How Quantum Tunneling Allows Particles to Pass Through Barriers

The Sun Should Not Be Burning

At 15 million degrees Celsius, the Sun's core is not hot enough for hydrogen nuclei to overcome their mutual electrostatic repulsion and fuse through classical physics alone. The protons simply don't have sufficient kinetic energy. Yet the Sun fuses 620 million metric tons of hydrogen into helium every second, radiating the energy that sustains all life on Earth. The explanation lies in quantum tunneling—a phenomenon in which particles pass through energy barriers that, according to classical mechanics, should be absolutely impenetrable. Without tunneling, stellar fusion rates would be negligible. Stars would not shine. The universe would be dark.

Classical Walls vs. Quantum Probability

In classical physics, a ball rolling toward a hill with insufficient speed will always roll back. The energy barrier is absolute. Quantum mechanics replaces this certainty with probability.

Particles are described by wave functions—mathematical expressions encoding the probability of finding a particle at any given location. When a particle's wave function encounters an energy barrier, it doesn't stop cleanly at the wall. Instead, the wave function decays exponentially within the barrier but doesn't reach zero on the other side. There is a non-zero probability that the particle exists beyond the barrier.

• Tunneling probability decreases exponentially with barrier width and height
• Lighter particles tunnel more readily than heavier ones (electrons tunnel far more easily than protons)
• The effect is significant only at atomic and subatomic scales—macroscopic objects have essentially zero tunneling probability
• Tunneling does not violate conservation of energy—the particle's total energy remains unchanged
• The time spent "inside" the barrier is a subject of ongoing theoretical debate

No classical analogy accurately captures tunneling. It is a purely quantum phenomenon with no everyday parallel.

Alpha Decay: Tunneling Out of a Nucleus

In 1928, George Gamow applied quantum tunneling to explain alpha decay—one of the earliest triumphs of quantum mechanics applied to nuclear physics. Inside a heavy nucleus like uranium-238, alpha particles (two protons and two neutrons) are trapped by the nuclear strong force. The potential energy barrier surrounding the nucleus is far higher than the alpha particle's kinetic energy.

The pattern is striking. Small differences in alpha particle energy produce enormous differences in half-life because tunneling probability depends exponentially on the energy deficit. Polonium-212's alpha particle has slightly higher energy, so it tunnels through the barrier almost immediately. Uranium-238's alpha particle has slightly lower energy, and the tunneling probability is so small that the average atom waits 4.5 billion years before an alpha particle escapes.

Powering the Sun: Proton-Proton Fusion

The Sun's core temperature of 15 million Kelvin gives protons an average kinetic energy of about 1.3 keV. The Coulomb barrier between two protons requires roughly 550 keV to overcome classically. That's a factor of 400 shortfall. Yet fusion occurs because of the quantum mechanical tail of the Maxwell-Boltzmann energy distribution combined with tunneling.

• Only protons in the high-energy tail of the distribution have any meaningful tunneling probability
• Even so, the probability of any two protons fusing is vanishingly small—about 1 in 10^28 per encounter
• The Sun compensates through sheer numbers: its core contains roughly 10^57 protons
• The low individual probability explains why the Sun burns steadily over billions of years rather than exploding

Arthur Eddington proposed in 1920 that stars are powered by nuclear fusion, but it was Gamow's tunneling framework that provided the physics explaining how fusion occurs at stellar temperatures. Without tunneling, the minimum temperature for hydrogen fusion would be roughly 10 billion degrees—conditions that don't exist in any main-sequence star.

Technology Built on Tunneling

Quantum tunneling is not just an exotic curiosity. It underpins multiple technologies used daily.

The scanning tunneling microscope deserves special attention. Gerd Binnig and Heinrich Rohrer at IBM Zurich built the first STM in 1981. By maintaining a needle-sharp metal tip angstroms above a surface and measuring the exponentially distance-sensitive tunneling current, they produced the first real-space images of individual atoms. The resolution was stunning—a direct consequence of tunneling's exponential sensitivity to barrier width.

Tunneling at the Limits of Miniaturization

As transistors shrink below 5 nanometers, quantum tunneling becomes a problem rather than a feature. Electrons tunnel through gate oxide layers and between source and drain regions, causing leakage currents that waste power and generate heat. This tunneling leakage is one of the fundamental barriers to continued Moore's Law scaling.

Chipmakers combat tunneling with high-k dielectrics (thicker effective barriers without increased physical thickness), FinFET and gate-all-around transistor architectures, and ultimately the exploration of entirely new computing paradigms. The very phenomenon that makes flash memory possible threatens to make conventional transistors impossible at atomic scales.

Where Classical Intuition Ends

Quantum tunneling sits at the boundary where human intuition breaks down entirely. A baseball cannot pass through a concrete wall. But an electron, a proton, or an alpha particle can pass through an energy barrier that classical physics declares impassable—not by breaking through, but by having a probability of simply being on the other side. The math works. The predictions match experiments to extraordinary precision. The Sun burns because of it. Hard drives store data because of it. Radioactive elements decay because of it. Tunneling is not a minor quantum curiosity—it is one of the mechanisms that makes the universe function as it does.