Quantum tunnelling

Quantum tunnelling, also known as barrier penetration, is a fundamental phenomenon in quantum mechanics. In our everyday world, objects follow the rules of classical mechanics. If you roll a ball toward a steep hill, it will only reach the other side if it has enough energy to go over the top. If the ball lacks that energy, it simply rolls back down. In the quantum world, however, particles like electrons or atoms do not always follow these rules. They can pass through a potential energy barrier even if they do not have enough energy to surmount it. This ability to cross an seemingly impassable barrier is what we call tunnelling.

To understand how this happens, we must look at the wave nature of matter. In quantum mechanics, a particle is described by a mathematical tool called a wave function. This wave function describes the possible states of a physical system. Scientists use equations, such as the Schrödinger equation, to describe how these wave functions change over time. The square of the absolute value of the wave function represents a probability distribution. This distribution tells us the likelihood of finding a particle at a specific position.

When a particle, represented as a wave packet, hits a narrow potential barrier, something strange occurs. Most of the wave packet is reflected back, much like a wave hitting a wall. However, a small portion of the wave function can penetrate the barrier and appear on the other side. This represents a non-zero probability that the particle will be measured outside the barrier. This process is highly sensitive to the physical properties of the system. The probability of transmission decreases exponentially as the barrier height increases. It also decreases as the barrier width increases or as the mass of the tunnelling particle increases. Because of this, tunnelling is most common in low-mass particles like electrons.

Our understanding of tunnelling grew through many important discoveries in the 20th century. The Schrödinger equation was published in 1926, providing the math needed to study these waves. In 1927, Friedrich Hund applied this equation to study tunnelling between two classically allowed regions. Around 1927 and 1928, other scientists like Lothar Nordheim, Ralph Fowler, Leonid Mandelstam, and Mikhail Leontovich also made significant contributions. A major breakthrough occurred in 1928 when George Gamow, Ronald Gurney, and Edward Condon used tunnelling theory to explain alpha radioactive decay. They showed that the half-life of a particle depends directly on the mathematical probability of tunnelling through the nuclear potential.

Experimental work later turned these theories into practical tools. In 1957, Leo Esaki demonstrated electron tunnelling through a semiconductor barrier. In 1960, Ivar Giaever showed that tunnelling also occurs in superconductors. Later, Brian Josephson predicted the tunnelling of superconducting Cooper pairs. These three scientists shared the Nobel Prize in Physics in 1973. In 1981, Gerd Binnig and Heinrich Rohrer developed the scanning tunnelling microscope (STM). This device uses tunnelling currents to create images of surfaces at the atomic level. They were awarded the Nobel Prize in 1986 for this discovery.

Quantum tunnelling is essential to many modern technologies and natural processes. It is a key mechanism in nuclear fusion, which powers stars. In electronics, tunnelling is used to program the floating gates in flash memory. It is also used in tunnel diodes and resonant tunnelling diodes. A resonant tunnelling diode uses two thin layers to create a quantum potential well. This allows electrons to flow like an open wire only at specific resonant voltages.

However, tunnelling also presents challenges for the future of computing. In very-large-scale integration (VLSI) electronics, tunnelling causes current leakage. This happens when insulating layers or transistors become thinner than about 1 nm. When this occurs, electrons tunnel through the layers, causing power drain and heat. Researchers are looking for ways to manage this, such as developing tunnel field-effect transistors. These could potentially reduce gate voltage from 1 volt to 0.2 volts, greatly improving energy efficiency. Most recently, in 2025, Nobel recognition was given to John Clarke, John M. Martinis, and Michel H. Devoret. They demonstrated that tunnelling can be observed on a macroscopic scale using complex electrical circuits with superconductors.