Scanning tunnelling microscope STM — seeing atoms

What just happened?

The scanning tunnelling microscope (STM) tip hovered above the sample surface at a distance of a fraction of a nanometre — too far for electrons to cross according to classical physics. And yet a current flows. This is a purely quantum effect: electrons have a certain probability of "hopping" across that vacuum gap, even though they do not have the energy to do so in the classical sense.

Quantum tunnelling — the formula:

— the tunnelling current I depends exponentially on the tip–surface distance d. I₀ and κ are constants that depend on the material and the voltage. The exponential dependence means that even a microscopic change in d (a fraction of a nanometre) produces a huge change in I — by orders of magnitude.

What is quantum tunnelling?

In classical physics a particle without enough energy cannot cross a barrier (here: the vacuum gap between the tip and the sample) — like a ball that cannot roll over a hill higher than its energy. In quantum mechanics an electron is described by a wavefunction, which does not vanish abruptly at the barrier boundary but instead decays exponentially inside it. If the barrier is very thin (a fraction of a nanometre), the wavefunction "reaches" the other side — and there is a non-zero probability that the electron will be found there. A phenomenon impossible in classical physics, but an everyday occurrence at the atomic scale.

How do you "see" a single atom?

STM does not take a photograph — it builds a map. The tip scans the surface line by line, and the electronics keep the tunnelling current at a constant level by gently raising or lowering the tip above each point. Because the current depends so strongly on d, keeping I constant means keeping the distance almost constant — so the tip literally "rides" along the contour of the surface. By recording the tip height at every point, you obtain a topographic map with single-atom resolution — something no optical microscope can achieve, because it is limited by the diffraction of light.

Nobel 1986 — Binnig and Rohrer:

In 1981 Gerd Binnig and Heinrich Rohrer, working at the IBM laboratory in Zurich, built the first working scanning tunnelling microscope. For this achievement they received the 1986 Nobel Prize in Physics "for their design of the scanning tunnelling microscope". Their invention gave humanity the first tool able to directly "see" and manipulate single atoms on the surface of a material.

What is STM used for today?

STM (and its relative, the atomic force microscope, AFM) is today a fundamental tool of nanotechnology and surface physics — it is used to study the structure of catalysts, defects in materials, atomic layers of graphene, and even to manipulate single atoms, arranging them into letters and patterns (the famous IBM demonstrations). It is a cornerstone of the research that enabled the development of electronics and materials at the nanometre scale.

Why you need this for the exam:

Remember the key qualitative fact: the tunnelling current depends EXPONENTIALLY (not linearly!) on distance. This is the most frequently asked point about STM — recognise the signal "enormous sensitivity despite tiny changes in distance" as quantum tunnelling, a phenomenon impossible in classical physics.

Remember: the tunnelling current in STM depends exponentially on the tip–surface distance — hence the enormous sensitivity that allows single atoms to be imaged. This is a purely quantum phenomenon (Binnig and Rohrer, Nobel 1986).