TiO2 based nanostructured memristor for RRAM and neuromorphic applications: a simulation approach
We report simulation of nanostructured memristor device using piecewise linear and nonlinear window functions for RRAM and neuromorphic applications. The linear drift model of memristor has been exploited for the simulation purpose with the linear and non-linear window function as the mathematical and scripting basis. The results evidences that the piecewise linear window function can aptly simulate the memristor characteristics pertaining to RRAM application. However, the nonlinear window function could exhibit the nonlinear phenomenon in simulation only at the lower magnitude of control parameter. This has motivated us to propose a new nonlinear window function for emulating the simulation model of the memristor. Interestingly, the proposed window function is scalable up to f(x) = 1 and exhibits the nonlinear behavior at higher magnitude of control parameter. Moreover, the simulation results of proposed nonlinear window function are encouraging and reveals the smooth nonlinear change from LRS to HRS and vice versa and therefore useful for the neuromorphic applications.
KeywordsMemristor Window function RRAM Neuromorphic applications
Memristor which is poised to establish as the fourth circuit element in addition to the R, L and C, was theorized way back in the year 1971 by Chua . Later in the year 2008 the same was validated by the HP research group . The peculiar characteristics of remembering the data in terms of low resistance state (LRS) and high resistance state (HRS) makes the memristor a unique attribute for many interesting applications not feasible with the conventional circuit elements. Moreover, the passivity and nonlinearity are some of the important characteristics of the memristor, which leads to its usage in the applications of diversified domains such as biomedical, resistive random access memory (RRAM), neural computing, nonlinear dynamics, neuromorphic computing realm etc. as reported widely in the literature [3, 4, 5, 6, 7, 8, 9, 10]. As these applications are important so is the accurate modelling of nonlinear memristor which has been the very basis of the scientific investigations. Incidentally many research group including ours are actively working in this direction as put forth briefly in the following paragraph to set the background of the present investigation.
Recently, Li et al. reported a new modelling method with multinomial window function. This method is derived through the statistical fitting of an experimental data of a memristor device . Batas et al. have come out with the behavioral model of magnetic flux-controlled memristor device. The reported model is simulated on integrated circuits emphasis i.e. SPICE platform . Valsa et al.  have investigated the analogue model of the memristor device which has been duly verified for various test signals with the results showing good resemblance with the ones reported in literature. Shin et al.  have put forth a compact circuit model and hardware emulator for memristor device with its applications for the arithmetic operations. Kolka et al.  reported the hardware emulator for the mem-systems based on the memristor, memcapacitor, and meminductor which can be further programmed to realize the above mentioned trio. Quite relevant to the theme of present paper are the investigations carried out by Biolek et al. and Yu et al. on the nonlinear and piecewise linear window function aspects for modelling the memristor respectively [16, 17].
Recently, our research group too has reported two new window functions for the modeling of the memristor device . The present research paper is an extension of our previously reported work [3, 4, 5, 6, 7, 8, 9, 10, 18]. While our previous papers report more of the details related to mathematical aspects, the present paper is a value addition as it actually showcases the simulation in light of the RRAM and neuromorphic applications. Both these applications are currently in profound demand. RRAM’s seems to be the only solution in the age of big data while a completely new paradigm of brain inspired computing is currently been explored through the neuromorphic domain. The main achievement of the present manuscript is the modified nonlinear window function which accurately models the nonlinearity of memristor device. The rest of the paper is as follows, after brief introduction in the first section, second section deals with the overview of piecewise linear and nonlinear window functions. The third section further divulges the simulation details of memristor with above mentioned window function. This section also deals with the modified nonlinear window function. At the end results and conclusion has been placed.
2 Overview of piecewise linear and nonlinear window functions
The reported literature reveals that drifting of vacancies has been highly nonlinear near the boundary interfaces. This is attributed to the nanoscale phenomena by which even a small voltage can produce large electric field across the device. This large electric field further generates nonlinear drifting of vacancies near the boundary interfaces . Another problem with linear drift model of memristor is that, the state variable ‘w’ never reaches to zero physical length which indicates that the oxygen vacancies are absent in the devices . The boundary problem can be minimized by adopting window function f(x). In general, the window function can be multiplied to state equation of memristor which is given as,
3 Simulation of memristor device using piecewise linear and nonlinear window functions
The main intent behind the modeling and simulation is to help the designers to come out with the apt device characteristics per application. In the present case the main rationale is to fine tune the memristor attributes through simulation for two fold purposes viz. fast transition from LRS to HRS for RRAM applications while slow transition from LRS to HRS for the neuromorphic domain. The modeling for the above mentioned attributes has been obtained by applying the piecewise linear and nonlinear window functions. After zeroing down on the technique for modeling the simulation was accomplished.
The present investigation reports the simulation of TiO2 nanostructured memristor device for RRAM and neuromorphic applications. The results strongly indicate the suitability of piecewise linear window function to carve the model of the nanostructured memristor device characteristics for RRAM application which is further been validated through simulation. Altering the control parameter from one state to another state makes the piecewise linear window function a best fit for the RRAM application. The modified nonlinear window function eliminates the scaling issue and thus accomplishes simulation of the memristor characteristics at higher magnitude of control parameters. The results are encouraging and show strong applicability towards neuromorphic engineering domains on which our research investigations are in progress.
TDD, PJP, and SMK designed the mathematical model. TDD, NKD, PPC, PPW, and PBP developed the MATLAB and Mathematica code. TDD, RSV, and MVT analyzed the results. RSV, MVT, PKG and RKK provided the advice on and coordinated the study. TDD and RKK documented the manuscript. All authors reviewed the manuscript. All authors read and approved the final manuscript.
The authors are very much thankful to Dr. S. S. Kumbhar for fruitful discussion on window functions. The authors are very much thankful to Prof. P. S. Patil for providing research facilities.
The authors declare that they have no competing interests.
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