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§ Phase vi · Tunneling · Chapter 03

Scanning tunneling microscopy

In a basement lab at IBM Zürich in the spring of 1981, two physicists hung a microscope on rubber bands, cooled their nerves, and tried to bring a sharpened tungsten wire to within a few atomic diameters of a clean metal surface. When the meter twitched, they were reading single atoms. Five years later they had a Nobel. A decade later, IBM had spelled its own name out of thirty-five xenon atoms.

The previous two chapters were about something strange happening inside other people’s experiments: alpha particles leaking out of uranium nuclei, electrons crossing barriers in diodes, fusion in the cores of stars. Tunneling was real, it was useful, it was measurable in bulk. But it was never something you could watch happen, and certainly not something you could aim. In 1981, two physicists in a Zürich basement turned tunneling into a paintbrush. They sharpened a metal wire to a single atom, brought it within a nanometer of a clean surface, and used the exponential sensitivity of the tunneling current as a ruler so precise that it could tell when the gap changed by less than the diameter of a hydrogen atom. The instrument they built, the scanning tunneling microscope, did not infer atoms from diffraction patterns. It drew their picture, one at a time.

The two physicists were Gerd Binnig, a young German postdoc fresh off his PhD in superconductivity, and Heinrich Rohrer, a Swiss experimentalist twenty years his senior who had spent most of his career on critical phenomena in magnetic systems. They had been hired by IBM’s Zürich research lab, a small but well-funded outpost of Big Blue tucked into the Alpine town of Rüschlikon, and were assigned a problem that was equal parts metallurgy and witchcraft: the thin oxide layers on the silicon wafers IBM was building chips out of were not uniform, and nobody could see them. The oxide was a few atomic layers thick, the bumps and dips that mattered were single-atom features, and every existing microscope (optical, electron, field-emission) either lacked the resolution or destroyed the surface looking at it. Binnig and Rohrer, in the way of people who have not yet been worn down by what is supposed to be possible, decided to invent a new kind of microscope from scratch.

Their key idea was to abandon the lens entirely. Every microscope before theirs (from Hooke’s compound scope to the transmission electron microscope) worked by collecting a wave that had already interacted with the sample and focusing it onto a detector. The resolution was always set by the wavelength of the wave: half a micron for visible light, picometers for energetic electrons. Binnig and Rohrer noticed that a tunneling current does not have a wavelength in the usual sense. It has a decay length. Bring a sharp metal tip close enough to a sample that the two electron clouds overlap, apply a small voltage, and a current flows whose magnitude depends not on a focused beam but on the exponentially decaying tail of a wavefunction leaking across a vacuum gap. Move the tip half an angstrom closer and the current grows by a factor of e. Half an angstrom farther and it shrinks by the same factor. Make the gap your signal and you have a ruler with sub-atomic precision. No lenses required.

The hard part was not the principle. It was the engineering. To hold a tungsten tip steady at a distance of half a nanometer above a surface, you have to suppress vibrations of every length and every frequency. A truck rumbling on a road three kilometers away can move the tip by a millionth of a meter, which is ten thousand times too far. A footstep in the hallway is worse. The hum of a fluorescent light, the breath of a passing colleague, the slow drift of room temperature changing the length of the support frame by parts per million per kelvin: all of it is fatal. Binnig and Rohrer suspended their first working microscope on a magnetically levitated lead plate floating over a superconducting bowl, the entire assembly kept at liquid-helium temperature inside a vacuum chamber the size of a kitchen oven. The lead plate hung there in mid-air, untouched, while piezoelectric ceramics inside it nudged the tip across the sample one angstrom at a time. The whole apparatus looked, as one colleague put it, like an experiment to detect the breathing of a butterfly.

It worked. On March 16, 1981, after months of crashed tips and false starts, the lab’s chart recorder produced a trace that climbed and fell with the periodicity of atomic terraces. Within weeks the team had imaged the famous 7×7 reconstruction of the silicon (111) surface, a fiendishly complicated pattern of dimers and adatoms that surface scientists had argued about for fifteen years on the basis of indirect diffraction data alone. The STM image settled the argument. You could just count the bumps.

Stop for a moment on that resolution claim. Zero point one nanometer laterally is roughly the spacing between adjacent atoms in a metal. Zero point zero one nanometer vertically, ten picometers, is about a tenth of the diameter of a hydrogen atom. The STM is not approximately atom-resolved. It overshoots single atoms by an order of magnitude in the vertical direction. The reason it can do this is the same reason it works at all: the exponential dependence of tunneling on distance. If the current changes by a factor of ten when the gap changes by one angstrom, and you can measure the current to one part in a hundred, you can resolve gap changes of one hundredth of an angstrom. Sensitivity at this scale is not a triumph of precision machining. It is a free gift from the exponential.

