing difference results in a larger increase in synaptic weight. The total weight change ∆*wi* induced by an impulse with pairs of pre- and postsynaptic spikes is considered as a function [42, 43]:

Synaptic Behavior in Metal Oxide-Based Memristors http://dx.doi.org/10.5772/intechopen.78408 7

$$
\Delta \mathbf{z} v\_i = \sum\_{j=1}^{N} \sum\_{u=1}^{N} \mathbb{W} \left( t\_j^u - t\_i' \right) \tag{1}
$$

where *W(x)* denotes the STDP function, *i,j* are the notes of the pre- and postsynapses, and *t i f* (*t j n* ) labels the firing times of the pre(post)synaptic neuron. An acceptable form of STDP function *W(x)* is given as

 $\mathcal{W}(\mathbf{x})$  is given as 
$$\mathcal{W}(\mathbf{x}) = \begin{cases} A\_{+} \exp(-\mathbf{x}/\tau\_{\star}), & \mathbf{x} > \mathbf{0} \\ -A\_{-} \exp(\mathbf{x}/\tau\_{\star}), & \mathbf{x} < \mathbf{0} \end{cases} \tag{2}$$

The parameters *A*<sup>+</sup> and *A*<sup>−</sup> depend on the current value of the synaptic weight *wi* where *τ*<sup>+</sup> and *τ*<sup>−</sup> are the time constants in the order of 10 *ms for* biological synapses [36]. Several recent reports have shown the STDP dependencies on rate, higher-order spiking motifs, and dendritic location [39]. This timing-centric view of plasticity is not meant to imply that spike rate is irrelevant. However, this timing-centric view of plasticity is not the only form responsible for synaptic learning in the biological brain. The learning rules may vary with different factors, such as the type, location of a synapse, firing rate, and spiking orders. Several other fundamental learning rules including rate-dependent synaptic plasticity, frequency-dependent synaptic plasticity, and cooperativity have also been studied extensively and believed to be very critical for biological neuron computation.

#### **3. Synaptic devices based on metal oxide memristors**

is excited by the surroundings. At the synapse, the plasma membrane of the signal-passing neuron (the presynaptic neuron) comes into close apposition with the membrane of the target (postsynaptic) cell. Both the presynaptic and postsynaptic sites contain extensive arrays of molecular machinery that links the two membranes together and carries out the signaling process. The presynaptic neuron will open the voltage-gated calcium channels as the action potentials arrive, and then the diffusion of Ca2+ ions will make the synaptic vesicle release neurotransmitters to the synaptic junction. Released neurotransmitters bind with their recep-

gated ion channels at postsynaptic neurons, which lead them to open and

ions to diffuse inside the cell. When the aggregated membrane potential reaches a

certain threshold, the neuron generates a spiking. The activation either potentiates or inhibits the postsynaptic neuron. The action potentials propagation, the neurotransmitters release and diffusion, and the neurons spiking activity constitute the ways whereby neurons communi-

In the biological brain, neurons and synapses are the two basic computational elements connected to each other. To perform different functions including visual, auditory, olfactory, gustatory and tactile means, as well as modulating and regulating a multitude of other physiological processes, the neuron system operates computation by integrating the inputs coming from other neurons and generating spikes across the synapses. In neuron computation, the synapses change their connection strength as a result of neuronal activity, which is known as synaptic plasticity. It is widely accepted that synaptic plasticity is the key mechanism of learning and memorizing for the biological brain [32]. In Hebbian's theory, both pre- and postsynaptic cells are activated coincidently, which results in modifications of synaptic strength between the two cells, thereby creating associative links between them [33]. In other words, the synapse plasticity is triggered by release of neurotransmitters of the presynaptic neurons and by diffusion of calcium ions into postsynaptic neurons, through excitatory amino-acid

How the brain can achieve learning and memory is a critical question in neuroscience. In 1949 [34], Hebbian postulated a concept of spike-timing-dependent plasticity (STDP), firstly, as a synaptic learning rule which has been demonstrated in various neural circuits over a wide spectrum including insects, animals, and humans, even plants [35–37]. It has attracted considerable interest in neuroscience from experiment to computation [38–41]. According to the asymmetric window of STDP, the synaptic plasticity depends on the order of pre- and postsynaptic spiking within a window of tens of milliseconds. Over the past decades, much progress has been made in understanding the mechanism of STDP. In general, the synapse will be excited (increases in synaptic strength or weight) if repeated presynaptic spikes arrive a few milliseconds before postsynaptic spikes, whereas the synapse will be inhibited (decreases in synaptic strength or weight) if repeated spikes arrive after postsynaptic spikes. In [35], Bi and Poo have plotted a figure of the synaptic weight change as a function of relative timing of pre- and postsynaptic spikes which is called the STDP function or learning window and varies

presynaptic spike and postsynaptic spikes. A smaller spike timing difference results in a larger

depends on the relative timing between

induced by an impulse with pairs of

cate and transmit information to one another and to nonneuronal tissues [31].

