Memristors and their potential applications 2012

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 done
by HP in 2008 by fabricating with TiO2 and Pt
electrode.

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 change
When p, q = 0,(ROFF, high res.), VQ = VSET, Q switched ON, q = 1
When 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 HPF
by appropriate selection of ON/OFF
states of Mij.
 Tuning of f‐3dB or pole/zero by
adjustment of memristance state.
 Cascading multiple stages can
provide for tunable band-pass
adjustment
 Dynamic PID controllers can be
implemented by connecting multiple
stages in parallel.

Programmable Analog ICs
1) Fine-Resolution Programmable Resistor or Memristor-
based digital potentiometer
2) Programmable Gain Amplifier
3) Programmable Threshold Comparator
4) Programmable Switching Thresholds Schmitt Trigger
5) 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 and
switches used to realize such programmable resistor; the MOS switches typically introduce large
parasitic capacitances and resistances. Furthermore, the parasitic values are dependent on the
switch state. The state-dependent large parasitics limit the resolution and the number of bits of
switching resistors.
 The usage of floating gate structures for realizing programmable resistor has long term
reliability 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 the
resolution step of resistance can be adjusted with VPT, duty ratio, and ωPT.
• Ease of programming and controllability due to the fact that memristance is
programmed by patterning the pulse waveform.
• The resistance programming with fine resolution and small parasitics is very useful in
many 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 potentiometer
consisting of the memristor M1 ,a couple
of FETs Q1 & Q2. The external control
signals Vpp & Vpn are used to program
the resistance of memristor between
two limiting values R1 & R2 . Vpr is the
memristor’s programming voltage that
should exceed the threshold voltage of
memristor, 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 when
the 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 is
Av = 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 by
M1∼M4

Programmable Gain Amplifier 3
(a) The Op-Amp A1 is connected in the standard non-inverting amplifier
configuration with a memristor replacing a resistor. Two FETs (Q1/Q2) are
used to program the resistance of the memristor thus selecting the amplifier
gain. 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 and
negative pulses change the state of memristor and correspondingly circuit’s
gain. 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 kΩ
and A1 is an operational amplifier.
(b) Programmable threshold comparator response to the input voltage
Vin = Vosin(2πft) with Vo = 1.3 V & f = 1 Hz, and several negative
programming pulses of 10 ms width applied in the time interval between
4 and 8 seconds. Each 10 ms voltage pulse changes RM by approximately
430 Ω causing a gradual decrease of the comparator threshold.
 It involves the memristor-based digital potentiometer
block
 The comparator threshold is determined by the voltage on
the memristor given by
 If the signal amplitude at the positive input exceeds, then
output signal is equal to the saturation voltage of the
operational 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 Schmitt
trigger with memristor. Here, R1 = 10 kΩ. (b) Programmable
switching thresholds Schmitt trigger response to the input
voltage Vin = Vo sin(2πft) with Vo = 1.3 V & f = 1 Hz, and several
positive programming pulses of 10 ms width applied in the time
interval between 2 and 4 s.
block
 This circuit behaves as an inverted comparator with
the switching thresholds given by
 When we apply programming pulses to M1, its
resistance RMchanges as well as the switching thresholds
of 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 programmable
frequency relaxation oscillator. The lower panel demonstrates an increase in the oscillation
frequency as RM is decreased by several negative pulses applied to V+ .
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.

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 of
possible waveforms.
• Software based solutions require a microprocessor which can be difficult and/or
expensive to miniaturize for several portable electronics applications.
Solution: Memristor Crossbar Drive Waveform Circuit
Advantages:
• Both timing and amplitude of o/p
waveform can be adjusted by binary switching of the
memristance states in the crossbar.
• Even with only binary memristance
switching, large number of possible drive waveforms
are available.
• Combined with techniques such as hill
climbing and genetic algorithms has potential for self
optimizing drive waveforms and real‐time adaption
of circuitry to effects of aging and temp variation.

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 of
pattern comparison and adjust allowable bit
error between resistance states and voltage
states.
• Allowing for bit error could
potentially be very useful to applications such
as facial recognition which can require
robustness 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)

Arithmetic Optimization Problems

Arithmetic Optimization Problems 1
Problems 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/8
Analog 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.

Signal Mixing

Signal Mixing
Problems with Conventional Modulation Systems:
• Increase in portable wireless electronics requires more efficient uses of spectrum
with 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 threshold
voltage, the resistance state of Mij and
voltage state of VinA can be used to
modulate signal transmission.
Advantages:
• Switching of carrier
frequencies allow more efficient use of
spectrum and compensation for
crowded channels.
• Potential exist for improved
signal encryption by sharing a
randomized memristance switching
pattern between sender and receiver.
Input Wiring

Artificial Intelligence

Artificial Intelligence
Potential 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).

Memristors and their potential applications 2012

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Memristors and their potential applications 2012