Scanning Tunneling Microscopy

The scanning tunneling microscope (STM), invented by Gerd Binnig and Heinrich Rohrer at IBM Zürich in 1981 (Nobel Prize, 1986), is one of the most direct applications of quantum tunneling in modern technology. It can image individual atoms on a conducting surface — a resolution that classical physics offers no mechanism to achieve.

The tunneling current

In the rectangular-barrier model from earlier lessons, a particle with energy $E$ encounters a barrier of height $V_0 \gt E$ and width $d$ . The transmission probability is well approximated, for a tall, wide barrier ( $\kappa d \gg 1$ ), by

T \approx 16 \frac{E}{V_0}\!\left(1 - \frac{E}{V_0}\right) e^{-2\kappa d},

where $\kappa = \sqrt{2m(V_0 - E)}/\hbar$ is the inverse decay length of the evanescent wave inside the barrier (Griffiths, Ch. 2.6). The exponential factor $e^{-2\kappa d}$ is the key: $T$ falls off exponentially with barrier width $d$ .

In an STM the "particle" is an electron, $m = 9.109 \times 10^{-31}\,\text{kg}$ . The barrier is the vacuum gap between a sharp metallic tip and a conducting sample. The effective barrier height is roughly the work function of the metal, typically $\phi \approx 4\text{–}5\,\text{eV}$ . At the Fermi level, $E \approx V_0 - \phi$ , so the relevant decay constant is

\kappa = \frac{\sqrt{2m\phi}}{\hbar}.

For $\phi = 4.5\,\text{eV} = 7.21 \times 10^{-19}\,\text{J}$ and using $\hbar = 1.055 \times 10^{-34}\,\text{J\,s}$ :

\kappa = \frac{\sqrt{2 \times 9.109\times10^{-31} \times 7.21\times10^{-19}}}{1.055\times10^{-34}} \approx 1.09 \times 10^{10}\,\text{m}^{-1}.

The factor $2\kappa \approx 2.18 \times 10^{10}\,\text{m}^{-1}$ . Each additional $\Delta d = 1\,\text{Å} = 10^{-10}\,\text{m}$ changes $2\kappa d$ by about $2.18$ , so the current changes by $e^{2.18} \approx 8.8$ — roughly one order of magnitude per angstrom. This extraordinary sensitivity is what makes atomic resolution possible.

How the microscope works

An STM has four main ingredients:

The tip. A metallic wire (often tungsten or platinum-iridium) etched or mechanically broken to leave just one or a few atoms at the apex. The sharpness of the tip determines lateral resolution.
Piezoelectric actuators. Ceramic elements that expand or contract by a precisely controlled fraction of a nanometre when a voltage is applied. The tip is mounted on three such elements (or a single tube), allowing sub-ångström positioning in all three dimensions.
The bias voltage. A small voltage (typically $0.01\text{–}1\,\text{V}$ ) is applied between tip and sample. This creates a net flow of electrons across the gap: some tunnel from the filled states of one electrode into the empty states of the other.
The feedback loop. A control circuit measures the tunneling current and adjusts the vertical piezo in real time to hold the current constant. As the tip scans the surface laterally, the vertical adjustments trace out a surface of constant local density of electron states — which, for a clean metal, tracks the atomic topography closely.

Constant-current vs. constant-height modes

Constant-current mode (described above) keeps $I$ fixed and records the tip height $z(x, y)$ . The image is a map of equal-probability surfaces for tunneling electrons. It is the preferred mode for rough surfaces because the feedback actively prevents the tip from crashing.

Constant-height mode keeps the tip at a fixed height and records the current $I(x, y)$ directly. Because no feedback correction is needed, the scan can be much faster — useful for watching atomic-scale dynamics in real time. However it requires an atomically flat sample to avoid tip crashes.

What STM images actually show

A subtle but important point: the STM does not image nuclear positions directly. It images the local density of electronic states (LDOS) near the Fermi energy at the tip location. On clean metallic surfaces these two quantities agree closely, and STM images are routinely interpreted as atomic maps.

On surfaces with adsorbed molecules or with electronic reconstructions the LDOS can differ significantly from the atom positions — a fact that makes STM both more subtle and more powerful as a tool, since it also gives information about electronic structure.

The IBM atom demonstration

In 1990 Donald Eigler and Erhard Schweizer at IBM Almaden used an STM not just to image but to position individual xenon atoms on a nickel surface, spelling out the letters "IBM". The experiment demonstrated that quantum tunneling, combined with precision piezo control, allows matter to be manipulated one atom at a time. It remains one of the most iconic illustrations that quantum mechanics is not merely an abstract theory but an engineering reality.

Broader impact

STM spawned an entire family of scanning probe microscopies: atomic force microscopy (AFM, which works on insulators by sensing van der Waals forces), Kelvin probe microscopy (surface potential), magnetic force microscopy, and many more. All share the same insight: bring a sharp probe close enough to a surface, measure a short-range interaction with extreme sensitivity, and scan to build a map.

Quantum tunneling — the same phenomenon that sets a lower bound on alpha-decay lifetimes and that flash memory cells exploit for electron injection — turns out to be the physical principle that lets humans see and arrange individual atoms.