Scanning Tunneling Microscope

The trick: distance becomes brightness

You cannot photograph an atom. Visible light has a wavelength of ~500 nm — thousands of times wider than an atom (~0.1–0.3 nm) — so no lens-based microscope can resolve one. The scanning tunneling microscope sidesteps optics entirely. It doesn't focus anything; it feels the surface with electrons.

Bring a metal tip to within about a nanometre of a conducting surface and apply a small voltage. Classically, no current flows — there's a vacuum gap and the electrons don't have the energy to cross it. But quantum mechanics lets electrons tunnel through that barrier, producing a measurable current. The magic is the steepness: the current depends exponentially on the gap width. Move the tip 0.1 nm closer and the current jumps roughly tenfold.

That exponential is the whole instrument. It means essentially all of the current squeezes through the single foremost atom of the tip — the one atom closest to the surface dominates because it's even a fraction of an ångström nearer than its neighbours. Raster that one-atom probe across the surface, record the current at every point, and the atomic corrugation of the surface paints itself out as a map of tunneling current. Distance has become a signal you can read.

How an STM works, end to end

1. The tip. A wire of tungsten or platinum–iridium is etched or cut so its apex ends in (ideally) a single atom. Sharpness in the chemical sense barely matters — what matters is that one atom protrudes.
2. The approach. A coarse motor brings the tip toward the surface; then a piezoelectric scanner takes over, advancing the tip in sub-ångström steps until a target current appears, signalling the ~1 nm gap.
3. The bias. A voltage (the bias, V) between tip and sample sets which electrons tunnel and in which direction. Positive sample bias lets tip electrons tunnel into empty sample states; negative bias probes filled states.
4. The scan. Piezo actuators sweep the tip in a raster — fast scan along x, slow step along y — covering an area that might be just a few nanometres across.
5. The feedback. An electronic loop reads the current and (in the usual mode) adjusts the tip height to keep it constant. The voltage sent to the z-piezo is recorded; that record, pixel by pixel, is the image.

The piezoelectric scanner is what makes sub-atomic positioning possible: a piezo crystal expands or contracts by a few picometres per millivolt applied, so applying a smoothly ramped voltage glides the tip across the surface with stability finer than the width of an atom.

The physics: tunneling through a barrier

Model the vacuum gap as a 1-D rectangular barrier of height φ (the average work function) and width d. An electron of energy E < φ has, inside the barrier, an exponentially decaying wavefunction ψ ∝ e^−κx, with decay constant

κ = √(2m(φ − E)) / ℏ   ≈ √(2mφ) / ℏ   (for E near the Fermi level)

The transmission probability through the barrier, and hence the current, scales as

I ∝ |ψ(d)|² ∝ e^(−2κd)

Put in numbers. For a typical metal work function φ ≈ 4 eV:

κ = √(2 · m_e · φ) / ℏ
  = √(2 · 9.11e−31 kg · 4 · 1.602e−19 J) / 1.055e−34 J·s
  ≈ 1.02 × 10^10 m⁻¹  =  1.02 Å⁻¹

So 2κ ≈ 2 Å⁻¹. Increasing the gap by 1 Å (0.1 nm) multiplies the exponent by e⁻² ≈ 1/7.4 — the current drops by about an order of magnitude. This single number is why the microscope works.

For quantitative imaging the proper description is the Tersoff–Hamann model (1983–85): treating the tip apex as a point s-orbital, the tunneling current is proportional to the surface local density of states (LDOS) at the tip position, integrated over the energy window opened by the bias:

I ∝ ∫₀^(eV) ρ_sample(r_tip, E) · ρ_tip(E) dE   ≈  V · ρ_sample(r_tip, E_F)   (small V)

The key consequence: an STM does not image atomic nuclei. It images where electrons are available to tunnel — the electron density at the energies your bias selects.

Operating modes and what they trade off

Property	Constant-current mode	Constant-height mode
Held fixed	Tunneling current (feedback adjusts z)	Tip height z (feedback off or slow)
Image is	z-piezo voltage vs (x, y)	Current vs (x, y)
Speed	Slower — limited by feedback bandwidth	Fast — no feedback lag
Surface roughness	Handles steps and bumps safely	Only very flat surfaces — tall features crash the tip
Crash risk	Low	High
Best for	General atomic imaging, stepped surfaces	Atomically flat regions, capturing moving atoms / fast video

A third family of measurements is scanning tunneling spectroscopy (STS): park the tip, sweep the bias V, and record I(V). The derivative dI/dV is proportional to the sample LDOS at energy eV — letting you read out a material's electronic band structure, superconducting gap, or molecular orbital spectrum at a single point.