To see why, recall the rectangular-barrier result from the previous chapter. The wavefunction inside the classically forbidden region decays as exp(-κz), where κ depends on the work function W of the metal:

κ = (1/ħ) √(2mₑ W)

For a typical metal with W ≈ 4 eV, κ comes out to roughly one inverse angstrom. The tunneling probability is the square of the wavefunction tail, so it scales as exp(-2κz). Plug in: a one-angstrom change in z multiplies the tunneling current by exp(-2) ≈ 7.4. That factor of seven for one angstrom is the whole magic. There is no other measurement in solid-state physics where a one-percent change in a controlled parameter produces a factor-of-seven change in the signal. It is what makes the STM the most position-sensitive instrument human beings have ever built that does not rely on interference.

In practice the microscope is run in one of two modes. In constant-current mode, an electronic feedback loop watches the tunneling current and adjusts the tip’s height in real time to keep the current pinned at a target value, say one nanoampere. The voltage commanded to the vertical piezo, recorded as the tip rasters left-to-right and top-to-bottom across the surface, is the image. Where the tip had to retract to keep the current constant, the surface is high; where it had to descend, the surface is low. In constant-height mode, the feedback is switched off and the tip is held at a fixed elevation while it scans. The current itself, mapped point by point, is the image. Constant-current mode is forgiving (it follows step edges without crashing the tip) but slow, because the feedback has to settle at every pixel. Constant-height mode is fast enough to catch atoms diffusing in real time but reckless on anything but the smoothest sample.

What appears in the image is not literally the surface. It is a contour of the local density of electronic states at the Fermi level, the cloud of mobile electrons available at the sample’s natural energy. On a flat metal, that contour does follow the atomic topography quite faithfully, so the picture looks like a corrugated landscape with bumps where atoms sit. On a chemically inhomogeneous surface (a molecule adsorbed on a metal, an impurity in a superconductor) the bumps and dimples can be shifted or even inverted, because what the STM sees is “where the electrons are” rather than “where the nuclei sit.” Tersoff and Hamann worked this out theoretically in 1985 and gave the modern interpretation: the STM current is proportional to the sample’s local density of states at the tip’s position. This is the foundation of scanning tunneling spectroscopy (STS), where instead of imaging at fixed bias you park the tip over one point, sweep the voltage, and read off dI/dV. That derivative is, to an excellent approximation, the local density of states as a function of energy. You can do solid-state physics one atom at a time.

T(d) = 16 ε (1 − ε) exp(−2κ d)

I(d) ≈ I₀ exp(−2 κ d)

d ln I / d d = −2κ

I(d + Δd) / I(d) = exp(−2κ Δd)

The story did not end with imaging. In 1989, Don Eigler and Erhard Schweizer at IBM Almaden showed that you could use the STM not just to look at atoms but to push them around. By cooling a nickel surface to four kelvin, dosing it with xenon atoms, and gently increasing the tip-sample interaction so that the tip pulled rather than tunneled, they discovered that they could drag a xenon atom across the surface from one adsorption site to the next. Then they spelled “IBM” out of thirty-five xenon atoms and published the picture in Nature. The image went around the world. It is, depending on how you count, the first photograph of single atoms arranged by a human being. It is also the most expensive logo in corporate history. Eigler’s team followed it with “quantum corrals” (rings of iron atoms on copper that trap surface electrons in standing-wave patterns visible directly in the STM image) which gave the first picture of an electron wavefunction confined in a custom-built potential. The Schrödinger equation, drawn from above.

The Nobel committee did not wait. The 1986 Physics Prize was split between Ernst Ruska (for the electron microscope, fifty years late) and Gerd Binnig and Heinrich Rohrer (for the STM, five years from invention to crown). Rohrer’s Nobel address is worth reading in full, but the heart of it is one sentence: “The whole instrument has fewer parts than a typewriter, and most of those parts you can buy at a hardware store.” The STM was, for a Nobel-winning experiment, almost embarrassingly simple. The hardness lived entirely in the engineering of stillness.

The STM was the seed of a whole family of scanning probe microscopes. The atomic force microscope (AFM), invented by Binnig in 1986, replaces the tunneling current with a mechanical force, allowing it to image insulating samples that the STM cannot touch. Magnetic force microscopy reads tiny stray fields. Near-field optical microscopy maps light below the diffraction limit. Today an undergraduate condensed-matter lab can buy an AFM the size of a coffee maker and routinely image biological membranes in water. None of this happens without the original STM. Eigler’s logo, the manipulation of single atoms, the field that calls itself “nanotechnology” with varying degrees of conviction: all of it descends from a tungsten wire in a Swiss basement, hanging on rubber bands, separated from a silicon wafer by half a nanometer of vacuum, and from the realization that exp(−2κd) is the most sensitive ruler in the world.

It is also a parable about what theoretical curiosity is good for. Gamow’s calculation of alpha decay in 1928 was, when he did it, a piece of nuclear-physics housekeeping with no connection to anything practical. Esaki’s tunnel diode was a working device but a niche one. Then in 1981 the same exponential decay (the same e^(−2κd), the same wavefunction leaking out into the forbidden region) became the foundation of an entire branch of experimental science. The leap from “classically impossible” to “industrially useful” took fifty-three years. The leap from “useful” to “lets us see single atoms” took, in Binnig and Rohrer’s hands, about two more.