MEMRISTOR by playboy14


									MEMRISTOR-THE                                                      and the flux linkage
                                                                  is introduced as the
MISSING CIRCUIT                              fourth basic circuit element. Many circuit-
                                             theoretic properties of memistors are
ELEMENT                                      derived. It is shown that this element
                                             exhibits some peculiar behavior different
                                             from that exhibited by resistors, inductors,
                                             or capacitors. These properties lead to a
                                             number of unique applications which
                                             cannot be realized with RLC networks

                                                         The first, as the name "memory
                                             resistor" implies, is for a type of non-
                                             volatile random access memory, or
                                             NVRAM. Such a memory would have
                                             very useful properties, in that it would not
                                             'forget' the data that it stores when the
                                             power is turned off.

                                                          This paper presents the logical
                                             and scientific basis for the existence of a
                                             new two terminal circuit element called
                                             memristor (a contraction for memory
                                             resistor) which has every right to be a
                                             basic as the three classical circuit elements
                                             already in existence, namely, the inductor,
                                             resistor and capacitor. Although the
                                             existence of a memristor in the form of a
                                             physical device without internal power
                                             supply has not yet been discovered it is
                                             realized using active circuit elements in

Abstract:                                    INTRODUCTION:
          A new two-terminal circuit         What is memristance?
element-called the memristor characterized
by a relationship between the charge
           Memristance is a property of an            An ideal memristor is a passive two-
electronic component. If charge flows in        terminal electronic device that is built to
one direction through a circuit, the            express only the property of memristance
resistance of that component of the circuit     (just as a resistor expresses resistance and
will increase, and if charge flows in the       an inductor expresses inductance).
opposite direction in the circuit, the          However, in practice it may be difficult to
resistance will decrease. If the flow of        build a 'pure memristor,' since a real
charge is stopped by turning off the            device may also have a small amount of
applied voltage, the component will             some other property, such as capacitance
'remember' the last resistance that it had,     (just as any real inductor also has
and when the flow of charge starts again        resistance).
the resistance of the circuit will be what it
was when it was last active.
                                                What is an analogy for a memristor?
Why is memristance important?                         A common analogy for a resistor is a
                                                pipe that carries water. The water itself is
        It turns out that memristance is        analogous to electrical charge, the pressure
becoming stronger as the feature sizes in       at the input of the pipe is similar to
circuits are getting smaller. At some point     voltage, and the rate of flow of the water
as we scale into the realm of nano              through the pipe is like electrical current.
electronics, it will be necessary to            Just as with an electrical resistor, the flow
explicitly take account of memristance in       of water through the pipe is faster if the
our circuit models in order to simulate and     pipe is shorter and/or it has a larger
design electronic circuits properly.            diameter. An analogy for a memristor is an
                                                interesting kind of pipe that expands or
                                                shrinks when water flows through it. If
Have people seen memristance before?            water flows through the pipe in one
                                                direction, the diameter of the pipe
         Yes, we are aware of over 100          increases, thus enabling the water to flow
published papers going back to at least the     faster. If water flows through the pipe in
early 1960's in which researchers observed      the opposite direction, the diameter of the
and reported unusual 'hysteresis' in their      pipe decreases, thus slowing down the
current-voltage plots of various devices        flow of water. If the water pressure is
and circuits based on many different types      turned off, the pipe will retain it most
of materials and structures. In retrospect,     recent diameter until the water is turned
we can understand that those researchers        back on. Thus, the pipe does not store
were actually seeing memristance, but they      water like a bucket (or a capacitor) – it
were apparently not aware of it.                remembers how much water flowed
                                                through it.

                                                Aren't there other fundamental passive
                                                devices that don't add energy to a
                                                circuit? What about diodes?

                                                      No, there are only four fundamental
                                                types of passive circuit elements. Diodes
What is a memristor?                            are just non-linear resistors - the resistance
                                                of a diode changes with the applied
                                                voltage, but if you turn off the voltage and
start back at 0 volts, the resistance of the   It can be inferred from this that
diode is the same as it was before at 0        memristance is simply charge-dependent
volts, not what it was when the voltage        resistance. If M (q (t)) is a constant, then
was turned off. This is also true of a         we obtain Ohm's Law R (t) = V (t)/ I (t). If
resistor that heats up and increases its       M (q (t)) is nontrivial, however, the
resistance because of a temperature            equation is not equivalent because q(t) and
increase. Thus, neither a diode nor a          M(q(t)) will vary with time. Solving for
heated resistor ‘remembers' their history.     voltage as a function of time we obtain
However, each type of fundamental circuit
element is actually a family of devices
with essentially an infinite number of
higher order members.

