Fakultät für Physik

ESA, ACT ESTEC April 29, 2015

Memristive Tunnel Junctions for

Neuromorphic CircuitsAndy Thomas

Acknowledgments

O. SimonN. Shepheard

O. Schebaum

I.-M. Imort

J. Münchenberger

M. SchäfersS. Fabretti

Z. Kugler

L. Schnatmann M. Schirmer

S. Niehörster

J. Sterz

2

G. Reiss A. Hütten

Ministerium für Innovation, Wissenschaft und Forschung des Landes Nordrhein-Westfalen

Center for Spinelectronic Materials and Devices

Collaborations

Spin electronic C. Felser, MPI Dresden J. Moodera, M.I.T. T. Kampfrath, FHI Berlin K. Nielsch, U Hamburg

Spin caloritronics M. Münzenberg, U Greifswald

S. Goennenwein, WMI Garching C. Heiliger, U Gießen M. Kläui, U Mainz

Memristive systems C. Kaltschmidt, U Bielefeld E. Chicca, U. Rückert, CITEC Bielefeld mem

ristor

−∞ −∞

3

Why neuromorphic circuits?

Bio-inspired neural networks

Andy Thomas and Christian Kaltschmidt

1 Introduction

Memristors have attracted great interest for a variety of applications in recent years.An obvious use would be as a memory device [17, 52, 50] or, more ambitiously,a reconfigurable logic device [88, 10, 89, 11, 64]. However, the most interestingimplementation of memristive devices is neuromorphic computing.

Neuromorphic computing aims to use biological mechanisms operating withinthe brain as a blueprint to construct novel computer architectures. Carver Meadbuilt the foundation of this field and proposed large-scale adaptive analogue systemsbecause of their robustness as well as good power efficiency [61]. The efficiency ofthese systems is particularly promising, as shown in Table 1.

Table 1 Comparison of the power consumption of three different technologies [74]. A biologicalneuron draws less power and consumes less area than a digital computer or silicon neuron.

Digital computer Silicon neuron Biological neuron

Energy consumption (J/spike) 10�5 10�8 10�11

Size (µm2) 108 3⇥103 10

Despite its power efficiency and robustness, some tasks are very challenging forthe human brain, e.g., solving coupled differential equations. However, it is veryeasy to find a solution for this problem with the help of a von-Neumann/Zuse com-puter [92, 67]. However, some tasks are also difficult for a state-of-the-art computer

Andy ThomasPhysics department, Bielefeld University, Germany, e-mail: andy.thomas@uni-bielefeld.de, andPhysics department, Osnabruck University, Germany

Christian KaltschmidtBiology department, Bielefeld University, Germany, e-mail: c.kaltschmidt@uni-bielefeld.de

1

[74] C.S. Poon, Frontiers in neuroscience 5 (2011) 1

Arithmetische Einheit

Kontrolleinheit

Speicher

Lochkartenleser

MCA

CC

R

Efficiency

Avoid von Neumann bottleneck

Scientific curiosity Maximum reduction?

presynaptic cell

postsynaptic cell

synapse

impulses

dendrite

axon

synapse

Biological neural networks

Biological neural networks

6

presynaptic cell

postsynaptic cell

synapse

impulses

dendrite

axon

synapse

presynaptic cell postsynaptic cell

synapse

impulses

need neurons and synapses neurons are connected via the synapses.

I(t)

CR

pulse triggersswitch

voltage thresholdtriggers pulse

Neurons integrate signals and fire when exceeding threshold

leaky integrate and fire

oversampled ΣΔ modulators= 1-Bit AD converter

I(t)

CR

pulse triggersswitch

voltage thresholdtriggers pulse

I(t)

CR

pulse triggersswitch

voltage thresholdtriggers pulse

Thomas, J. Phys D: Appl. Phys. 46 (2013) 093001, Thomas, Kaltschmidt, Memristor Networks, Ed. Adamatzky, Chua (2014) 151-172

Biological synapse

7

Axon

Pre-synpase

synaptic cleft

Post-synapse

vesicles containing neurotransmitters

vesicle fusion Glu

Glu

Glu

Glu

GluGlu

Ca2+

gene expression via CREB, NF-kappaB

Simplify the mechanisms via a simple model: One effective connection strength.

Mayford, Siegelbaum, Kandel, Cold Spring Harbor Perspectives in Biology 4(6), a005,751 (2012)

Electronic symbols

8

J. Phys. D: Appl. Phys. 46 (2013) 093001 Topical Review

I(t)

CR

pulse triggersswitch

voltage thresholdtriggers pulse

Figure 12. Integrate-and-fire circuits: the perfect integrate-and-firemodel consists of a capacitor, threshold detector and switch (withoutresistor). Once the voltage reaches a threshold, the spike is fired andthe switch is closed to shunt the capacitor. In the leaky version, aresistor is added that slowly drains the capacitor with time. Thiscorresponds to leakage current through a membrane in a living cell.

integrate-and-fire [68–71]. The rather simple model capturestwo of the most important aspects of neuronal excitability;specifically, the neuron integrates the incoming signals andgenerates the spikes once a certain threshold is exceeded(figure 12).

This behaviour is often explained using two simple electriccircuits [72]. The perfect integrate-and-fire circuit consistsof a capacitor, threshold detector and switch. Once a spikeis fired, the switch closes and shunts the capacitor. Anadditional resistor is included in the leaky integrate-and-fire circuit. The resistor slowly drains the capacitor andcorresponds to leakage currents in the membrane. However,the integrate-and-fire functionality of a neural network isconsiderably simpler to implement than the synaptic efficacy.For example, oversampled Delta-Sigma modulators, which are1-bit analogue- digital converters, can mimic the integrate-and-fire behaviour [73, 74]. Therefore, the following paragraphsprimarily describe the use of memristive systems as synapsesbecause the integrate-and-fire functionality can be achievedusing conventional CMOS-technology.

2.5. Minimal requirements

We can summarize the primary requirements for a bio-inspiredneural network as follows.

(i) Devices that act as neurons and devices that behave likesynapses are needed, and the neurons are interconnectedvia the synapses.

(ii) The neurons integrate inhibitory and excitatory incomingsignals and fire once a threshold is exceeded.

(iii) The synapses exhibit LTP (cooperative, associative, andinput-specific), LTD, and STDP.

