Current Voltage Relation of Different Memristor Models

Current Voltage Relation of Different Memristor Models lineation Memristor a two terminal passive non volatile whirl is considered as the fourth circuit ingredient and underside be used in many applications which includes fund, logic and neuromorphic systems. The memristor provides many advantages like scalability, compatibility with CMOS and offers no wetting accredited. Various personates of memristor have been discussed in this paper. The main focus is on the Current-Voltage (IV) relation of different manikins and its simulation is through with(p) in Cadence Virtuoso.Index Terms- memristor, VerilogA, window function, SPICE, doorway.INTRODUCTIONIn 1971, L. O. Chua introduced the fourth passive circuit fixings named memristor which is two terminal non volatile device with a property of uncertain enemy known as memristance 1. The memristance provides the relation in the time integrals of potential difference and present-day(prenominal). Originally, current controlled time invariant memristor is expressed aswhere w is conjure variable, v(t) is the device voltage, i(t) is the memristor device current, R(w, i) is the memristance and t is the time period.Since HP labs proclaimed the physical working manikin of memristor 2, it opens the doors to the new type of electronics. Some of the applications includes logic design 3 4, memory 5, neuromorphic systems 6.Different lays of memristor have been deigned. Formally knowing sit arounds does not contain threshold 2 7 8 (i.e. resistance modifications for any current or voltage). The doorstep Adaptive Memristor sit down ( group )9 and Voltage Threshold Adaptive Memristor pattern (VTEAM) 10 lays exhibits the threshold current and threshold voltage respectively, argon the roughly expeditious models and less computational complexity.In this paper current-voltage relation of different models is implemented development VerilogA code. voice II describes the different types of memristor models. Comp arison of memristor model is provided in theatrical role III. The paper is concluded in section IV.DIFFERENT MEMRISTOR MODELSLinear Ion Drift ModelThis is the first and basic model of memristor proposed by HP Labs 3. This model has width which is splitted in two regions as shown in Figure 1. The region with width w is narcotized with positive oxygen ions (originally TiO2) and has low resistance therefore is more conductive and other side is undoped. distributively region is modeled with resistor (in series). Various assumptions are considered i.e. ohmic conductance, uniform field and average ion mobility.RON is the resistance at w(t) = D and R finish is the resistance at w(t) = 0 The assure variable w(t) is restrained within the detachment 0,D. To prevent w from going beyond the physical dimensions of the device, the derivative of w is required to multiply by the window function.The IV relationship hoist of elongated ion drift model of memristor for sinusoidal input is show n in account 2.Figure1 HP memristor model 1Figure 2 IV influence of linear memristor model with 2-window function.(frequency=20MHz,source bountifulness=0.003A, Ron=100ohm, Roff=2e5ohm, v=10e-14m2/Vs, D=10e-9m, P_coeff=2, initial offer=0.5, j=1, w_multiplied=1e9, P_window_noise=1e-18) no Linear Ion Drift ModelAlthough the linear ion drift model of memristor is simple and satisfies the basic memristor equations. But as per the experiments of the fabricated device, it behaves differently i.e. it is highly non linear 11 12. The non linearity is desirable for logic circuits, therefore another memristor model have been proposed based on data-based results concluded in 11. A model is 13 proposed. The relation between current and voltage for this model isWhere , , are known as fitting parameters and parameter n describes the influence of state variable (w) on the currents. . Here, the state variable w is normalized within the interval 0,1. The model shows asymmetric shift behaviour, in a port that during the ON state, w is near one and the first term of, is the dominant part of the current, which is a cut intoing phenomenon. During the OFF state, w is near zero and the second term, has the dominant part of the current, which is similar to an ideal diode equation. The state variable differential equation is written aswhere a, m are constants, f(w) is the window function and m is an odd integer. And there is a nonlinear dependency on voltage.The IV characteristics of this model is shown in figure 3.Figure3 IV curve of non linear ion drift model with 2-window function(frequency=20MHz,source amplitude=1V, P_coeff=1, initial state=0.5, j=1, Alpha=2, Beta=9, C=0.01, g=4, n=13, q=13,a=4, w_multiplied=1, P_window_noise=1e-18)Figure 4 IV curve of simmons tunnel barrier model.