How the Scanning Tunneling Microscope 'Sees' Individual Atoms

The scanning tunneling microscope images single atoms not by focusing light or electrons onto a surface, but by measuring an exponentially sensitive quantum tunneling current across a vacuum gap a few atomic diameters wide.

A microscope with no lens

Every microscope you met in school works the same way: light or electrons bounce off a sample, pass through a lens, and form a magnified image on a detector or screen. The scanning tunneling microscope (STM), invented in 1981 by Gerd Binnig and Heinrich Rohrer at IBM Zurich, throws that whole approach out. It has no lens and does not image light reflected from a surface at all. Instead, it drags an atomically sharp metal needle across a conducting surface, holding the tip so close — typically 0.4 to 1 nanometre, a few atomic diameters — that electrons spontaneously leak across the empty gap between tip and sample. That leakage current is quantum tunneling in its most direct, measurable, everyday-laboratory form, and it is sensitive enough to resolve individual atoms sitting on a surface. Binnig and Rohrer shared half of the 1986 Nobel Prize in Physics for the invention.

Why a gap of empty space isn't really empty to an electron

Classically, an electron confined inside a metal needs a certain minimum energy — the work function, typically 4–5 electron-volts for most metals — to escape into the vacuum outside. An electron with less energy than that should be completely unable to leave the tip, the same way a ball rolled at a hill without enough speed can never get over the top and roll down the other side. In quantum mechanics, though, an electron is described by a wavefunction, not a point particle, and the region of vacuum between tip and sample is what physicists call a potential barrier: a zone where the electron's energy is lower than the potential energy it would need to be there classically. Solving the Schrödinger equation for this situation shows that the wavefunction doesn't stop dead at the tip's surface. It decays smoothly and exponentially into the barrier region, meaning there's a small but genuinely nonzero probability of finding the electron on the far side of the gap, inside the sample, even though it never had enough energy to climb over the barrier in the classical sense. This is the same phenomenon modelled in the tunneling-probability simulation on this page: a particle wave meeting a barrier taller than its own energy still has amplitude beyond it.

The exponential that makes atomic resolution possible

The key equation is deceptively simple. For a rectangular barrier of height V above the electron's energy E and width d, the transmission probability falls off as T ∝ exp(−2κd), where κ = √(2m(V−E))/ħ. The important detail is that this is an exponential in the gap width d, not a linear or polynomial dependence. A change in tip-sample separation of just one ångström — roughly the radius of a hydrogen atom — can change the tunneling current by a full order of magnitude. That extreme sensitivity is precisely what turns a leaking electron current into an atomic-resolution imaging tool: as the tip scans line by line across a surface and a feedback loop adjusts its height to keep the tunneling current constant, the tip's vertical position traces out the sample's electron-density landscape with sub-ångström precision, revealing individual atoms as bumps and rows.

Two ways to scan: constant current and constant height

Most STM imaging is done in constant-current mode. A feedback circuit continuously compares the measured tunneling current to a setpoint (often around 1 nanoamp) and moves the tip up or down with a piezoelectric actuator to hold that current fixed as it rasters across the surface. Because current depends exponentially on gap width, holding it constant means holding the gap width almost constant, so the tip's vertical trajectory becomes a direct map of surface topography and, more precisely, of the local density of electron states at the Fermi level. The alternative, constant-height mode, switches the feedback off and scans the tip in a flat plane while simply recording how the current varies; it's faster but only works on very flat samples, since any large bump risks crashing the tip into the surface.

What the barrier's height and width represent physically

In the simulation on this page, the two sliders governing barrier height and particle energy aren't abstract knobs — they map onto real STM quantities. The barrier height corresponds to the average of the tip and sample work functions (how much energy an electron needs to leave each material), and the barrier width corresponds directly to the physical tip-sample separation, the single parameter an STM operator controls by moving the tip. Lower the barrier (approach a material with a smaller work function) or narrow it (bring the tip closer), and the tunneling probability — and hence the measured current — rises sharply. This is also why STM requires ultra-high vacuum and vibration isolation: any stray gas molecule or mechanical vibration that shifts the gap by even a fraction of an ångström swamps the signal you're trying to measure.

Beyond imaging: pushing atoms and reading spins

Once researchers had a tip that could sense individual atoms, it turned out they could also nudge them. In 1990, IBM scientists used an STM tip to drag 35 individual xenon atoms into position on a nickel surface, spelling out the company's logo — the first time humans arranged matter one atom at a time on purpose. Modern variants extend the same tunneling principle further: scanning tunneling spectroscopy varies the bias voltage at a fixed position to map the local electronic density of states, revealing band gaps and molecular orbitals, while spin-polarized STM uses a magnetic tip so that the tunneling current itself depends on the relative alignment of electron spins, allowing individual atomic magnetic moments to be imaged directly.

A gateway phenomenon, not a curiosity

It's worth remembering that STM is only the most visually dramatic demonstration of a phenomenon that underlies enormous swaths of modern technology. The same barrier-penetration mathematics governs alpha decay of atomic nuclei (Gamow's 1928 explanation, decades before STM existed), the flash memory in every phone and SSD (electrons tunnel through a thin oxide layer to be trapped on or read from a floating gate), tunnel diodes and Josephson junctions used in superconducting quantum computers, and even enzyme-catalysed reactions in biochemistry where protons tunnel between molecules faster than classical reaction-rate theory predicts. The STM simply makes the effect directly visible and controllable at the scale of a single atom, which is why it remains one of the clearest teaching examples of quantum mechanics behaving unlike anything in everyday classical experience.

Frequently Asked Questions

How small is the tip-sample gap in a real STM?

Typically 4 to 10 ångströms (0.4–1 nanometre) — a distance comparable to just a few atomic diameters. The tip itself is ideally terminated in a single atom, which is what gives the instrument its atomic lateral resolution.

Does the STM tip ever actually touch the sample?

No. If it did, the instrument would be operating in a completely different, contact-based regime (closer to atomic force microscopy) rather than measuring a tunneling current. A feedback loop actively holds the tip back at the gap that produces the target current.

Why does tunneling current depend so sensitively on distance?

Because the transmission probability falls off exponentially with barrier width, not linearly. Each additional ångström of separation multiplies the current by roughly the same fractional factor, so even sub-ångström height changes on a surface show up as large, easily measured current changes.

Can STM image any material?

Only conducting or semiconducting surfaces, because the technique relies on a measurable electron tunneling current flowing between tip and sample. Insulators are typically imaged instead with atomic force microscopy, which senses mechanical force rather than electron flow.

Is the tunneling probability in this simulation realistic?

It follows the same exponential dependence on barrier width, barrier height, and particle energy as the real quantum-mechanical formula, though the displayed values are scaled for visual clarity rather than reporting true STM current magnitudes, which range over many orders of magnitude.