IEEE Spectrum December, 2008 - 27

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Bow ties

eOn cHuA'S original graph of the hypothetical memristor's behavior is shown at top right; the graph of
r. Stanley Williams's experimental results in the Nature
paper is shown below. The loops map the switching behavior of
the device: it begins with a high resistance, and as the voltage
increases, the current slowly increases. As charge flows through
the device, the resistance drops, and the current increases more
rapidly with increasing voltage until the maximum is reached.
Then, as the voltage decreases, the current decreases but more
slowly, because charge is flowing through the device and the
resistance is still dropping. The result is an on-switching loop.
When the voltage turns negative, the resistance of the device
increases, resulting in an off-switching loop. -R.S.W.

immobile until we again applied a positive
or negative voltage. That's memristance:
the devices remembered their current
history. We had coaxed Chua's mythical
memristor off the page and into being.

mulating the behavior of a single
memristor, Chua showed, requires a
circuit with at least 15 transistors and
other passive elements. The implications
are extraordinary: just imagine how many
kinds of circuits could be supercharged by
replacing a handful of transistors with one
single memristor.
The most obvious benefit is to memories.
In its initial state, a crossbar memory has
only open switches, and no information is
stored. But once you start closing switches,
you can store vast amounts of information compactly and efficiently. Because
memristors remember their state, they
can store data indefinitely, using energy
only when you toggle or read the state of
a switch, unlike the capacitors in conventional DRAM, which will lose their stored
charge if the power to the chip is turned off.
Furthermore, the wires and switches can
be made very small: we should eventually
get down to a width of around 4 nm, and
then multiple crossbars could be stacked
on top of each other to create a ridiculously
high density of stored bits.
Greg Snider and I published a paper
last year showing that memristors could
vastly improve one type of processing
circuit, called a field-programmable gate
array, or FPGA. By replacing several specific transistors with a crossbar of memristors, we showed that the circuit could
be shrunk by nearly a factor of 10 in area
and improved in terms of its speed relative to power-consumption performance.
Right now, we are testing a prototype of
this circuit in our lab.

current, mA

turns the TiO2 layer into TiO2-x and makes
it conductive, thus turning the device on.
A negative voltage has the opposite effect:
the vacancies are attracted upward and
back out of the TiO2 , and thus the thickness of the TiO2 layer increases and the
device turns off. This switching polarity
is what we had been seeing for years but
had been unable to explain.
On 20 August 2006, I solved the two
most important equations of my career-
one equation detailing the relationship
between current and voltage for this
equivalent circuit, and another equation
describing how the application of the voltage causes the vacancies to move-thereby
writing down, for the first time, an equation for memristance in terms of the physical properties of a material. This provided
a unique insight. Memristance arises in a
semiconductor when both electrons and
charged dopants are forced to move simultaneously by applying a voltage to the system. The memristance did not actually
involve magnetism in this case; the integral
over the voltage reflected how far the dopants had moved and thus how much the
resistance of the device had changed.
We finally had a model we could
use to engineer our switches, which we
had by now positively identified as memristors. Now we could use all the theoretical machinery Chua had created to help
us design new circuits with our devices.
Triumphantly, I showed the group
my results and immediately declared that
we had to take the molecule monolayers
out of our devices. Skeptical after years
of false starts and failed hypotheses, my
team reminded me that we had run control samples without molecule layers for
every device we had ever made and that
those devices had never switched. And
getting the recipe right turned out to be
tricky indeed. We needed to find the exact
amounts of titanium and oxygen to get the
two layers to do their respective jobs. By
that point we were all getting impatient. In
fact, it took so long to get the first working
device that in my discouragement I nearly
decided to put the molecule layers back in.
A month later, it worked. We not only
had working devices, but we were also
able to improve and change their characteristics at will.
But here is the real triumph. The resistance of these devices stayed constant
whether we turned off the voltage or just
read their states (interrogating them with
a voltage so small it left the resistance
unchanged). The oxygen vacancies didn't
roam around; they remained absolutely

Voltage

And memristors are by no means
hard to fabricate. The titanium dioxide structure can be made in any semiconductor fab currently in existence.
(In fact, our hybrid circuit was built in
an HP fab used for making inkjet cartridges.) The primary limitation to manufacturing hybrid chips with memristors is that today only a small number of
people on Earth have any idea of how to
design circuits containing memristors.
I must emphasize here that memristors
will never eliminate the need for transistors: passive devices and circuits
require active devices like transistors
to supply energy.
The potential of the memristor goes
far beyond juicing a few FPGAs. I have
referred several times to the similarity of
memristor behavior to that of synapses.
Right now, Greg is designing new circuits that mimic aspects of the brain. The
neurons are implemented with transistors,
the axons are the nanowires in the crossbar, and the synapses are the memristors
at the cross points. A circuit like this could
perform real-time data analysis for multiple sensors. Think about it: an intelligent
physical infrastructure that could provide structural assessment monitoring
for bridges. How much money-and how
many lives-could be saved?
I'm convinced that eventually the
memristor will change circuit design in
the 21st century as radically as the transistor changed it in the 20th. Don't forget
that the transistor was lounging around
as a mainly academic curiosity for a
decade until 1956, when a killer app-the
hearing aid-brought it into the marketplace. My guess is that the real killer app
for memristors will be invented by a curious student who is now just deciding what
EE courses to take next year.
o
dEcEmbEr 2008 * iEEE SpEctrum * NA

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