MEMRISTOR THEORY:                              This equation reveals that memristance
                                               defines a linear relationship between
                                               current and voltage, as long as charge does
                                               not vary. Of course, nonzero current
                                               implies time varying charge. Alternating
                                               current, however, may reveal the linear
                                               dependence in circuit operation by
                                               inducing a measurable voltage without net
                                               charge movement—as long as the
                                               maximum change in q does not cause
        Memristor symbol.                      much change in M.

The memristor is formally defined as a         Furthermore, the memristor is static if no
two-terminal element in which the              current is applied. If I(t) = 0, we find V(t)
magnetic flux Φm between the terminals is      = 0 and M(t) is constant. This is the
a function of the amount of electric charge    essence of the memory effect.
q that has passed through the device. Each
memristor is characterized by its              The power consumption characteristic
memristance function describing the            recalls that of a resistor, I2R.
charge-dependent rate of change of flux
with charge.
                                               As long as M (q (t)) varies little, such as
                                               under alternating current, the memristor
                                               will appear as a resistor. If M(q(t))
                                               increases rapidly, however, current and
Noting from Faraday's law of induction         power consumption will quickly stop.
that magnetic flux is simply the time          Magnetic flux in a passive device in
integral of voltage, and charge is the time    circuit theory, magnetic flux Φm
integral of current, we may write the more     typically relates to Faraday's law of
convenient form                                induction, which states that the voltage
                                               in terms of energy gained around a loop
                                               (electromotive force) equals the negative
                                               derivative of the flux through the loop:
                                                 to connect pairs of the four fundamental
                                                 circuit variables (current, i; voltage, v;
Appendix: Ohm's law and its three                charge, q; magnetic flux, )1. Of these, five
siblings                                         are well known. Two arise from the
       finally, let me wrap up by a table        definitions of two of the variables
that makes it clear why there are four basic     concerned: charge and magnetic flux are
elements. For the sake of simplicity, we         the time integrals of current and voltage
will be assuming that the relationships are      (dq = i dt and d = v dt), respectively. The
linear. In reality, they are nonlinear. In all   other three lead to the axiomatic properties
four cases, they are relationships between       of three classic circuit elements:
the current I (or its integral over time,        resistance, R, is the rate of change of
namely the charge Q) and the voltage V           voltage with current; capacitance, C, that
(or its integral over time, a sort of            of charge with voltage; and inductance, L,
magnetic flux Φ or flux linkages).               that of flux with current.

There are two places where you can put
the integral sign (or you don't have to): in
front of "I" and/or in front of "V". So there
are clearly 2 x 2 = 4 combinations how to
construct a version of Ohm's law:

