History Of Quantum Tunneling, How It Works And Applications
Quantum Tunnelling
A particle can bypass an energy barrier through “quantum tunnelling” even without energy. Classical physics states that a ball needs energy to climb a hill or roll back down. Particles behave differently in quantum space.
How Quantum Tunnelling Works
Quantum tunnelling is caused by the Schrödinger equation's wave-particle duality. Wave functions, which predict the possibility of finding a particle at a given place, characterise particles in quantum physics.
Wave Function Penetration: A particle's wave function does not stop when it hits a potential barrier. Instead, it decays rapidly inside the barrier. Importantly, the wave function exhibits a small but non-zero amplitude over the barrier. This suggests the particle will seem far away.
Penetration likelihood: The square of the wave function's amplitude gives the likelihood of finding the particle across the barrier. This chance decreases exponentially with barrier height, width, and tunnelling particle mass. Tunnelling is particularly visible when low-mass particles like protons or electrons move through microscopically tight barriers, which are usually 0.1 nm for heavier particles and 1-3 nm for electrons.
This phenomenon breaks classical physics, which stipulates that a particle must have energy larger than the barrier height to pass through. The finite transmission is exponentially affected by the potential barrier's width and height.
Quantum tunnelling can be explained using Heisenberg's uncertainty principle, which states that electromagnetic particles can bypass classical physics and propagate without crossing the potential energy boundary due to uncertainty in their location. Tunnelling and the uncertainty principle are compatible by characterising a quantum material as a wave and particle.
Quantum Tunnelling Features
Non-Classical: It contradicts the classical physics rule that a particle must have more energy than the barrier height to cross.
The fact that matter is a wave causes wave-particle duality.
The particle may tunnel or reflect because the result is probabilistic. We eliminate no particles or waves during the procedure.
Mathematics Foundation
The time-independent Schrödinger equation describes quantum tunnelling mathematically. This equation can be solved in several ways depending on the particle's potential energy V(x) and total energy E. Solutions where V(x) – E is negative represent travelling waves. When V(x) – E is positive, the particle is inside the barrier where its energy is smaller than the potential energy, causing rising and falling exponentials, or evanescent waves. The semiclassical WKB approximation helps change potential barriers by approximating this challenging mathematical issue. This helps calculate the transmission coefficient, which indicates tunnelling likelihood.
History Of Quantum Tunnelling
In 1926, Schrödinger published his equation. Friedrich Hund originally utilised it in 1927 to analyse double-well potentials and molecular spectra for tunnelling over a potential barrier. In 1928, Mikhail Leontovich and Leonid Mandelstam independently discovered tunnelling.
Tunnelling theory triumphed after George Gamow's 1928 mathematical explanation of alpha decay, which Ronald Gurney and Edward Condon independently explained. By solving the Schrödinger equation for a nuclear potential model, they found a correlation between particle half-life and emission energy, which affects tunnelling. Walter Schottky coined “wellenmechanischer Tunneleffekt” in 1931, and Yakov Frenkel's textbook popularised “tunnel effect” in 1932.
After Leo Esaki demonstrated electron tunnelling in a semiconductor structure in 1957, the tunnel diode was invented. Brian Josephson predicted Cooper pairs would tunnel in 1962, and Ivar Giaever demonstrated superconductor tunnelling in 1960. Solids quantum tunnelling won Esaki, Giaever, and Josephson the 1973 Physics Nobel Prize. 1981 STM inventors Heinrich Rohrer and Gerd Binnig awarded the 1986 Physics Nobel.
Quantum Tunnelling Uses
Many natural and technological processes involve quantum tunnelling.
Nuclear Fusion: Stars like the Sun need it. For atomic nuclei to overcome their mutual electrostatic repulsion (Coulomb barrier) and fuse conventionally, star cores are usually too cold. Despite the modest individual chance, quantum tunnelling dramatically increases the chances of crossing this barrier and continuing star-driving fusion events.
Alpha decay is explained by quantum tunnelling, in which alpha particles leave the atomic nucleus through the strong nuclear force barrier. This provides astrobiology with energy in various cases.
Quantum tunnelling generates atomic-level surface pictures in scanning tunnelling microscopes (STM). Using a voltage bias, a conductive surface and a sharp conducting tip can be placed close together to detect tunnelling current. This current is increasingly sensitive to distance, allowing STMs to resolve surface features with 0.001 nm precision.
Tunnelling leaks current in very-large-scale integration (VLSI) circuits, causing power loss and warmth. It sets a minimum microelectronic device component size. Programming flash memory floating gates requires it. The following electronics employ tunnelling:
Tunnel diodes: Quantum tunnelling gives these devices unique current-voltage features. High-speed applications can have a voltage range where current declines with voltage. Different tunnelling is utilised in resonant tunnelling diodes.
Cold Emission (Field Electron Emission): Strong electric fields tunnel electrons out of atomic states, creating an exponentially changing current. This includes vacuum tubes, flash memory, and electron microscopes.
Tunnel Junctions: Josephson junctions use thin insulators as barriers between conductors, which require tunnelling for precise measurements.
Tunnel Field-Effect Transistors (TFETs): Quantum tunnelling regulates its gate (channel) instead of thermal injection, lowering gate voltage and power usage.
Quantum tunnelling helps explain electron collisions and electron transport through metals, especially impurities. Chemistry:
In interstellar clouds, chemical reactions occur at extremely low energy. Quantum tunnelling sustains hydrogen ion and molecule processes.
Quantum tunnelling is needed to explain large isotopic effects in chemical kinetics that classical theories cannot, especially when a heavier isotope is replaced with a lighter one.
Biology: Quantum biology's quantum tunnelling is important.
Enzymatic catalysis, photosynthesis, and cellular respiration depend on electron tunnelling.
Proton Tunnelling: Required for spontaneous DNA mutation. A proton burrows past a potential energy barrier in a DNA hydrogen bond, generating a “tautomeric transition.” DNA replication in this changed form may cause a mutation, threatening the base pairing rule. This process is linked to cancer and ageing.
