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Scanning Tunnelling Microscopy

How Quantum Tunnelling Lets Us Map Individual Atoms

Big Question: How can a current through empty space tell us where individual atoms and electronic states are on a surface?

Quick Answer

An STM holds an atomically sharp conducting tip within roughly a nanometre of a conducting or semiconducting surface. A small voltage is applied between tip and sample. Quantum tunnelling allows electrons to cross the vacuum gap, creating a tiny current.

The tunnelling current depends exponentially on tip–sample separation. Move the tip by a tiny fraction of a nanometre and the current can change greatly. A feedback system moves the tip vertically while it scans sideways, keeping current constant or recording current changes. The resulting data map the surface with atomic-scale sensitivity.

Gerd Binnig and Heinrich Rohrer received half of the 1986 Nobel Prize in Physics for the design of the scanning tunnelling microscope.

Nobel Prize — The 1986 Physics Prize and scanning tunnelling microscopy →

What You Will Learn

• What an energy barrier is.
• Why classical particles cannot cross some barriers.
• Why quantum wavefunctions can penetrate barriers.
• What tunnelling probability means.
• Why tunnelling current is extremely sensitive to distance.
• How an atomically sharp tip is used.
• What constant-current and constant-height scanning mean.
• Why an STM image is not a simple photograph of atoms.
• How local density of electronic states influences contrast.
• What scanning tunnelling spectroscopy measures.
• How individual atoms can sometimes be manipulated.
• Why vibration, cleanliness and tip condition matter.

Part 1 — The Classical Barrier

In classical mechanics, a ball with less energy than the top of a hill cannot cross the hill. It rolls back.

An electron facing an energy barrier would seem to obey the same rule: if its energy is lower than the barrier height, it should not appear beyond the barrier.

Quantum mechanics changes the model because an electron is described by a wavefunction rather than a precise little ball following one path.

Part 2 — The Wavefunction Enters the Forbidden Region

Inside a classically forbidden barrier, the electron’s wavefunction does not instantly become zero. It decays exponentially with distance.

If the barrier is thin enough, some amplitude remains at the far side. That produces a finite probability of transmission.

barrier too high classically ≠ zero transmission quantum mechanically.

Part 3 — Vacuum Is the Barrier

In an STM, the sharp metal tip does not touch the sample. A tiny vacuum or insulating gap separates them.

Electrons in the metal face an energy barrier associated with leaving the material. When tip and sample are close enough and a bias voltage is applied, electrons tunnel across.

The resulting current may be only picoamps or nanoamps, but modern electronics can measure it.

Part 4 — Exponential Sensitivity Is the Superpower

Tunnelling current changes approximately exponentially with separation:

I ∝ e^−2κs

Here s is the tip–sample gap and κ depends on barrier properties.

Because of the exponential dependence, changing the gap by a fraction of an ångström can produce a measurable current change.

That sensitivity is what makes atomic-scale vertical resolution possible.

Part 5 — The Tip Must End in Almost One Atom

An STM tip is sharpened so that one atom or a tiny cluster at the apex dominates the tunnelling current.

If many tip atoms contribute equally, the image becomes blurred or duplicated.

This means the instrument’s “eye” is not a lens. It is the electronic structure of the last few atoms at the tip.

Part 6 — Constant-Current Mode

In constant-current mode, the tip moves sideways across the surface while a feedback controller continually raises or lowers it to keep tunnelling current at a chosen value.

The vertical motion of the tip is recorded.

surface feature changes current → feedback changes height → height signal becomes the image.

Part 7 — Constant-Height Mode

For very flat surfaces, feedback can be slowed or disabled and the tip can scan at nearly constant height.

The tunnelling current itself becomes the recorded signal.

This can be faster, but it is riskier: a sudden surface bump can crash the tip into the sample.

Part 8 — An STM Image Is Not Simply Topography

The current depends not only on distance but also on the electronic states available in the tip and sample.

A bright feature can therefore mean:

• the surface is physically higher;
• the local electronic density of states is larger at the chosen bias;
• the tip structure changed;
• some combination of these.

This is why scientists should say STM measures a tunnelling-current landscape, not that it simply photographs hard atomic spheres.

Part 9 — Bias Voltage Selects Electronic States

Changing the sign and magnitude of bias changes which occupied or unoccupied electronic states contribute to tunnelling.

The same atomic surface can therefore look different at different bias voltages.

This is not necessarily an imaging error. It can reveal real electronic structure.

Part 10 — Scanning Tunnelling Spectroscopy

Hold the tip over one location and sweep the bias voltage while measuring current. This produces an I–V curve.

The derivative dI/dV is often related to the local density of electronic states.

Scanning tunnelling spectroscopy can therefore map electronic properties such as energy gaps, surface states and local defects, not just surface shape.

Part 11 — Why Conductivity Is Required

A steady tunnelling current requires an electrical path through the sample.

STM therefore works naturally on conducting and semiconducting surfaces. Truly insulating samples are much more difficult because charge cannot easily be replenished.

Other scanning-probe methods, especially atomic force microscopy, are often better for insulating materials.

Part 12 — The Instrument Must Fight Vibration

If a fraction-of-a-nanometre change alters current strongly, then footsteps, building vibration, sound and thermal drift can ruin the measurement.

STM systems therefore use vibration isolation, rigid mechanical design, temperature control and often vacuum environments.

Atomic resolution is as much an engineering achievement as a quantum-mechanical one.

