The Tunneling Needle

Gerd Binnig, Heinrich Rohrer, and the Scanning Tunneling Microscope

Inside a stainless-steel vacuum bell jar at the IBM Zurich Research Laboratory in Rüschlikon, Switzerland, in the spring of 1981, a heavy permanent-magnet cradle hung from two nested rings of soft coil springs above a pair of water-cooled oxygen-free copper plates. Whenever a passing freight train on the Zurich railway line or a footstep in the hallway shook the building, the moving magnets induced opposing eddy currents in the copper plates below, damping vertical floor vibrations of several microns down to less than a hundredth of an angstrom. Sitting atop that magnetically levitated stage, a tiny tripod of lead-zirconate-titanate piezoelectric ceramic bars held an electrochemically etched tungsten wire needle just five angstroms—half a nanometer, or roughly the diameter of two silicon atoms—above a polished gold crystal surface without touching it.

For a century after Ernst Abbe derived the optical diffraction limit in 1873 ($d = \lambda / 2 \text{NA}$), physicists knew that no microscope built with lenses could ever resolve details smaller than roughly half the wavelength of the illuminating wave. For visible light, any feature smaller than 200 nanometers blurs into an Airy diffraction disk. Ernst Ruska's transmission electron microscope of the 1930s pushed past the optical limit by firing high-energy electrons whose de Broglie wavelengths were picometers across, yet high-voltage electron beams penetrated deep into solid crystals, averaging over dozens of subsurface atomic layers and often blasting delicate surface atoms out of position. Individual atoms sitting on the top layer of a bulk solid remained essentially invisible in real space.

In late 1978, the Swiss physicist Heinrich Rohrer and his German colleague Gerd Binnig set out to examine microscopic pinholes in ultra-thin insulating oxide layers grown for experimental Josephson-junction computer switches. Rather than focusing a wave with a lens from afar, they decided to bring a blind mechanical probe directly into the near-field regime, closer to the sample surface than the wavelength of an electron itself.

In classical physics, if a metal needle and a conducting sample separated by five angstroms of empty vacuum are wired to a low-voltage battery ($V \approx 0.01\text{ to }1\text{ volt}$), zero electrical current can flow between them because the electrons lack the four to five electron-volts of thermal or kinetic energy (the metal's work function $\phi$) needed to leap out of the metal into empty space. In quantum mechanics, however, the electron wavefunctions $\psi$ do not drop to zero abruptly at the metal surface; they leak exponentially into the forbidden vacuum barrier. When the needle tip approaches to within a few angstroms ($d \approx 4\text{ to }7\text{ \AA}$) of the surface, the decaying wavefunction tails of the tip and the sample overlap, allowing electrons to tunnel continuously across the vacuum gap with a current $I(d)$ that varies exponentially with separation distance $d$:

Here $m$ is the electron mass, $\hbar$ is the reduced Planck constant, and $\phi$ is the average work function of the tip and sample (around $4\text{ eV}$ for tungsten and gold). Plugging in those physical constants yields a decay rate of roughly $2\text{ \AA}^{-1}$ inside the exponent. In practical terms, pulling the tungsten needle back by just a single angstrom ($0.1\text{ nanometers}$, less than the radius of one atom) slashes the tunneling current by an entire order of magnitude—nearly tenfold. Move the needle back by three angstroms, and the current drops by a factor of a thousand.

That extreme exponential sensitivity turned two seemingly fatal engineering obstacles into advantages. First, Binnig, Rohrer, and their technician Christoph Gerber did not need to manufacture a needle polished to a one-atom point from top to bottom; because tunneling current drops tenfold per angstrom of height, whichever single tungsten atom happened to protrude slightly farthest at the very bottom of a jagged microscopic tip carried more than ninety percent of the entire nanoampere current. Second, by wiring the tunneling current into an electronic servo loop that drove the vertical $z$-axis piezoelectric bar (which expanded or contracted by angstroms per applied volt) to keep the current strictly constant as the $x$ and $y$ piezo bars raster-scanned the needle across the sample, the voltage fed to the $z$-piezo traced a direct three-dimensional contour map of the surface electron clouds with vertical resolution reaching $0.01\text{ angstroms}$ ($1\text{ picometer}$).

In autumn 1982, Binnig and Rohrer scanned a clean crystal of silicon in ultra-high vacuum and produced a real-space topographical relief map resolving every single atom of the long-debated $7 \times 7$ surface reconstruction unit cell. In November 1989, Donald Eigler and Erhard Schweizer at IBM Almaden cooled a scanning tunneling microscope to four kelvins and used its tungsten tip to drag thirty-five individual xenon atoms into place on a nickel crystal, spelling out three letters five nanometers tall.