Name            Law              Constant k      Implementations:
resistor         I=k V           k = 1/R
                                                 1. Titanium dioxide memristor
capacitor       ∫I = k V         k=C
inductor         I = k ∫V        k = 1/L         Interest in the memristor revived in 2008
memristor       ∫I = k ∫V        k = 1/M         when an experimental solid state version
                                                 was reported by R. Stanley Williams of
                                                 Hewlett Packard. A solid-state device
Once again, the resistor and the memristor       could not be constructed until the unusual
could look like the same thing but it is not     behavior of nano scale materials was better
quite the case because you can't quite           understood. The device neither uses
cancel the integral sign - because the           magnetic flux as the theoretical memristor
constant of integration can be nonzero.          suggested, nor stores charge as a capacitor
                                                 does, but instead achieves a resistance
                                                 dependent on the history of current using a
                                                 chemical mechanism.
There are six independent permutations of
two objects from a bank of four. Thus, six       The HP device is composed of a thin (50
mathematical relations might be construed        nm) titanium dioxide film between two 5
nm thick electrodes, one Ti, the other Pt.      10−10 cm2/(V·s). In comparison, the
Initially, there are two layers to the          highest known drift ionic mobilities occur
titanium dioxide film, one of which has a       in advanced superionic conductors, such as
slight depletion of oxygen atoms. The           rubidium silver iodide with about 2×10−4
oxygen vacancies act as charge carriers,        cm2/(V·s) conducting silver ions at room
meaning that the depleted layer has a much      temperature. Electrons and holes in silicon
lower resistance than the non-depleted          have a mobility ~1000 cm2/(V·s), a figure
layer. When an electric field is applied, the   which is essential to the performance of
oxygen vacancies drift (see Fast ion            transistors. However, a relatively low bias
conductor), changing the boundary               of 1 volt was used, and the plots appear to
between the high-resistance and low-            be generated by a mathematical model
resistance layers. Thus the resistance of the   rather than a laboratory experiment.
film as a whole is dependent on how much
charge has been passed through it in a          2.Polymeric memristor
particular direction, which is reversible by
changing the direction of current. Since the    In July 2008, Victor Erokhin and Marco P.
HP device displays fast ion conduction at       Fontana, in Electrochemically controlled
nanoscale, it is considered a nanoionic         polymeric device: a memristor (and more)
device.                                         found two years ago, claim to have
                                                developed a polymeric memristor before
Memristance is displayed only when both         the titanium dioxide memristor more
the doped layer and depleted layer              recently announced.
contribute to resistance. When enough
charge has passed through the memristor         3. Spin memristive systems
that the ions can no longer move, the
device enters hysteresis. It ceases to          A fundamentally different mechanism for
integrate q=∫Idt but rather keeps q at an       memristive behavior has been proposed by
upper bound and M fixed, thus acting as a       Yuriy V. Pershin and Massimiliano Di
resistor until current is reversed.             Ventra in their paper "Spin memristive
                                                systems". The authors show that certain
Memory applications of thin-film oxides         types of semiconductor spintronic
had been an area of active investigation for    structures belong to a broad class of
some time. IBM published an article in          memristive systems as defined by Chua
2000 regarding structures similar to that       and Kang.The mechanism of memristive
described by Williams. Samsung has a            behavior in such structures is based
pending U.S. patent application for several     entirely on the electron spin degree of
oxide-layer based switches similar to that      freedom which allows for a more
described by Williams. Williams also has a      convenient control than the ionic transport
pending U.S. patent application related to      in nanostructures. When an external
the memristor construction.                     control parameter (such as voltage) is
                                                changed, the adjustment of electron spin
Although the HP memristor is a major            polarization is delayed because of the
discovery for electrical engineering theory,    diffusion and relaxation processes causing
it has yet to be demonstrated in operation      a hysteresis-type behavior. This result was
at practical speeds and densities. Graphs in    anticipated in the study of spin extraction
Williams' original report show switching        at semiconductor/ferromagnet interfaces,
operation at only ~1 Hz. Although the           but was not described in terms of
small dimensions of the device seem to          memristive behavior. On a short time
imply fast operation, the charge carriers       scale, these structures behave almost as an
move very slowly, with an ion mobility of       ideal memristor. This result broadens the
 possible range of applications of              ability to retain information.
 semiconductor spintronics and makes a
 step forward in future practical               "This opens up a whole new door in thinking
 applications of the concept of memristive      about how chips could be designed and
 systems.                                       operated," Williams says.

 4. Manganite memristive systems                Engineers could, for example, develop a new
                                                kind of computer memory that would
 Although not described using the word          supplement and eventually replace today's
 "memristor", a study was done of bilayer       commonly used dynamic random access
 oxide films based on manganite for non-        memory (D-RAM). Computers using
 volatile memory by researchers at the          conventional D-RAM lack the ability to
 University of Houston in 2001. Some of         retain information once they are turned off.
 the graphs indicate a tunable resistance       When power is restored to a D-RAM-based
 based on the number of applied voltage         computer, a slow, energy-consuming "boot-
 pulses similar to the effects found in the     up" process is necessary to retrieve data
 titanium dioxide memristor materials           stored on a magnetic disk required to run the
 described in the Nature paper "The             system.
 missing memristor found".
                                                Memristor-based computers wouldn't require
 5. Resonant tunneling diode memristor          that process, using less power and possibly
 In 1994, F. A. Buot and A. K. Rajagopal        increasing system resiliency and reliability.
                                                Chua believes the memristor could have
 of the U.S. Naval Research Laboratory
                                                applications for computing, cell phones,
 demonstrated that a ‘bow-tie’ current-         video games - anything that requires a lot of
 voltage (I-V) characteristics occurs in        memory without a lot of battery-power
 AlAs/GaAs/AlAs quantum-well diodes             drain.
 containing special doping design of the        Brain-like systems?
 spacer layers in the source and drain
 regions, in agreement with the published
 experimental results.      This ‘bow-tie’
 current-voltage (I-V) characteristic is sine
 qua non of a memristor although the term
 memristor is not explicitly mentioned in
 their papers. No magnetic interaction is
                                                As for the human brain-like characteristics,
                                                memristor technology could one day lead to
What types of applications                      computer systems that can remember and
could memristors have?                          associate patterns in a way similar to how
                                                people do.
Possible replacement for D-RAM
                                                This could be used to substantially improve
                                                facial recognition technology         or to
By providing a mathematical model for the       provide     more     complex       biometric
physics of a memristor, the team makes          recognition systems that could more
possible for engineers to develop integrated    effectively restrict access to personal
circuit designs that take advantage of its      information.
                                                How does this Memristor technology
                                                compare to existing Flash memory, which
                                                appears to have similar properties?
                                                Flash and hard disk are non-volatile but very
                                                slow. There exists a significant opportunity
                                                for a new memory technology that is *both*
                                                fast and non-volatile. Memristor technology
                                                is an excellent candidate for this role.