Part 13 — Atoms Can Sometimes Be Moved

The STM tip can do more than observe. By adjusting tip position, voltage and current, researchers can sometimes move individual adsorbed atoms or molecules across a surface.

Famous experiments arranged xenon atoms into deliberate patterns, demonstrating direct atomic manipulation.

This does not mean atoms are picked up like marbles by hand. The tip alters local forces and tunnelling conditions at atomic scale.

Part 14 — Follow One Pixel

1. The sharp conducting tip approaches the surface.
2. A bias voltage creates an energy difference between tip and sample states.
3. The electron wavefunction extends into the vacuum gap.
4. Some electrons tunnel across.
5. A tiny current is measured.
6. The tip moves sideways to the next location.
7. Current changes because distance and local electronic states changed.
8. The feedback loop adjusts the tip height.
9. The vertical correction is stored.
10. Thousands or millions of positions build a map.
11. Repeat at another bias and the electronic contrast changes.

Think Like a Scientist: How Do We Know We Are Seeing Atomic Structure?

• Repeat scans and verify lattice periodicity.
• Rotate or translate the scan and check that the surface lattice remains consistent.
• Change bias voltage and compare electronic contrast.
• Use known crystal surfaces as calibration standards.
• Compare with diffraction and theoretical surface structures.
• Change or recondition the tip to test whether features are tip artefacts.
• Acquire spectroscopy at selected locations.

Observation vs Inference

• Observation: tunnelling current changes strongly with tip position.
• Measurement: periodic features match known lattice spacings.
• Observation: contrast changes with bias voltage.
• Inference: image structure reflects both surface topography and local electronic states.
• Boundary: bright spots are not automatically literal pictures of spherical atoms.

Common Misconceptions and Better Models

Misconception	Better model
Electrons physically drill through the barrier.	Tunnelling is a quantum transmission probability from wavefunction overlap.
The tip touches the sample.	A tiny gap must remain for tunnelling.
An STM image is a photograph of atoms.	It maps tunnelling current influenced by height and electronic states.
Any material can be scanned.	Electrical conductivity is normally required.
Atomic resolution means no uncertainty.	Tip shape, vibration, drift and electronic contrast still matter.
Tunnelling violates energy conservation.	The quantum state obeys energy conservation; the barrier is crossed probabilistically without borrowing macroscopic energy.

Checkpoint Questions

1. What is quantum tunnelling?
2. Why is the vacuum gap an energy barrier?
3. Why is tunnelling current so sensitive to distance?
4. Why must the tip be extremely sharp?
5. How does constant-current mode work?
6. Why isn’t an STM image simply topography?
7. What does bias voltage select?
8. What does scanning tunnelling spectroscopy measure?
9. Why is vibration control essential?
10. Why are insulators difficult for STM?

Answer Key

Open after attempting the questions

1. Finite quantum transmission through a classically forbidden barrier.
2. Electrons must leave one conducting material and cross a region of higher potential energy.
3. The wavefunction decays exponentially through the barrier.
4. A tiny apex localises the current and improves lateral resolution.
5. A feedback loop adjusts tip height to maintain a chosen current.
6. Current also depends on local electronic density of states.
7. Which occupied or unoccupied electronic states contribute to tunnelling.
8. Local current–voltage behaviour and electronic states.
9. Sub-ångström changes can alter current strongly.
10. They cannot easily sustain the required electrical current path.

Primary Science Bridge

• objects can be measured without ordinary visible contact;
• electric current is movement of charge;
• microscopes reveal structures too small for the eye;
• models can change at very small scales;
• measurements can be indirect.

Secondary and JC Bridge

Core idea	Higher-resolution route
Electrons	Wavefunctions and probability amplitude
Potential energy	Quantum barriers
Current	Tunnelling current
Feedback	Piezoelectric positioning and control loops
Microscopy	Scanning-probe imaging
Atomic structure	Local density of electronic states

Deep Science Window — WKB Approximation

The exponential dependence of tunnelling probability on barrier width can be derived approximately using semiclassical methods such as the WKB approximation. It explains why angstrom-scale distance control creates orders-of-magnitude current changes.

Deep Science Window — Surface Electronic States

A crystal surface breaks the periodic environment that exists inside the bulk. New electronic states can appear at the surface. STM is unusually powerful because it probes these local states directly in real space.

Deep Science Window — Atomic Manipulation

By changing tip–surface forces and bias, scientists can move selected atoms or molecules. This turns the microscope into both a measurement tool and a nanoscale actuator.

Evidence Boundaries

• STM image ≠ ordinary photograph.
• Bright feature ≠ automatically a physically higher atom.
• Tunnelling ≠ energy-law violation.
• Atomic resolution ≠ exact atomic nucleus position in every image.
• One tip state ≠ permanent calibration. Tip condition can change.
• STM ≠ X-ray diffraction. One maps local surface tunnelling; the other measures reciprocal-space scattering from many atoms.

Manual Summary — KNOW → CONNECT → EXPLAIN → APPLY → CHECK

KNOW: quantum tunnelling, barrier, tunnelling current, bias, feedback, local density of states.

CONNECT: wavefunction decay to current sensitivity and current sensitivity to atomic-scale imaging.

EXPLAIN: how electrons cross a gap without classical contact.

APPLY: predict how gap width, bias and tip condition alter the signal.

CHECK: separate topographic claims from electronic-state claims.

Research Sources and Further Reading

• Nobel Prize — Scanning Tunnelling Microscope
• NIST — Scanning Tunnelling Microscopy