What is a memristor?

One of the most hyped devices of the past few years has been the memristor, and in comparison to other circuit elements I think you’ll agree it’s pretty weird, and interesting!

The existence of the memristor was first predicted in 1971 by Leon Chua. The behavior of basic circuit elements had long been described mathematically, with each circuit element having a given relationship between two of four quantities: charge (q), current (I), voltage (V), and flux (φ). Chua noticed that the mathematical equations could be tabulated and had a symmetry of sorts, but that one equation seemed to be missing, for a device that related current to a change in magnetic flux.  The behavior of such a device would change depending on how much current had passed through it, and for this reason Chua called it a ‘memristor’, a contraction of ‘memory’ and ‘resistor’. You can see the mathematical relationships represented below as the edges of a tetrahedron. Resistor behavior is quantified by the resistance R and capacitor behavior is quantified by the capacitance C, in the two equations near the top. And on either side, we have relations for the inductance L and the memristance M. It’s not crucial to understand these equations intimately, just to see that they have a certain symmetry and completeness to them as a set of relations between these four key variables. Five of these relationships had been experimentally observed in devices, and mathematically suggested the sixth, the memristance equation on the right. But having the equation doesn’t tell you how to make a device that will exhibit that behavior!

Chua’s initial proposals to physically create a memristor used external power to store the remembered information, making the component active rather than passive. However, in 2008 a real-world memristor was created using a nanoscale film with embedded free charge that could be moved by applying an electric field that exerts a force on the charge. How much of the film contains the extra charge determines how much of the device has high resistance and low resistance, which causes the total resistance to depend on how much current has passed through.

This isn’t the only implementation of a memristor available, because as many researchers realized once the first results were announced, memory of past measurements is a common nanoscale feature. Current flow can often cause small changes in materials, but while these changes may not be noticeable in the properties of a bulk material, when the material has very small thickness or feature size, the changes can affect material properties in a measurable way. Since this constitutes a form of memory that lasts for a significant amount of time, and there is a large market for non-volatile electronic memory for computers, the commercial interest in these devices has been considerable. HP expects to have their version memristor-based computer memory on the market by 2014, and it remains to be seen what other novel electronics may come from the memristor.

Active and Passive Circuit Components

Now that we have several different circuit components under our belts, it’s helpful to try to classify the behavior that we’ve seen so far. Resistors, capacitors, and inductors respond in a reliable way to any applied voltage that induces an electric field. Resistors dissipate heat, capacitors store charge, and inductors store magnetic flux.  These responses always occur and cannot be manipulated without manipulating the very structure of the material which causes the response. They don’t add energy or electrons to a circuit, but merely redirect the electrons provided by an external source. Thus these are called “passive circuit components”.

Transistors also have a predictable response to a given voltage, but that response can be changed by tuning the gate voltage in order to open or close the conducting channel. Effectively, the transistor can be in one of two states:

1. Functioning like a wire with a small resistance, passing most current through while dissipating a small amount of heat.
2. Functioning like an insulator with a high resistance, blocking most current and dissipating more heat.

The controlling gate which allows us to pick between these two states can actually add energy to the system, increasing the current output, thus the transistor is called an “active circuit component”. Circuits that do calculations or perform operations are usually a combination of active and passive circuit components, where the active components add energy and act as controls, whereas the passive components process the current in a predetermined way. There are other system analogues to this, such as hydrodynamic machines. Instead of controlling the flow of electrons, we can control the flow of water to provide energy, remove waste products, and even perform calculations. An active component would be a place where water was added or accelerated, whereas a passive component might be a wheel turned by the water or a gate that redirects the water. But in electronics, with electrons as the medium, active components add energy and passive components modify existing signals.

How Resistors and Capacitors Work

Now that we have started out with atoms and gone all the way to electronic band theory, which uses available energy states to explain why some materials are good at conducting electrons and others are not, we can start to discuss actual electronic devices! After all, fancy materials aren’t much good unless you have some way to use them.

Broadly speaking, we want devices that do something worthwhile, like light a room, make calculations, or power a motor. Most electrical devices work by manipulating a flow of electrons to extract some useful behavior. If we apply an electrical potential (which is also called voltage) to a device, then it will be energetically favorable for electrons to move through the device; this charge flow is called electrical current. The potential difference is often provided by something like a battery, where the differing chemical potential within the battery provides the voltage, and the device itself is connected to both terminals of the battery. Connecting a device to a battery forms a physical loop that electrons travel through, hence the name circuit. The battery itself is a circuit element, and so is the device that does something useful. There are quite a few interesting circuit elements but let’s start simple.

While the high electrical conduction of metals is extremely useful, sometimes it can be useful to have something that does not conduct electrons quite so well. Why? Because poor conductors offer the opportunity to convert electrical energy into other forms of energy, such as light or heat. This is the idea behind resistors, circuit elements that resist the flow of electrons without quite stopping it. Some resistor materials convert excess energy into heat, which can be the basis of electric heaters or electric stovetops. And the filament in an incandescent light bulb is acting as a resistor, one which heats up so much that it emits light (the reason for this is a whole other sack of beans). Resistors can be made by combining a conductive material with a non-conductive material, and are manufactured across an incredibly broad range of resistances. And independent of their heating or light-emitting properties, they are often used because the electrical current through them depends linearly on voltage.

And what happens if we push resistance to its limit, such that no electrons can actually pass through an insulating device? Applying a voltage drop would cause electrons to build up on one side of the device, attempting to pass through, until the repulsive force from the assembled electrons was enough to deter additional electrons from building up. The charge imbalance creates an electric field across the device, and this is what we call a capacitor. You can build a capacitor by bringing two parallel conducting plates close to each other and applying voltage. Since current can’t cross the gap between the plates, charge is stored on the capacitor plates, which can be discharged upon connection to a circuit. This is somewhat similar to a battery, although most batteries have stored chemical energy rather than electrical, and the speed of the chemical reaction which discharges a battery is usually much slower than the speed of electrons rushing to equilibrium when a capacitor is discharged. An older example of a capacitor is shown below; modern capacitors use thin films to create an insulating gap, and are considerably smaller than the capacitor pictured.

Resistors and capacitors are two of the most basic pieces that you can put into a circuit, and two of the most widely used. But some of the more complicated elements are interesting as well, and we’ll get into those in the next few posts!