3. Implementations using memristive systems

The question may be asked as to why we want to constructneuromorphic systems that emulate the presented biologicalmechanisms. Carver Mead pioneered a considerable amount

excitatory

inhibitatoryneuronsynapse

Figure 13. Schematic symbols for synapses and neurons as used inthe following paragraphs.

of the research on this topic and explained the reasoning in thefollowing way [75]: For many problems, particularly those inwhich the input data are ill-conditioned and the computationcan be specified in a relative manner, biological solutions aremany orders of magnitude more effective than those we havebeen able to implement using digital methods. [...] Large-scale adaptive analog systems are more robust to componentdegradation and failure than are more conventional systems,and they use far less power. The need for less power isparticularly obvious if we compare the performance of thebrain of even an invertebrate with a computer CPU and contrastthe power consumption. However, there are some tasks thatare difficult for a human and easy for a computer, such asmultiplying two long numbers, and other problems that ahuman can easily solve but computers fail to solve.

In 2008, the use of memristors to mimic biologicalmechanisms, such as STDP, was already hypothesized[76]. Snider implemented the spike time dependence usingmemristive nanodevices as synapses and conventional CMOStechnology as neurons. He also suggested two electronicsymbols for neurons and synapses [76] that have been adaptedby some groups as well as in this paper; the symbols aredepicted in figure 13. Furthermore, Snider indicated thatwe should note that STDP alone might not be sufficient toimplement stable learning; more complex synaptic dynamicsand additional state variables may be required and refers towork by Carpenter et al [77] as well as Fusi and Abbott [78].

Although Snider suggested a new paradigm that useslarge-scale adaptive analogue systems, the approach still uses aglobal clock signal. In 2010, Pershin and Di Ventra described asmall system composed of three neurons and two synapses thatis fully asynchronous [79, 80]. The memristive behaviour wasemulated by a microcontroller combined with other commonelectronic components. They demonstrated how Ivan Pavlov’sfamous experiment [81] can be imitated with the basic circuitdepicted in figure 14 [79].

Initially, the output signal (salivation) is recorded independence on the sight of food or a bell sound. Only thesight of food (input signal 1) leads to salivation (neuron 3output); the bell (input signal 2) is not associated with food.There is a subsequent learning period where the input 1and input 2 signals are applied simultaneously. Afterwards,both individual input signals induce salivation. The elegantexperiment demonstrates how an important function of thebrain, namely associative memory [79], can be constructedwith a circuit, as shown in figure 14.

A similar simulation was conducted by Cantley et al usingSPICE (UC Berkeley, CA, USA) and MATLAB (Natick, MA,USA), and they noted Also, it should be pointed out that theassociation as presented (in figure 4) can be unlearned. This

6

presynaptic cell postsynaptic cell

synapse

impulses

J. Phys. D: Appl. Phys. 46 (2013) 093001 Topical Review

I(t)

CR

pulse triggersswitch

voltage thresholdtriggers pulse

Figure 12. Integrate-and-fire circuits: the perfect integrate-and-firemodel consists of a capacitor, threshold detector and switch (withoutresistor). Once the voltage reaches a threshold, the spike is fired andthe switch is closed to shunt the capacitor. In the leaky version, aresistor is added that slowly drains the capacitor with time. Thiscorresponds to leakage current through a membrane in a living cell.

integrate-and-fire [68–71]. The rather simple model capturestwo of the most important aspects of neuronal excitability;specifically, the neuron integrates the incoming signals andgenerates the spikes once a certain threshold is exceeded(figure 12).

This behaviour is often explained using two simple electriccircuits [72]. The perfect integrate-and-fire circuit consistsof a capacitor, threshold detector and switch. Once a spikeis fired, the switch closes and shunts the capacitor. Anadditional resistor is included in the leaky integrate-and-fire circuit. The resistor slowly drains the capacitor andcorresponds to leakage currents in the membrane. However,the integrate-and-fire functionality of a neural network isconsiderably simpler to implement than the synaptic efficacy.For example, oversampled Delta-Sigma modulators, which are1-bit analogue- digital converters, can mimic the integrate-and-fire behaviour [73, 74]. Therefore, the following paragraphsprimarily describe the use of memristive systems as synapsesbecause the integrate-and-fire functionality can be achievedusing conventional CMOS-technology.

2.5. Minimal requirements

We can summarize the primary requirements for a bio-inspiredneural network as follows.

(i) Devices that act as neurons and devices that behave likesynapses are needed, and the neurons are interconnectedvia the synapses.

(ii) The neurons integrate inhibitory and excitatory incomingsignals and fire once a threshold is exceeded.

(iii) The synapses exhibit LTP (cooperative, associative, andinput-specific), LTD, and STDP.

3. Implementations using memristive systems

The question may be asked as to why we want to constructneuromorphic systems that emulate the presented biologicalmechanisms. Carver Mead pioneered a considerable amount

excitatory

inhibitatoryneuronsynapse

Figure 13. Schematic symbols for synapses and neurons as used inthe following paragraphs.

of the research on this topic and explained the reasoning in thefollowing way [75]: For many problems, particularly those inwhich the input data are ill-conditioned and the computationcan be specified in a relative manner, biological solutions aremany orders of magnitude more effective than those we havebeen able to implement using digital methods. [...] Large-scale adaptive analog systems are more robust to componentdegradation and failure than are more conventional systems,and they use far less power. The need for less power isparticularly obvious if we compare the performance of thebrain of even an invertebrate with a computer CPU and contrastthe power consumption. However, there are some tasks thatare difficult for a human and easy for a computer, such asmultiplying two long numbers, and other problems that ahuman can easily solve but computers fail to solve.

In 2008, the use of memristors to mimic biologicalmechanisms, such as STDP, was already hypothesized[76]. Snider implemented the spike time dependence usingmemristive nanodevices as synapses and conventional CMOStechnology as neurons. He also suggested two electronicsymbols for neurons and synapses [76] that have been adaptedby some groups as well as in this paper; the symbols aredepicted in figure 13. Furthermore, Snider indicated thatwe should note that STDP alone might not be sufficient toimplement stable learning; more complex synaptic dynamicsand additional state variables may be required and refers towork by Carpenter et al [77] as well as Fusi and Abbott [78].

Although Snider suggested a new paradigm that useslarge-scale adaptive analogue systems, the approach still uses aglobal clock signal. In 2010, Pershin and Di Ventra described asmall system composed of three neurons and two synapses thatis fully asynchronous [79, 80]. The memristive behaviour wasemulated by a microcontroller combined with other commonelectronic components. They demonstrated how Ivan Pavlov’sfamous experiment [81] can be imitated with the basic circuitdepicted in figure 14 [79].

Initially, the output signal (salivation) is recorded independence on the sight of food or a bell sound. Only thesight of food (input signal 1) leads to salivation (neuron 3output); the bell (input signal 2) is not associated with food.There is a subsequent learning period where the input 1and input 2 signals are applied simultaneously. Afterwards,both individual input signals induce salivation. The elegantexperiment demonstrates how an important function of thebrain, namely associative memory [79], can be constructedwith a circuit, as shown in figure 14.