6 Advances in Memristor Neural Networks – Modeling and Applications

receptors and possibly voltage-gated calcium channels (VGCCs).

in synapse types. The change of synaptic weight ∆*wi*

increase in synaptic weight. The total weight change ∆*wi*

pre- and postsynaptic spikes is considered as a function [42, 43]:

tor sites of the Na+

allow Na+

To imitate the learning and memorization of the biological system, new materials as well as architectures exhibiting memristive behavior fit the need well. Memristor, an abbreviation of memory and resistor, is the fourth fundamental passive circuit elements, the others being the resistor, the capacitor, and the inductor, which were proposed theoretically by Professor Leon Chua [22]. It is a kind of a nonlinear, two-terminal element that cannot be replicated with any combination of other fundamental electrical elements. Memristors behaves like a resistor with resistance depending on the history of the current passing through. In fact, it maintains a relationship between the time integrals of current and voltage across a two-terminal element, and the resistance remains in the value as it had earlier when the current stopped. In other words, the memristor has a memory of the current that was last turned on. In 2008, HP Labs realized memristors physically in nanoscale titanium dioxide cross-point resistive switches [24]. In this operation, the device exhibits pinched current-voltage(I-V) hysteresis indicating a resistive memory effect, and the conductive area is adjusted by the concentration of oxygen vacancies, which determine the whole conductive states (resistive switching state), that is, high resistance state (HRS) and low resistance state (LRS). This work invoked a renewable research of new materials and devices that have memristive effects, such as NiO, WO<sup>3</sup> ZrO2 , ZnO, HfO2 , TaO2, and TiO2 [44–50] binary oxides, BiFeO3 , SrTiO3 , ZnSO3 , and LiNbO<sup>3</sup> [51–54] ternary oxides, and CuO/ZnO, HfO2 /TiO2, and TaOx /NiOx [55–57] heterostructures. **Table 1** gives a summary of the recent work of oxide-based memristors including memristive properties.


broad spectrum of material systems [25–28, 60–62]. According to the switching mechanism, the memristors can be categorized into phase change, valence change, conductive bridge, electrochemical metallization, and ferroelectric devices. Due to the simple structure, biological plausibility, and excellent properties for memory, the scientific researchers explored the application of memristors from data storage to analogy neuromorphic computing for spatialtemporal pattern recognition, sequence learning, navigation, and direction selectivity. As for the human brain-like characteristics, memristor technology could one day lead computer systems to a new state that can remember and associate patterns in a way similar to how people do. Next, we will focus on several kinds metal oxide-based memristors with analog synaptic

The first physical instantiation of the memristor was generally acknowledged that was made

by Strukov et al. [24], but as early as in 1968, it was found that the TiO<sup>2</sup>

device shows memristive properties [63]. In literature [63], the work demonstrated that thin films exhibited resistive switching (RS) effects with pinched hysteretic current-voltage (I–V) curves during repeated tests. And also, there are several experimental researches on the RS

/Pt [65] devices. For memristors, the distinctive property is the pinched hysteretic loop indicating no energy dissipation. In [62], the prototype of memristor showed bipolar RS I–V curves with pinched points, which are a result of local stoichiometric change caused by the migration of oxygen vacancies. As oxygen vacancies act as donors in the TiO2

in the depletion zone, the conductance of the device could be modulated by the depletion or accumulation of Vos. Specifically, when the device undergoes a set process from a high resistance state to a low resistance state by the external electric field, the Vos will accumulate resulting in an increase of the conductive layer width. When applying electric pulse with reverse polarity, the Vos will be driven back thereby the conductive layer will become thin.

Later it was demonstrated in some studies that the accumulation of Vos in TiO<sup>2</sup>

O7

reported. In this work, it showed that oxygen vacancies were introduced by the aluminum electrodes, and if a noble metal (Au) electrode was used, the form and reversibility of switching will change. The mechanism of the memristive effect strongly depends on the synthesis method, the choice of metal electrodes, and their interfacial properties. Many suggested that an understanding has been put forward through a series of experimental analyses from the view of film composition, microcrystalline structure, and switching zones. It also should be noted that the RS effect of the devices will be affected by device architecture, electrode

As a prototype of the memristor, TiO2−based devices show their potential in neuromorphic computing. Seo et al. [69] used titanium oxide as the active material to perform synaptic behavior in

structure was fabricated by atomic layer deposition and the sol-gel method, respectively. In the device, the titanium oxide bilayer works as a progressive resistance-changing medium with Al and W as the top and bottom electrodes. The multilevel conductance states were achieved by

the context of analog memory, synaptic plasticity and STDP function. A bilayer of TiO<sup>x</sup>

thin-film

9

layer

may cause

and TiOy

/Ru [64] and sputter-deposited Pt/

Synaptic Behavior in Metal Oxide-Based Memristors http://dx.doi.org/10.5772/intechopen.78408

) that is metallic and directly studied by TEM

/Al memristor fabricated by solution processing was

behavior which are intensively studied for neuromorphic computing.


**-based memristors**

the formation of a new Magneli phase (Ti4

[66, 67]. In 2009 [68], a flexible Al/TiO<sup>2</sup>

materials, and layer stacks.

