Memristors and the future

by Jim Walker
Originated: 11 May 2010

I first heard news about Hewlett Packard's new type of memory storage device about two years ago but I didn't take much notice because the news at that time was mostly about the advances being made in NAND flash. My interest changed dramatically, however, after watching a video presentation by R. Stanley Williams describing the properties of the memristor. This is one of the most interesting science & technology stories I've heard in a long time. The presentation is highly technical and most of it goes way above my layman's head, but Williams did a great job conveying the importance and fundamental nature of this electronic element. If you understand electronics, please watch the video of Williams presentation [click here]. If you don't understand electronics, and don't want to suffer through the technical jargon I will try to give a description and the importance of the memristor in a dumbed down version, so that a layman can understand.

From my understanding the memristor might not only revolutionize computer memory as we know it, but it could forever change the nature of logic circuit design, including artificial intelligence and artificial brains that work like real biological brains. Perhaps my speculations goes too far here but memristor devices appear to me as the first glimpse of a possible means for not just artificial brains but artificial consciousness, including the understanding of the elusive qualia.

It all started in 1971 in a paper written by Leon O. Chua, who some consider today as the "father of nonlinear circuit theory." Williams claims that, "Leon Chua is to circuit theory, what Albert Einstein was to relativity."

Leon Chua

Leon O. Chua

During the time of Chua's 1971 seminal paper on memristors, only three passive circuit elements were known: the resistor, the capacitor, and the inductor (one might think that the transistor would count as a distinct circuit element but it actually consists of doped semiconductor resistors, nothing fundamentally new).


Chua's interest involved the mathematical theory of electronics rather than circuit design and after examining the mathematical relationships between the three known circuit elements, he saw something missing. He observed a mathematical symmetry and predicted that there should exist a fourth element to complete the symmetry (similar to the way Paul Dirac predicted antimatter in the 1920s). He coined the missing element, the memristor (a contraction of the words "memory" and "resistor.")


At the time, no one had yet invented an actual memristor and, in fact, Chua wrote in his 1971 paper:

"Although no physical memristor has yet been discovered in the form of a physical device without internal power supply, the circuit-theoretic and quasi-static electromagnetic analyses. . . make plausible the notion that a memristor device with a monotonically increasing curve. . . could be invented, if not discovered accidentally."

Chua not only foresaw the memristor but he predicted how they should behave. One of its signatures, and indeed a fundamental identifier of memristors comes from its "pinched hysteresis loop":


  A diagram of a pinched hysteresis loop

Now I haven't a clue as to why a pinched hysteresis loop predicts a memory function, but whatever this kind of loop does, it serves as a requirement to identify a memristor. As it turns out, electrical engineers had long observed pinched hysteresis loops as far back as 1910, but they didn't understand why they occurred. They thought of these loops as anomalous behavior in their devices, something to be worked around, not something to take advantage of. At the time of Chua's 1971 paper and many years after, the engineers still did not understand these hysteresis loops because the engineers didn't read mathematical papers, much less Chua's paper, and the mathematician Chua did not read device specifications. In fact, as more and more semiconductors became smaller, the observation of these hysteresis loops became more common, but they remained a mystery. So for forty years no one understood what was going on until Stanley Williams at Hewlett Packard Laboratories put two and two together.

Williams had read Chua's paper and had also observed the problematic pinched hysteresis loops in the devices he was working on. On 20 August 2006, Williams solved two of the most important equations of his career that led to an understanding of the relationship between current and voltage in the physical properties he was working on. With Chua's theory and an understanding of the semiconductor materials, within a short while, Williams and his team constructed working circuits using memristors. Like the discovery of anti-matter, proving Paul Dirac's theory correct, Williams proved Chua's theory with functioning memristors.

Interestingly, the scale of the electronic circuit affects the observable behavior of memristance because, apparently, it obeys an inverse square law. Williams says that "memristance is a million times as important at the nanometer scale as it is at the micrometer scale, and it’s essentially unobservable at the millimeter scale and larger." No wonder no one observed memristance in the last two hundred years! As engineers build smaller circuits, especially integrated semiconductor circuits, memristance becomes more noticeable and in some cases, dominant. This gives another reason why memristors are so important for the future of electronics. If we ever want to design and build larger memories in smaller packages, it will be required to understand memristance.

A physical memristor consists of a two-terminal device whose resistance depends on the magnitude, polarity and length of time of the voltage applied to it. When the voltage is turned off, the resistance remains as it did just before it was turned off. This makes the memristor a non-linear, nonvolatile memory device.