A similar simulation was conducted by Cantley et al usingSPICE (UC Berkeley, CA, USA) and MATLAB (Natick, MA,USA), and they noted Also, it should be pointed out that theassociation as presented (in figure 4) can be unlearned. This

6

J. Phys. D: Appl. Phys. 46 (2013) 093001 Topical Review

I(t)

CR

pulse triggersswitch

voltage thresholdtriggers pulse

Figure 12. Integrate-and-fire circuits: the perfect integrate-and-firemodel consists of a capacitor, threshold detector and switch (withoutresistor). Once the voltage reaches a threshold, the spike is fired andthe switch is closed to shunt the capacitor. In the leaky version, aresistor is added that slowly drains the capacitor with time. Thiscorresponds to leakage current through a membrane in a living cell.

integrate-and-fire [68–71]. The rather simple model capturestwo of the most important aspects of neuronal excitability;specifically, the neuron integrates the incoming signals andgenerates the spikes once a certain threshold is exceeded(figure 12).

This behaviour is often explained using two simple electriccircuits [72]. The perfect integrate-and-fire circuit consistsof a capacitor, threshold detector and switch. Once a spikeis fired, the switch closes and shunts the capacitor. Anadditional resistor is included in the leaky integrate-and-fire circuit. The resistor slowly drains the capacitor andcorresponds to leakage currents in the membrane. However,the integrate-and-fire functionality of a neural network isconsiderably simpler to implement than the synaptic efficacy.For example, oversampled Delta-Sigma modulators, which are1-bit analogue- digital converters, can mimic the integrate-and-fire behaviour [73, 74]. Therefore, the following paragraphsprimarily describe the use of memristive systems as synapsesbecause the integrate-and-fire functionality can be achievedusing conventional CMOS-technology.

2.5. Minimal requirements

We can summarize the primary requirements for a bio-inspiredneural network as follows.

(i) Devices that act as neurons and devices that behave likesynapses are needed, and the neurons are interconnectedvia the synapses.

(ii) The neurons integrate inhibitory and excitatory incomingsignals and fire once a threshold is exceeded.

(iii) The synapses exhibit LTP (cooperative, associative, andinput-specific), LTD, and STDP.

3. Implementations using memristive systems

The question may be asked as to why we want to constructneuromorphic systems that emulate the presented biologicalmechanisms. Carver Mead pioneered a considerable amount

excitatory

inhibitatoryneuronsynapse

Figure 13. Schematic symbols for synapses and neurons as used inthe following paragraphs.

of the research on this topic and explained the reasoning in thefollowing way [75]: For many problems, particularly those inwhich the input data are ill-conditioned and the computationcan be specified in a relative manner, biological solutions aremany orders of magnitude more effective than those we havebeen able to implement using digital methods. [...] Large-scale adaptive analog systems are more robust to componentdegradation and failure than are more conventional systems,and they use far less power. The need for less power isparticularly obvious if we compare the performance of thebrain of even an invertebrate with a computer CPU and contrastthe power consumption. However, there are some tasks thatare difficult for a human and easy for a computer, such asmultiplying two long numbers, and other problems that ahuman can easily solve but computers fail to solve.

In 2008, the use of memristors to mimic biologicalmechanisms, such as STDP, was already hypothesized[76]. Snider implemented the spike time dependence usingmemristive nanodevices as synapses and conventional CMOStechnology as neurons. He also suggested two electronicsymbols for neurons and synapses [76] that have been adaptedby some groups as well as in this paper; the symbols aredepicted in figure 13. Furthermore, Snider indicated thatwe should note that STDP alone might not be sufficient toimplement stable learning; more complex synaptic dynamicsand additional state variables may be required and refers towork by Carpenter et al [77] as well as Fusi and Abbott [78].

Although Snider suggested a new paradigm that useslarge-scale adaptive analogue systems, the approach still uses aglobal clock signal. In 2010, Pershin and Di Ventra described asmall system composed of three neurons and two synapses thatis fully asynchronous [79, 80]. The memristive behaviour wasemulated by a microcontroller combined with other commonelectronic components. They demonstrated how Ivan Pavlov’sfamous experiment [81] can be imitated with the basic circuitdepicted in figure 14 [79].

Initially, the output signal (salivation) is recorded independence on the sight of food or a bell sound. Only thesight of food (input signal 1) leads to salivation (neuron 3output); the bell (input signal 2) is not associated with food.There is a subsequent learning period where the input 1and input 2 signals are applied simultaneously. Afterwards,both individual input signals induce salivation. The elegantexperiment demonstrates how an important function of thebrain, namely associative memory [79], can be constructedwith a circuit, as shown in figure 14.

A similar simulation was conducted by Cantley et al usingSPICE (UC Berkeley, CA, USA) and MATLAB (Natick, MA,USA), and they noted Also, it should be pointed out that theassociation as presented (in figure 4) can be unlearned. This

6

J. Phys. D: Appl. Phys. 46 (2013) 093001 Topical Review

I(t)

CR

pulse triggersswitch

voltage thresholdtriggers pulse

Figure 12. Integrate-and-fire circuits: the perfect integrate-and-firemodel consists of a capacitor, threshold detector and switch (withoutresistor). Once the voltage reaches a threshold, the spike is fired andthe switch is closed to shunt the capacitor. In the leaky version, aresistor is added that slowly drains the capacitor with time. Thiscorresponds to leakage current through a membrane in a living cell.

integrate-and-fire [68–71]. The rather simple model capturestwo of the most important aspects of neuronal excitability;specifically, the neuron integrates the incoming signals andgenerates the spikes once a certain threshold is exceeded(figure 12).

This behaviour is often explained using two simple electriccircuits [72]. The perfect integrate-and-fire circuit consistsof a capacitor, threshold detector and switch. Once a spikeis fired, the switch closes and shunts the capacitor. Anadditional resistor is included in the leaky integrate-and-fire circuit. The resistor slowly drains the capacitor andcorresponds to leakage currents in the membrane. However,the integrate-and-fire functionality of a neural network isconsiderably simpler to implement than the synaptic efficacy.For example, oversampled Delta-Sigma modulators, which are1-bit analogue- digital converters, can mimic the integrate-and-fire behaviour [73, 74]. Therefore, the following paragraphsprimarily describe the use of memristive systems as synapsesbecause the integrate-and-fire functionality can be achievedusing conventional CMOS-technology.

2.5. Minimal requirements

We can summarize the primary requirements for a bio-inspiredneural network as follows.

(i) Devices that act as neurons and devices that behave likesynapses are needed, and the neurons are interconnectedvia the synapses.

(ii) The neurons integrate inhibitory and excitatory incomingsignals and fire once a threshold is exceeded.

(iii) The synapses exhibit LTP (cooperative, associative, andinput-specific), LTD, and STDP.