**3.1. TiO2**

from TiO2

effect of TiO<sup>2</sup>

TiO2

**- and WO3**

**Table 1.** Recent work on metal oxide-based memristors.

Nowadays, the memory is usually referred to as resistive random-access memory (RRAM) devices which can be traced as early as the 1960s [58]. In general, these devices are nanoscale in dimensions and offer excellent performance for data storage in terms of operation speed, nonvolatility, and read/write cycling [59]. Amounts of work have been performed to elucidate types of switching mechanisms that underlie resistive switching phenomena in a broad spectrum of material systems [25–28, 60–62]. According to the switching mechanism, the memristors can be categorized into phase change, valence change, conductive bridge, electrochemical metallization, and ferroelectric devices. Due to the simple structure, biological plausibility, and excellent properties for memory, the scientific researchers explored the application of memristors from data storage to analogy neuromorphic computing for spatialtemporal pattern recognition, sequence learning, navigation, and direction selectivity. As for the human brain-like characteristics, memristor technology could one day lead computer systems to a new state that can remember and associate patterns in a way similar to how people do. Next, we will focus on several kinds metal oxide-based memristors with analog synaptic behavior which are intensively studied for neuromorphic computing.

#### **3.1. TiO2 - and WO3 -based memristors**

Nowadays, the memory is usually referred to as resistive random-access memory (RRAM) devices which can be traced as early as the 1960s [58]. In general, these devices are nanoscale in dimensions and offer excellent performance for data storage in terms of operation speed, nonvolatility, and read/write cycling [59]. Amounts of work have been performed to elucidate types of switching mechanisms that underlie resistive switching phenomena in a

/Pt 50 2 × 10<sup>3</sup> s 650 [102]

**Material (architecture) Endurance (cycles) Retention On/off ratio Reference**

/Pt 8000 — 1.2 [50]

/Pt 1000 10 years 10<sup>6</sup> [49]

/ITO 320 2 × 10<sup>4</sup> s 10 [45]

/Pt 200 3 × 10<sup>4</sup> s ~50 [79]

/Pt 150 3 × 10<sup>4</sup> s ~10 [79]

/Pt 50 3 × 10<sup>4</sup> s ~100 [79]

Cu/WO3-x/ITO 1000 5 × 10<sup>4</sup> s 10<sup>5</sup> [80] Al/ZnO/Al 5 — 54.8 [47] Al/ZnO1-x/Al 5 — 4.8 [47]

Ti/ZnO/Pt 1000 — 100 [107]

/Pt 100 — 10<sup>4</sup> [109]

/Pt 10<sup>11</sup> 10 years ~100 [111]

/Pt 50 3 × 10<sup>3</sup> s 100 [100]

/HfO2-x/TiN 100 — 1000 [103]

/Pt 50 2 × 10<sup>3</sup> s ~100 [51]

s 2 [69]

s 65 [50]

s 10<sup>7</sup> [106]

s 10<sup>4</sup> [108]

s 162 [44]

s 30 [44]

s ~7 [110]

s 40 [110]

s ~15 [112]

s ~10<sup>3</sup> [105]

s 10 [56]

s 100 [104]

