Scanning Tunnelling Microscopes (STM) Revision Notes | A Level AQA Physics

1. The Instrument That Saw Individual Atoms

Before 1981, no one had ever directly imaged individual atoms on a surface. The scanning tunnelling microscope changed that — and it did so by exploiting one of the strangest predictions of quantum mechanics: the ability of electrons to pass through barriers they have no classical right to cross.

The STM sits at the intersection of two major themes in the AQA A-level turning points topic: wave-particle duality and the quantum mechanical description of matter. Understanding how it works requires you to connect the wave nature of electrons directly to a measurable electrical signal.

2. Quantum Tunnelling — The Core Mechanism

Picture a ball rolling towards a hill. Classically, if the ball does not have enough kinetic energy to reach the top, it rolls back — it cannot pass through the hill. Now replace the ball with an electron and the hill with a thin potential energy barrier. Quantum mechanics tells a different story.

Because electrons have wave-like properties, their wave function does not abruptly drop to zero at the edge of a barrier. Instead, it decays exponentially through the barrier. If the barrier is thin enough, the wave function has a non-zero amplitude on the other side — meaning there is a finite probability of finding the electron there. This is quantum tunnelling.

The exponential dependence on barrier width is the key to the STM's extraordinary sensitivity. A tiny change in the gap between the probe tip and the surface produces a large, measurable change in the tunnelling current. This is what makes atomic-resolution imaging possible.

3. Principle of Operation of the STM

The STM consists of an extremely sharp conducting probe tip — ideally terminating in a single atom — held very close to a conducting sample surface, typically within 0.3 nm to 1 nm. A small voltage (the bias voltage) is applied between the tip and the surface. Because the gap is so narrow, electrons tunnel quantum mechanically across the vacuum between them, producing a measurable tunnelling current.

The tunnelling current is extraordinarily sensitive to the tip-surface separation. For typical metal surfaces, reducing the gap by just 0.1 nm roughly doubles the tunnelling current, though the exact factor depends on the work function of the material. This sensitivity is what gives the STM its atomic-scale resolution — variations in surface height of a fraction of a nanometre produce clearly detectable changes in current.

The tip is mounted on piezoelectric transducers — materials that expand or contract by precise, controllable amounts when a voltage is applied to them. Three transducers control movement in the x, y, and z directions, allowing the tip to be scanned across the surface in a raster pattern while its height is regulated with sub-atomic precision.

3a. The Two Operating Modes

The STM can be operated in two distinct modes, and it is worth knowing both for exam purposes.

In constant current mode, the feedback voltage sent to the z-transducer traces the surface topography. Plotting this voltage against the x-y position of the tip produces an image of the surface at atomic resolution. In constant height mode, the current map itself is the image.

4. The Role of the Work Function and the Potential Barrier

The vacuum gap between the STM tip and the surface acts as a potential energy barrier for electrons. The height of this barrier is related to the work function of the surface material — the minimum energy needed to remove an electron from the surface into the vacuum.

Electrons near the Fermi level of the tip have energies below the vacuum level, so classically they cannot cross the gap. Quantum mechanically, their wave functions extend into and through the vacuum, and if the gap is narrow enough, the wave function reaches the surface with sufficient amplitude to produce a tunnelling current. The bias voltage applied between tip and surface shifts the energy levels slightly, determining the direction of net electron flow.

A higher work function means a taller barrier, which causes the wave function to decay more steeply through the gap. This reduces the tunnelling probability for a given gap width. Different surface materials therefore produce different tunnelling currents even at the same tip-surface separation — a fact that means the STM image reflects both topography and local electronic structure.

5. Piezoelectric Control — Achieving Sub-Atomic Precision

The mechanical precision required by the STM is extraordinary. To image individual atoms separated by roughly 0.2–0.3 nm, the tip must be positioned and moved with a resolution better than 0.01 nm. No conventional mechanical system can achieve this. Piezoelectric transducers make it possible.