3. Implementations using memristive systems

The question may be asked as to why we want to constructneuromorphic systems that emulate the presented biologicalmechanisms. Carver Mead pioneered a considerable amount

excitatory

inhibitatoryneuronsynapse

Figure 13. Schematic symbols for synapses and neurons as used inthe following paragraphs.

of the research on this topic and explained the reasoning in thefollowing way [75]: For many problems, particularly those inwhich the input data are ill-conditioned and the computationcan be specified in a relative manner, biological solutions aremany orders of magnitude more effective than those we havebeen able to implement using digital methods. [...] Large-scale adaptive analog systems are more robust to componentdegradation and failure than are more conventional systems,and they use far less power. The need for less power isparticularly obvious if we compare the performance of thebrain of even an invertebrate with a computer CPU and contrastthe power consumption. However, there are some tasks thatare difficult for a human and easy for a computer, such asmultiplying two long numbers, and other problems that ahuman can easily solve but computers fail to solve.

In 2008, the use of memristors to mimic biologicalmechanisms, such as STDP, was already hypothesized[76]. Snider implemented the spike time dependence usingmemristive nanodevices as synapses and conventional CMOStechnology as neurons. He also suggested two electronicsymbols for neurons and synapses [76] that have been adaptedby some groups as well as in this paper; the symbols aredepicted in figure 13. Furthermore, Snider indicated thatwe should note that STDP alone might not be sufficient toimplement stable learning; more complex synaptic dynamicsand additional state variables may be required and refers towork by Carpenter et al [77] as well as Fusi and Abbott [78].

Although Snider suggested a new paradigm that useslarge-scale adaptive analogue systems, the approach still uses aglobal clock signal. In 2010, Pershin and Di Ventra described asmall system composed of three neurons and two synapses thatis fully asynchronous [79, 80]. The memristive behaviour wasemulated by a microcontroller combined with other commonelectronic components. They demonstrated how Ivan Pavlov’sfamous experiment [81] can be imitated with the basic circuitdepicted in figure 14 [79].

Initially, the output signal (salivation) is recorded independence on the sight of food or a bell sound. Only thesight of food (input signal 1) leads to salivation (neuron 3output); the bell (input signal 2) is not associated with food.There is a subsequent learning period where the input 1and input 2 signals are applied simultaneously. Afterwards,both individual input signals induce salivation. The elegantexperiment demonstrates how an important function of thebrain, namely associative memory [79], can be constructedwith a circuit, as shown in figure 14.

A similar simulation was conducted by Cantley et al usingSPICE (UC Berkeley, CA, USA) and MATLAB (Natick, MA,USA), and they noted Also, it should be pointed out that theassociation as presented (in figure 4) can be unlearned. This

6

Symbols

presynaptic cell postsynaptic cell

Biological synapses

9

100

50

0

-50

pote

ntia

tion

(%)

43210time (h)

input

output

3

2

1

γ

β

α

(a)

(b)100

50

0

-50-60 -40 -20 0 20 40 60

spike timing (ms)

change (%)

1.0

0.5

0.0

syna

ptic

stre

ngth

3020100-10time (min)

Exhibit LTP, LTD, STDP

T. Bliss at al, Nature 361 (1993) 31, Y. Goda et al, Neuron 16 (1996) 103, S. Cassenaer et al, Nature 448 (2007) 709

Long-term potentiation (LTP)

Long-term depression (LTD)

Spike-time dependent plasticity (STDP)

Observations in a biological neural network

The synapses exhibit LTP (cooperative, associative, and input-specific), LTD, and STDP. CONTENTS 7

Bliss and Collingridge also reported that ltp is characterized by three basic

properties: cooperativity, associativity and input-specificity [43]. We will discuss these

three characteristics in the following paragraphs.

Figure 7. A low- (a) and high-intensity stimulus (b) was applied to a fibre. The low-intensity stimulus produced a reaction, but it was short lasting. The high-intensitystimulation lasted for a longer time. Reprinted from Brain Res. [46], with permissionfrom Elsevier.

Cooperativity means that there is an intensity threshold to induce ltp, and this

threshold is above the stimulus threshold that leads to a minimal synaptic response [46].

This process is illustrated in figure 7. A small-intensity stimulus was used in figure 7a.

While there is a reaction, the potentiation disappeared approximately 5 minutes after

application of the stimulus. This behaviour changes if a stimulus of higher intensity is

used (figure 7b.). The potentiation lasts a longer time, although the initial potentiation

is of comparable size. The stimulation in a biological system is usually a tetanus,

i.e., rapidly repeated impulses. Therefore, the threshold for inducing ltp is a complex

[complicated] function of the intensity and pattern of the tetanic stimulation (Bliss and

Collingridge [43]). This concept is discussed in more detail by [47].

Associativity indicates that many weak tetani in separate but convergent inputs

still trigger ltp [49]. Figure 8 depicts the potentiation resulting from the application

of two stimuli at the same time. First, the weak stimulus W is used, and no long-term

potentiation can be observed. The same is true if another strong, solitary stimulus S

is applied. However, a combined W plus S tetanus results in a long-term potentiation,

which is visible in figure 8.

Finally, input-specificity means that only the plasticity of the active connection is

potentiated [51, 50]. This was investigated using a tetanized pathway and a control path

in 17 matched-pair experiments by Lynch et al. [50]. The result is shown in table 1. The

CONTENTS 8

Figure 8. The application of the weak stimulus W or a strong stimulus S does notlead to a potentiation. If W and S are applied at the same time, long-term potentiationcan be observed. Reprinted from Proc. Nat. Acad. Sci. [48], Copyright (1983).

post tetanus (min) Pre 5 10 15

Tetanised pathway (%) 100 390 380 332

Control pathway (%) 100 74 67 73

Table 1. Population spike amplitude of tetanised and control pathways before andafter stimulation (N=17). Adapted by permission from Macmillan Publishers Ltd:Nature [50], copyright (1977).

tetanized path changed its amplitude by more than a factor of three, while the control

pathway remained approximately constant.

2.2. Long term depression ( ltd) and retention

We have to distinguish two di↵erent types of processes to investigate the term long-

term depression (ltd) and compare it with ltp. The first process is the antagonist of

ltp, which is consequently labelled ltd. The similarity of ltd to ltp is apparent in

figure 9, where the current traces were recorded before and after the stimulus. Although

the synaptic strength initially remains constant, the stimulus weakens the connection.

Afterward, the synaptic strength recovers over the course of several minutes, but it

remains less than its initial value. This result is indeed the analogue of ltp with an

opposite sign of the change in connection strength.

