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Physik-Institut

Tunneling

In quantum physics, particles can cross an energy barrier even when they lack the necessary energy. This phenomenon does not exist in classical physics.

In classical physics, the situation is clear: if a particle has insufficient energy to cross an energy barrier, such as a wall, it cannot do so. In quantum physics, the wave function describes the probability of where the particle could be. The wave function can extend beyond the barrier and have a non-zero probability on the other side. This means there is a chance the particle will "tunnel through" the barrier even if its energy is less than the barrier's height. The probability depends on the height and thickness of the barrier.

The tunneling effect is used in many electronic components, such as tunnel diodes, and in scanning tunneling microscopes. It also provides an explanation for alpha decay. However, tunneling is also a prerequisite for nuclei in the sun to come close enough for fusion to occur; without it, the sun would not shine!

Tunneling - an example

In everyday life, it is inconceivable that a ball without enough energy to roll over a hill would still make it to the other side. However, quantum objects can tunnel through a barrier with a certain probability.

For example: An electron accelerated with a voltage of 0.01 volts encounters a 0.5-nm-wide barrier with ten times its energy. There is a 34% probability that it will overcome the barrier. A ping-pong ball traveling at 1 m/s can reach a height of 5 cm. The probability that the ball will overcome a 10-cm-wide, 50-cm-high barrier using the tunneling effect is a number with 10³⁰ zeros after the decimal point. It is much more likely that the ping-pong ball will gain enough energy to overcome the barrier through thermal fluctuation in the air (10²⁰ zeros), but neither will ever happen.

tunneling
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Illustration of tunnel effect:
Left: In classical physics, a ball cannot get over the wall unless it has enough energy; otherwise, it is reflected off the wall.
Right: In quantum mechanics, however, there is a certain probability that the ball can 'tunnel' to the other side.
Picture: Ruth Bründler, UZH

 

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More on Scanning Tunnelling Microscopes

A scanning tunnelling microscope (STM) uses the tunnelling effect to image the atomic-level surface structure of materials. To achieve this, an extremely fine tip is positioned close to the surface of the sample. When an electrical voltage is applied between the tip and the surface, a tiny tunnel current will flow if the distance between them is small enough. The size of this current depends exponentially on the distance, enabling the precise reconstruction of the atomic topography by scanning the surface.

STM
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Schematische Darstellung eines Rastertunnelmikroskops, Michael Schmid and Grzegorz Pietrzak, CC BY-SA 2.0 AT https://creativecommons.org/licenses/by-sa/2.0/at/deed.en via Wikimedia Commons href="https://commons.wikimedia.org/wiki/File:Rastertunnelmikroskop-schema.svg

 

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