IEEE Circuits and Systems Magazine - Q4 2019 - 12

Real devices show behaviors that may not be represented
by current models, yet they can affect the function
of the circuit and the system.
state drift discussed here regards the state changes in
the absence of any input.
There are several suggestions regarding compensation of read-out mechanism, nonetheless, there are no
concrete solutions addressing the leakage. To evaluate
these effects we designed and implemented (shown in
Fig. 5) a memory write and read circuit [95] and measured the maximum retention time of Knowm "BS-AF-W"
memristors [96]. Our measurement showed 81 hours
of retention time (488 reads, 10 minutes apart) for our
memory system. In our experiments, the read operations were not compensated and hence could affect the
retention time. However, in a different experiment with
more frequent reads (every 1 second), we managed to
have 6000 correct reads before a state change. Therefore, even though the 488 read operations contribute in
reduction of retention time, the two experiments prove
the presence of a different effect which we associate
with the leakage. Since currently, no models for this effect exist, we could not simulate this effect. Similarly, no
other memristive memory system design can be thoroughly verified in simulation (e.g., regarding its retention time). At least not using the models currently available to the public and academia. This indicates the need
for developing new and more comprehensive models.
More importantly, it highlights the importance of the
physical implementation and verification of memristive
systems. We note that there are memory products in

Figure 5. Our implementation of a complete memory system on PCB, populated with memristor chip and required
circuits to read and write.
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IEEE CIRCUITS AND SYSTEMS MAGAZINE

the market, e.g., [97], which use memristors. Therefore,
there is no doubt that there are and can be more memristive memory systems, for which similar characterization experiments are done. However, we could not find
any similar reports accessible to the public, reporting
those important characteristics we measured.
B. Logic Example-IMPLY
As one of the most prominent memristor-based logic
design methods, IMPLY has been extensively used [31],
[34], [38], [48], [49], [99]-[102]. There are also various
works in the literature on its design and implementation as well, e.g. [34], [35], [38], [45]. This also includes
closed-form formulas and determined boundaries regarding the value of various circuit elements necessary
to implement an IMPLY [38], [45]. In the literature, however, often the circuit simulation of systems using IMPLY
is skipped (see e.g., [45], [48], [99], [100]), given the assumption that the basic gate implementation as shown
in [34] is functional. However, to verify our IMPLY based
system published in [48], we tried to run the respective
simulation in SPICE. The common assumption in p " q
(p IMPLY q) is that p maintains its state while q changes
its state to hold the result [31], [45], [48], [100]-[102]. Despite the fact that many of the designed systems work
strictly based on this assumption, to our surprise, this
does not seem to be always the case.
One of the problems with the closed-form calculations
is that they assume a resistive switch with fixed resistance
before and after crossing the threshold voltage. Whereas
in reality, the memristors experience state drift on both
sides of this threshold, which on itself affects the switching process. According to our simulations using four different models (namely, Biolek [98], Yakopcic [103], Joglekar
[104] and TEAM [105]), in a single operation, or as shown
in [34] in a few step operation, the parameters could be set
such that p can be considered (in some cases only marginally) as keeping its previous states. However, the state
drift in a sequence of operations leads to a potential loss of
state for p and consequently false results (see Fig. 6). The
only model in which we managed to simulate IMPLY with a
small enough state drift that does not cause a loss of state
is TEAM [105]. However, we notice that for doing so we had
to set the model parameters arbitrarily and far from the
characteristics of the real memristors we have at hand.
Taking all the above into account, the question of
the practicality of a physical implementation of IMPLY
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