The second process is more involved and could possibly be described by the

depotentiation (reversal) of the ltp at the single-neuron level. However, beginning with

a top-bottom approach may be instructive. Therefore, it appears natural to connect

the potentiation of the various synaptic inputs with learning and, consequently, the

depotentiation with forgetting. This process occurs on a more extended timescale and

is of great interest to psychological researchers. In their review, Rubin and Wenzel

collected one hundred years data regarding forgetting. They provided a quantitative

Cooperative Associative

Input-specific: required by general causalityB.L. McNaughton, Brain. Res. 157 (1978) 277

G. Barrioneuvo, Natl. Acad. Sci. 80 (1983) 7347

Spike timing dependent plasticity (STDP)

11

input

output

3

2

1

γ

β

α

(a)

(b)100

50

0

-50-60 -40 -20 0 20 40 60

spike timing (ms)

change (%)

S. Cassenaer et al, Nature 448 (2007) 709

Spike-time dependent plasticity (STDP)

potentiate α

output

1

output

1

2

depress α

coincidence detector

2

α

Memristor

Thin film samples @ Bielefeld

Materials ‘development’: Ferromagnets, e.g. Heusler (HMF) SC: e.g. Heusler, MgB2 Oxides: e.g. Ta-O, HfO2, MgO

Spintronic devices: sensors memory logic

Spin caloritronics: TMS vs TMR thermal spin transfer torque spin pumping

Memristors: artificial neural networks integration with CMOS hybrid samples with biological neurons

Metal

Insulator

Lithography: optical e-beam ion beam etching

Thin film devices

13

Sample preparation

Thin film (co-)deposition on Si-wafer, MgO, STO, ..., substrates

Optional in- and ex-situ anneal, ex-situ optional field cool

Lithography (e-beam, optical), subsequent ion-beam etching

Transport measurements (0.3-500K, up to 4T)

Insulator

Ferromagnet

Superconductor

Meservey-Tedrow- Tunnel Junction

Metal

Metal

Insulator

Memristor

Ferromagnet

Ferromagnet

Insulator

Magnetic Tunnel Junction

Examples of the prepared thin film devices14

Memristive tunnel junctions

15

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v=v0 sin(ωt)

•

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152

151

150

149

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ce (Ω

)

806040200flux (Vs)

•

••

••

•

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•

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+I: resistance up

current flows other direction => turn knob other direction

-I: resistance down

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Abbildung 1: Stack

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Abbildung 2: Loop mit Switching Effekt von 120% (MgO 12%)

Die oberen 3 Kurven wurden aus der gleichen Probe generiert. Die Barrierewurde hergestellt indem 2nm Ta mit Sauerstoffplasma oxidiert wurden. DieBeschleunigugnsspannung betrug -80V und die Oxidationszeit betrug 200s.

1

Ta/TaO/Pd

Metal

Metal

Insulator

Electrically controlled, two terminal, bipolar, analog devices

Thomas, J. Phys D: Appl. Phys. 46 (2013) 093001, Krzysteczko,..., AT, Appl. Phys. Lett. 95 (2009) 112508 Semicond. Sci. Technol. 29 (2014), guest Editor: A. Thomas

Memristor based synapses

Long term potentiation and depression

17

-0.5

0.0

0.5

1050time (min)

2

1

0

cond

ucta

nce

chan

ge (%

) LTP

LTD

excitatory

inhibitatoryneuronsynapse

I

excitatory

inhibitatoryneuronsynapse

I

220

219

218

217

R(Ω)

121086420

Time (min)

-15

0Flux(Vs)

-0.5

0.0v

(V)

Figure 49: Memristive mtj

activated by a standard spiketrain of negative polarity. Theposition of the applied trainis shown by the bottom trace.The resulting flux is givenby the middle trace, the to-tal flux-contend of the train is�15 Vs. The resistance of thememristive synapse is mod-ulated by the train and re-mains stable when the activ-ity is terminated.

in figure 48 are applied. They are characterized by only two pa-rameters: the amplitude of the sine profile vmax and the numberof spikes per train Nsp.

A typical measurement is shown in figure 49. The graph con-sists of three traces. The bottom trace plots the applied voltage.The middle trace displays the corresponding flux. The top traceshows that due to the voltage treatment, the resistance is drivenfrom a lower stable level to a higher stable level. This is ex-actly how an artificial synapse should respond. The activity atthe synaptic connection leads a stable modification thereof—theactivity is remembered.

223

222

221

220

219

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217

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50403020100

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0

1

23

4Figure 50: The effect ofsubsequent train application.The resistive states are num-bered. The state zero is theresult of the refreshing pro-cedure shown in fig. 51. Theother states are induced bystandard spike trains.

Figure 50 shows the effect of repeated treatment (4 times) witha 30-spike train and vmax = �500 mV. To control the barrier qual-ity, every 12 minutes (dashed lines) the constant magnetic field isreleased to measure the magnetic minor loop. If the minor loopshows a tmr ratio close to 100 % the data measured so far is con-

59

Successive pulses cause successive potentiation/ depression

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T. Bliss at al, Nature 361 (1993) 31, Y. Goda et al, Neuron 16 (1996) 103

Pulse shaping for spike timing dependent plasticity

18

�t > 0 �t < 0

�

vpre

vpost vpost

vpre

vMR vMR

t

t

t

t

t

t-vth

+vth

�

Figure 61: Flux-dependentplasticity induced by thevoltage at the memristorv

mr

= vpost � vpre. The fluxcalculated from v

mr

>vth canbe defined as positive forDt > 0 and negative for Dt <0. This asymmetry is thebasis of stdp of memristivemtjs. Reproduced from B.Linares-Barranco et al., Na-ture Precedings (2009)

in the first chapter and use the well-defined dependence of theresistance on the flux as discussed on page 62.

We follow the scheme proposed by Linares-Barranco et al.85

85 B. Linares-Barranco andT. Serrano-Gotarredona,Nature Precedings (2009)

The action potential (spike) is assumed to have the form presentedin figure 61. It consists of an on-set side and an off-set side. Bothmight be described by exponential functions and characterizedby parameters like amplitude and curvature. The exact shape ofthe spike is irrelevant at this point. The important features are(i) a not vanishing temporal extent of the pulse and (ii) an am-plitude higher than the threshold voltage for memristor activa-tion vth. The meaning of vth is visualized in figure 62 where thehysteresis of the R(f)-curve opens only within a critical windowdefined by the fth values.

The temporal extend of the pulses is important because wewant to use the temporal overlap of both pulses. If vpre is appliedto one terminal of the memristor and vpost to the other terminalthen the net voltage at the synaptic mtj will be v

mr

= vpost� vpre.If furthermore, the spike timing Dt is small enough—this is theHebbian rule for synaptic plasticity—the two overlapping spikeswill create a signal as shown on the bottom of figure 61. The pre-eminent role of vth is visualized by the reddish area. This areaenclosed by vth and v

mr

can be identified with the over-thresholdflux fth.

th

188.0

183

177.6

R (!)