/Pt 83 10<sup>4</sup>

8 Advances in Memristor Neural Networks – Modeling and Applications

/Pt 120 10<sup>4</sup>

Ag/ZnO/Pt 100 10<sup>7</sup>

Al/ZnO/Pt 300 10<sup>5</sup>

/Pt 200 10<sup>4</sup>

/Pt 50 10<sup>4</sup>

/ITO 150 10<sup>3</sup>

/ZrO2-x/TiN 50 10<sup>4</sup>

/Pt 1000 10<sup>4</sup>

/Pt 100 10<sup>5</sup>

/Pt 1000 10<sup>3</sup>

/FTO 100 10<sup>4</sup>

**Table 1.** Recent work on metal oxide-based memristors.

Pt/TiO<sup>2</sup>

Pt/TiO<sup>x</sup>

Pt/Ta<sup>2</sup> O5

Ti/TaOx

ITO/WO3

Al/WO3

Cu/WO3

Pt/WO<sup>3</sup>

Pt/ZrO<sup>2</sup>

Cu/ZrO2

Ti/ZrO2

ITO/ZrO2

TiN/ZrO2

Ta/HfO2

TiN/HfO2

Ti/HfO2

Pt/HfO<sup>2</sup>

Pt/BiFeO<sup>3</sup>

Cu/HfO2

Pt/NiO<sup>x</sup>

Pt/Ti/Ta<sup>2</sup> O5 /HfO2

Pt/Ti/Nb:SrTiO<sup>3</sup>

/TiO2

/TiO2

The first physical instantiation of the memristor was generally acknowledged that was made from TiO2 by Strukov et al. [24], but as early as in 1968, it was found that the TiO<sup>2</sup> thin-film device shows memristive properties [63]. In literature [63], the work demonstrated that thin films exhibited resistive switching (RS) effects with pinched hysteretic current-voltage (I–V) curves during repeated tests. And also, there are several experimental researches on the RS effect of TiO<sup>2</sup> -based devices before 2008, such as Pt/TiO<sup>2</sup> /Ru [64] and sputter-deposited Pt/ TiO2 /Pt [65] devices. For memristors, the distinctive property is the pinched hysteretic loop indicating no energy dissipation. In [62], the prototype of memristor showed bipolar RS I–V curves with pinched points, which are a result of local stoichiometric change caused by the migration of oxygen vacancies. As oxygen vacancies act as donors in the TiO2 layer in the depletion zone, the conductance of the device could be modulated by the depletion or accumulation of Vos. Specifically, when the device undergoes a set process from a high resistance state to a low resistance state by the external electric field, the Vos will accumulate resulting in an increase of the conductive layer width. When applying electric pulse with reverse polarity, the Vos will be driven back thereby the conductive layer will become thin. Later it was demonstrated in some studies that the accumulation of Vos in TiO<sup>2</sup> may cause the formation of a new Magneli phase (Ti4 O7 ) that is metallic and directly studied by TEM [66, 67]. In 2009 [68], a flexible Al/TiO<sup>2</sup> /Al memristor fabricated by solution processing was reported. In this work, it showed that oxygen vacancies were introduced by the aluminum electrodes, and if a noble metal (Au) electrode was used, the form and reversibility of switching will change. The mechanism of the memristive effect strongly depends on the synthesis method, the choice of metal electrodes, and their interfacial properties. Many suggested that an understanding has been put forward through a series of experimental analyses from the view of film composition, microcrystalline structure, and switching zones. It also should be noted that the RS effect of the devices will be affected by device architecture, electrode materials, and layer stacks.

As a prototype of the memristor, TiO2−based devices show their potential in neuromorphic computing. Seo et al. [69] used titanium oxide as the active material to perform synaptic behavior in the context of analog memory, synaptic plasticity and STDP function. A bilayer of TiO<sup>x</sup> and TiOy structure was fabricated by atomic layer deposition and the sol-gel method, respectively. In the device, the titanium oxide bilayer works as a progressive resistance-changing medium with Al and W as the top and bottom electrodes. The multilevel conductance states were achieved by the movement of oxygen between the TiOy and the TiOx layer. In the report, the thickness of the less conductive layer TiOy was controlled by the applied bias which finally resulted in multilevel conductance and analog memory characteristics. As a positive bias was applied to the top electrode, the oxygen ions were driven from TiOy to TiOx and the effective thickness of the TiOy layer is reduced, which resulted in an increased conductance. Conversely, by applying negative bias to the device, the oxygen ions are moved from TiOx to TiOy , which caused a reduction of conductance. Due to the easy controlling of conductance, the analog characteristics of this device have been intensively studied. By applying sets of identical positive (negative) pulses, conductance can be progressively increased (decreased) as well as the potentiation (depression) in biological synapse. **Figure 2** illustrated the continuous potentiating and depressing characteristics of the device which were extremely useful for precisely modulating the device's synaptic weight. Also, the prior conductance state dependence of the subsequent conductance change is shown in **Figure 2b**. The results confirmed that the device showed the behavior as in the biological synaptic STDP model [70]: prior synaptic weight states affect the subsequent weight change. Furthermore, the time dependence of the device conductance change was studied which resembled that of the biological synapse. This indicated the titanium oxide bilayer's resistive switching device had great potential for mimicking biological synapses.

the memristive synapse elements according to a spike-based perceptron plasticity rule. In 2016, Park developed a Mo-/TiOx-based interface RRAM with 64-level conductance states and proposed a hybrid pulse mode for the synaptic application [75]. Under the stimuli of

Although many investigations have been carried out on the resistive switching mechanism of

is used in bilayer or multi-layer stacks' synaptic device to optimize the performance.

pattern recognition accuracy, which was confirmed through synaptic simulation.

Another great candidate for memristors as artificial synapses is tungsten oxides (WO<sup>x</sup>

of their high endurance, CMOS compatibility, and memorization and learning functions.

oxide and can be served as n-type semiconductors depending on its stoichiometry and morphology. Due to its attractive properties, it has been studied for both digital and analog mem-

storage properties by the application of suitable compliance current values. In that study, the device exhibited pronounced RS effects with an endurance of over 100 cycles and a retention of over 10<sup>4</sup> s. During the set process, the conductive filament is modulated by the compliance

positive bias will aid the creation of oxygen vacancies resulting in conductive filaments. The applied negative bias will drive back the oxygen ions to recombine with the vacancies, making the device turn OFF. Meanwhile, the role of electrodes on RS effect has also been studied,

material of the electrodes, the RS effects originate from the formation or annihilation of oxygen vacancies. Under positive bias, the non-inert electrode is oxidized and the ions diffuse toward another electrode to expand a conductive filament and *vice versa*. That is to say, a continuous concentration gradient of oxygen vacancies will be introduced during the oxidation process for the inert electrodes, which can result in low or high resistance states of the devices. In

studied [81, 82]. The conductance will decrease as the temperature increases due to higher oxygen vacancies' diffusion. In addition to the temperature, the memristive effects of tungsten oxide are also highly humidity dependent. The adsorbed moisture on the surface of WO3

/W memristor shows reliable synaptic operations with robust endurance behavior. The

/W memristor [84]. It was found that the memristor device retention can be

a necessary characteristic for practical applications in neuromorphic systems. Furthermore, the conductance change is governed by the history of the applied voltage signals, leading to synaptic behaviors including long-term potentiation and depression. The memristor behavior was explained by a novel model that takes both drift and diffusion effects into consideration. **Figure 3** presents the retention loss curve and memory loss in a human memory curve

resulted in decreasing conductances as the H cation induces an increase in barrier heights.