                                                I would have liked to see a more in-depth
These same pattern-matching capabilities        explanation of how a memristor actually
could enable appliances that learn from         works. Also explain more clearly how a
experience and computers that can make          memristor emulates human neuronal
decisions.                                      activity and how the memory state is
Nanoscale electronics experience                maintained when the current is shut off to
                                                such                   a                device.
                                                The mathematical description of a memristor
In the memristor work, the researchers built    is explained in some detail within the Nature
on their extensive experience - Williams        scientific journal article. A model system of
founded the precursor lab to IQSL in 1995 -     mobile ions and electrons is used to illustrate
in building and studying nanoscale              the simple and more complicated dynamical
electronics and architectures.                  memristor behavior. References to the
                                                original memristor theory work from 1971
One goal of this work has been to move          are included there as well.
computing beyond the physical and fiscal
limits of conventional silicon chips. For       Could have used a bit more info. Does the
decades, increases in chip performance have     memristor lend itself to FPGA or PLA-like
come about largely by putting more and          designs? What are the energy requirements
more transistors on a circuit. Higher           for switching the memristor, and what is
densities, however, increase the problems of    the energy required to read it?
heat generation and defects and affect the      Fundamental science is always the most
basic physics of the devices.                   interesting                    information.
                                                A perceptive question -- yes, the memristor
"Instead of increasing the number of            is well suited for FPGA designs. Energy
transistors on a circuit, we could create a     requirements for switching the nanoscale
hybrid circuit with fewer transistors but the   memristor compare very favorably with
addition of memristors - and more               Flash; energy requirements to read it can be
functionality," Williams says. Alternately,     even lower. A detailed description of the
memristor technologies could enable more        nanoscale physics leading to memristor
energy-efficient high-density circuits.         action will be published in the near future
                                                and include a great deal more experimental
In 2007, the team developed an architecture     evidence
for such a hybrid chip using conventional
CMOS technology and nano scale switching
devices.                                        True news from H-P-- memristor nano-
                                                memory element
                                               resistor memristor circuits have been
                                               presented, it is not unreasonable to expect
                                               that the most interesting applications will be
                                               found in circuits containing resistors,
                                               inductors, capacitors, and memristors.

                                                               Although   no    physical
                                               memristors has not yet been discovered in
                                               the form of a physical device without
                                               internal power supply.


                                                     L.O. Chua, Introduction to Non-
Seems Berkeley might be hanging a new
                                                      linear network theory. New York:
Nobel plaque above some mantel soon.
                                                      McGraw-hill, 1969
37 years ago, Dr. Leon Chua, a professor in
the University of California's Electrical
Engineering and Computer Sciences                 
Department, noticed an unfilled symmetry              ntum_systems.html
between      fundamental    electromagnetic
equations relating charge and flux and their
corresponding passive circuit elements. He
filled this blank with a conjectural passive
element he termed a memristor, a device
with a hysteretic (history-dependent)
behavior that changes its electrical
characteristics based on past current-flow

  The memristor has been introduced as the
fourth basic circuit element. Three types of
mutators have been introduced for realizing
memristors in form of active circuits. The
applications of memristors in modeling
unconventional      devices    shows    that
memristors are useful even if they are used
as conceptual tool of analysis. While only

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