Memristors

Introduction Theoretically, Memristors, a concatenation of “memory resistors”, are a type of passive circuit elements that maintain a relationship between the time integrals of current and voltage across a two terminal element. Electronic symbol

Simplified Definition It is the consolidation of two words namely, MEMORY and RESISTOR. As the name suggests its resistance (dV/dI) depends on the charge that HAD flowed through the circuit. When current flows in one direction the resistance increases, in contrast when the current flows in opposite direction the resistance decreases. However resistance cannot go below zero. When the current is stopped the resistance remains in the value that it had earlier. It means MEMRISTOR “REMEMBERS” the current that had last flowed through it.

History Professor Leon Chua Theory was developed in 1971 by Professor Leon Chua at University of California, Berkeley. In 2008, a team at HP Labs under R.Stanley Williams claimed to have found Chua's missing memristor based on an analysis of a thin film of titanium dioxide. In March 2012, a team of researchers from HRL Laboratories and the University of Michigan announced the first functioning memristor array built on a CMOS chip. R. Stanley Williams

Analogy Memristors behaves like a pipe whose diameter varies according to the amount and direction of the current passing through it If the current is turned OFF, the pipes diameter stays same until it is switched ON again It Remembers what current has flowed through it

Fundamental Passive Linear Elements

Background Leon Chua extrapolated a conceptual symmetry between the nonlinear resistor (voltage vs. current), nonlinear capacitor (voltage vs. charge) and nonlinear inductor (magnetic flux linkage vs. current). He then inferred the possibility of a memristor as another fundamental nonlinear circuit element linking magnetic flux linkage and charge.

Theory The memristor was originally defined in terms of a non-linear functional relationship between magnetic flux linkage Φm(t) and the amount of electric charge that has flowed, q(t) f(Φm (t),q(t)) = 0 The variable Φm ("magnetic flux linkage") is generalized from the circuit characteristic of an inductor. It does not represent a magnetic field here. The symbol Φm may be regarded as the integral of voltage over time.

M(q(t)) = Φm/𝒅𝒕 𝒅𝒒/𝒅𝒕 = V(t) I(t) Memristance In the relationship between Φm and q, the derivative of one with respect to the other depends on the value of one or the other So each memristor is characterized by its memristance function describing the charge-dependent rate of change of flux with charge. M(q) = dΦm dq Substituting the flux as the time integral of the voltage, and charge as the time integral of current M(q(t)) = Φm/𝒅𝒕 𝒅𝒒/𝒅𝒕 = V(t) I(t)

Device Characteristic property (units) Differential equation Resistor Resistance (V per A, or Ohm, Ω) R = dV / dI Capacitor Capacitance (C per V, or Farads) C = dq / dV Inductor Inductance (Wb per A, or Henrys) L = dΦm / dI Memristor Memristance (Wb per C, or Ohm) M = dΦm / dq The above table covers all meaningful ratios of differentials of I, Q, Φm, and V. No device can relate dI to dq, or dΦm to dV, because I is the derivative of Q and Φm is the integral of V.

Current-voltage characteristics for the resistor, capacitor, inductor and memristor.

It can be inferred from this that memristance is charge-dependent resistance. If M(q(t)) is a constant, then we obtain Ohm's Law R(t) = V(t)/ I(t). If M(q(t)) is nontrivial, however, the equation is not equivalent because q(t) and M(q(t)) can vary with time. Solving for voltage as a function of time produces V(t)= M(q(t)) I(t) This equation reveals that memristance defines a linear relationship between current and voltage, as long as M does not vary with charge.

Memory Effect V(t)= M(q(t)) I(t) The memristor is static if no current is applied. V(t)= M(q(t)) I(t) If I(t) = 0, we find V(t) = 0 and M(t) is constant. This is the essence of the memory effect.

P(t) = V(t) I(t) = I2(t) M(q(t)) Power Equation The power consumption characteristic recalls that of a resistor, I2R. P(t) = V(t) I(t) = I2(t) M(q(t)) As long as M(q(t)) varies little, such as under alternating current, the memristor will appear as a constant resistor. If M(q(t)) increases rapidly, however, current and power consumption will quickly stop.

Contribution of HP Labs PT TiO(2-x) TiO2 3 nm 2 nm Oxidized Reduced (-)ve (+)ve TiO2-x region doped with oxygen vacancies In the TiO2-x region, the ratio between titanium atoms and oxygen atoms has been altered such that there is less oxygen than in a regular TiO2 sample The resistance of the device when w = D will be designated RON and when w = 0 the resistance will be designated as ROFF .

Resistance Naming Convention Effective Electrical Structure of the HP Memristor The effective IV behaviour of the structure can be represented as equation

Contribution of HP Labs Further Calculations leads to: For RON<< ROFF the memristance function was determined to be M(q(t)) = ROFF . (1- μv RON D2 q(t)) where ROFF represents the high resistance state RON represents the low resistance state μv represents the mobility of dopants in the thin film D represents the film thickness.

An array of 17 purpose-built oxygen-depleted titanium dioxide memristors built at HP Labs, imaged by an atomic force microscope. The wires are about 50 nm, or 150 atoms, wide.

Applications of a Memristor Non-volatile memory applications Memristors can retain memory states, and data, in power-off modes. Non-volatile random access memory, or NVRAM is the first application that comes to mind when we hear about memristors. There are already 3nm Memristors in fabrication now.

Low-power and remote sensing applications. Coupled with memcapacitors and meminductors, the complementary circuits to the memristor which allow for the storage of charge. Memristors can possibly allow for nano-scale low power memory and distributed state storage, as a further extension of NVRAM capabilities. These are currently all hypothetical in terms of time to market.

Programmable Resistances While the Memristor can be used at its extreme resistance values in order to provide digital memory, it can also be made to behave in an analog manner. One potential application of this behaviour is that of a dynamically adjustable electric load . Thus, existing electronic circuit topologies with characteristics that depend on a resistance can be made with Memristors that behave as variable, programmable resistances.

Memristor patents include applications in Programmable Logic Signal Processing Neural Networks Control Systems Reconfigurable Computing Brain-computer Interfaces RFID.

Advantages of Memristors Has properties which can not be duplicated by the other circuit elements (resistors, capacitors, and inductors Capable of replacing both DRAM and hard drives Smaller than transistors while generating less heat Works better as it gets smaller which is the opposite of transistors Devices storing 100 gigabytes in a square centimeter have been created using memristors Quicker boot-ups Requires less voltage (and thus less overall power required)

Disadvantages of Memristors Not currently commercially available Current versions only at 1/10th the speed of DRAM Has the ability to learn but can also learn the wrong patterns in the beginning. Since all data on the computer becomes non-volatile, rebooting will not solve any issues as it often times can with DRAM. Suspected by some that the performance and speed will never match DRAM and transistors.

References http://en.wikipedia.org/wiki/Memristor http://spectrum.ieee.org/semiconductors/processors/how-we-found-the- missing-memristor http://innovativeblood.blogspot.in/2011/02/memristor-missing-circuit- element.html http://whatis.techtarget.com/definition/memristor http://www.memristor.org/reference/research/13/what-are-memristors http://www.channelregister.co.uk/2011/12/27/memristors_and_mouttet/ http://thefutureofthings.com/4060-flexible-memristor-chips/ http://www.vrg.utoronto.ca/~shortena/documents/memristor.pdf

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