A memristor

The two terminal memristor above uses titanium dioxide (TiO2) as the resistive material (other materials can be used such as SiO2, but apparently TiO2 works better). When a voltage is applied across the platinum electrodes, oxygen atoms in the material diffuse left or right, depending on the polarity of the voltage, which makes the material thinner or thicker, thus causing a change in resistance. (Don't ask me why doping makes a change in thickness. I can only guess that adding more oxygen atoms makes the material thicker because you're adding more material, and vice versa: removing oxygen makes the material thinner. Remember, at nanoscales even a small change in thickness can result in a dramatic resistance change.)

How do memristors read and write data? I'm not sure but I suspect that low voltages don't cause a change in resistance, therefore the resistance can be measured during low voltage (the read state). Higher voltages, however, cause oxygen diffusion, thus changing resistance (the write state). If anyone knows differently, please let me know.

Note, transistors use fixed doped junctions also, but unlike a transistor, a memristor, can change the doped region on the fly. The important thing about it is that when the voltage is turned off, the oxygen atoms stays put, thus the resistance is "remembered." Nor is a memristor simply a digital on-or-off device (although it can be). Since the doped region acts like a variable resistor, its state can be anywhere from 0 to 1, and this makes it a true analog device. You might think that oxygen atoms diffusing within a material is slow, but according to Williams, the diffusion rate is 1 meter per second. That might sound slow but it means that at nanometer scales, switching speeds can occur within nanoseconds!

Not only that but since this kind of memristor is made out of titanium dioxide, a mineral that occurs in nature in materials such as rutile, anatase, brookite, etc., we should be able to extrapolate the life span from these materials. The life of the state of a titanium dioxide memristor could last as long as geological times. Williams estimates a stability of around 100 million years!

Consider that the best recording materials we have today are stone (as in cuneiform tablets) and acid-free paper, which can last thousands of years at best. Magnetic tape, disks, CDs, etc. only last for a few dozen years or so. Imagine a storage device lasting millions of years (why not billions of years?). Memristors can be designed to be virtually immune to radiation; they are not affected by magnetism and the bottom line: there's no reason why they shouldn't last as long as geological minerals.

So here we have a fundamentally new device that promises a dramatically new form of fast, inexpensive, low power, universal, and long lasting nonvolatile memory. Memristors require less energy, faster than flash memory, and contain far more data per area than any other present memory. Memristor technology should replace not only hard drives, but DRAM and Flash drives as well.

Imagine turning on your computer and, like turning on a light switch, it instantly displays all the information you had on it when it was last turned off. No more boot up time. [2] No more moving parts. RAM would not be needed. Backup memory could be made automatically and quicker and easier than Apple's "Time Machine." Computers, laptops, cell phones, and iPods could be made much smaller with much larger memories.

memristor circuit

Electron photo of 17 titanium dioxide memristors

The photo above shows only seventeen memristors on a two-dimensional chip but they can also be made on a 2D crossbar array. These 2D layers can also be stacked on top of each other producing very dense three-dimensional memory chips.

So what's holding up the technology? According to Williams, it's not a problem with manufacturing because any semiconductor fabrication company could start making memristors within three days (memristor arrays are low power CMOS devices). The problem is with knowledge; there are only a handful of engineers capable of designing memristors at the time of this writing. Nor is it difficult to do; it just takes awareness and training. The other problem is compatibility issues and designing protocols and standards. Lastly it is a problem of traditional beliefs and an unwillingness to drop old ways. Even scientists and engineers can be stubborn in this area. As Edward O. Wilson once said, "Old beliefs die hard even when demonstrably false."

This is just the beginning

The incredible potential of memristors as memory devices is not necessarily the most interesting thing about them. They can also be used as logic devices. Transistors, for many years, have performed with a full set of logic operations using a combination of NAND (not-and) gates. At first it was thought that memristors could not perform a full set of logic operations but it has now been found that a memristor can utilize other memristors to reprogram themselves in a manner that depends on the evaluation of other logic operations, hence memristors can use NAND gates for logic operations, but in a new way with a combination of three memristors. This opens up the possibility that memristor circuits could be used, not just for memory retention, but as CPUs as well! The first CPU applications would probably use a hybrid of transistors with memristors, but perhaps in the future, even the transistors could be replaced by memristor combinations. Williams claims that changing between memory and logic operations constitutes a new computing paradigm thus "enabling calculations to be performed in the same chips where data is stored, rather than in a specialized central processing unit." If this statement holds true, then -- wow! This is beginning to look very much like a neural brain.

As it turns out, the synapses of the brain are, memristors! Voltage gated calcium channels, potassium and sodium ion channel conductance, and electrical conductance in synapses act very much like semiconductor memristance where there also occurs coupled ion-electron motions (albeit, simpler).

Leon Chua said: "Since our brains are made of memristors, the flood gate is now open for commercialization of computers that would compute like human brains, which is totally different from the von Neumann architecture underpinning all digital computers."

