Analysis of memristors with nonlinear memristance versus state maps

Summary According to the axiomatic definition of the memristor from 1971, its properties are unambiguously determined by the memristance versus charge (or flux) map. The original model of the ‘HP memristor’ introduces this map via a linear function that represents this memristor as a variable resistor whose resistance is linearly dependent on the amount of charge flowing through. However, some analog applications require nonlinear, frequently exponential or logarithmic dependence of the resistance on an external controlling variable. The memristor with nonlinear memristance versus charge map is analyzed in the paper. The results are specified for the exponential type of this nonlinearity, which may be useful for future applications. Analytic formulae of the area of the pinched hysteresis loop of such a memristor are derived for harmonic excitation. It is also shown that the current flowing through such a memristor, which is driven by a voltage of arbitrary waveform, conforms to the Abel differential equation, and its closed-form solution is found. Copyright © 2017 John Wiley & Sons, Ltd.

[1]  Uri C. Weiser,et al.  TEAM: ThrEshold Adaptive Memristor Model , 2013, IEEE Transactions on Circuits and Systems I: Regular Papers.

[2]  Dalibor Biolek,et al.  Memristor models for SPICE simulation of extremely large memristive networks , 2016, 2016 IEEE International Symposium on Circuits and Systems (ISCAS).

[3]  Dalibor Biolek,et al.  Computing Areas of Pinched Hysteresis Loops of Mem-Systems in OrCAD PSPICE , 2013 .

[4]  Chris Yakopcic,et al.  Generalized Memristive Device SPICE Model and its Application in Circuit Design , 2013, IEEE Transactions on Computer-Aided Design of Integrated Circuits and Systems.

[5]  Leon O. Chua,et al.  History Erase Effect in a Non-Volatile Memristor , 2016, IEEE Transactions on Circuits and Systems I: Regular Papers.

[6]  Dalibor Biolek,et al.  Specification of one classical fingerprint of ideal memristor , 2015, Microelectron. J..

[7]  Chris Yakopcic,et al.  Memristor SPICE Modeling , 2012 .

[8]  Ronald Tetzlaff,et al.  Memristor-based filtering applications , 2013, 2013 14th Latin American Test Workshop - LATW.

[9]  E. Lehtonen,et al.  CNN using memristors for neighborhood connections , 2010, 2010 12th International Workshop on Cellular Nanoscale Networks and their Applications (CNNA 2010).

[10]  Alon Ascoli,et al.  The First Ever Real Bistable Memristors—Part I: Theoretical Insights on Local Fading Memory , 2016, IEEE Transactions on Circuits and Systems II: Express Briefs.

[11]  Leon O. Chua,et al.  A Theoretical Approach to Memristor Devices , 2015, IEEE Journal on Emerging and Selected Topics in Circuits and Systems.

[12]  Massimiliano Di Ventra,et al.  Practical Approach to Programmable Analog Circuits With Memristors , 2009, IEEE Transactions on Circuits and Systems I: Regular Papers.

[13]  D. Biolek,et al.  Improved Model of TiO2 Memristor , 2015 .

[14]  Leon O. Chua.  Resistance switching memories are memristors , 2011 .

[15]  Siegfried Selberherr,et al.  Domain-wall spintronic memristor for capacitance and inductance sensing , 2011, 2011 International Semiconductor Device Research Symposium (ISDRS).

[16]  Siddharth Gaba,et al.  Synaptic behaviors and modeling of a metal oxide memristive device , 2011 .

[17]  L.O. Chua,et al.  Memristive devices and systems , 1976, Proceedings of the IEEE.

[18]  Saha Gourav.  Theory of Memristive Controllers: Design and Stability Analysis for Linear Plants , 2011 .

[19]  Takashi Mukai,et al.  高出力255/280/310nm深紫外発光ダイオードとその寿命特性 , 2014 .

[20]  Ronald Tetzlaff,et al.  Nonlinear Dynamics of a Locally-Active Memristor , 2015, IEEE Transactions on Circuits and Systems I: Regular Papers.

[21]  Dalibor Biolek,et al.  (Co)content in Circuits With Memristive Elements , 2015, IEEE Transactions on Circuits and Systems I: Regular Papers.

