arXiv subjects

V. A. Slipko

Publications and source records attributed to V. A. Slipko.

At least 19 recordsLinked to original sources

arXiv2023

A probabilistic model of resistance jumps in memristive devices

Resistance switching memory cells such as electrochemical metallization cells and valence change mechanism cells have the potential to revolutionize information processing and storage. However, the creation of deterministic resistance switching devices is a challenging problem that is still open. At present, the modeling of resistance switching cells is dominantly based on deterministic models that fail to capture the cycle-to-cycle variability intrinsic to these devices. Herewith we introduce a state probability distribution function and associated integro-differential equation to describe the switching process consisting of a set of stochastic jumps. Numerical and analytical solutions of the equation have been found in two model cases. This work expands the toolbox of models available for resistance switching cells and related devices, and enables a rigorous description of intrinsic physical behavior not available in other models.

cond-mat.mes-hall↗

arXiv2022

Analytic and SPICE modeling of stochastic ReRAM circuits

The modeling of conventional (deterministic) electronic circuits - ones consisting of transistors, resistors, capacitors, inductors, and other traditional electronic components - is a well-established subject. The cycle-to-cycle variability of emerging electronic devices, in particular, certain ReRAM cells, has led to the concept of stochastic circuits. Unfortunately, even in relatively simple cases, the direct transient analysis of stochastic circuits is computationally demanding and potentially impractical, if possible at all. An important development in this area has been the application of a master equation that is easily implemented in SPICE. In this conference paper, we briefly review the master equation approach and present an improved implementation of this approach in SPICE. Moreover, we find an attractor state in a periodically driven memristive circuit - a stochastic counterpart of deterministic memristor attractors.

cs.ET↗

arXiv2021

Theory of heterogeneous circuits with stochastic memristive devices

We introduce an approach based on the Chapman-Kolmogorov equation to model heterogeneous stochastic circuits, namely, the circuits combining binary or multi-state stochastic memristive devices and continuum reactive components (capacitors and/or inductors). Such circuits are described in terms of occupation probabilities of memristive states that are functions of reactive variables. As an illustrative example, the series circuit of a binary memristor and capacitor is considered in detail. Some analytical solutions are found. Our work offers a novel analytical/numerical tool for modeling complex stochastic networks, which may find a broad range of applications.

cs.ET↗

arXiv2020

Probabilistic Memristive Networks: Application of a Master Equation to Networks of Binary ReRAM cells

The possibility of using non-deterministic circuit components has been gaining significant attention in recent years. The modeling and simulation of their circuits require novel approaches, as now the state of a circuit at an arbitrary moment in time cannot be precisely predicted. Generally, these circuits should be described in terms of probabilities, the circuit variables should be calculated on average, and correlation functions should be used to explore interrelations among the variables. In this paper, we use, for the first time, a master equation to analyze the networks composed of probabilistic binary memristors. Analytical solutions of the master equation for the case of identical memristors connected in-series and in-parallel are found. Our analytical results are supplemented by results of numerical simulations that extend our findings beyond the case of identical memristors. The approach proposed in this paper facilitates the development of probabilistic/stochastic electronic circuits and advance their real-world applications.

cs.ET↗

arXiv2020

Modeling networks of probabilistic memristors in SPICE

Efficient simulation of probabilistic memristors and their networks requires novel modeling approaches. One major departure from the conventional memristor modeling is based on a master equation for the occupation probabilities of network states [arXiv:2003.11011 (2020)]. In the present article, we show how to implement such master equations in SPICE - a general-purpose circuit simulation program. In the case studies, we simulate the dynamics of ac-driven probabilistic binary and multi-state memristors, and dc-driven networks of probabilistic binary and multi-state memristors. Our SPICE results are in perfect agreement with known analytical solutions. Examples of LTspice codes are included.

cs.ET↗

arXiv2019

Bifurcation analysis of a TaO memristor model

This paper presents a study of bifurcation in the time-averaged dynamics of TaO memristors driven by narrow pulses of alternating polarities. The analysis, based on a physics-inspired model, focuses on the stable fixed points and on how these are affected by the pulse parameters. Our main finding is the identification of a driving regime when two stable fixed points exist simultaneously. To the best of our knowledge, such bistability is identified in a single memristor for the first time. This result can be readily tested experimentally, and is expected to be useful in future memristor circuit designs.

