Effect of write voltage and frequency on the reliability aspects of memristor-based RRAM
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In this paper, we report the effect of the write voltage and frequency on memristor-based resistive random access memory (RRAM). The above-said parameters have been investigated on the linear drift model of the memristor. With a variation of write voltage from 0.2 to 1.2 V and a subsequent frequency modulation from 1, 2, 4, 10, 100 and 200 Hz, the corresponding effects on memory window, low resistance state (LRS) and high resistance state (HRS) have been reported. Thus, the lifetime (τ) reliability analysis of memristor-based RRAM is carried out using the above results. It is found that the HRS is independent of the write voltage, whereas LRS shows dependency on write voltage and frequency. The simulation results showcase the fact that the memristor possesses higher memory window and lifetime (τ) in the higher voltage with lower frequency region, which has been attributed to less data losses in the memory architecture.
KeywordsMemristor RRAM Memory window Lifetime reliability Write voltage
Traditionally, the passive circuit family in electrical engineering consists of three lumped elements, viz., resistor, inductor, and capacitor. In 2008, HP research group reported the first physical realization of a fourth fundamental circuit element named as Memristor , which was postulated mathematically four decades earlier by Chua . Memristor is a nonlinear circuit element and possesses nonvolatile memory property, which is not observed in any other circuit elements. The inherent memory property of memristor is distinctly observed in the nanoscale and therefore, it is considered as a strong candidate for the next generation memories . Along with its applications in memory, there are many interesting applications explored around memristors such as neuromorphic computations , in-memory computing , biomedical application  and much more.
Recently, Nickel et al.  developed the nonlinear, bipolar memristor crossbar structures and demonstrated the high scalability in the developed device. Emara et al.  reported the 1T2 M differential memory cell for single and multi-bit data storage. Ning et al.  proposed the nonvolatile threshold adaptive transistors model with embedded RRAM for neuromorphic application. Dongale et al.  reported the TiO2 thin film memristor with the low symmetric voltage switching. Hoessbacher et al.  reported a novel application of memristor in the plasmonic domain. The reported plasmonic memristor can be used as electrically activated optical switches with a memory effect. Murali et al. reported the zinc–tin–oxide (ZTO) based memristor. Good switching ratio, long retention time, and good endurance have been observed in the developed memory device . Against the backdrop of the international research scenario, our research group is also striving hard to model and realize memristor using different methods and come out with useful applications [13, 14, 15, 16]. Previously we have reported the effect of device size as a function of frequency on memristor-based RRAM . We have also investigated the conduction mechanism and frequency dependency of nanostructured memristor device [18, 19].
In the present paper, we have reported the effect of write voltage as a function of frequency on memristor-based resistive random access memory (RRAM) and thereby ensured the reliability of the device. The proposed investigation is based on linear drift model of memristor proposed by HP research group . The rest of the paper is as follows: After a brief introduction in the first section, the second section deals with the computational details, followed by the effect of write voltage as a function of frequency on memristor-based RRAM in the third section. The fourth section investigates the effect of write voltage as a function of frequency variation on lifetime (τ) reliability of memristor device. At the end, the conclusion is portrayed.
The memristor properties are simulated using linear drift model . For the present investigation, the drift velocity of oxygen vacancies is considered as a state variable ‘w’. The details of conduction mechanism and device structure have been investigated thoroughly by many researchers [14, 15, 20, 21, 22]. Considering the linear ionic drift with the average drift velocity of oxygen vacancies μ V leads us to memristor current and voltage relation represented by the following mathematical equations :
Effect of write voltage and frequency on memristor-based RRAM
The write voltage plays a key role in the resistive switching of memristor device. The properties of memristor are distinctly observed in the nanoscale regions and at this region, small bias can produce large electric field across the device which accelerates the drift velocity of charge carriers. In other words, this kind of effect can be understood by nanoscopic drift–diffusion model and not by macroscopic drift–diffusion model. In this scenario, an application of a small bias (few volts) on the nanoscale device results in the generation of the extremely strong electric field in the active region of a device (~1 MV cm−1) . This strong electric field reduces the activation barrier which results in an increase in the drift velocity of charge carriers or nanoscopic nonlinear ionic transport . Furthermore, this strong electric field produces nonlinear drifting of vacancies near the boundary interfaces [20, 21, 22].
The results of the present simulations suggest that the current multiplier factor plays an important role in resistive switching and is found to be 10−5 A for 0.2–0.6 V. The same becomes 10−4, 10−3 A for the 0.8–1.0, and 1.2 V, respectively. At the nanoscale, current threshold for resistive switching seems to be operational and the rate of drifting of oxygen vacancies (state variable of memristor) is higher at a particular range of bias and lower for other bias. The simulation results are clearly evident that memristor is a very apt fundamental building block of the nonvolatile memory with a high degree of symmetry. The lower resistive switching voltage makes it a promising candidate for future low power consumption memories.
Thus, the results clearly depict the existence of higher memory window only at higher write voltage with lower frequency. This results in fewer read/write errors in the memristor-based RRAM. The results also suggested that the memory window becomes very small at higher frequency; therefore, read/write errors become dominant and, hence, memristor-based RRAM cannot be used in this region.
Effect of bias or write voltage and frequency on memristor lifetime (τ) reliability
The data-handling capacity of a memory device, in general, is characterized by its data retention property. The data are supposed to be retained for a very long period of time and it is one of the primary requirements for any memory device. The external or internal malfunction or faults can be responsible for data losses [17, 27]. Furthermore, this fault also affects the lifetime (τ) reliability of the memory device. The lifetime of the memristor, as well as data retention, can be increased by taking proper care of faults and malfunctions. Against this backdrop, we have investigated the effect of write voltage and frequency on the reliability of memristor-based RRAM. The results described in the previous sections confirm the important role of write voltage in the memristor-based RRAM. With reference to the write voltage scenario, the value of LRS is very low for lower voltage region, and it becomes high for higher voltage region. At the same time, the value of LRS increases as the frequency of applied signal increases which is shown in Fig. 5.
The present paper portrayed the effect of the write voltage and frequency on memristor-based resistive random access memory (RRAM). It is found that the LRS is a function of write voltage and frequency but HRS is independent of write voltage and frequency. It is further revealed that memory window tends to increase with an increase in the write voltage. Furthermore, the memory window is found to be the function of frequency and higher memory window is achieved at the lower frequency region. In the present investigation, memory window is found to be ~200 for frequency value ≤2 Hz and it decreases after 4 Hz. The lifetime (τ) reliability analysis of memristor-based RRAM is carried out using LRS results. It is observed that memristor possesses higher lifetime (τ) at higher voltage with lower frequency region, i.e., the magnitude of the current is found to be ~0.01 A for frequency value ≤2 Hz and it decreases for higher frequencies. The simulation results confirm that the higher frequency region is responsible for the lower memory window and higher errors in the memory architecture.
TDD, KVK, SVM, NDD, and SSS investigated the mathematical model. TDD, VLP, SAV, AVM and KYR developed the MATLAB code. PNB, PSP, PKG and RKK analyzed the results. TDD, KVK, AVM, KYR, and RKK documented the manuscript. All authors reviewed the manuscript.
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