Vive la memristance!

Researchers have created a fourth fundamental circuit element that could supersede Ram and Flash memory and enable instant-on computers. It could also lead to computers that work more like our brains.

The existence of the element was predicted in 1971 by a young University of California engineer, Leon Chua, in a brilliant revisiting of basic circuitry. Most PCW readers will be aware of Ohm’s Law, giving the simple relationship between the voltage (V) across a resistance (R) and the current (I) passing through it: V = IR.

Less well known are similar relationships involving the two other classic two-terminal circuit elements, the capacitor and the inductor. The charge (Q) in a capacitance C is given by Q = CV; and the magnetic flux (Φ) in an inductance (L) is Φ = LI.

Chua postulated a fourth element displaying a similar relationship between charge and magnetic flux: Φ = MQ, where M represents something he called ‘memory resistance’ or memristance. The notional new element was accordingly called a memristor.

These relationships are more accurately described using calculus, the mathematics of change. This shows that, at any instant, Chua’s equation is identical to Ohm’s Law: V = IM, with this strange quality called M acting like pure resistance (see here for fuller explanation).

The same will hold true of the next instant. Only this time the resistance of M will have changed. The resistance of a classic resistor is constant; the resistance of a memristor depends on the charge that has flowed into it. Stranger still, the memristor ‘remembers’ this value if you stop the current.

Chua’s work was largely forgotten, except by specialists, because no device exhibiting the effect could be found - or rather it was not recognised. Resear chers investigating the electrical properties of nanostructures reported odd behaviour over the years but no-one linked it to Chua.

Then Greg Snider, part of a team headed by Stan Williams at HP’s Information and Quantum Systems Laboratory in California, pointed out that some of the results they were getting mirrored those predicted by Chua.

“We all struggled to work out the microphysics involved,” his colleague Donald Stewart told me. “Stan Williams, myself and [fourth team member] Dmitri Strukov wrote down some equations, edited them and finally agreed they might be right.

Then we saw that the equations we had written were identical to those proposed by Chua.”

If memristance is so fundamental, why has it proved so elusive when even a simple piece of wire can be shown to have some degree of capacitance, resistance and inductance?

The reason is that the effect is evident only at very small scales, where electric fields can be enormous (one volt across a nanometre is a field strength of a billion volts per metre).

The HP memristor consists of a 5nm film of a titanium dioxide sandwiched between platinum contacts. The titanium dioxide, like silicon in transistors, is doped to make it more conductive. But while transistors exploit the movement of charges within the doped silicon, entire dopant atoms shift when current flows in a memristor. And they stay where they are when it stops, which is what gives rise to the memory effect.

The effect works in both directions. “Let’s say you push a charge through the memristor and the resistance doubles. If you push the same charge in the opposite direction it will have halved,” said Stewart.

Switching times are of the order of a thousand times faster than Flash, which is why there is so much interest in their use as memory. And like Flash, they do not need to draw power to retain information.

This could lead to computers that simply freeze their current state when switched off and return instantly to that state when switched on again.

Stewart points out that memristors are only one of several promising technologies competing to supersede Flash. But while memristors could be used as simple digital switches, or even multi-level memory cells, they can represent a continuous set of values and so can be used in analogue mode. One intriguing application would be to model the behaviour of the synapses that link the neurons of the brain, which become more conductive the more they are used.

“The strength of signal from the neuron is the same every time. How much gets through depends on the strength [conductance] of the synapse,” said Stewart. This structure could be replicated to perform tasks like pattern recognition, at which the brain outperforms digital computers.

The discovery of the memristor, announced in Nature magazine, caused great excitement and threw the spotlight back on Chua, now a professor at Berkeley, and the remarkable inferences he drew from what began almost as a game.
Stewart said: “He must be pretty smart guy.”