Memristors & Their Potential Applications

A Literature Review

Introduction• What is Memristor

Stands for ‘Memory Resistor’

Fourth basic passive circuit element (2-terminal) with R, L & C

First theoretically predicted by Leon Chua from UC Berkeley back in 1971.

Provide missing link between Flux-linkage ø, and charge, q

Introduction (Cont…)Properties of Memristor

Function of amount of charge flowing through it.

Can remember it’s last electrical state (Memristance) even if power is turned OFF.

Voltage & current waves have same zero crossings (no phase shift between them)

Pinched Hysteresis loop shrinks with increased in frequency, w

Purely dissipative device, no storage of energy

Introduction (Cont…) First passive realization of memristor was doneby HP in 2008 by fabricating with TiO2 and Ptelectrode.

Advantages of Memristor• Can work as both memory and logic functions• Higher data density due to nano-scale size• Requires less energy and dissipate less heat• Combines the jobs of working memory and hard drives

into one tiny device (Non-volatile memory)• Faster and less expensive than MRAM• Provides greater reliability when power is interrupted in

data centers• Would allow for a quicker boot up since information is not

lost when the device is turned off• Can use anything between 0 and 1 (0.3, 0.8, 0.5, etc.)• Compatible with CMOS process and provide innovating

nanotechnology due to the fact that it performs better the smaller it becomes.

Non-Volatile Memristor Memory 4

The concept of Universal Memory can be realized by using Memristor alone as it combines the advantages of both memories residing on top most and bottom of the hierarchy.

Memristor Based IMPLY Logic Tradeoff between speed (fast write times) and correct logic behavior

|VCOND| < |VSET |When p = 1 (RON, low res.), VQ = VSET - VCOND , so q = no changeWhen p, q = 0,(ROFF, high res.), VQ = VSET, Q switched ON, q = 1When p = 0, q =1 , VQ = VSET , so q = no change

Potential Application #1

FPAAs (Field Programmable Analog Arrays)

FPAAs (Field Programmable Analog Arrays)1

Limitations of Conventional FPAAs:

limited in the range of configurable states

Lacks ability to electrically tune the resistance

Solutions: By including memristor crossbar junctions in the input and feedback path of an op‐amp capacitor array, a transfer function can be tuned to adjust the gain, pole and/or zero of a filter.

Advantages: Conversion between LPF and HPFby appropriate selection of ON/OFFstates of Mij.

Tuning of f‐3dB or pole/zero byadjustment of memristance state.

Cascading multiple stages canprovide for tunable band-passadjustment

Dynamic PID controllers can beimplemented by connecting multiplestages in parallel.

Potential Application #2

Programmable Analog ICs

1) Fine-Resolution Programmable Resistor or Memristor-based digital potentiometer

2) Programmable Gain Amplifier3) Programmable Threshold Comparator4) Programmable Switching Thresholds Schmitt Trigger5) Programmable Frequency Relaxation Oscillator

Fine-Resolution Programmable Resistor 2

Pulse-coded programmable resistor using a memristor.

Need of a Programmable Resistor:In many high-frequency circuits such as amplifiers and filters, resistors need to be programmed for adaptation to particular applications or for compensation for PVT variations.

Problems with Conventional Ones:

In the switch-controlled resistors composed of an array of weighted resistors andswitches used to realize such programmable resistor; the MOS switches typically introduce largeparasitic capacitances and resistances. Furthermore, the parasitic values are dependent on theswitch state. The state-dependent large parasitics limit the resolution and the number of bits ofswitching resistors. The usage of floating gate structures for realizing programmable resistor has long termreliability problems as the stored charge on the floating gate may slowly leak away with time.

Advantages: • The most distinct feature of this memristor-based programmable resistor is that theresolution step of resistance can be adjusted with VPT, duty ratio, and ωPT.

• Ease of programming and controllability due to the fact that memristance isprogrammed by patterning the pulse waveform.• The resistance programming with fine resolution and small parasitics is very useful inmany midband and RF-range differential circuits.

Fine-Resolution Programmable Resistor 2 (Cont…)• In order to block any dc mismatch or even order mismatches, which can cause

unbalanced flux between the differential signals, two blocking capacitors (CB) are used to isolate the even-order mismatch effects

• Memristance is programmed by patterning the pulse waveform.• The flux can be linearly controlled by determining the number of pulses (NPULSE),

duty ratio, pulse amplitude (VPT), and pulse frequency (ωPT).

Memristor-based Digital Potentiometer 3

Main idea of using memristors in analog circuits is based on the fact that the rate of memristance change depends essentially on the magnitude of applied voltage. At voltages below a certain threshold, the change of memristance is extremely slow, whereas at voltages above the threshold, , it is fast.

Programmable memristors operate basically as digital potentiometers that has several advantages over traditional potentiometer:

(i) Higher density chips/smaller electronic components due to very small memristor size (e.g. 30 x 30 nm2)

(ii) The operation of potentiometer requires less transistors as the information about resistance is written directly into a memristive medium.