0 42 84

Flux (Vs)

�

th�

Figure 62: (cf. fig. 14)Typical resistance hysteresis.The hysteresis is open withina critical flux-window as in-dicated by the reddish lines.

The timing sensibility is introduced by the reversed sign of theover-threshold part of vMR for reversed temporal order of presy-naptic and postsynaptic spike. This is visualized on the right side

65

Take real properties into account

190.9188

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-0.55 0.0 0.55Voltage (V)

RH,P

RL,P

R H

R L

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We next turned our attention from synapses to neurons and from the barrier properties to the magnetic electrodes of the MTJs. With a new perspective on a phenomenon known as back-hopping,[8–11] we were able to demonstrate that memris-tive MTJs can emulate the behavior of neurons. Figure 4 shows an STT measurement, where the free magnetic electrode was switched by a spin-polarized current. At t 0.2 min, the mag-netic configuration was switched from the parallel state to an intermediate state with R 360 . For this first switching, a voltage of 420 mV was applied, which drove a current density of j 1.8 106 A cm 2. The occurrence of an intermediate state can be explained by the presence of magnetic domains within the free magnetic layer.[32–34] The intermediate state, however, was unstable. The magnetization of the free layer switched repeatedly between the intermediate state and the antiparallel state, indicating that back-hopping had been activated. When the positive bias was released (note the color scale), the sample remained in the antiparallel magnetic state of approximately 440 . Under negative bias, no switching or back-hopping was

A striking qualitative similarity between bio-logical synapses and memristive MTJs can be observed from the resistance traces presented in Figure 1 and 2 (compare, e.g., references [29,30]). The electrical activity at the memris-tive MTJ (synapse) led to a nonvolatile modu-lation of resistivity (synaptic strength). This is analogous to LTP and LTD, depending on the polarity of the bias. The next logical step was to verify a learning rule similar to the STDP observed for biological synapses (Figure 3A). To accomplish this step, we employed the voltage pulses described by v t. Given that u1(t) is the potential at the bottom electrode (presynaptic spike) and u2(t) is the poten-tial at the top electrode (postsynaptic spike), the bias at the memristive MTJ (synapse) is defined as the time delay-dependent func-tion v t(t). Provided that the amplitudes of the sawtooth functions are well chosen, a timing-dependent resistance modulation is observed. For high t, the bias does not exceed vth at any time, and resistance remains unchanged. For low t, however, negative or positive bias in excess of vth is applied, depending on the sign of t. The resulting STDP of memris-tive MTJs is presented in Figure 3B. Using sawtooth spikes with an amplitude of 0.3 V, we found a critical time delay of t 100 s for the resistance to be modified. The resist-ance change reached 4.59% for positive t and 3.48% for negative t. Note that because of the well-defined dependence of R on the flux, one is not restricted to sawtooth-shaped spikes. The actual shape of the stimulus is not decisive, since the resistance change R is determined by the flux, i.e., by the area enclosed by v t.

Figure 2. Resistance increase induced by a stimulus resulting from two sawtooth spikes with a positive delay of 40 s. The sawtooth spikes are presented on the top trace. The resulting difference signal is shown on the right axis. The resistance trace is colored according to the applied bias; the color scale is given by the inset. The activation threshold vth is indicated by dotted lines. See the Supporting Information for details on the estimation of the activation threshold.

173176179182

R (

)

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u (V

)

-0.5

0.0

0.5

v (V

)

t u1

u2

0.5-0.5v (V)

Figure 3. The STDP of biological and artificial synapses. A) The STDP observed for cultures of dissociated embryonic rat hippocampal neurons, data from reference [14]. B) The STDP of memristive MTJs. An initial state of 173.77 0.73 was modulated by R depending on the value of the positive delay t. For negative delays, the initial state was set to 180.26 0.21 . Selected voltage traces are presented in the insets; dotted lines indicate vth. See the Supporting Information for details on the initial state setting and all voltage and resistance traces.

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()

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wileyonlinelibrary.com © 2012 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim Adv. Mater. 2012, 24, 762–766

We next turned our attention from synapses to neurons and from the barrier properties to the magnetic electrodes of the MTJs. With a new perspective on a phenomenon known as back-hopping,[8–11] we were able to demonstrate that memris-tive MTJs can emulate the behavior of neurons. Figure 4 shows an STT measurement, where the free magnetic electrode was switched by a spin-polarized current. At t 0.2 min, the mag-netic configuration was switched from the parallel state to an intermediate state with R 360 . For this first switching, a voltage of 420 mV was applied, which drove a current density of j 1.8 106 A cm 2. The occurrence of an intermediate state can be explained by the presence of magnetic domains within the free magnetic layer.[32–34] The intermediate state, however, was unstable. The magnetization of the free layer switched repeatedly between the intermediate state and the antiparallel state, indicating that back-hopping had been activated. When the positive bias was released (note the color scale), the sample remained in the antiparallel magnetic state of approximately 440 . Under negative bias, no switching or back-hopping was

A striking qualitative similarity between bio-logical synapses and memristive MTJs can be observed from the resistance traces presented in Figure 1 and 2 (compare, e.g., references [29,30]). The electrical activity at the memris-tive MTJ (synapse) led to a nonvolatile modu-lation of resistivity (synaptic strength). This is analogous to LTP and LTD, depending on the polarity of the bias. The next logical step was to verify a learning rule similar to the STDP observed for biological synapses (Figure 3A). To accomplish this step, we employed the voltage pulses described by v t. Given that u1(t) is the potential at the bottom electrode (presynaptic spike) and u2(t) is the poten-tial at the top electrode (postsynaptic spike), the bias at the memristive MTJ (synapse) is defined as the time delay-dependent func-tion v t(t). Provided that the amplitudes of the sawtooth functions are well chosen, a timing-dependent resistance modulation is observed. For high t, the bias does not exceed vth at any time, and resistance remains unchanged. For low t, however, negative or positive bias in excess of vth is applied, depending on the sign of t. The resulting STDP of memris-tive MTJs is presented in Figure 3B. Using sawtooth spikes with an amplitude of 0.3 V, we found a critical time delay of t 100 s for the resistance to be modified. The resist-ance change reached 4.59% for positive t and 3.48% for negative t. Note that because of the well-defined dependence of R on the flux, one is not restricted to sawtooth-shaped spikes. The actual shape of the stimulus is not decisive, since the resistance change R is determined by the flux, i.e., by the area enclosed by v t.