Memristor technology also promises dense, compact memory packages, on par with the density capability of a biological brain. Memristors can be made extremely small, at nanometer scales. Already HP labs have designed circuits that mimic aspects of the brain. Transistors are used as neurons, nanowires in a crossbar network act as axons and the memristors at the cross points act as synapses. In the future, even the transistors might be replaced by memristors.

Far future speculations

Memristor technology brings out a whole new set of possibilities. All the AI circuits and neural networks in the past have been built on digital 1s and 0s, and although they can do a great job in intelligent operations, they are still basically zombies. No one has come even close to simulating consciousness (qualia, sensations, feelings, emotions, etc.).

In my opinion the question of how consciousness and feelings occur in dead matter represents one of the most important scientific questions yet to be answered. Many philosophers think that this is an impossible goal. However, memristors, because they act similar to synapses, might be used to test emulated neurotransmitter functions.

I think the key to understanding conscious feelings involves pain and pleasure centers in the brain along with neurotransmitters (serotonin, dopamine, melatonin, glycine, etc.) Biologists know that neurotransmitters play an important role in consciousness and feeling centers because, you only need to take a drug like cocaine or LSD (that mimic natural neurotransmitters) to dramatically change the state of consciousness. But how can a simple chemical affect (or cause) conscious states?

[In my opinion, consciousness requires pain and pleasure centers, along with the neurotransmitters. My hypothesis is that it is impossible to achieve consciousness with digital computers alone, no matter how complex or intelligent the outcome (unless they can duplicate neurotransmitter activity). In this, I disagree with Dennett, et al. I do not think that consciousness just emerges out of thinking systems. Yes, I think computers can be very intelligent, even more intelligent than a human being, but not conscious with feelings and emotions. Sensations, in my opinion, form the baseline of consciousness, not thinking (evolutionary history shows that intelligence evolved after sensations, not before). After all, meditators (as in Zen meditation) have consciousness, awareness, and feelings, all without having a single conscious thought during meditation.]

Do the chemicals that make up neurotransmitters directly affect consciousness, or do they indirectly cause feelings from neurotransmitters acting as semiconductors, thereby changing the function of synaptic activity? Are the oxygen atoms diffusing in a TiO2 material acting like a neurotransmitter in a similar way? Can it be possible that we could build pain and pleasure centers with memristors to the point of achieving consciousness? I don't know but memristor technology looks like a promising first step for this kind of study.

Readers who have read my speculations on Death and time travel, know that in order to achieve duty-cycle spacetime travel, we (or an interstellar aliens) would need to achieve low power switchable on-off conscious brain states. Manufacturing artificial brains is the most technologically difficult problem to solve in regards to practical space travel, in my opinion. If consciousness can be achieved by memristor circuitry, this would be an ideal candidate for duty-cycle space travel because it appears that memristors can last for millions of years and they can live off low power (possibly from the energy of distant starlights).



Leon O. Chua, "Memristor: The missing circuit element," IEEE Transactions on Circuit Theory, September, 1971

Memristor and Memristive Systems Symposium videos: (Part 1), (Part 2), (Part 3), (Part 4)

Finding the Missing Memristor - R. Stanley Williams, video

R. Stanley Williams, "How We Found the Missing Memristor"

Hewlett-Packard Unveils Real-World memristor, Chip of the Future

Memristics: Memristors again?

New approaches for emerging technologies; memristor comments by Dr. Leon Chua

HP Discovery Could Fundamentally Change Computer Systems

A Synapse is a Memristor and Memcapacitors have no Resistance : New Era in AI and Electronics

Memristor YouTube website (lots of video information on memristors)

Pictures of the brain's activity during Yoga Midra by Robert Nilsson

O.M. Corbino (Phys. Z. II, 413, 1910) [first known observance of pinched hysteresis loops, but Corbino didn't understand them.]


[1] Leon Chua also speculated that one day capacitors and inductors with memory could be discovered or invented. If so then perhaps the term "memristor" could be misleading (memristors involve only resistors, not capacitors and inductors). Perhaps a better term could be used to include the memory capacitors and inductors. Prof. B. Widrow coined the term "Memistor (without the r) to describe his device designed to emulate synapses in brain cells. Perhaps a more inclusive term like this would serve better?

[2] My first computer, an Apple II, worked this way. When I turned it on, it was ready to program. I've been disappointed by boot up times ever since. Of course I still had to load in a program serially by using a cassette tape recorder!

[3] In 2008, Williams predicted the realization of commercial memristors within three years. Since this article was written in 2010, we should be seeing commercial memristors within one year, but to be cautious, I'm guessing up to five years.