Knock-on damage

In plain words

Damage done by the beam of an electron microscope when fast electrons knock atoms out of the sample. Imaging with lower-energy electrons avoids much of it.

Going deeper

Electron microscopy of a monolayer is a collision experiment as much as an imaging one. Above a threshold energy, an imaging electron transfers enough momentum to knock an atom out, so the picture is partly of the damage the beam has already done.

Momentum, not heat

Knock-on damage is a direct mechanical process: an incoming electron scatters from a nucleus and transfers momentum. Because the electron is so much lighter, only a small fraction of its energy passes to the nucleus, but that fraction grows with the beam energy and falls with the mass of the target atom. If the energy the nucleus receives exceeds the displacement threshold – the energy needed to remove that atom from its site – the atom leaves.

This makes the damage sharply threshold-like rather than cumulative in the way heating or ionisation damage is. Below the threshold, more dose gives a better picture; above it, more dose gives more . In the is the vulnerable one, being much lighter than the metal, and the lighter the chalcogen the lower the voltage at which it starts to go.

Where the thresholds sit

calculations have produced displacement threshold energies for atoms in 21 different dichalcogenides, and converted them into the electron energies required to produce defects – which is the practical form, since a microscopist chooses an accelerating voltage, not a displacement energy.

The result worth remembering is that the familiar advice to “image at 80 kV” is not a guarantee. In the same study, high-resolution of MoS₂ at 80 keV showed vacancies forming under the beam, confirming the calculation rather than escaping it. Lower voltages help, but they also lower the resolution, and at some point the only sound approach is to bound the dose, image quickly, and treat defect densities measured after prolonged imaging as an upper limit on what was there to begin with.

Turning it into a tool

The flip side of controlled damage is controlled modification. Vacancies created by the beam are reactive sites, and they can be filled with impurity atoms from the residual gas or from deliberately supplied precursors, which dopes the material where the beam was pointed. The same calculations that predict where damage begins therefore also predict where this kind of patterning becomes possible.

It connects to the wider defect story: are the most commonly discussed defect in these materials, and it is worth keeping straight which ones were grown in and which were made by the microscope used to look for them. That is not a hypothetical confusion – the instrument used to count defects is also a machine for making them.

For specialists

Atom displacement caused by momentum transfer from high-energy electrons – for sulfur in TMDCs it becomes severe at high accelerating voltages.

Where this comes from

Two-dimensional transition metal dichalcogenides under electron irradiation: defect production and doping Komsa et al. · Physical Review Letters 109, 035503 (2012) cited by 1,174

Point defect

A flaw in a crystal that involves a single atomic site: an atom missing (a vacancy), an atom of the wrong kind in a site (a substitution, or an antisite when the crystal’s own two kinds of atom swap places), or an extra atom squeezed in between (an interstitial). Every real crystal has some. In a sheet a few atoms thick each one sits at the surface, so a handful of them can change how the material conducts, glows or reacts far more than in a thick crystal.

A defect confined to one or a few lattice sites – vacancy, interstitial, substitutional impurity, antisite or adatom – or a small complex of them. What it does is set by the levels it introduces: shallow levels dope, deep levels trap carriers and act as non-radiative recombination centres, and an isolated deep level in a wide gap can emit single photons. Formation energies and charge states depend on the chemical conditions of growth and on the Fermi level. In 2D materials every defect is a surface defect, less screened and more exposed to the environment, and densities of 10¹² to 10¹³ per cm² are typical of TMDC monolayers.

Full explanation

Chalcogenide, halide and pnictide

Family names for compounds, taken from the element in them that carries the negative charge. Chalcogenides contain sulfur, selenium or tellurium; halides contain fluorine, chlorine, bromine or iodine; pnictides contain phosphorus, arsenic, antimony or bismuth. Most layered crystals belong to one of these families, and the catalogue groups many of them that way.

Compounds named for their most electronegative constituent: chalcogenides of group 16 (S, Se, Te; oxides are conventionally counted apart), halides of group 17 (F, Cl, Br, I) and pnictides of group 15 (P, As, Sb, Bi; nitrides usually keep their own name). Down each group the anion grows larger and less electronegative, so bonding turns more covalent, gaps shrink and spin–orbit coupling grows. Chalcogenides give the MX₂ semiconductors and metals, halides mostly ionic, often magnetic insulators built from edge-sharing octahedra, and pnictides many metals, semimetals and the parents of the iron-based superconductors; mixed-anion compounds such as oxychalcogenides and chalcohalides combine two.

Full explanation

Density functional theory (DFT)

The workhorse calculation of materials physics. Rather than following every electron, it works with the electron density and a recipe for how electrons avoid one another – which makes a whole crystal cheap enough to compute, and makes the accuracy depend entirely on that recipe.

Ground-state electronic structure from the density, exact in principle by Hohenberg–Kohn and made practical by the Kohn–Sham equations with an approximate exchange–correlation functional. Two dimensions need care: a vacuum gap wide enough that periodic images stop interacting or a truncated Coulomb interaction, a dispersion correction for interlayer binding, and the knowledge that semi-local functionals underestimate gaps – hybrid functionals narrow that error at far higher cost, and quantitative gaps and optical spectra need GW and Bethe–Salpeter on top.

Full explanation