/Pd, and Pt/WO<sup>3</sup>

addition, the temperature and humidity impact on the performance of WOx


into standard manufacturing processes [76]. Additionally, WO3

apse is still limited when compared to PCMO, HfO<sup>x</sup>


, and TaOx

is also extensively studied as a memristor due to its CMOS compatibility


Synaptic Behavior in Metal Oxide-Based Memristors http://dx.doi.org/10.5772/intechopen.78408

/Pt structure devices and demonstrated multilevel

/ITO [79, 80]. In these studies, no matter the

memristors were reported by Chang [83]. The Pd/

potentiation/depression pulses without degradation which is

interface. In addition to the work of Celano [78], the applied

materials. In most situations,

is a kind of transition metal

memristors were

has

) because

11

the hybrid pulse mode, the TiO<sup>2</sup> <sup>−</sup> <sup>x</sup>

, WO3

current between the Cu and WO3

ory. Liu et al. [77] have fabricated Cu/WO3

/ITO, W/WO3

Synaptic behaviors and modeling of WOx

devices can endure at least 10<sup>5</sup>

the TiO2

Similar to TiO2

such as Ag/WO3

WOx

of the Pd/WO<sup>x</sup>

TiOx

In 2012 [71], Yu fabricated TiOx /HfOx /TiOx /HfOx multi-layer RRAM stacks and showed that the resistance states of the stacks could be gradually modulated by using identical pulses. The gradual resistance modulation behavior is useful for learning with high fault tolerance. Berdan in 2016 [72] demonstrated that TiO2 memristors can exhibit nonassociative plasticity. The transition between long-term plasticity (LTP) and short-term plasticity (STP) of this device was presented. The rate-limiting volatility in TiO<sup>2</sup> RRAM devices was very essential to capture short-term synaptic dynamics. In addition to Seo's works on the bilayer TiO<sup>x</sup> /TiOy device [69], Bousoulas studied the role of interfaces in TiOx /TiOy RRAM structures for high multilevel switching and synaptic properties [73]. A CMOS-memristor architecture composed of the 8\*8 array of the neuron was demonstrated by Mostafa [74]. The proposed system comprises CMOS neurons interconnected through TiO<sup>2</sup> <sup>−</sup> <sup>x</sup> memristors and spike-based learning circuits which modulate the conductance of

**Figure 2.** (a) The potentiation and depression for the device and (b) conductance dependence on history. Reprinted with permission from [69].

the memristive synapse elements according to a spike-based perceptron plasticity rule. In 2016, Park developed a Mo-/TiOx-based interface RRAM with 64-level conductance states and proposed a hybrid pulse mode for the synaptic application [75]. Under the stimuli of the hybrid pulse mode, the TiO<sup>2</sup> <sup>−</sup> <sup>x</sup> -based devices show good performance and enhanced pattern recognition accuracy, which was confirmed through synaptic simulation.

the movement of oxygen between the TiOy and the TiOx

10 Advances in Memristor Neural Networks – Modeling and Applications

bias to the device, the oxygen ions are moved from TiOx

electrode, the oxygen ions were driven from TiOy

less conductive layer TiOy

In 2012 [71], Yu fabricated TiOx

works on the bilayer TiO<sup>x</sup>

TiOx

TiO<sup>2</sup> <sup>−</sup> <sup>x</sup>

/TiOy

permission from [69].

layer. In the report, the thickness of the

and the effective thickness of the TiOy

multi-layer RRAM stacks and showed

device [69], Bousoulas studied the role of interfaces in

memristors can exhibit non-

RRAM

, which caused a reduction

was controlled by the applied bias which finally resulted in multi-

to TiOy

level conductance and analog memory characteristics. As a positive bias was applied to the top

layer is reduced, which resulted in an increased conductance. Conversely, by applying negative

of conductance. Due to the easy controlling of conductance, the analog characteristics of this device have been intensively studied. By applying sets of identical positive (negative) pulses, conductance can be progressively increased (decreased) as well as the potentiation (depression) in biological synapse. **Figure 2** illustrated the continuous potentiating and depressing characteristics of the device which were extremely useful for precisely modulating the device's synaptic weight. Also, the prior conductance state dependence of the subsequent conductance change is shown in **Figure 2b**. The results confirmed that the device showed the behavior as in the biological synaptic STDP model [70]: prior synaptic weight states affect the subsequent weight change. Furthermore, the time dependence of the device conductance change was studied which resembled that of the biological synapse. This indicated the titanium oxide bilayer's

resistive switching device had great potential for mimicking biological synapses.

