Quantum tunnelling is the name given to a phenomenon that becomes important in the microscopic world*. Quantum tunneling can occur when a quantum system has two low-enregy states seperated by a high energy state, or barrier. To illustrate this, imagine a car faced with a hill on an otherwise flat road. To get over this barrier, the car must use energy (from whatever type of fuel it runs on) to get to the top of the hill. Now if you can do fancy things with regenerative braking you might get back some of that energy as the car wheels down the other side, but you still need the energy to get to the top of the hill in the first place.

However, if the road goes through the hill in a tunnel, then you do not need to expend any energy to get to the other side of the hill (well, ok, there are inconvenient things like friction and so on, but in the best tradition of physics demonstrations we shall ignore this for the moment). In the quantum world something similar can happen, except you don't need to build a tunnel. To get an electron to jump over a gap (the "hill") between two conductors normally requires a healthy voltage difference (to give the electron enough energy to get to the top of the "hill"). The spark plugs in a petrol engine normally require between 10000 and 20000 Volts to create sparks, for example. However, if you bring the conductors really close together (say 1 nm, which is about 6 atoms in length) a voltage difference of just 1 V is enough to create a small current flow between the two ("small" being only a few nanoamps, but this is measurable). This occurs because the electrons are now "tunnelling" through the energy "hill" that seperates the two conductors. The resulting tunnelling current is dependant on the voltage applied (as with normal electronics)and also the width and the height of the energy barrier. In particular, the current varies exponentially with the width of the energy barrier, meaning that very small changes in the seperation of the two conductors results in a large change in the current.

The more advanced version

The more physics-y explaination reads as follows: when the wavefunction* of an electron encounters a finite energy barrier, the wavefunction decays exponentially into the barrier region and therefore the function is non-zero at the other side of the barrier (assuming the barrier has a finite width). The result of this is a finite probability that the electron will, at some point, find itself on the other side of the barrier. As this probability depends exponentially on the width of the barrier, it follows that the barrier width must be very narrow for this to happen (or rather, that the probability of it happening is not negligible).

So can this actually be used for anything useful? (MRAM, HD tunnel junction read heads, single-electron transistors)