Numbers: how an STM compares to other microscopes

Microscope	Probe	Lateral resolution	Sees	Needs vacuum?
Optical (light)	Visible photons (~500 nm)	~200 nm	Bulk features, cells	No
SEM (scanning electron)	Electron beam	~1 nm	Surface morphology	Yes
TEM (transmission electron)	Electron beam through thin sample	~0.05 nm	Projected atomic columns	Yes
STM	Tunneling current	~0.1 nm (~1 pm vertical)	Surface electron density (LDOS)	Best in UHV
AFM	Tip–sample force	~0.1 nm	Surface topography (insulators too)	No (works in air/liquid)

Concrete scales for an STM: tunneling current ~0.01–10 nA; bias ~10 mV to ~2 V; gap ~5–10 Å; tip speed during a scan ~10–1000 nm/s; a single atomic-resolution image (say 256×256 pixels in constant-current mode) takes from seconds to several minutes depending on feedback bandwidth. Vertical stability must beat ~1 pm — which is why the instrument hangs on springs, sits on a magnetic-eddy or air damping stage, and is frequently cooled to 4 K to freeze out thermal drift and surface atom motion.

Worked example: reading a single atomic step

Suppose the feedback loop is set to hold I = 1.0 nA, and the tip moves over a monatomic step on a metal surface that is Δd = 0.20 nm = 2.0 Å tall. In constant-height mode (feedback briefly off), how much does the current change as the tip passes over the step edge before the loop can react?

I_after / I_before = e^(−2κ·Δd)
                   = e^(−2 · 1.02 Å⁻¹ · 2.0 Å)
                   = e^(−4.08)
                   ≈ 0.017

The current collapses to ~1.7% of its value — roughly a 60-fold drop — for a step just two ångströms tall. Equivalently, the current swings by ~×7.4 for each ångström. In constant-current mode the loop instead retracts the tip by exactly 0.20 nm to keep I = 1.0 nA, and that 0.20 nm shows up directly in the recorded z-image as the height of the step. Either way, a feature one atom tall is screaming-loud in the signal.

Where STM shows up

• Surface science. The original killer app — resolving the famous Si(111)-7×7 reconstruction in real space settled debates that diffraction alone couldn't.
• Atom manipulation. In 1989 IBM's Don Eigler spelled "IBM" with 35 individual xenon atoms; the same precision builds quantum corrals and single-molecule logic.
• Superconductivity and correlated materials. STS maps the superconducting energy gap, vortex lattices, and the local density of states in high-T_c cuprates and graphene moiré systems.
• Molecular electronics and catalysis. Imaging single molecules adsorbed on surfaces, watching reactions site by site, measuring single-molecule conductance.
• Semiconductor metrology. Characterising dopant atoms, defects, and band bending at the atomic scale on silicon and III–V surfaces.
• Spin-resolved STM. A magnetic tip senses spin polarisation, imaging individual magnetic moments and skyrmions atom by atom.

Common misconceptions and edge cases

• "It photographs atoms." No light, no lens, no magnification in the optical sense. It maps electron tunneling probability point by point and reconstructs an image from a scan.
• "Bright spots are atomic nuclei." Bright spots are high local density of states. On some surfaces the maxima sit between atoms, and flipping the bias polarity can swap which atoms look bright (filled vs empty states).
• "It works on anything." Only conductors. Insulators charge up and kill the current — use AFM for those.
• "Resolution comes from a sharp tip." It comes from the exponential current–distance law concentrating tunneling onto the single foremost atom. A blunt tip with one lucky protruding atom still gives atomic resolution; a "double tip" gives ghost images.
• "The image is pure geometry." STM topography mixes geometry and electronics. A region that's electronically denser can look "taller" even if it's geometrically flat. Disentangling the two requires spectroscopy (STS) or comparison with AFM.
• "Vacuum is mandatory." Ultra-high vacuum gives the cleanest surfaces, but STM also runs in air, liquid, and electrochemical cells — important for biology and electrochemistry, at the cost of surface contamination.