/TiOx

plasticity (STP) of this device was presented. The rate-limiting volatility in TiO<sup>2</sup>

/HfOx

that the resistance states of the stacks could be gradually modulated by using identical pulses. The gradual resistance modulation behavior is useful for learning with high

associative plasticity. The transition between long-term plasticity (LTP) and short-term

devices was very essential to capture short-term synaptic dynamics. In addition to Seo's

CMOS-memristor architecture composed of the 8\*8 array of the neuron was demonstrated by Mostafa [74]. The proposed system comprises CMOS neurons interconnected through

**Figure 2.** (a) The potentiation and depression for the device and (b) conductance dependence on history. Reprinted with

RRAM structures for high multilevel switching and synaptic properties [73]. A

memristors and spike-based learning circuits which modulate the conductance of

/HfOx

fault tolerance. Berdan in 2016 [72] demonstrated that TiO2

/TiOy

to TiOx

Although many investigations have been carried out on the resistive switching mechanism of the TiO2 -based memristor, the demonstration of TiO2 -based memristor for the artificial synapse is still limited when compared to PCMO, HfO<sup>x</sup> , and TaOx materials. In most situations, TiOx is used in bilayer or multi-layer stacks' synaptic device to optimize the performance. Another great candidate for memristors as artificial synapses is tungsten oxides (WO<sup>x</sup> ) because of their high endurance, CMOS compatibility, and memorization and learning functions.

Similar to TiO2 , WO3 is also extensively studied as a memristor due to its CMOS compatibility into standard manufacturing processes [76]. Additionally, WO3 is a kind of transition metal oxide and can be served as n-type semiconductors depending on its stoichiometry and morphology. Due to its attractive properties, it has been studied for both digital and analog memory. Liu et al. [77] have fabricated Cu/WO3 /Pt structure devices and demonstrated multilevel storage properties by the application of suitable compliance current values. In that study, the device exhibited pronounced RS effects with an endurance of over 100 cycles and a retention of over 10<sup>4</sup> s. During the set process, the conductive filament is modulated by the compliance current between the Cu and WO3 interface. In addition to the work of Celano [78], the applied positive bias will aid the creation of oxygen vacancies resulting in conductive filaments. The applied negative bias will drive back the oxygen ions to recombine with the vacancies, making the device turn OFF. Meanwhile, the role of electrodes on RS effect has also been studied, such as Ag/WO3 /ITO, W/WO3 /Pd, and Pt/WO<sup>3</sup> /ITO [79, 80]. In these studies, no matter the material of the electrodes, the RS effects originate from the formation or annihilation of oxygen vacancies. Under positive bias, the non-inert electrode is oxidized and the ions diffuse toward another electrode to expand a conductive filament and *vice versa*. That is to say, a continuous concentration gradient of oxygen vacancies will be introduced during the oxidation process for the inert electrodes, which can result in low or high resistance states of the devices. In addition, the temperature and humidity impact on the performance of WOx memristors were studied [81, 82]. The conductance will decrease as the temperature increases due to higher oxygen vacancies' diffusion. In addition to the temperature, the memristive effects of tungsten oxide are also highly humidity dependent. The adsorbed moisture on the surface of WO3 has resulted in decreasing conductances as the H cation induces an increase in barrier heights.

Synaptic behaviors and modeling of WOx memristors were reported by Chang [83]. The Pd/ WOx /W memristor shows reliable synaptic operations with robust endurance behavior. The devices can endure at least 10<sup>5</sup> potentiation/depression pulses without degradation which is a necessary characteristic for practical applications in neuromorphic systems. Furthermore, the conductance change is governed by the history of the applied voltage signals, leading to synaptic behaviors including long-term potentiation and depression. The memristor behavior was explained by a novel model that takes both drift and diffusion effects into consideration. **Figure 3** presents the retention loss curve and memory loss in a human memory curve of the Pd/WO<sup>x</sup> /W memristor [84]. It was found that the memristor device retention can be improved with the application of repeated stimulations and bears remarkable similarities to the STM-to-LTM transition in biological systems. Among other transition metal oxides, WOx is a great candidate material for synaptic device application. For further exploring its applications in neuromorphic computing, the enhancement of synaptic operation time (endurance) is of importance.

which experiences sharp and first-order metal-to-insulator transition (MIT) at the around 68°C

devices, which can be integrated with the RRAM device to mitigate sneak-path current. The

The modulation of the device resistance with memory effects is essential to mimic biological synapse. And the understanding of switching mechanism is also important to incorporate memristors as a bionic synapse into the neuromorphic computing system. Many suggestions have been put forward to elucidate the causes of resistive memory effects of those oxidebased memristors. The most popular views on RS mechanism are taken as ionic diffusion and

For the mechanism of ionic drift and diffusion, under the stimulation of applied bias, the ions will migrate, and the conductance of memristors will be enhanced or depressed [96–98]. Actually, there are two types of ionic drift: cation and or anion drift, which depends on the

tor, both electrodes have inert Pt; the movement of oxygen vacancies causes the whole active