(iii) The resistance is remembered in the analog form potentially allowing for higher resolution.

Memristor based digital potentiometerconsisting of the memristor M1 ,a coupleof FETs Q1 & Q2. The external controlsignals Vpp & Vpn are used to programthe resistance of memristor betweentwo limiting values R1 & R2 . Vpr is thememristor’s programming voltage thatshould exceed the threshold voltage ofmemristor, Vth.

Programmable Gain Amplifier 2

Circuit schematic of programmable gain amplifier using memristor, RL is the equivalent resistance of the pulse-programmed memristance.

Mid-band equivalent circuit, where Ci and Co are parasitic input and output capacitances, respectively.

Features: Designed together with a 0.18-μm CMOS process and utilizing the memristor based programmable resistor

With the memristor-based load resistance (RL ), the ac voltage gain is easily programmable by controlling the flux amount across the memristor

This circuit becomes more advantageous whenthe application frequency is in the RF range, since the blocking capacitors can be integrated together with CMOS active devices for higher input frequencies.

The mid-band ac voltage gain isAv = gm(ro || RL )

neglecting high-frequency effect of Ci & Co ,where gm is diff transconductance of M1 &M2,ro is amplifier’s o/p impedance formed byM1∼M4

Programmable Gain Amplifier 3

(a) The Op-Amp A1 is connected in the standard non-inverting amplifierconfiguration with a memristor replacing a resistor. Two FETs (Q1/Q2) areused to program the resistance of the memristor thus selecting the amplifiergain. The capacitor C1 = 0.1 uF is used for noise suppression.(b) Programming of gain using 10-ms width pulses. In these measurements,the input voltage Vin =0.2 V is permanently supplied while positive andnegative pulses change the state of memristor and correspondingly circuit’sgain. As a result, we observe a set of steps in the output signal.(c) Coarser control of gain using 20 ms width pulses.

The gain of such amplifier is given by:

The gain is determined by memristance RM which can be programmed between two limiting values Rmin & Rmax using two FETs. The desirable regime of operation that minimizes the voltage applied to the memristor is RM << R1

The amplifier’s gain is controlled using pulses of constant width.

Longer pulses produce larger changes in allowing for coarser control of the gain (Fig c).

Programmable Threshold Comparator 3

(a) Schematics of a programmable threshold comparator. Here R1 = 10 kΩand A1 is an operational amplifier.

(b) Programmable threshold comparator response to the input voltageVin = Vosin(2πft) with Vo = 1.3 V & f = 1 Hz, and several negativeprogramming pulses of 10 ms width applied in the time interval between4 and 8 seconds. Each 10 ms voltage pulse changes RM by approximately430 Ω causing a gradual decrease of the comparator threshold.

It involves the memristor-based digital potentiometerblock

The comparator threshold is determined by the voltage onthe memristor given by

If the signal amplitude at the positive input exceeds, thenoutput signal is equal to the saturation voltage of theoperational amplifier (which in the present case is close to V).In the opposite case, is close to 2.5 V.

Programmable Switching Thresholds Schmitt Trigger 3

(a) Schematics of a programmable switching thresholds Schmitttrigger with memristor. Here, R1 = 10 kΩ. (b) Programmableswitching thresholds Schmitt trigger response to the inputvoltage Vin = Vo sin(2πft) with Vo = 1.3 V & f = 1 Hz, and severalpositive programming pulses of 10 ms width applied in the timeinterval between 2 and 4 s.

It involves the memristor-based digital potentiometerblock

This circuit behaves as an inverted comparator withthe switching thresholds given by

When we apply programming pulses to M1, itsresistance RMchanges as well as the switching thresholdsof Schmitt trigger.

Programmable Frequency Relaxation Oscillator 3

(a) Schematics of a programmable frequency relaxation oscillator with memristor. Here, R1 = R2 =10 kΩ and C1 = 10 µF. (b) Oscillating signals in the different points of the programmablefrequency relaxation oscillator. The lower panel demonstrates an increase in the oscillationfrequency as RM is decreased by several negative pulses applied to V+ .

It involves the memristor-based digital potentiometer block and Schmitt trigger.

The relaxation oscillator is a well-known circuit which automatically oscillates because of the negative feedback added to a Schmitt trigger by an RC circuit.

The period of oscillations is determined by both the RC components and switching thresholds of the Schmitt trigger. Therefore, in order to control the relaxation oscillator frequency, a memristor-based digital potentiometer is used to vary switching thresholds of the Schmitt trigger.

Potential Application #3

Programmable Drive Waveforms

Programmable Drive Waveforms 1

Assuming RLOW of memristors << RF, R

Problems with Conventional Drive Waveform Circuits:• In many electronics applications, variation of circuit parameters due to temp.

change, aging, etc. require adjustment of drive waveforms.• Waveform adjustment is also desirable for mode adjustment in various apps.• Timing modulation and amplitude modulation circuits implemented in

hardware can require complex circuitry and have limitations in adaptability and the range ofpossible waveforms.