Figure 2. Resistance increase induced by a stimulus resulting from two sawtooth spikes with a positive delay of 40 s. The sawtooth spikes are presented on the top trace. The resulting difference signal is shown on the right axis. The resistance trace is colored according to the applied bias; the color scale is given by the inset. The activation threshold vth is indicated by dotted lines. See the Supporting Information for details on the estimation of the activation threshold.

173176179182

R (

)

121086420

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-0.30.00.3

u (V

)

-0.5

0.0

0.5

v (V

)

t u1

u2

0.5-0.5v (V)

Figure 3. The STDP of biological and artificial synapses. A) The STDP observed for cultures of dissociated embryonic rat hippocampal neurons, data from reference [14]. B) The STDP of memristive MTJs. An initial state of 173.77 0.73 was modulated by R depending on the value of the positive delay t. For negative delays, the initial state was set to 180.26 0.21 . Selected voltage traces are presented in the insets; dotted lines indicate vth. See the Supporting Information for details on the initial state setting and all voltage and resistance traces.

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Biological system Memristor system

S. Cassenaer et al, Nature 448 (2007) 709

Memristors as artificial synapses

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T. Bliss at al, Nature 361 (1993) 31, Y. Goda et al, Neuron 16 (1996) 103S. Cassenaer et al, Nature 448 (2007) 709

Memristive System

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Neuromorphic circuits

Memristor plus CMOS

22

I(t)

CR

pulse triggersswitch

voltage thresholdtriggers pulse

J. Phys. D: Appl. Phys. 46 (2013) 093001 Topical Review

I(t)

CR

pulse triggersswitch

voltage thresholdtriggers pulse

Figure 12. Integrate-and-fire circuits: the perfect integrate-and-firemodel consists of a capacitor, threshold detector and switch (withoutresistor). Once the voltage reaches a threshold, the spike is fired andthe switch is closed to shunt the capacitor. In the leaky version, aresistor is added that slowly drains the capacitor with time. Thiscorresponds to leakage current through a membrane in a living cell.

integrate-and-fire [68–71]. The rather simple model capturestwo of the most important aspects of neuronal excitability;specifically, the neuron integrates the incoming signals andgenerates the spikes once a certain threshold is exceeded(figure 12).

This behaviour is often explained using two simple electriccircuits [72]. The perfect integrate-and-fire circuit consistsof a capacitor, threshold detector and switch. Once a spikeis fired, the switch closes and shunts the capacitor. Anadditional resistor is included in the leaky integrate-and-fire circuit. The resistor slowly drains the capacitor andcorresponds to leakage currents in the membrane. However,the integrate-and-fire functionality of a neural network isconsiderably simpler to implement than the synaptic efficacy.For example, oversampled Delta-Sigma modulators, which are1-bit analogue- digital converters, can mimic the integrate-and-fire behaviour [73, 74]. Therefore, the following paragraphsprimarily describe the use of memristive systems as synapsesbecause the integrate-and-fire functionality can be achievedusing conventional CMOS-technology.

2.5. Minimal requirements

We can summarize the primary requirements for a bio-inspiredneural network as follows.

(i) Devices that act as neurons and devices that behave likesynapses are needed, and the neurons are interconnectedvia the synapses.

(ii) The neurons integrate inhibitory and excitatory incomingsignals and fire once a threshold is exceeded.

(iii) The synapses exhibit LTP (cooperative, associative, andinput-specific), LTD, and STDP.

3. Implementations using memristive systems

The question may be asked as to why we want to constructneuromorphic systems that emulate the presented biologicalmechanisms. Carver Mead pioneered a considerable amount

excitatory

inhibitatoryneuronsynapse

Figure 13. Schematic symbols for synapses and neurons as used inthe following paragraphs.

of the research on this topic and explained the reasoning in thefollowing way [75]: For many problems, particularly those inwhich the input data are ill-conditioned and the computationcan be specified in a relative manner, biological solutions aremany orders of magnitude more effective than those we havebeen able to implement using digital methods. [...] Large-scale adaptive analog systems are more robust to componentdegradation and failure than are more conventional systems,and they use far less power. The need for less power isparticularly obvious if we compare the performance of thebrain of even an invertebrate with a computer CPU and contrastthe power consumption. However, there are some tasks thatare difficult for a human and easy for a computer, such asmultiplying two long numbers, and other problems that ahuman can easily solve but computers fail to solve.

In 2008, the use of memristors to mimic biologicalmechanisms, such as STDP, was already hypothesized[76]. Snider implemented the spike time dependence usingmemristive nanodevices as synapses and conventional CMOStechnology as neurons. He also suggested two electronicsymbols for neurons and synapses [76] that have been adaptedby some groups as well as in this paper; the symbols aredepicted in figure 13. Furthermore, Snider indicated thatwe should note that STDP alone might not be sufficient toimplement stable learning; more complex synaptic dynamicsand additional state variables may be required and refers towork by Carpenter et al [77] as well as Fusi and Abbott [78].

Although Snider suggested a new paradigm that useslarge-scale adaptive analogue systems, the approach still uses aglobal clock signal. In 2010, Pershin and Di Ventra described asmall system composed of three neurons and two synapses thatis fully asynchronous [79, 80]. The memristive behaviour wasemulated by a microcontroller combined with other commonelectronic components. They demonstrated how Ivan Pavlov’sfamous experiment [81] can be imitated with the basic circuitdepicted in figure 14 [79].

Initially, the output signal (salivation) is recorded independence on the sight of food or a bell sound. Only thesight of food (input signal 1) leads to salivation (neuron 3output); the bell (input signal 2) is not associated with food.There is a subsequent learning period where the input 1and input 2 signals are applied simultaneously. Afterwards,both individual input signals induce salivation. The elegantexperiment demonstrates how an important function of thebrain, namely associative memory [79], can be constructedwith a circuit, as shown in figure 14.

A similar simulation was conducted by Cantley et al usingSPICE (UC Berkeley, CA, USA) and MATLAB (Natick, MA,USA), and they noted Also, it should be pointed out that theassociation as presented (in figure 4) can be unlearned. This

6

J. Phys. D: Appl. Phys. 46 (2013) 093001 Topical Review

I(t)

CR

pulse triggersswitch

voltage thresholdtriggers pulse

Figure 12. Integrate-and-fire circuits: the perfect integrate-and-firemodel consists of a capacitor, threshold detector and switch (withoutresistor). Once the voltage reaches a threshold, the spike is fired andthe switch is closed to shunt the capacitor. In the leaky version, aresistor is added that slowly drains the capacitor with time. Thiscorresponds to leakage current through a membrane in a living cell.

integrate-and-fire [68–71]. The rather simple model capturestwo of the most important aspects of neuronal excitability;specifically, the neuron integrates the incoming signals andgenerates the spikes once a certain threshold is exceeded(figure 12).