The second mechanism is about the heating effect [99, 100]. In the set or reset process, the active layer material is changed by the application of an electric field and flowing current heat. As the current is applied, the heat is released and the ions drift, forming an electron path to develop the conductive filament. At the same time, due to the collision of electrons, a new boundary may be created that inhibits the formation of the filament with excess heat [100]. Joule heating effects have been credited both in unipolar and in bipolar switching memories. In unipolar switching, under the high current passing through the memory devices, the heating fuses the conductive filaments in the reset process which is similar to that in bipolar switching. In bipolar switching, Joule heating dissolves the filament when sufficiently high current flows through the device. If this rupture happens in the SET process, it becomes a valid operation since the resistance did not stay in LRS and result in threshold switching [101]. However, large current should be avoided in the device which will introduce bad effects to performance or lead to a permanent failure because large current flowing through the filament will generate severe Joule heating, and a steep increase of the temperature in the

 layer to separate into two parts, with one part rich in oxygen vacancies and being more conductive. Hence, the difference in the concentration of oxygen vacancies leads to oxygen ion (anions) diffusion. Oxygen ions move to the anode and more oxygen vacancies are created. The increase of oxygen vacancies then makes the device more conductive to a low resistance state. Meanwhile, there is some evidence that the noninert electrode can hinder the combination of oxygen ions and serve as an oxygen vacancy reservoir. In the set process, the metal is oxidized and the metal ions diffuse into the insulating layer to develop a conducting filament.

materials used for active layers and electrodes. For example, for Strukov's [24] TiO2

Under negative bias, the filaments are ruptured by the increase of the electric field.

/Pt selector has been integrated with NiO unipolar RRAM by Lee et al. [93] in 2007 and

bipolar RRAM by Son et al. [94] in 2011. In 2016, 1S-1R configuration of W/VO<sup>2</sup>

as RRAM materials had been explored by Drisoll et al. [92] through

/Pt RRAM was demonstrated by zhang et al. [95]. However,

for practical applications [13].

so far focus on its use for select

Synaptic Behavior in Metal Oxide-Based Memristors http://dx.doi.org/10.5772/intechopen.78408

/

13

memris-

[91]. The application of VOx

Pt selection device and Ti/HfO<sup>2</sup>

filament will finally melt the filament.

thermal instability is a major challenge with VO<sup>2</sup>

Pt/VO<sup>2</sup>

/HfOx

**3.3. Mechanisms**

thermal effect.

TiO2

ZrOx

the sol-gel technique. Nevertheless, most researches on VOx

#### **3.2. Other metal oxide memristor-based synaptic devices**

Besides titanium oxide- and tungsten oxide-based memristors discussed above, a variety of other materials has been studied to implement the neural network as a synaptic device. Similar to TiOx , NiOx is one of the earliest materials found to exhibit restive switching behavior. Although NiOx -based RRAM devices have been reported with high endurance (10<sup>6</sup> ) and retention, its application for neuromorphic computing is restricted due to poor uniformity. Akoh fabricated synaptic devices with bipolar NiO<sup>x</sup> memristors [85]. This device also has the ability to update the synaptic conductance according to the difference of pre- and postneuron spike timing. Hu *et al.* studied the paired-pulse-induced response of an NiOx-based memristor, which is similar to the paired-pulse facilitation(PPF) of biological synapse [86]. In addition to PPF, the synaptic LTP of NiOx-based memristors was also studied by Hu et al. [87]. The LTP effect of the memristor has a dependence on pulse height, width, interval, and number of pulses. An artificial neural network is constructed to realize the associative learning and LTP behavior in the extinction of association in Pavlov's dog experiment.

AlOx is of interest in memristor materials due to its large band gap (~9 eV) and low RESET current (~ μA). For neuromorphic application, AlOx can also be used alone or stacked with other RRAM materials to improve the uniformity of the synaptic device characteristics. A GdOx and Cu-doped MoOx stack with platinum top and bottom electrodes was reported by Choi [88]. The weighted sum operation was carried out on an electrically modifiable synapse array circuit based on the proposed stacks [89]. The biological synaptic behavior was demonstrated by Chang through integrating SiOx -based RRAM with Si diodes. The proposed one-diodeone-resistor (1D-1R) architecture not only avoids sneak-path issues and lowers standby power consumption but also helps to realize STDP behaviors [90]. VOx is a well-known Mott material,

**Figure 3.** (a) Retention loss curve of Pd/WOx/W-based memristor and (b) forgetting memory of the human memory curve. Reprinted with permission from [44].

which experiences sharp and first-order metal-to-insulator transition (MIT) at the around 68°C [91]. The application of VOx as RRAM materials had been explored by Drisoll et al. [92] through the sol-gel technique. Nevertheless, most researches on VOx so far focus on its use for select devices, which can be integrated with the RRAM device to mitigate sneak-path current. The Pt/VO<sup>2</sup> /Pt selector has been integrated with NiO unipolar RRAM by Lee et al. [93] in 2007 and ZrOx /HfOx bipolar RRAM by Son et al. [94] in 2011. In 2016, 1S-1R configuration of W/VO<sup>2</sup> / Pt selection device and Ti/HfO<sup>2</sup> /Pt RRAM was demonstrated by zhang et al. [95]. However, thermal instability is a major challenge with VO<sup>2</sup> for practical applications [13].