• Software based solutions require a microprocessor which can be difficult and/orexpensive to miniaturize for several portable electronics applications.

Solution: Memristor Crossbar Drive Waveform Circuit

Advantages:• Both timing and amplitude of o/pwaveform can be adjusted by binary switching of thememristance states in the crossbar.• Even with only binary memristanceswitching, large number of possible drive waveformsare available.• Combined with techniques such as hillclimbing and genetic algorithms has potential for selfoptimizing drive waveforms and real‐time adaptionof circuitry to effects of aging and temp variation.

Potential Application #4

Pattern Recognition

Pattern Recognition 1

Advantages:• O/P voltage from 1st op‐amp is

analogous to XNOR (bit comparator) function.

• Tuning Vref can adjust sensitivity ofpattern comparison and adjust allowable biterror between resistance states and voltagestates.

• Allowing for bit error couldpotentially be very useful to applications suchas facial recognition which can requirerobustness to a large percentage of bit errors.

Problems with Conventional Pattern Recognition Solutions:• Software‐based solutions require time for data transfer between memory and

processor circuits which causes a lag in responsiveness.• Hardware solutions can be faster but have limits in adaptability and limits in the

range of patterns that can be classified.• Memristors offer a route to a “morphware” pattern recognition solution

combining both memory storage and data processing in a common circuit.

Solution: Memristor Crossbar Pattern Comparison Circuit (V>Vth for Write Mode and V<Vth for Detect Mode)

Potential Application #5

Arithmetic Optimization Problems

Arithmetic Optimization Problems 1Problems with Conventional Arithmetic Processor Designs :

• Segmentation between memory and processor circuitry may produce a bottleneck in speed. New clock independent designs are desirable.

• Logic based arithmetic is inefficient for some network optimization problems involving repeated recalculation of sums

Assuming RLOW of memristors << R/8Analog output representative of 2+4

Solution: Memristor Crossbar Arithmetic Circuit

Advantages:• Although op‐amps are slower than

logic circuits, the combination of memory and processing in a single circuit reduces the reliance on a clock.

• May be scalable to provide real time solutions to network optimization.

Potential Application #6

Signal Mixing

Signal Mixing Problems with Conventional Modulation Systems:

• Increase in portable wireless electronics requires more efficient uses of spectrumwith techniques such as frequency hopping.

• Simpler but more secure signal encryption methods are desirable.

Solution: Back‐to‐back diode memristor crossbar

Equivalent circuit at each crossbar junction

For VinB less than the diode thresholdvoltage, the resistance state of Mij andvoltage state of VinA can be used tomodulate signal transmission.

Advantages:• Switching of carrier

frequencies allow more efficient use ofspectrum and compensation forcrowded channels.

• Potential exist for improvedsignal encryption by sharing arandomized memristance switchingpattern between sender and receiver.

Input Wiring

Potential Application #7

Artificial Intelligence

Artificial IntelligencePotential Routes to Strong A.I. with Memristor Crossbars:

• Neural Networks (feed-forward of nonlinear weighted sums of memristance states)

• Genetic Algorithms (selection, crossover, and mutation of memristance states)• Emergent Complexity from Memory‐Prediction Framework (Hawkins

approach)• Fuzzy Logic implementation

Memristor Crossbar Circuit Design for Sensor Stimulated Emergent Behavior

References[1] Blaise Mouttet, “Proposals for Memristor Crossbar Design and Applications”, Memristors and

Memristive Systems Symposium, UC Berkeley, Nov, 2008.

[2] S. Shin, K. Kim, and S.M. Kang, “Memristor Applications for Programmable Analog ICs”, IEEE

Tran. on Nanotech., vol. 10, no. 2, Mar 2011.

[3] Y. V. Pershin and M. D. Ventra, “Practical Approach to Programmable Analog Circuits With

Memristors” , IEEE Tran on Circuits & Systems, vol. 57, no. 8, Aug 2010.

[4] Yenpo Ho, Garng M. Huang and Peng Li, “Nonvolatile Memristor Memory: Device Characteristics

and Design Implications”, ICCAD’09, Nov 2–5, 2009, San Jose, California, USA.

[5] S. Kvatinsky, A. Kolodny and E. G. Friedman, “Memristor-based IMPLY Logic Design Procedure”,

ICCD '11 Proceedings, p.p. 142-147, 2011, USA

[6] D. B. Strukov, G. S. Snider, D. R. Stewart and R. S. Williams, “The missing memristor found”, Nature

Letters, vol 453, May, 2008.

[7] Chua, L. O., “Memristor - the missing circuit element”, IEEE Trans. Circuit Theory, 18, 507–519

(1971).

Thank You

Q & A