IEEE Circuits and Systems Magazine - Q4 2019 - 15

While real devices are hard to access, awareness of potential challenges
and thorough low-level simulations are crucial for a reliable design.
and issues such as amplifier noise are introduced. A
simple solution is adding a transistor to switch a memristor in or out of the crossbar. The main problem
with this structure, also called 1T1M, is the additional
transistor gate wire which makes the crossbar less
compact compared to a cell structure that requires
only a memristor. The required transistors can have
an even larger effect in the total area of the crossbar.
Device level solutions such as larger OFF/ON ratios
also could alleviate the sneak path problem. In that
case, 1T1M could change from a functional necessity
to a luxurious addition for applications which require
higher reliability and can accept the additional costs
of 1T1M structures.
At the circuit and system level, the following steps
can help the design and implementation process;
Models Memristor models still have a long way to completion. Modeling temperature effects, device variations
(particularly the variations in the absolute value of R on
and R off ), threshold variation, cyclic variations, leakage
(retention time), and endurance are some of the practical
effects which, to the best of our knowledge, are not reflected in any of the existing models. Modeling these effects -
especially in one integrated model- can enable more realistic simulations, particularly corner simulations.
Parasitics More often than not, memristor models are
developed in a laboratory environment and are based
on on-die measurements. They do not consider any of
the parasitics which can be formed due to the wires and
connections as well as the layout of the circuits. Creating and using models for these effects can help in the
design process and lead to more realistic simulations
which better represent implementations.
Functional Simulations Using better models which
reflect the reality better, in terms of values and variations and include leakage, extracted parasitics, and
unideal initial states (memristors that enter an operation without having reached their full ON or OFF states
in previous operations), the circuits can be thoroughly
tested to see whether they are functional under all those
circumstances or not. If not, the range of functional operations, as well as more problematic issues, can be
identified. The former allows selecting suitable applications or technologies and the latter helps in devising solutions to address the relevant functional issues.
Corner Simulation Evaluating a circuit in different
corners, such as the ones mentioned above, help in
predicting the chances of prototypes being functional,
FOURTH QUARTER 2019

or selection of the technology to fabricate the designed
circuit, as well as the universality of the design. That
is, how much of variation in those parameters the design can tolerate before showing functional problems?
Consequently, this helps to find suitable technologies
since technologies which have a variation within those
bounds can be used to implement that design.
Design and Test Awareness Once designers are
aware of the challenges of practical implementations,
as we discussed in this paper, they can design their
circuits such that they can overcome or better tolerate
these adversities. Whether these solutions be at circuit
level, or at system level (e.g., the one we proposed here
for the practical problems of the IMPLY gate). It is also
important to test the circuits and systems against them,
both in simulations and in practice.
Integration Many of working implementations are
based on Integrated Circuit (IC) solutions [107], [108].
That is, the memristors and the CMOS circuits are on
the same die or in the same package. This seems to be
a possible solution for more reliable implementations.
This facility is hardly available to the public but it seems
to have a considerable effect since most published practical implementations are ICs. With the announcement
of TSMC [27] regarding their new fabrication rounds
which include memristive devices, this could change
and we hope to see more practical implementations.
VI. Conclusions
Our experiments above show critical issues to which the
community needs to pay more attention to create more
effective and realistic memristive circuits and systems.
First, is the necessity of developing improved, more
comprehensive and more realistic memristor models
which represent the behavior of real-world memristors
better. In particular, factors such as device, threshold
and cyclic variations, as well as temperature effects,
leakage (retention time) and endurance. This point was
presented in the example of the memory system we have
developed. There, we showed factors such as retention
time or realistic refresh cycles cannot be simulated
since parameters such as leakage or device variation are
not fully or properly represented in the existing models.
Completion of models presents a longer-term challenge
since the memristive technology itself is evolving. This
process of evolution requires renewing respective
models to better represent the physical behavior of
newer technologies.
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IEEE Circuits and Systems Magazine - Q4 2019

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