cs.ET↗

arXiv2019

Transient dynamics of pulse-driven memristors in the presence of a stable fixed point

Some memristors are quite interesting from the point of view of dynamical systems. When driven by narrow pulses of alternating polarities, their dynamics has a stable fixed point, which may be useful for future applications. We study the transient dynamics of two types of memristors characterized by a stable fixed point using a time-averaged evolution equation. Time-averaged trajectories of the Biolek window function memristor and resistor-threshold type memristor circuit (an effective memristor) are determined analytically, and the times of relaxation to the stable fixed point are found. Our analytical results are in perfect agreement with the results of numerical simulations.

cs.ET↗

arXiv2019

Importance of the window function choice for the predictive modelling of memristors

Window functions are widely employed in memristor models to restrict the changes of the internal state variables to specified intervals. Here we show that the actual choice of window function is of significant importance for the predictive modelling of memristors. Using a recently formulated theory of memristor attractors, we demonstrate that whether stable fixed points exist depends on the type of window function used in the model. Our main findings are formulated in terms of two memristor attractor theorems, which apply to broad classes of memristor models. As an example of our findings, we predict the existence of stable fixed points in Biolek window function memristors and their absence in memristors described by the Joglekar window function, when such memristors are driven by periodic alternating polarity pulses. It is anticipated that the results of this study will contribute toward the development of more sophisticated models of memristive devices and systems.

cs.ET↗

arXiv2019

Dynamical attractors of memristors and their networks

It is shown that the time-averaged dynamics of memristors and their networks periodically driven by alternating-polarity pulses may converge to fixed-point attractors. Starting with a general memristive system model, we derive basic equations describing the fixed-point attractors and investigate attractors in the dynamics of ideal, threshold-type and second-order memristors, and memristive networks. A memristor potential function is introduced, and it is shown that in some cases the attractor identification problem can be mapped to the problem of potential function minimization. Importantly, the fixed-point attractors may only exist if the function describing the internal state dynamics depends on an internal state variable. Our findings may be used to tune the states of analog memristors, and also be relevant to memristive synapses subjected to forward- and back-propagating spikes.

nlin.CD↗

arXiv2017

Switching synchronization in 1-D memristive networks: An exact solution

We study a switching synchronization phenomenon taking place in one-dimensional memristive networks when the memristors switch from the high to low resistance state. It is assumed that the distributions of threshold voltages and switching rates of memristors are arbitrary. Using the Laplace transform, a set of non-linear equations describing the memristors dynamics is solved exactly, without any approximations. The time dependencies of memristances are found and it is shown that the voltage falls across memristors are proportional to their threshold voltages. A compact expression for the network switching time is derived.

nlin.AO↗

arXiv2017

Kinks and antikinks of buckled graphene: A testing ground for phi^4 field model

Kinks and antikinks of the classical phi^4 field model are topological solutions connecting its two distinct ground states. Here we establish an analogy between the excitations of a long graphene nanoribbon buckled in the transverse direction and phi^4 model results. Using molecular dynamics simulations, we investigated the dynamics of a buckled graphene nanoribbon with a single kink and with a kink-antikink pair. Several features of phi^4 model have been observed including the kink-antikink capture at low energies, kink-antikink reflection at high energies, and a bounce resonance. Our results pave the way towards the experimental observation of a rich variety of phi^4 model predictions based on graphene.

cond-mat.mes-hall↗

arXiv2016

Metastable Memristive Lines for Signal Transmission and Information Processing Applications

Traditional studies of memristive devices have mainly focused on their applications in non-volatile information storage and information processing. Here, we demonstrate that the third fundamental component of information technologies { the transfer of information { can also be employed with memristive devices. For this purpose, we introduce a metastable memristive circuit. Combining metastable memristive circuits into a line, one obtains an architecture capable of transferring a signal edge from one space location to another. We emphasize that the suggested transmission lines employ only resistive components. Moreover, their networks (for example, Y-connected lines) have an information processing capability.

