Quantum tunnelling

In classical mechanics, a particle whose energy is lower than the height of a potential-energy barrier cannot cross it. Quantum mechanics instead describes a particle by a wave function, whose amplitude can extend into a region that is classically forbidden. If the barrier is finite, the amplitude may remain nonzero on its far side, giving a measurable probability that the particle will be detected beyond it. This process is called tunnelling or barrier penetration. It does not mean that the particle carves a literal passage or that it follows a known classical path through the barrier.

Tunnelling is probabilistic, not guaranteed. In general, the probability of transmission falls as the barrier becomes wider or higher and as the particle's mass increases. The details depend on the shape of the barrier and the particle's energy and quantum state. These relationships help distinguish tunnelling from simply having enough energy to pass over a barrier: a particle may tunnel even when its energy is below the barrier's height.

Alpha decay provides an important nuclear example. An alpha particle confined within a radioactive nucleus can have a finite probability of escaping through the nuclear potential barrier, even when classical mechanics would not give it enough energy to climb over the barrier. Quantum tunnelling also occurs in electron transport through thin insulating layers and at semiconductor junctions. In each case, the relevant outcome is a probability of transmission, whose size depends on the physical system.

A scanning tunnelling microscope uses quantum tunnelling of electrons between a sharp conductive tip and a conductive sample separated by a very small gap. The tunnelling current depends sensitively on the separation and the electronic properties of the surfaces. Scanning the tip and measuring the current allows a surface map to be constructed at atomic-scale resolution under suitable conditions. The instrument was developed by IBM researchers Gerd Binnig and Heinrich Rohrer and earned them a share of the 1986 Nobel Prize in Physics.