Quantum tunneling is a phenomenon in quantum mechanics where a particle can pass through a potential energy barrier, even if it does not have the energy to surmount it. This possibility fundamentally contradicts the rules of classical physics, which govern the motion of everyday objects. The effect is a reality that is mathematically predicted and repeatedly observed in nature and technology. It is a direct consequence of matter possessing wave-like properties, a core principle of the quantum world.
Setting the Stage: The Potential Barrier
The concept of a potential barrier is easily understood through everyday experience. Imagine trying to roll a ball over a hill; if the ball does not have enough kinetic energy to reach the top, it will simply roll back down. The hill represents a potential energy barrier, and the ball’s motion is entirely governed by classical mechanics. For the ball to get to the other side, its total energy must be greater than the maximum potential energy at the hill’s peak.
In the classical view of the microscopic world, a particle facing an energy barrier it cannot overcome would behave exactly like the ball. It would be reflected back, unable to penetrate the region where its potential energy exceeds its total energy. This region is considered “classically forbidden.” The particle’s trajectory is determined and predictable, leaving zero probability that it will ever be found on the far side of the obstacle.
The Probability Principle: How Tunneling Works
The mechanics of quantum tunneling become clear when considering that subatomic particles possess wave-like characteristics. The state of a particle is described by the wave function, which is a probability wave that determines the likelihood of finding the particle at a specific location in space.
When a particle encounters an energy barrier, its wave function does not abruptly drop to zero at the barrier’s edge. Instead, the wave function decays exponentially as it penetrates the barrier region. This means the probability of finding the particle decreases rapidly the deeper it gets into the forbidden zone.
If the barrier is sufficiently thin, the wave function’s amplitude will still be non-zero on the other side. This small but finite amplitude translates directly into a non-zero probability that the particle will appear on the far side without having overcome the energy threshold. The particle exploits its fundamental wave nature to briefly exist in a state impossible under classical rules. The probability of this event is highly sensitive to the barrier’s thickness and height, with thinner, lower barriers allowing a much higher tunneling rate.
Observing the Phenomenon
Quantum tunneling is a fundamental process that governs various phenomena in the natural world. One example is alpha decay, a form of radioactive decay where an alpha particle (a helium nucleus) escapes a larger atomic nucleus. The alpha particle is held inside the nucleus by the strong nuclear force, which forms a significant potential barrier.
Classically, the alpha particle lacks the energy to break free from this barrier. However, tunneling gives it a small but finite chance of penetrating the barrier and being emitted. This process determines the half-lives of many radioactive elements.
Stellar Fusion
Another naturally occurring example is stellar fusion, the energy source of stars like the Sun. In the Sun’s core, hydrogen nuclei must fuse to form helium, but they are prevented from doing so by their mutual electrostatic repulsion, known as the Coulomb barrier. The kinetic energy of the protons is too low to overcome this barrier classically. Only by tunneling through the Coulomb barrier can the protons get close enough for the strong nuclear force to bind them, allowing fusion to occur and sustaining the star’s energy output.
Ammonia Inversion
A third example is ammonia inversion, a chemical process where the nitrogen atom in an ammonia molecule (\(\text{NH}_3\)) tunnels through the plane formed by the three hydrogen atoms, causing the molecule to rapidly flip its pyramidal shape.
Technology That Relies on Tunneling
Scientists and engineers harness the properties of quantum tunneling to create devices with high sensitivity and speed. The Scanning Tunneling Microscope (STM) is a direct application, using tunneling to image surfaces at the atomic level. The STM operates by bringing an extremely sharp conducting tip within a few nanometers of a sample surface.
A small voltage is applied, and electrons tunnel through the vacuum gap between the tip and the sample, creating a measurable current. Because this current changes exponentially with the distance, the STM creates a topographical map with atomic-scale resolution as the tip scans across the material.
Tunnel diodes are another technology built entirely on this quantum effect, advancing high-speed electronics. These semiconductor devices are engineered with a very thin junction, allowing electrons to tunnel through it even when the applied voltage is low. This results in unique electrical properties, such as negative resistance, making tunnel diodes valuable for use in ultra-high-frequency circuits and fast switching applications.
The ability of electrons to tunnel through extremely thin insulating layers is also the operating principle behind modern flash memory, which underpins data storage in most consumer electronics.