The tunnel effect is a quantum phenomenon where particles pass through potential barriers.In 1928, George Gamow, Ronald Gurney and Edward Condon independently explained alpha decay: a particle inside the nucleus does not have enough energy to escape according to classical laws, but thanks to the wave properties of matter, there is a small probability of finding it outside — as if it passed through a wall without breaking it. Later, the effect found application in electronics: in 1957, Leo Esaki created the tunnel diode, where current flows through the forbidden zone of a semiconductor.
In 1927, Friedrich Hund first discovered tunneling while analyzing a double potential well. In 1928, George Gamow, and independently Ronald Gurney and Edward Condon, applied the concept to explain alpha decay. Later, in 1957, Leo Esaki invented the tunnel diode, demonstrating practical use of the effect in semiconductors, for which he received the Nobel Prize.
The tunnel effect manifests at scales on the order of the de Broglie wavelength of the particle. As the particle mass and barrier width decrease, the tunneling probability increases. It is used in scanning tunneling microscopes, tunnel diodes, flash memory cells, and in nuclear fusion in stars (overcoming the Coulomb barrier). Limits of applicability: requires quantum description; not observed in the macroscopic world due to exponential suppression for large masses and thicknesses.
Tunnel diodes, flash memory, scanning tunneling microscopes, radioactive alpha decay, quantum computers.
In a USB flash drive, electrons tunnel through an oxide layer just a few nanometers thick, changing the cell charge — that's how your files are stored.
| B | variable | Euclidean action difference — action difference |
| S_E | variable | Euclidean action of a field configuration — action |
| \phi_b | variable | Field configuration of the bounce (instanton) — field configuration |
| \phi_{\text{vacuum}} | variable | Field configuration of the vacuum state — field configuration |
| T | variable | tunneling probability — transmission probability |
| z1 | variable | left turning point of the barrier — position metre |
| z2 | variable | right turning point of the barrier — position metre |
| m | variable | mass of the tunneling particle — mass kilogram |
| V | variable | potential energy as a function of position — potential energy joule |
| E | variable | energy of the particle — energy joule |
| ħ | constant | fundamental quantum of action divided by 2π — reduced planck constant = 1.054571817e-34 joule second |
| ∫ | operator | sums the integrand over the interval — integral |
| √ | operator | takes the non-negative root — square root |
| exp | operator | raises e to the given power — exponential |
| \Gamma | variable | Tunneling rate (probability per unit time) — rate per second |
| S | variable | Euclidean action of the bounce solution — action joule second |
| \propto | operator | Indicates proportionality — proportional to |
| e^{-S} | operator | Exponential function with exponent -S — exponential |




















