IEEE Circuits and Systems Magazine - Q2 2018 - 74

well-established system-theoretic concept first introduced
by Boyd and Chua [41] back in 1985, if it exhibits a unique
asymptotic behaviour irrespective of its initial state. In
2015 fading memory was discovered in the tantalum oxide memristor nano-device fabricated at Hewlett Packard
Labs [33] after numerical simulations on its physics-based
model [17], conducted by Ascoli and Tetzlaff [42] unveiled
the emergence of the memory loss phenomenon. Despite
the TaO resistance switching memory is non-volatile, its DC
or AC periodic stimulation results in a progressive history
erase leading to a unique steady-state dynamic behaviour.
Through the analysis of a graphic tool named Dynamic
Route Map [54], this paper reveals that the history erase
phenomenon is ubiquitous in real-world memristor nanodevices ([15], [16], [19], [20], [21]), irrespective of material
composition and physical mechanisms underlying the peculiar memristive dynamics18. The unchanged sign of the
state evolution function under a DC stimulus with constant
polarity, combined with the resulting asymptotic saturating
behaviour for the device memory state, explains the origin
of fading memory effects in a DC-driven memristor nanodevice. With reference to the aforementioned TaO memristor, this was recently confirmed through the derivation and
study of the analytical solution of Strachan's model [17]
under positive DC excitation [27]. In this work a clearer
understanding for the emergence of the memory loss phenomenon under AC periodic stimuli is gained through the
analysis of the Wei Lu's memristor model [16], in which the
on- and off-switching kinetics are modelled by the same
equation, where, however, a device parameter, namely the
ion hopping barrier height, assumes distinct values depending upon the input polarity. The hypothetical memristor, obtained from Wei Lu's original model equations
(32)-(33) by considering a same value for such device
parameter under on and off switching, displays symmetric dynamics under positive and negative DC inputs, and
experiences no memory loss, similarly to ideal and ideal
generic memristors [44], revealing that the typical asymmetry in the on and off switching dynamics of real-world
memristors may be one factor at the origin of the progressive history erase phenomenon at AC. As a further remark,
it is crucial to observe that, in general, the observation of
AC fading memory effects in physical memristor nano-devices is not merely induced by the existence of boundary
conditions, as may be evinced by inspecting Fig. 14(b), referring to a numerical simulation of Strachan's model [17],
18
Employing numerical simulations on their mathematical descriptions, we
observed DC and AC fading memory also in other real-world memristor models, including the hafnium oxide-based resistive random access
memory (ReRAM) nano-device from Politecnico di Milano [18] and the
TiOx/HfOx bilayer memristor from Stanford Nanoelectronics Lab [22]
from Stanford, but, due to lack of space, the presentation of the relative
results is omitted from this contribution, and will be partially reported
elsewhere [65].

IEEE cIrcuIts and systEms magazInE

and showing how, irrespective of the initial condition, the
memory state of the TaO memristor from Hewlett Packard
Labs in response to a two-tone input oscillates well within
its allowable variation range at steady state. For the sake of
completeness, some extended memristors [40] may also
display a local form of the fading memory property, theoretically introduced in [47] through a purely-mathematical
memristor model, and further investigated in [48] through
the application of circuit- and system-theoretic techniques
to a memristor emulator.
Acknowledgments
This work has been supported by the Czech Science Foundation under grant no. 18-21608S The authors would like
to acknowledge the contribution of the EU COST Action
IC1401 "Memristors-Devices, Models, Circuits, Systems
and Applications" (MemoCiS). The authors wish to thank
L.O. Chua from University of California Berkeley, V. Ntinas, and G.Ch. Sirakoulis from Democritus University of
Thrace, M.D. Pickett, J.P. Strachan, and R.S. Williams from
Hewlett Packard Enterprise, D. Ielmini from Politecnico di
Milano, as well as A. Siemon, and R. Waser from RWTH
Aachen for the fruitful collaboration towards a better understanding of the fading memory dynamic phenomenon
emerging in real-world memristor nano-devices.
Alon Ascoli received a Ph.D. Degree in
Electronic Engineering from University
College Dublin in 2006. From 2006 to
2009 he worked as RFIC analog engineer at CSR Sweden AB. From 2009 to
2012 he was Research Assistant in the
Department of Electronics and Telecommunications at
Politecnico di Torino. Since 2012 he is Assistant Professor in the Faculty of Electrical and Computer Engineering, Technische Universität Dresden. Since 2018 he is
Scientific Collaborator with the Department of Microelectronics, Brno University of Technology, Brno, Czech
Republic. His research interests lie in the area of nonlinear circuits and systems, networks of oscillators, Cellular Nonlinear Networks and memristors. Dr. Ascoli was
honored with the IJCTA 2007 Best Paper Award. In April
2017 he was conferred the habilitation title as Associate
Professor in Electrical Circuit Theory from the Italian
Ministry of Education. In November 2017 he was conferred a High-Performance Award from Technische Universität Dresden. Since 2014 he is Management Committee Substitute for Germany in the COST Action IC1401
MemoCIS "Memristors-Devices, Models, Circuits, Systems, and Applications". He has been Program Chair and
Special Session Chair for the 15th International Workshop on Cellular Nanoscale Networks and their Applications (CNNA) in 2016.
sEcOnd quartEr 2018

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