cs.ET↗

arXiv2015

Reconfigurable Transmission Lines with Memcapacitive Materials

We study transmission lines made of memory capacitive (memcapacitive) materials. The transmission properties of these lines can be adjusted on demand using an appropriate sequence of pulses. In particular, we demonstrate a pulse combination that creates a periodic modulation of dielectric properties along the line. Such a structure resembles a distributed Bragg reflector having important optical applications. We present simulation results demonstrating all major steps of such a reconfigurable device operation including reset, programming and transmission of small amplitude signals. The proposed reconfigurable transmission lines employ only passive memory materials and can be realized using available memcapacitive devices.

cond-mat.mes-hall↗

arXiv2015

Switching Synchronization in One-Dimensional Memristive Networks

We report on an astonishing switching synchronization phenomenon in one-dimensional memristive networks, which occurs when several memristive systems with different switching constants are switched from the high to low resistance state. Our numerical simulations show that such a collective behavior is especially pronounced when the applied voltage slightly exceeds the combined threshold voltage of memristive systems. Moreover, a finite increase in the network switching time is found compared to the average switching time of individual systems. An analytical model is presented to explain our observations. Using this model, we have derived asymptotic expressions for memory resistances at short and long times, which are in excellent agreement with our numerical calculations.

cond-mat.mes-hall↗

arXiv2013

Hybrid Spin Noise Spectroscopy and the Spin Hall Effect

Here we suggest a novel hybrid spin noise spectroscopy technique, which is sensitive to the spin Hall effect. It is shown that, while the standard spin-spin correlation function is not sensitive to the spin Hall effect, spin-transverse voltage and transverse voltage-voltage correlation functions provide the missing sensitivity being linear and quadratic in the spin Hall coefficient, respectively. The correlation between transverse voltage and spin fluctuations appears as a result of spin-charge coupling fundamental for the spin Hall effect. We anticipate that the proposed method could find applications in the studies of spin-charge coupling in semiconductors.

cond-mat.mes-hall↗

arXiv2012

Changing the state of a memristive system with white noise

Can we change the average state of a resistor by simply applying white noise? We show that the answer to this question is positive if the resistor has memory of its past dynamics (a memristive system). We also prove that, if the memory arises only from the charge flowing through the resistor -- an ideal memristor -- then the current flowing through such memristor can not charge a capacitor connected in series, and therefore cannot produce useful work. Moreover, the memristive system may skew the charge probability density on the capacitor, an effect which can be measured experimentally.

cond-mat.mes-hall↗

arXiv2012

Decay of Persistent Spin Helix due to the Spin Relaxation at Boundaries

We study electron spin relaxation in one-dimensional structures of finite length in the presence of Bychkov-Rashba spin-orbit coupling and boundary spin relaxation. Using a spin kinetic equation approach, we formulate boundary conditions for the case of a partial spin polarization loss at the boundaries. These boundary conditions are used to derive corresponding boundary conditions for spin drift-diffusion equation. The later is solved analytically for the case of relaxation of a homogeneous spin polarization in 1D finite length structures. It is found that the spin relaxation consists of three stages (in some cases, two) -- an initial D'yakonov-Perel' relaxation is followed by spin helix formation and its subsequent decay. Analytical expressions for the decay time are found. We support our analytical results by results of Monte Carlo simulations.

cond-mat.mes-hall↗

arXiv2012

Complex dynamics and scale invariance of one-dimensional memristive networks

Memristive systems, namely resistive systems with memory, are attracting considerable attention due to their ubiquity in several phenomena and technological applications. Here, we show that even the simplest one-dimensional network formed by the most common memristive elements with voltage threshold bears non-trivial physical properties. In particular, by taking into account the single element variability we find i) dynamical acceleration and slowing down of the total resistance in adiabatic processes, ii) dependence of the final state on the history of the input signal with same initial conditions, iii) existence of switching avalanches in memristive ladders, and iv) independence of the dynamics voltage threshold with respect to the number of memristive elements in the network (scale invariance). An important criterion for this scale invariance is the presence of memristive systems with very small threshold voltages in the ensemble. These results elucidate the role of memory in complex networks and are relevant to technological applications of these systems.

cond-mat.dis-nn↗