This behaviour is often explained using two simple electriccircuits [72]. The perfect integrate-and-fire circuit consistsof a capacitor, threshold detector and switch. Once a spikeis fired, the switch closes and shunts the capacitor. Anadditional resistor is included in the leaky integrate-and-fire circuit. The resistor slowly drains the capacitor andcorresponds to leakage currents in the membrane. However,the integrate-and-fire functionality of a neural network isconsiderably simpler to implement than the synaptic efficacy.For example, oversampled Delta-Sigma modulators, which are1-bit analogue- digital converters, can mimic the integrate-and-fire behaviour [73, 74]. Therefore, the following paragraphsprimarily describe the use of memristive systems as synapsesbecause the integrate-and-fire functionality can be achievedusing conventional CMOS-technology.

2.5. Minimal requirements

We can summarize the primary requirements for a bio-inspiredneural network as follows.

(i) Devices that act as neurons and devices that behave likesynapses are needed, and the neurons are interconnectedvia the synapses.

(ii) The neurons integrate inhibitory and excitatory incomingsignals and fire once a threshold is exceeded.

(iii) The synapses exhibit LTP (cooperative, associative, andinput-specific), LTD, and STDP.

3. Implementations using memristive systems

The question may be asked as to why we want to constructneuromorphic systems that emulate the presented biologicalmechanisms. Carver Mead pioneered a considerable amount

excitatory

inhibitatoryneuronsynapse

Figure 13. Schematic symbols for synapses and neurons as used inthe following paragraphs.

of the research on this topic and explained the reasoning in thefollowing way [75]: For many problems, particularly those inwhich the input data are ill-conditioned and the computationcan be specified in a relative manner, biological solutions aremany orders of magnitude more effective than those we havebeen able to implement using digital methods. [...] Large-scale adaptive analog systems are more robust to componentdegradation and failure than are more conventional systems,and they use far less power. The need for less power isparticularly obvious if we compare the performance of thebrain of even an invertebrate with a computer CPU and contrastthe power consumption. However, there are some tasks thatare difficult for a human and easy for a computer, such asmultiplying two long numbers, and other problems that ahuman can easily solve but computers fail to solve.

In 2008, the use of memristors to mimic biologicalmechanisms, such as STDP, was already hypothesized[76]. Snider implemented the spike time dependence usingmemristive nanodevices as synapses and conventional CMOStechnology as neurons. He also suggested two electronicsymbols for neurons and synapses [76] that have been adaptedby some groups as well as in this paper; the symbols aredepicted in figure 13. Furthermore, Snider indicated thatwe should note that STDP alone might not be sufficient toimplement stable learning; more complex synaptic dynamicsand additional state variables may be required and refers towork by Carpenter et al [77] as well as Fusi and Abbott [78].

Although Snider suggested a new paradigm that useslarge-scale adaptive analogue systems, the approach still uses aglobal clock signal. In 2010, Pershin and Di Ventra described asmall system composed of three neurons and two synapses thatis fully asynchronous [79, 80]. The memristive behaviour wasemulated by a microcontroller combined with other commonelectronic components. They demonstrated how Ivan Pavlov’sfamous experiment [81] can be imitated with the basic circuitdepicted in figure 14 [79].

Initially, the output signal (salivation) is recorded independence on the sight of food or a bell sound. Only thesight of food (input signal 1) leads to salivation (neuron 3output); the bell (input signal 2) is not associated with food.There is a subsequent learning period where the input 1and input 2 signals are applied simultaneously. Afterwards,both individual input signals induce salivation. The elegantexperiment demonstrates how an important function of thebrain, namely associative memory [79], can be constructedwith a circuit, as shown in figure 14.

A similar simulation was conducted by Cantley et al usingSPICE (UC Berkeley, CA, USA) and MATLAB (Natick, MA,USA), and they noted Also, it should be pointed out that theassociation as presented (in figure 4) can be unlearned. This

6

Use existing CMOS Use memristors

mem

ristor

−∞−∞

Implementation of memristors

23

Neuromorphic nanoscale memristor synapses 13

VddVddVdd

VddVdd

Ith

I�

Isyn

Vin3

Vin2

Vw

IwN

Vin1

Vin4

VinNVw

Vw

Vw

VwIw

(a) (b)

Figure 6: Neuromorphic memristive synapse. (a) Schematic circuit implementing an

array of memristive synapses, with independent inputs and synaptic weights, but with

shared temporal dynamics. (b) SPICE simulations of the circuit in Fig. 6a showing the

output Isyn EPSC in response to a pre-synaptic input spike, for 4 di↵erent memristor

conductance values.

produce. Larger memristor conductances, which represent a larger number of open

proteic channels in real synapses, correspond to larger synaptic weights.

Figure 6b shows the results of SPICE simulations of the circuit in Fig. 6a, for a

180 nm CMOS process. The Ithr and I⌧ current sources were implemented with p-type

MOSFETs, biased to produce 2 pA and 10 pA respectively, and the Vw voltage bias was

set to 700mV. The data was obtained by simulating the response of one input memristive

branch to a single input spike, while sweeping the memristor impedance from 1K⌦ to

7K⌦. In these simulations we set the memristor in its LRS, and assumed we could

modulate the value of the resistance to obtain four distinct analog states analogous to

the ones measured experimentally in Fig. 2b. Of course the circuit supports also the

operation of the memristor as a binary device, working in either the HRS state or the

LRS one. This bi-stable mode of using the memristor would encode only an “on” or

“o↵” synaptic state, but it would be more reliable and it is compatible with biologically

plausible learning mechanisms, such as those proposed in [71], and implemented in [69].

The circuit of Fig. 6a shows only the circuit elements required for a “read” operation,

i.e., an operation that stimulates the synapse to generate an EPSC with an amplitude set

by the conductance of the memristor. Additional circuit elements would be required to

change the value of the memristor’s conductance, e.g., via learning protocols. However

the complex circuitry controlling the learning mechanisms would be implemented at the

Input/Output (I/O) periphery of the synaptic array, for example with pulse-shaping

circuits and architectures analogous to the ones described in Section 3, or with circuits

that check the state of the neuron and of it’s recent spiking history, such as those

G. Indiveri et al., Nanotech. 24 (2013) 384010

existing neuromorphic chip design + memristor pads + additional electronics

= neuronal circuit with synaptic weights

Existing neuromorphic chips often lack synaptic weights (>1000 Neurons)

Neuromorphic chip design (AG E. Chicca, Citec Bielefeld),

Memristor preparation and lithography (AG A. Thomas, U Bielefeld)

Take home message

25

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T. Bliss at al, Nature 361 (1993) 31, Y. Goda et al, Neuron 16 (1996) 103S. Cassenaer et al, Nature 448 (2007) 709

Memristive System

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