(frequency=20MHz,source amplitude=0.003A, Ron=100ohm, Roff=2e5ohm, D=3e-9m, initial state=0.5, aon=2e-9,aoff =1.2e-9, ion=8.9e-6, ioff=115e-6,con=40e-6, coff=3.5e-6,b=500e-6,Xc=107e-12 w_multiplie d=1e9, P_window_noise=1e-18)Simmons Tunnel barricade Modelanother(prenominal) model having more accuracy than previous discussed model was proposed in 14. The assumptions of this new model includes non-linearity and asymmetric fault behavior because of an exponential dependency of movement of ionized dopants i.e. changes in state variable. Physical model of this type has a resistor in series with electron tunnel barrier. The simmons tunnel barrier width x, is the state variable. So the derivative of x can be represented as oxygen vacancy drift velocity, and iswhere b, con, coff, ion, ioff, aon, aoff are known as fitting parameters. Con is always greater than coff and they both effect the magnitude of change of x. The parameters ioff and ion define the current threshold. Another parameter aoff and aon gives the upper and lower bounds of x respectively. Within the graze defined, the derivative of state variable x, is significantly smaller than state variable itself. Therefore, ther e is no compulsion of window function that is the biggest advantage of this model.According to the simmons tunnel model, the relation between voltage and current can be expressed asWhere V is applied voltage and v is internal voltage of the device (it is not necessary that both voltages are equal 15 ). ground on the fitting parameters, the IV characteristics curve of the simmons tunnel barrier model is shown in figure 4.TEAM ModelBefore 2013, it was claimed that Simmons Tunnel Barrier model is the most accurate memristor model but it too has some limitations of complication, unexplicit relation in voltage and current and is not in general. Therefore a model with accuracy and simpler expressions is the main demand.The TEAM ( Threshold Adaptive Memristor model) is proposed by Shahar Kvatinsky 16. This is simple and general model, physically similar to predefined model. Some assumptions can be make for analysis and for computational efficiency.Based on assumptions, state variable deri vative of this model is expressed aswhere aon,aoff, kon,and koff are constants (koff is positive and kon is negative). foff(x) and fon (x) are the window functions, depends on state variable x.by assuming the current voltage relation is same as memristance of memristor which changes linearly in x. Therefore,but if Simmons Tunnel Barrier model is assumed then memristance changes exponentially and given aswhere is the fitting parameter. The parameter Ron and Roff are resistances at bound and satisfiesBy tuning different parameters of the model, the VI curve of this model is showm in figure11.According to 9, it is claimed that the accuracy of TEAM model is more enough having mean error of 0.2%.VTEAM ModelMany experiments on memristive devices shown the existence of threshold voltage 2 16 17 instead of threshold current. Therefore, Shahar Kvatinsky designs the new model i.e. VTEAM model 10 (Voltage Threshold Adaptive Memristor model), contains threshold voltage. Another reason for the existence of this model is that a memristor exhibiting threshold voltage is more desirable than the threshold current in many applications of memory and logic 10.The advantages of TEAM model (i.e. general, accurate, simple, designer friendly) combines with threshold voltage in spite of threshold current gives the VTEAM model.Similar to the state variable derivative of TEAM model, the state variable derivative of VTEAM model iswhere koff, kon off and on are constants. Parameters voff and von are threshold voltages. The window functions fon and foff defines the dependency of state variable derivative on state variable w.for VTEAM model, the current voltage relation is not flop defined but the linear dependency of state variable and resistance can be attained, from where current voltage relation iswhere woff and won gives bounds of state variable w.The curve for the IV relation of VTEAM memristor model is depicted as in figure 6.Figure 5 IV curve of TEAM model with 4-window type.(fre quency=20MHz,source amplitude=0.003A, Ron=100ohm, Roff=2e5ohm, v=10e-14m2/Vs, D=10e-9m, P_coeff=2, initial state=0.5, j=1.5, aon=2.3e-9, aoff =1.2e-9, ion=-1e-6, ioff=1e-6, kon=-8e-13, koff=8e13, xon=0, xoff=3e-9, aon=3,aoff=3, Xc =107e-12 w_multiplied=1e9, P_window_noise=1e-18)Figure6 IV curve of VTEAM model without window function.(frequency=20MHz,source amplitude=1V, Ron=100ohm, Roff=2e5ohm, v=10e-14m2/Vs, D=10e-9m, P_coeff=2, initial state=0.5, j=1.5, aon=2e-9, aoff =1.2e-9, von=-0.2 voff=0.02, kon=-8e-13, koff=8e13, xon=0, xoff=3e-9, aon=3,aoff=3, Xc =107e-12 w_multiplied=1e9, P_window_noise=1e-18)COMPARISONComparison of different models of memristor is listed in table1.Table 1 Comparison between diffent memristor models.CONCLUSIONIn this paper, different models of memristor- linear ion drift model, non linear ion drift model, simmons tunnel barrier model, TEAM model and VTEAM model are described. Moreover the VI characteristics of each model is simulated. The VI curve for VTEA M model is most efficient and desirable. Also VTEAM and TEAM models are simple, general and accurate.The VI characteristics of each model is implemented by using verilogA code 18 because of its effiency regarding computational time than SPICE model.REFERENCESL. O. Chua, Memristor The Missing Circuit Element, IEEE Transactions on Circuit Theory, Vol. 18, No. 5, pp. 507-519, 1971.D. B. Strukov, G. S. Snider, D. R. Stewart, and R. S. Williams, The Missing Memristor Found, Nature, Vol. 453, No. 7191, pp. 80-83, 2008.G. Snider, Computing with hysteretic resistor crossbars, employ Physics A, Material Science Process, vol. 80, rascal 1165-1172, 2005.S. Kvatinsky, E. G. Friedman, A. Kolodny, and U. C. Wieser, Memristor-based demand logic design procedure, minutes IEEE International Conference Computational Design, page 142-147, 2011.G. M. Huang, Y. Ho, and P. 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