[22]  Dalibor Biolek,et al.  Interpreting area of pinched memristor hysteresis loop , 2014 .

[23]  Derek Abbott,et al.  Memristive Device Fundamentals and Modeling: Applications to Circuits and Systems Simulation , 2012, Proceedings of the IEEE.

[24]  Dalibor Biolek,et al.  Fourth Fundamental Circuit Element: SPICE Modeling and Simulation , 2014 .

[25]  Dalibor Biolek,et al.  Reliable Modeling of Ideal Generic Memristors via State-Space Transformation , 2015 .

[26]  Fernando Corinto,et al.  Analysis of current–voltage characteristics for memristive elements in pattern recognition systems , 2012, Int. J. Circuit Theory Appl..

[27]  J. Yang,et al.  Switching dynamics in titanium dioxide memristive devices , 2009 .

[28]  Eby G. Friedman,et al.  VTEAM – A General Model for Voltage Controlled Memristors , 2014 .

[29]  D. Strukov,et al.  Phenomenological modeling of memristive devices , 2014, 1406.4219.

[30]  L. Chua.  Memristor-The missing circuit element , 1971 .

[31]  Leon O. Chua,et al.  If it’s pinched it’s a memristor , 2014 .

[32]  Ronald Tetzlaff,et al.  Generalized boundary condition memristor model , 2016, Int. J. Circuit Theory Appl..

[33]  Leon O. Chua,et al.  The First Ever Real Bistable Memristors—Part II: Design and Analysis of a Local Fading Memory System , 2016, IEEE Transactions on Circuits and Systems II: Express Briefs.

[34]  Matthew D. Pickett,et al.  SPICE modeling of memristors , 2011, 2011 IEEE International Symposium of Circuits and Systems (ISCAS).

[35]  Dalibor Biolek,et al.  Analytical Solution of Circuits Employing Voltage- and Current-Excited Memristors , 2012, IEEE Transactions on Circuits and Systems I: Regular Papers.

[36]  Anne Siemon,et al.  Applicability of Well-Established Memristive Models for Simulations of Resistive Switching Devices , 2014, IEEE Transactions on Circuits and Systems I: Regular Papers.

[37]  Fernando Corinto,et al.  Memristor Circuits: Flux—Charge Analysis Method , 2016, IEEE Transactions on Circuits and Systems I: Regular Papers.

[38]  Leon O. Chua,et al.  Fading memory and the problem of approximating nonlinear operators with volterra series , 1985 .

[39]  Mauricio Barahona,et al.  Device Properties of Bernoulli Memristors , 2012, Proceedings of the IEEE.

[40]  Dalibor Biolek,et al.  Hysteresis versus PSM of ideal memristors, memcapacitors, and meminductors , 2016 .

[41]  Leon O. Chua,et al.  Everything You Wish to Know About Memristors But Are Afraid to Ask , 2015 .

[42]  Dalibor Biolek,et al.  Differential Equations of Ideal Memristors , 2015 .

[43]  Baker Mohammad,et al.  Robust Hybrid Memristor-CMOS Memory: Modeling and Design , 2013, IEEE Transactions on Very Large Scale Integration (VLSI) Systems.

[44]  Fernando Corinto,et al.  A Boundary Condition-Based Approach to the Modeling of Memristor Nanostructures , 2012, IEEE Transactions on Circuits and Systems I: Regular Papers.

[45]  Darko Veberic,et al.  Having Fun with Lambert W(x) Function , 2010, ArXiv.

[46]  J. Yang,et al.  State Dynamics and Modeling of Tantalum Oxide Memristors , 2013, IEEE Transactions on Electron Devices.

[47]  D. Stewart,et al.  The missing memristor found , 2008, Nature.

[48]  Dalibor Biolek,et al.  Computation of the Area of Memristor Pinched Hysteresis Loop , 2012, IEEE Transactions on Circuits and Systems II: Express Briefs.

[49]  D. Biolek,et al.  Pinched hysteretic loops of ideal memristors, memcapacitors and meminductors must be 'self-crossing' , 2011 .

[50]  J. Simmons.  Electric Tunnel Effect between Dissimilar Electrodes Separated by a Thin Insulating Film , 1963 .