Scanning tunnelling microscopy (STM)

Also called scanning tunnelling spectroscopy

In plain words

A needle sharpened to a single atom is brought so close to a surface that electrons tunnel across the gap – a quantum effect by which they pass through a barrier they could never climb over. The current maps the surface atom by atom, and how it changes with voltage tells you which energies electrons are allowed to have at that exact spot.

Going deeper

The tunnelling current depends so steeply on distance that the last atom of the tip does almost all the work, giving atomic resolution. Held at one spot while the voltage is swept, the tip measures the local density of states, including the quasiparticle gap and states that defects place inside it.

How it images

A bias voltage is applied between a sharp metal tip and a conducting sample, and the tip is brought within a nanometre of the surface. Electrons tunnel across the vacuum gap, and the current falls by roughly a factor of ten for every 0.1 nm of extra distance, so almost all of it flows through the single atom closest to the surface. That is the origin of atomic resolution, which earned Binnig and Rohrer the 1986 Nobel Prize.

In the usual constant-current mode, a feedback loop adjusts the tip height to keep the current fixed as it scans. The resulting image mixes geometry and : bright means more states available to tunnel into or out of at that voltage, not simply higher. A defect can look like a bump at one bias and a hole at another.

Spectroscopy: energy at a single spot

Stopping the tip over one point and sweeping the bias gives scanning tunnelling spectroscopy. The derivative dI/dV, measured with a lock-in amplifier, is roughly proportional to the sample’s local at the corresponding energy. Negative sample bias probes filled states, positive bias empty ones.

STS therefore measures the directly – the energy to add or remove an electron – rather than the optical gap. Measurements on on graphene found gaps far larger than their optical gaps, a direct view of strong binding and of the screening a provides. Maps of dI/dV at chosen energies show defect states, , and , and interference patterns around defects reveal band structure.

Practical limits

The sample has to conduct. Semiconducting monolayers are placed on graphite or graphene, or contacted through graphene in a device; thick block tunnelling. The surface must be clean, so samples are cleaved or grown in vacuum or annealed there, and measurements run in ultrahigh vacuum, usually at low temperature. Temperature also sets energy resolution, about a millielectronvolt at 4 K.

The tip is a source of error. Double tips repeat features, a tip that changes during a scan alters the contrast, and the electric field of the tip bends the bands of a , shifting the apparent . Images cover small areas, so defect densities and domain sizes need many images before they are representative.

For specialists

Tunnelling between a sharp tip and a conducting surface, giving atomic-resolution topography and, in spectroscopy mode, the local density of states against energy. On it resolves defect levels, moiré potentials, edge modes and quasiparticle gaps site by site. The sample has to be clean and conducting, so it is run on films or on placed on graphite, in vacuum and often at cryogenic temperature.

Where this comes from

Surface studies by scanning tunneling microscopy Binnig et al. · Physical Review Letters 49, 57 (1982) cited by 4,743
Giant bandgap renormalization and excitonic effects in a monolayer transition metal dichalcogenide semiconductor Ugeda et al. · Nature Materials 13, 1091 (2014) cited by 1,870

Band structure

The map of the energies an electron may have in a crystal. The allowed energies come in ranges called bands, with forbidden gaps between them – like the decks of a multi-storey car park, where a car can stand on a deck but never between two. Whether a material conducts, gives off light or lets its electrons move easily can all be read from it, and in a layered material the map changes with the number of layers.

The electron energies E(k) of a periodic crystal as functions of crystal momentum, one branch per band, usually plotted along high-symmetry lines of the Brillouin zone. Band edges, slopes and curvatures give the gap, group velocities and effective masses; crossings and inversions give the topology. In layered crystals interlayer hybridisation makes it depend on thickness: the valence-band maximum of MoS₂ moves from Γ in the bulk to K in the monolayer, turning an indirect gap into a direct one.

Full explanation

Density of states

A count of how many states electrons can occupy at each energy – like a chart of how many seats each row of a stadium has. Where the count is high, many electrons can join in whatever happens at that energy; inside a band gap it is zero. Flat bands pile many states onto one energy, which is why they favour unusual behaviour, and a scanning tunnelling microscope can measure the count at a single spot.

