IEEE Circuits and Systems Magazine - Q4 2019 - 11

Be aware of limitations! Abstractions for high-level simulations
are very little reliable, so are the low-level simulations
using only nominal values.
it does not show how good or bad they may model a
specific physical memristor (of this or any other type).
Additionally, this set of criteria does not provide a full
insight to the behavior of a memristor.
As mentioned above, some models do consider the
non-linearity and kinetics, which to some extent reflects
the speed of the device. However, even for speed, more
works such as extracting layout and wire parasitics and
considering them in the models are missing. In addition,
noise, variability, and temperature are also not reflected
properly in the models. It is known that temperature can
affect properties such as the mobility in the devices [57],
which can, in turn, affect its behavior. This effect is stronger in some materials such as VO2 and NbO2, leading to
the observation of negative differential resistance [57]. A
property which has been used to create oscillation [84]
and neurons [54], [84]. Although this behavior for these
specific types has been modeled [85], [86], main-stream
generic models do not consider any temperature effects.
C. The Nature of Designed Circuits
Memristive circuits such as neuromorphic systems [24],
[53], [60], [91] or Threshold Logic [28], [37], and some
other custom circuits [53], [92] treat memristors as a device with a continuous range of values. This is in nature
similar to analog circuits rather than digital circuits and
therefore, requires similar care and approach as in analog circuits. That is, new designs and concepts need to be
backed up by physical implementation and verification in
order to be reliable. On the other hand, in many of the
digital memristive circuits, a highly non-linear behavior
(sharp switching based on thresholds) is assumed and
used. In reality the extent of this non-linearity is more limited and the analog continuous nature of memristors has
a strong presence, making a notable difference in practice.
For example, in IMPLY Logic [31], [35], [64], the state
change operation heavily depends on the voltage difference between VCOND and VSET, which is significantly
smaller than the power supply, providing a very weak
non-binary drive for the change. On the other hand, it is
assumed that if the voltage across a memristor is below
the threshold, that memristor will not experience any
changes. Whereas, in practice, that memristor can experience a state drift (we will show and discuss this more
in Section IV-B). Although the input and output are considered as digital values, the dynamic of the operation
is significantly closer to the traditional analog circuits
FOURTH QUARTER 2019

than the digital circuits. Again, requiring considerations
that are common in the analog domain but are often
omitted in the digital domain.
IV. Reproducibility Challenge
Shortcomings discussed in Section II and Section III
negatively affect reproducibility of designs in the real
world and consequently, put a question mark on the extent of their practicality and usefulness. In some cases,
these issues lead to inconsistencies and reproduction issues in simulations as well, which poses an even greater
challenge to the community. We have tried to reproduce
some of the existing works in the literature and faced
certain problems which we briefly report here. We note
that to answer questions such as "which logic is more
reliable in practice?" a comprehensive set of studies is in
order. In such a study one should test them in practice
at the presence of practical challenges, and assess the
difficulty to come up with solutions to resolve any problems they may face in practice. Only then a good perspective of the advantages or disadvantages of one logic
or another can be discussed. Even though, we hope that
this paper and particularly this section will ignite such
discussions and plant the seed for such studies, such indepth analysis and discussion is not in the scope of the
present paper. Here we narrate our limited experiences
to highlight the challenges of practical implementation
and attract the attention of researchers and engineers
to their importance while leaving comprehensive comparative studies for future works.
A. Memory Example
There are several papers in the literature on various
aspects of using memristors as memories [9], [13], [15],
[16], [19]-[22]. Although various models capture different characteristics of memristors, interestingly enough,
so far and to the best of our knowledge, none of the
existing ones model the leakage or state drift fully and
properly. A factor that substantially affects the performance of memristors as memory. We bear in mind that
there have been works on "history effect" [93], [94], however, that is a different concept. History effect concerns
the eventuality of a steady state in memristors, which is
independent of its initial state, after application of a certain input pattern. In studying history effect, the authors
explicitly mention that they do not consider state changes in the absence of input [93], whereas the leakage or
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