Current Voltage Relation of Different Memristor Models

Current potential difference Relation of Different Memristor computer simulationsAbstract Memristor a two terminal passive non volatile device is considered as the fourth circuit element and can 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 leakage ongoing. Various ideals of memristor have been discussed in this paper. The main focus is on the Current-Voltage (IV) tattle of different mildews and its simulation is done in Cadence Virtuoso.Index Terms- memristor, VerilogA, windowpane function, SPICE, threshold.INTRODUCTIONIn 1971, L. O. Chua introduced the fourth passive circuit element named memristor which is two terminal non volatile device with a proportion of variable resistance cognize as memristance 1. The memristance provides the apprisal in the time integrals of voltage and menses. Originally, current controlled time invariant memristo r is expressed aswhere w is landed e pronounce 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 sample 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 models of memristor have been deigned. Formally designed models does non contain threshold 2 7 8 (i.e. resistance changes for any current or voltage). The Threshold Adaptive Memristor model (team )9 and Voltage Threshold Adaptive Memristor model (VTEAM) 10 models exhibits the threshold current and threshold voltage respectively, atomic number 18 the most efficient models and less computational complexity.In this paper current-voltage relation of different models is implemented using VerilogA code. Section II describes the different types of memristor models. Comparison of memristor model is provi ded in section III. The paper is concluded in section IV. assorted 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 sections as shown in image 1. The region with width w is doped with positive oxygen ions (originally TiO2) and has low resistance therefore is much conductive and other side is undoped. Each region is modeled with resistor (in series). Various assumptions be considered i.e. ohmic conductance, uniform field and average ion mobility.RON is the resistance at w(t) = D and ROFF is the resistance at w(t) = 0 The land variable w(t) is bounded within the interval 0,D. To prevent w from going beyond the physical dimensions of the device, the derived function of w is required to multiply by the window function.The IV relationship curve of linear ion rove model of memristor for sinusoidal input is shown in figure 2. interpret1 HP memristor model 1Figure 2 IV curve of li near memristor model with 2-window function.(frequency=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, w_multiplied=1e9, P_window_noise=1e-18)Non 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 experimental 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 noninterchangeable switching behavior, in a way that during the ON state, w is near one and the first ter m of, is the dominant part of the current, which is a tunneling phenomenon. During the OFF state, w is near zero and the second term, has the dominant part of the current, which is alike 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_multiplied=1e9, P_window_noise=1e-18)Simmons Tunnel Barrier ModelAnother model ha ving more accuracy than previous discussed model was proposed in 14. The assumptions of this new model includes non-linearity and asymmetric switching 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 differential 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 termination 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 range defined, the differential of state variable x, is significantly smaller than state variable itself. Therefore, there is no need of window function that is the biggest advantage of this mod el.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 ).Based 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 made for analysis and for computational efficiency.Based on assumptions, state variable derivative of this model is expressed aswhere aon,aoff, kon,and koff are constants (ko ff 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 primer coat 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 properly 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.(frequency=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. 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