The number of single-particle states per unit energy (and per unit area in 2D), g(E) = Σ_n ∫ δ(E − ε_n(k)) d²k/(2π)². For a parabolic 2D band it is constant, m*/(2πħ²) per spin and valley; for graphene’s Dirac cone it rises linearly from zero; van Hove singularities appear at saddle points. Its value at the Fermi level sets the electronic heat capacity, Pauli susceptibility, screening and the tendency to Stoner or superconducting instabilities; scanning tunnelling spectroscopy measures the local density of states through dI/dV.

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Substrate

The base a thin film or flake sits on – often a polished slice of silicon, glass or sapphire. For a crystal one atom thick, the substrate is not just a table: its bumps, stray charges and vibrations reach right into the sheet and change how it conducts and glows. That is why the same material can behave differently on two substrates, and why the flattest, cleanest one – boron nitride – gives the best results.

The material beneath a 2D layer. It acts on the layer through surface roughness, charged impurities, surface optical phonons, dielectric screening, strain and charge transfer, and during growth it sets orientation through epitaxy. Replacing SiO₂ with hexagonal boron nitride, which is atomically flat and nearly free of dangling bonds and charge traps, improved the mobility and charge homogeneity of graphene by close to an order of magnitude.

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Edge state

Electrons that can only travel along the border of a sheet while its interior stays insulating. In a topological material these border lanes are guaranteed to exist, and in the cleanest cases they carry current without losing energy to scattering.

States localised at a sample boundary and dispersing inside the bulk gap. In quantum Hall and Chern insulators they are chiral, one-way channels; in a quantum spin Hall insulator they are helical, counter-propagating with opposite spins and protected by time reversal, giving e²/h per edge in the ideal case – monolayer 1T′-WTe₂ keeps that edge conduction up to about 100 K. Trivial edges carry states too, from dangling bonds, reconstructions and graphene’s zigzag edge, so the evidence for topology is quantised conductance and its magnetic-field dependence, not conduction at the edge alone.

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Dielectric

An electrical insulator used for what it does in an electric field rather than for carrying current – the thin layer inside a capacitor, or the insulator that separates a transistor’s gate from its channel. A good dielectric blocks current completely, withstands a strong field without breaking down and, for gates, has a high permittivity, so that a voltage on the gate pulls many charges into the channel. For 2D transistors the dielectric is as hard to get right as the 2D layer itself.

An insulator characterised by its permittivity κ, band gap and band offsets to the channel, breakdown field, leakage, and density of fixed charge and traps at the interface and in the bulk (border traps). Silicon technology moved from SiO₂ (κ ≈ 3.9) to hafnium-based high-κ oxides (κ ≈ 20–25) to keep gate control at sub-nanometre equivalent oxide thickness. For 2D channels, hBN gives clean, trap-poor interfaces but a low κ of about 3–4 and is hard to grow at wafer scale; ALD oxides nucleate poorly on basal planes; alternatives include crystalline CaF₂, native oxides such as Bi₂SeO₅ on Bi₂O₂Se, and molecular crystals. Reliability – hysteresis, bias-temperature instability and time-dependent breakdown – is the yardstick for any dielectric meant for products.

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Epitaxy

Growing a crystal on top of another so that its atoms line up with the ones underneath and carry on the pattern of the crystal below. It is how most semiconductor chips, lasers and LEDs are built, and it works cleanly only when the two crystals’ atomic spacings match closely – a restriction that layered 2D materials largely escape.

Growth of a crystalline film whose orientation is fixed by a single-crystal substrate: homoepitaxy on the same material, heteroepitaxy on a different one. A covalently bonded film strains to the substrate’s lattice until, beyond a critical thickness that falls steeply with mismatch, misfit dislocations relax it, so mismatches above a few percent permit only very thin coherent films. In van der Waals epitaxy the film is aligned but not bonded and mismatch is largely irrelevant; in remote epitaxy the substrate’s potential aligns the film through a graphene interlayer.

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