#### **3.3. Mechanisms**

improved with the application of repeated stimulations and bears remarkable similarities to the STM-to-LTM transition in biological systems. Among other transition metal oxides,

Besides titanium oxide- and tungsten oxide-based memristors discussed above, a variety of other materials has been studied to implement the neural network as a synaptic device.

retention, its application for neuromorphic computing is restricted due to poor uniformity.

the ability to update the synaptic conductance according to the difference of pre- and postneuron spike timing. Hu *et al.* studied the paired-pulse-induced response of an NiOx-based memristor, which is similar to the paired-pulse facilitation(PPF) of biological synapse [86]. In addition to PPF, the synaptic LTP of NiOx-based memristors was also studied by Hu et al. [87]. The LTP effect of the memristor has a dependence on pulse height, width, interval, and number of pulses. An artificial neural network is constructed to realize the associative learn-

is of interest in memristor materials due to its large band gap (~9 eV) and low RESET

other RRAM materials to improve the uniformity of the synaptic device characteristics. A GdOx

[88]. The weighted sum operation was carried out on an electrically modifiable synapse array circuit based on the proposed stacks [89]. The biological synaptic behavior was demonstrated

one-resistor (1D-1R) architecture not only avoids sneak-path issues and lowers standby power

**Figure 3.** (a) Retention loss curve of Pd/WOx/W-based memristor and (b) forgetting memory of the human memory

ing and LTP behavior in the extinction of association in Pavlov's dog experiment.

is one of the earliest materials found to exhibit restive switching behav-

stack with platinum top and bottom electrodes was reported by Choi


) and

memristors [85]. This device also has

can also be used alone or stacked with

is a well-known Mott material,


 is a great candidate material for synaptic device application. For further exploring its applications in neuromorphic computing, the enhancement of synaptic operation time

WOx

AlOx

Similar to TiOx

ior. Although NiOx

and Cu-doped MoOx

by Chang through integrating SiOx

curve. Reprinted with permission from [44].

(endurance) is of importance.

, NiOx

**3.2. Other metal oxide memristor-based synaptic devices**

12 Advances in Memristor Neural Networks – Modeling and Applications

Akoh fabricated synaptic devices with bipolar NiO<sup>x</sup>

current (~ μA). For neuromorphic application, AlOx

consumption but also helps to realize STDP behaviors [90]. VOx

The modulation of the device resistance with memory effects is essential to mimic biological synapse. And the understanding of switching mechanism is also important to incorporate memristors as a bionic synapse into the neuromorphic computing system. Many suggestions have been put forward to elucidate the causes of resistive memory effects of those oxidebased memristors. The most popular views on RS mechanism are taken as ionic diffusion and thermal effect.

For the mechanism of ionic drift and diffusion, under the stimulation of applied bias, the ions will migrate, and the conductance of memristors will be enhanced or depressed [96–98]. Actually, there are two types of ionic drift: cation and or anion drift, which depends on the materials used for active layers and electrodes. For example, for Strukov's [24] TiO2 memristor, both electrodes have inert Pt; the movement of oxygen vacancies causes the whole active TiO2 layer to separate into two parts, with one part rich in oxygen vacancies and being more conductive. Hence, the difference in the concentration of oxygen vacancies leads to oxygen ion (anions) diffusion. Oxygen ions move to the anode and more oxygen vacancies are created. The increase of oxygen vacancies then makes the device more conductive to a low resistance state. Meanwhile, there is some evidence that the noninert electrode can hinder the combination of oxygen ions and serve as an oxygen vacancy reservoir. In the set process, the metal is oxidized and the metal ions diffuse into the insulating layer to develop a conducting filament. Under negative bias, the filaments are ruptured by the increase of the electric field.

The second mechanism is about the heating effect [99, 100]. In the set or reset process, the active layer material is changed by the application of an electric field and flowing current heat. As the current is applied, the heat is released and the ions drift, forming an electron path to develop the conductive filament. At the same time, due to the collision of electrons, a new boundary may be created that inhibits the formation of the filament with excess heat [100]. Joule heating effects have been credited both in unipolar and in bipolar switching memories. In unipolar switching, under the high current passing through the memory devices, the heating fuses the conductive filaments in the reset process which is similar to that in bipolar switching. In bipolar switching, Joule heating dissolves the filament when sufficiently high current flows through the device. If this rupture happens in the SET process, it becomes a valid operation since the resistance did not stay in LRS and result in threshold switching [101]. However, large current should be avoided in the device which will introduce bad effects to performance or lead to a permanent failure because large current flowing through the filament will generate severe Joule heating, and a steep increase of the temperature in the filament will finally melt the filament.

Generally, the physical origin of the switching effect in memristors depends on architectures, materials, and interfaces. The comprehensive study of the mechanism is very helpful to the manipulation of memory and to extend the application of memristors. In terms of conductance modulation in memristors, many metal oxide-based memristors can perform not only on digital memory but also on analog memory which is similar to biological functions.

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