Quantum Tunneling: How Particles Pass Through Walls

The Sun Burns Because of a Quantum Trick

Nuclear fusion in the Sun's core requires protons to collide at energies that classical physics says are impossible at the Sun's temperature. The actual mechanism is quantum tunneling — protons borrow enough probability amplitude to pass through the Coulomb barrier without ever having the classical energy to do it. Without tunneling, stars wouldn't shine.

Why Classical Physics Forbids It

In classical mechanics, a ball rolling toward a hill either has enough energy to clear it or bounces back. The total energy must exceed the potential energy of the barrier. Full stop. Quantum mechanics rewrites this completely.

Particles in quantum mechanics are described by wave functions — mathematical objects that encode probability. The wave function doesn't abruptly stop at a barrier's edge. It decays exponentially inside the barrier. If the barrier is thin enough, a non-zero wave function exists on the other side, which means there's a non-zero probability of finding the particle there.

The Mathematics of Tunneling Probability

The tunneling probability T depends on three factors:

• Barrier width — probability drops exponentially with thickness
• Barrier height — the higher the energy difference, the lower the probability
• Particle mass — heavier particles tunnel far less readily (electrons tunnel far more than protons)

For a rectangular barrier, the transmission coefficient is approximately:

T ≈ e^(−2κL), where κ = √(2m(V₀−E))/ℏ, L is barrier width, m is mass, V₀ is barrier height, and E is particle energy.

Alpha Decay: Tunneling in Action

Alpha decay was the first phenomenon explained by quantum tunneling (George Gamow, 1928). An alpha particle inside a uranium nucleus is trapped by the nuclear strong force — but classical calculations showed it shouldn't have enough energy to escape. In reality, the alpha particle tunnels through the Coulomb barrier thousands of times per second, and probability slowly adds up until it escapes. This gives radioactive isotopes their characteristic half-lives.

A tiny increase in alpha energy produces a dramatic drop in half-life. That exponential sensitivity is exactly what the tunneling equation predicts.

Tunneling in Electronics

Modern transistors operate at feature sizes of 3–5 nanometers. At those scales, electrons tunnel through gate oxides that are only a few atoms thick, causing leakage currents that limit how small conventional transistors can go. This is a fundamental barrier to further miniaturization of silicon chips.

Tunnel diodes exploit this effect deliberately. They allow current to flow at very low voltages through quantum tunneling and switch at speeds far exceeding ordinary semiconductor junctions. Flash memory storage also uses controlled tunneling to trap and release charge on floating gates.

The Scanning Tunneling Microscope

Invented by Gerd Binnig and Heinrich Rohrer in 1981 (Nobel Prize, 1986), the scanning tunneling microscope (STM) resolves individual atoms. A metal tip is brought to within 0.5–1 nm of a conducting surface. Electrons tunnel between the tip and surface; the tunneling current varies exponentially with distance. By moving the tip to maintain constant current, the STM maps surface topography atom by atom.

• Lateral resolution: ~0.1 nm
• Vertical resolution: ~0.01 nm (about 1% of an atomic diameter)
• Requires conducting surfaces; insulating materials need related techniques (AFM)

Tunneling in Biology

Enzyme catalysis is faster than classical transition-state theory predicts for proton and hydrogen transfer reactions. Experimental evidence shows that hydrogen tunnels through activation energy barriers in enzymes like alcohol dehydrogenase. Photosynthesis also exploits quantum coherence and tunneling to transfer energy with near-perfect efficiency through light-harvesting complexes.

Tunneling in Quantum Computing

D-Wave's quantum annealing processors use tunneling as a computational resource. Instead of classically hopping over energy barriers to find optimal solutions, the system tunnels through them, potentially exploring solution spaces more efficiently than classical algorithms for certain optimization problems.

Temperature and Tunneling

Classical reaction rates drop sharply at low temperatures because fewer particles have enough thermal energy to surmount barriers. Tunneling rates are largely temperature-independent — the particle doesn't need the energy. At very low temperatures, tunneling often dominates reaction kinetics entirely, which is why some chemical reactions proceed even near absolute zero.