IEEE Circuits and Systems Magazine - Q4 2019 - 10

20 pulses of 800 mV amplitude and 25 μs width were
used to drive the memristors to their ON state (or low
resistance, shown in solid circles) and 20 pulses of
-400 mV amplitude and 25 μs width were used to drive
them to the OFF state (or high resistance, denoted by
hollow circles). Each memristor was driven to the two
opposite states and measured ten times for each state.
We see that for the first 3-4 memristors (each column/
group depicts the measurements of one memristor),
shown in (shades of) blue, R on and R off values overlap in
some measurements. This trend improves with a somewhat smaller or larger gap between the two values for
other memristors, shown in different shades of green.
Using memristors with overlapping R on and R off values
is practically impossible. Therefore, either they should
be identified beforehand and avoided, or other mechanisms should be devised to drive them into two distinct
states. We note that the ratio of R off /R on also varies from
57 to 1. This wide range of variation makes working even

1,800
1,600
Resistance (kΩ)

1,400
1,200
1,000
800
600
400
200
0

Measurements

Figure 4. Ron and Roff measurement results for 8 ReRAMs in
a single package. Each column represent measurements of
one memristive device. Solid circles denote ON resistance,
whereas hollow circles mark OFF resistances.

Fading

Stanford [89]

RWTH [90]

Flexibility

State-Depe.

Multi-Bit

VTEAM [88]

CRS

Kinetics

Strachan [87]

I-V/I-t

Table I.
Comparison of generic behaviors of four prominent
models [6]. Where , , and l show unacceptable,
acceptable, and good performance, respectively.

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with "functional" memristors (that is, memristors without overlapping values of R on and R off ) very difficult.
Another difficulty is the variation in absolute values.
The minimum R on in this set of measurements is 17 kX,
whereas the maximum was 1.17 MX, which shows a
# 68 difference. The smallest observed R off was 172 kX
and the largest 1.59 MX, a # 9 difference, which is very
large but significantly better than variations in R on . It
goes without saying that as the technology matures, we
can hope to see more of the green memristors than the
blue ones and more uniformity in fabrication.
B. Immaturity of Models
As mentioned, referring to memristors does not imply
any specific technology, material or fabrication process. Even more specific terms such as ReRAM (or PCM)
do not imply the same material or properties in that
category. Various memristors have different properties
and since they are often fabricated in research laboratories in small quantities, they are not available to other
researchers and potential users for additional tests,
experiments, or modeling. Consequently, the quality,
verifiability, and scalability of respective models remain
often very limited due to restricted experiments and
modeling efforts possible at the research institute fabricating the memristor. A major issue, in this case, is that
most models are developed at single device level under a few typical test scenarios (such as characterizing
hysteresis loops, e.g. [80]-[83]). Although these models
capture certain characteristics of the memristors, they
rarely manage to sufficiently predict the behavior of the
device under real application scenarios where the usage
is substantially different from the tests. Moreover, the
interaction between the devices and the environment
is often neglected, leading to further inaccuracies when
it comes to circuits involving more memristive devices,
working in an uncontrolled environment.
We should bear in mind that even if the basic principles of operations of the memristor are known to us,
some physical details, especially regarding the switching process, are yet rather unknown [6]. Based on this
premise, very recently Menzel et al. [6] conducted an
investigation of the quality of various prominent models on modeling the generic behavior of Redox-based
memristive devices. This behavior includes voltage and
current characteristics (I-V/I-t), non-linear switching
kinetics, complementary resistive switching, multi-bit
data storage, state-dependency, fading memory capability (asymptotic behavior), and model flexibility. Table I
provides a summary of their study. We note that the
performance is not measured against any real memristor, rather against generic behaviors of Redox based
memristors (thus excludes any other types). Therefore,
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IEEE Circuits and Systems Magazine - Q4 2019

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