Memristors MATLAB Modeling

Memristors MATLAB Modeling

Jeetendra Lekhraj Singh

Department of Electronics & Telecommunication Engineering

Dhole Patil college of Engineering Pune, India

Prof. Manoj. S. Kakade

Department of Electronics & Telecommunication Engineering

Sinhgad college of Engineering Pune, India

AbstractMemristor is the fourth two terminal fundamental passive element and memristive effect was first published by Leon Chua in early 1970, Since then students and researchers are interested in exploring more practical possibilities and design application circuits But to design Memristors based circuits, an Accurate simulating models are very important. Testing circuits on practical Memristors will take few more years since its still in researchers stage. In this paper we provide near accurate Computer models of memristor which will act as a tool to speed up its behavioral analysis and this will further help student and enthusiastic community to design innovative circuits and interesting applications with Memristors. This MATLAB model is derived from HP based Mathematical model and its functionality can be shown on computer by simulation.

KeywordsMemristors, MATLAB, Mathematical model, ADALINE, HDL, Hysteresis , Eflux and Echarge.

1. INTRODUCTION

   The concept of a resistor with memory existed even before Leon Chua's publication on the memristor in 1970. In 1960, Prof. Bernard Widrow of Stanford University developed a new circuit element named the memristor. This memristor proposed was three terminal device for which the conductance between two of the terminals was controlled by current flow (time-integral) in third terminal. Thus, the resistance of the memristor was controlled by charge. Memristors formed the basic components of the neural-network architecture called ADALINE (ADAptive Linear Neuron).

   Between 1994 and 2008 there were many other devices developed with behavior similar to that of the memristor, but only the HP scientists were successful in finding link between their work and the memristor explained by Chua.

   The purpose of this paper is to provide and accurate MATLAB model of Memristor. The paper structure is as follows: Section II,After Introduction part provides information about physical and mathematical models for memristor, already published in [1] and [4]. Section III describes MATLAB Model, After explanation of mathematical model in Section III, Section IV shows process flow and ends with results from MATLAB simulations for the proposed model and last section VI describes application of Memristor.

2. LITERATURE SURVEY

   Memristors is also known to be the fourth passive element after Resistor ( R ), Capacitor ( C ) and Inductor ( L ). Its logical to develop a MATLAB model, Since with reduction in die size ( below 20nm ) the effect of memristor will be eminent and cannot be ignored and hence conventional circuits will have to consider memristive effect into consideration and will provide opportunity to design circuits more effectively and which will also bring new design challenges. Hence accurate simulation tools will help foresee and overcome these design challenges.

   In May 2008 HP-Lab based research group led Dr. Williams, published a report [1] on memristor, Its the fourth two terminal fundamental passive element and it was predicted in year 1970 by professor Chua in his paper [2] and reference from original work [1] has been taken for our analysis, the information like physical model of memristor.

   Fig. 1. Memristor model according to [1].

   The Memristors physical model [1], shown in Fig 1, is a thin film of D = 10 nm of consist of two TiO2 layers sandwiched between platinum contacts. one layers is undoped and other layer is doped so that it behaves like an semiconductor. The undoped layer has insulator property. And due to this complex material process consequence the doped region width (w) is proportional to electric charge passed through the device, The direction of electric current passing moves the boundary between them in same direction.

   Thus cumulative resistance of the memristor Rmem is sum of two regions (doped and undoped regions), w is width of doped region with reference to total length D of both layer of TiO2 layer, And limiting values are Roff and Ron for memristor resistance when w = 0 and w = D. Usually the ratio

   is 10^2 -10^3 for these two resistances. The resistance of doped layer depends on the current and other factors stated in Eq. 1.

   Rmem (x) = Ron x + Roff (1-x), (1)

   where x = w / D (0,1) (2) As per Ohmic relation voltage and current: for memristor.

   v (t) = Rmem (w)i(t) (3)

   Rmem (x) which is also proportional to movement of speed of the boundary between the undoped and doped regions (dx/dt).

   dx/dt = k i(t)f(x) k=constant = (vRon)/D^2 (4)

   where v = 10 14 m^2 s^ – 1 V^-1 is dopant mobility. As mentioned in [1], Small voltages in nanotechnology can produce enormous electric fields enough for a significant nonlinear in ionic transport. At thin film edges these nonlinear manifest themselves, where boundary's movement decreases gradually to zero. This nonlinear dopant drift can be modeled by the window function f(x) from the right side of Eq. 4. The window function is:

   f (x) = 1 (2x 1)^2 p (5)

   where p is a positive integer.

3. EXPERIMENTATION

   There are various ways to model the electrical characteristics of the Memristors (RMEM) listed below are few models which can be help provide memristive simulation models.

   1. MATLAB MICRO MODEL

      The first approach, MATLAB macro-models, is more readable for most of the readers and compatible to all MATLAB versions. Apart this model can be readily used to simulate Analog subsystem and circuits in combination with memristive element which can help primarily to redesign conventional circuits.

