IEEE Circuits and Systems Magazine - Q4 2019 - 14

how a more reliable and repeatable implementation of
MAGIC can be made possible? Be it a solution at device
level (e.g., less variation could help), circuit level (e.g.,
could any extra circuit help?), or system level. For example, at system level, the state drifts of input memristors due to longer operation time (which improves the
state change in output memristor) can be compensated
by refreshing the state of the input memristors (as we
suggested for IMPLY too). Similar to the IMPLY example
above, practical issues may be therefore overcome with
certain considerations which affect the system at higher
(e.g., at algorithm) levels too.
V. Moving Forward
In previous sections, we discussed major challenges
that memristive circuits and systems face in practice.
We would like to emphasize that this is not meant to
undermine the practicality of building memristive circuits and systems. It has been repeatedly proven that
it is possible to build memristive circuits which work
in practice, for example, see [107] and [108], among
many others. Our intention here is to raise awareness
about these challenges and by considering these issues,
empower engineers and designers to design circuits and
systems which have a shorter path to practical implementations. Other than taking the challenges of the current
state into account, there are certain steps that we, as a
community, could take to alleviate these adversities and
reduce the existing challenges. In this section, we summarize some of these potential steps, which provide formidable research questions and challenges. Addressing
them could have a positive effect on the design and implementation of memristive circuits and systems. Some
of the challenges to be addressed at the device level are:
Device Variability As we saw in Section A, particularly the example of Fig. 4, the variation between devices,
even within the same package, is so large that the R off
of a memristor can be smaller than the R on of another in
the same package. This makes it impossible to consider
even an arbitrary range of these values, within which
both memristors can be considered either ON or OFF.
Therefore, the biggest hurdle of practical implementations is this extremely large variation between device
characteristics. Reducing the size of memristors seems
to be a key solution to this problem. Material research
also could lead to improvements [109]-[111].
OFF/ON Ratio Even in a single memristor, it is important to have a minimum of R off /R on so that the two different states can be distinguished. As evident in our example, Fig. 4, this ratio undergoes a large variation too.
Values equal to or smaller than 1, which speak of practically indistinguishable states, are the major problem. In
addition, certain applications require much larger ratios.
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IEEE CIRCUITS AND SYSTEMS MAGAZINE

This issue, even though has a different effect in practice,
solution-wise, follows the previous issue closely. Solutions which could alleviate the problem of device variability could help in improving the OFF/ON ratio as well.
Cyclic Variability Variations during the lifetime of
the memristor is a well-known phenomenon as well
[112]. This challenge might be significantly more difficult than the device and ratio variation to address at
the device level. Considering it at circuit and system
level may be a somewhat easier approach. However, in
the presence of the previous two issues, this challenge
has little priority. Moreover, in many cases, its pattern
is hardly distinguishable. For example, we could not see
a particular pattern of cyclic variations in our measurements, however, once this pattern is distinguished and
modeled, circuit and system designers could better consider it in their designs.
Endurance Currently, the lifetime of memristors is
not very high in all technologies. In some cases, it could
be as low as 10,000 cycles [112], [113]. That is certainly
a limitation which could affect the wide-spread use of
them, particularly in applications such as in-memory
logic and computations which come with frequent
changes of state. Therefore, device level research is
needed to improve this aspect too. However, this problem seems to be of a secondary priority compared to
device variability and OFF/ON ratio.
Retention This problem mainly concerns memory applications. However, given that in future architectures
under investigation (which try to use in-memory computation), memristors are going to act both as memory and
computation unit, retention becomes an important aspect
for them as well. At this stage, this is also a secondary
concern, but very important for the wide-spread use of
these devices in consumer electronics. Material and device research seems to hold the answer to this question.
Device Speed In the literature a large range (from
sub-nanosecond to microseconds) of device speeds
can be observed [96], [114], [115]. This affects the performance and power consumption of the systems using
memristive circuits and systems. Improving the speed
of state changes at device level can make memristive
circuits and systems more competitive in the CMOSdominated market and hence improve its reception by
the industry and users.
Sneak Path is a well-known issue in the literature
[116], [117] and there have been efforts in reducing the
effect of sneak path [118], [119]. For example, in [118]
the authors use a system with buffer amplifiers to reduce the number of memristors which would normally
be affected by the sneak path. Thus, they alleviate the
problem, even though it does not go completely away.
In addition, the complexity of the system is increased
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