A piezoelectric material deforms — expands or contracts — by an amount proportional to the applied voltage. By applying carefully controlled voltages to three orthogonal piezoelectric elements (x, y, and z), the STM moves the tip in three dimensions with the required precision. Typical piezoelectric sensitivities allow movements of a fraction of a nanometre per volt, giving the instrument the control it needs.

The STM must also be isolated from external vibrations — even the vibration from a person walking nearby could displace the tip by more than the atomic spacings being measured. In practice, STMs are mounted on vibration-damping systems, and many operate at low temperatures to reduce thermal noise.

6. Building the Atomic Image

As the tip scans across the surface in a series of parallel lines (a raster scan), the feedback system records the z-transducer voltage at each x-y position. A computer converts this data into a false-colour map where height is represented by colour or brightness. The result is a real-space image of the surface at atomic resolution.

The first STM images, produced by Gerd Binnig and Heinrich Rohrer at IBM Zurich in 1981, showed the 7×7 reconstruction of the silicon (111) surface — a complex atomic arrangement that had been debated for years. The STM resolved it directly. Binnig and Rohrer were awarded the Nobel Prize in Physics in 1986, a recognition of how fundamentally the instrument changed surface science.

The STM does not use lenses or electromagnetic radiation to form its image. Resolution is not limited by diffraction — it is limited only by the sharpness of the tip and the stability of the instrument. This is a conceptually different approach to microscopy, and it is worth being able to compare it with optical and electron microscopes in an exam context.

7. Exam Technique and Mark-Winning Guidance

STM questions on AQA papers tend to target three areas: the mechanism of tunnelling, the relationship between current and separation, and the role of piezoelectric control. Knowing the physics precisely — rather than vaguely — is what separates a top-band answer from a mid-band one.

Worked example: Answering a 6-Mark 'Explain the Principle of Operation of the STM' Question

Explain the principle of operation of the scanning tunnelling microscope. [6 marks]

1. A sharp conducting tip is brought to within approximately 1 nm of a conducting surface. A bias voltage is applied between tip and surface. — [B1] Sets up the physical arrangement. Always state the gap is of order 1 nm — this signals you know the scale involved.
2. Electrons have wave-like properties. Their wave functions decay exponentially through the vacuum gap. Because the gap is narrow enough, the wave function has a non-zero amplitude at the surface, giving a finite probability of electrons tunnelling across. — [B1] for wave function decay; [B1] for linking non-zero amplitude to finite tunnelling probability. These two points are often awarded separately.
3. The tunnelling current depends exponentially on the tip-surface separation. A decrease in separation of 0.1 nm approximately doubles the tunnelling current. — [B1] The word 'exponential' is essential here. Vague language such as 'the current changes significantly' will not gain this mark.
4. Piezoelectric transducers move the tip in x, y, and z directions with sub-nanometre precision in response to applied voltages. The tip is scanned across the surface in a raster pattern. — [B1] Naming piezoelectric transducers and their function is a distinct mark point.
5. In constant current mode, a feedback circuit adjusts the z-transducer voltage to keep the tunnelling current constant. The z-voltage required at each x-y position is recorded and plotted to produce an atomic-resolution map of the surface topography. — [B1] Specifying that it is the z-voltage that is recorded — not the current — distinguishes a top-band answer.

Answer: A complete 6-mark answer covers: (1) tip-surface geometry and bias voltage; (2) wave function decay through the vacuum gap; (3) non-zero tunnelling probability; (4) exponential current-separation dependence; (5) piezoelectric transducer control; (6) feedback mechanism and image formation in constant current mode.

Notice how each mark point maps to a distinct physical idea. Examiners award marks for specific, precise statements — not for general descriptions of 'a very sensitive instrument'. Every sentence in your answer should earn its place by naming a mechanism, a relationship, or a component.

The STM is a direct experimental demonstration that quantum tunnelling is real and measurable — it is not merely a theoretical curiosity. That connection between quantum wave mechanics and a working instrument is exactly the kind of evaluative point that distinguishes an A-grade response in the turning points section of the paper.