   2. HDL HARDWARE DESCRIPTION LANGUAGE

      The second approach, HDL models, is more appropriate for detailed analysis since its low level language but language is comparatively most difficult.

   3. C PROGRAMMING

   The third approach, C PROGRAMING based modeling is simpler but least accurate since this model doesn't include parametric details.

   1. MATLAB MICRO MODEL :

      The memristor block level orientation shown in Fig 2, Its memory effect is modeled via a feedback-controlled integrator. The influence of boundary conditions and nonlinear drift are simulated by feedback function, f ( ) via nonlinear window.

      Fig. 2. The memristor block level orientation.

      The MATLAB model is As per Eq 1 the V I relation of memristor is modeled as :

      Rmem (x) = Roff -x R , R = Roff – Ron (6)

      The model is implemented as a MATLAB sub circuit with parameters like Ron, Roff resistance and initial resistance Rinit, width D of thin film, the windows function exponent p and v the dopant mobility.

      The MATLAB model passes parameters for direct computation of the various integral quantities like the time integrations of charge and flux. These parameters are key for results of MATLAB analysis. These are available as internally controlled sources of Echarge and Eflux.

4. PRAPOSED APPROACH

   The process flowchart to generate MATLAB model of Memristor and simulating its results is shown in Fig 3.

   We have used the Memristor mathematical model in first place to design a working MATLAB model and later the MATLAB simulation tool has been used to do simulation and Analysis of the generated Memristive MATLAB model.

   MATHWORK tool is used to simulate te MATLAB model Circuit / MATLAB Model .

   Rmem Parameters are adjusted in order to achieve the perfect MATLAB model.

   Fig.3. Process flowchart for MATLAB model simulation.

5. RESULT

   The Simulations of MATLAB Memristor model Driven by Voltage using PMATLAB, the width D of the TiO2 film is considered to be 10 nm and the dopant mobility v = 1^-14 cm^2 s^-1 V^-1. The values assumed are Ron=100, Roff=16K. The input frequency considered is 3 rad/s The simulation results are shown below in Fig. 5, 6, and 7.

   From Fig. 5, we can see that the fluxcharge curve is a monotonically increasing curve. We can also observe the currentvoltage pinched hysteresis loop and the hysteresis loop is shrinking with the increase in the input frequency in

   Fig. 5 and Fig. 6. Thus, all the properties that are said to be a signature of a memristor are satisfied.

   Fig. 4.Plot of Eflux Vs Echarge

   Fig. 5. Plot of current versus voltage for = 3rad/s.

   Fig. 6. Plot of current versus voltage for = 8rad/s.

6. APPLICATION OF MEMRISTORS

   Its implications are extraordinary. A few applications of Memristors are

   • NVRAM

   • FPGA's

   • MIMICING THE BRAIN (neural network)

   • ANALOG PARALLEL COMPS

7. CONCLUSION

The properties of the memristor and its model is simulated by subjecting it to various input voltages and noting the results obtained.

By redesigning certain elements of circuits by including Memristors, it's possible to obtain the same circuit function with fewer components, making the circuit itself cost effective and significant reduction in its power consumption. In fact, it can be hoped to combine traditional circuits elements with Memristors to produce a device to perform similar computation. Simulation tools and various models will help built efficient analog circuits. The MATLAB models will empower to develop innovative circuits. With Possibility of fabricating Memristor and circuits on single CMOS wafer will make electronic system much cheaper and efficient.

Nanoscale devices will automatically bring in memristive effect which cannot be ignored to design a functioning circuits. Thus, 21st century might be revolutionize by Memristors as transistor did in 20th century.

REFERENCES

1. STRUKOV, D.B., SNIDER, G.S., STEWART, D.R., WILLIAMS,R.S. The missing memristor found. Nature, 2008, vol. 453, 1 May 2008, p. 80

   83.

2. CHUA, L.O. Memristor the missing circuit element. IEEE Trans. Circuit Theory, 1971, vol. CT- 18, no. 5, p. 507 519.

3. JOGLEKAR, Y.N., WOLF, S. J. The elusive memristor : properties of basic electrical circuits.arXiv:0807.3994 v2 [cond-mat.meshall] 13 January 2009, p.1-24.

4. WANG, F.Y. Memristor for introductory physics. arXiv:0808.0286 v1 [physics.class-ph], 4 August 2008, p.1-4.

5. Kenneth M. Shultz, "Memristor",VCU SCHOOL OF ENGINEERING, summer 2009.

6. O. Kavehei, A. Iqbal, Y. S. Kim, K. Eshraghian, S. F. AL-Sarawi and D. Abbott, "The fourth element: Characteristics, modelling and electromagnetic theory of the memristor" Proc. R. Soc. A published online 17 March 2010 doi: 10.1098/rspa.2009.0553