Two-dimensional (2D) material
A crystal so thin that it is only one or a few atoms thick – a sheet rather than a lump. Graphene, a single layer of carbon atoms, is the best-known example: about 300,000 of its layers stacked up would be as thick as one sheet of paper. At that thickness a material can conduct, glow or respond to magnetism quite differently from the same substance in bulk.
A crystalline material whose thickness is one or a few unit cells, so that electrons, phonons and other excitations are confined in one direction. Most are obtained from layered bulk crystals in which strong in-plane bonds coexist with weak van der Waals bonding between layers.
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Dispersions and inks
Flakes of a 2D material floating in a liquid, and that liquid used like paint or ink. Stirring or shaking a layered crystal in the right liquid splits it into flakes that stay suspended; spinning away the thick ones leaves a dispersion of thin flakes, which can be sprayed, printed or coated onto almost anything. It is the cheapest way to make 2D materials by the kilogram, but the flakes are small and overlap in a film, so they never match a perfect continuous sheet.
Colloidal suspensions of nanosheets made by liquid-phase exfoliation of layered crystals in solvents whose surface energy matches the crystal (NMP, DMF, cyclohexanone) or in water with surfactants, by electrochemical exfoliation, or – for graphene oxide and MXenes – by chemical routes that leave hydrophilic surfaces. Centrifugation sorts flakes by size and thickness (liquid cascade centrifugation), and optical spectra give mean thickness and lateral size in the liquid. Formulated as inks with tuned viscosity and surface tension, they are inkjet-, screen- or spray-printed or coated into films limited by flake–flake junctions, porosity, residual solvent or surfactant, and oxidation in storage. Powders and dispersions sold as graphene range from monolayers to graphite, which ISO/TS 21356-1 addresses by defining how they are characterised.
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Chemical bond
The glue that holds atoms together. In a covalent bond two atoms share electrons, as within a sheet of graphene; in an ionic bond one atom hands electrons to another and the resulting charges attract, as in table salt; in a metal the outer electrons are shared by all the atoms at once. Much weaker van der Waals forces hold molecules and the layers of a layered crystal together. A 2D material is a crystal with strong bonds within its layers and only weak ones between them – which is why it can be peeled.
The attractive interactions that hold atoms in molecules and solids, classified by how electrons are shared: covalent bonds, from overlapping orbitals holding shared electron pairs, strong and directional (sp2 carbon, Mo–S in TMDCs); ionic bonds, from electron transfer and electrostatic attraction (halides, oxides); metallic bonding, with electrons delocalised in a partly filled band; and the weak, non-directional van der Waals interaction from correlated charge fluctuations, besides hydrogen bonds. Real bonds are mixtures, characterised by electronegativity differences and charge analyses. Layered crystals combine in-plane bonds of several electronvolts with interlayer binding of only about 20 meV per Å2 (some 0.3 J/m2 ), the criterion high-throughput screens use to identify exfoliable compounds.
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Coordination polyhedron
The small shape traced by the atoms that surround a metal atom in a crystal. In many layered materials each metal sits inside an octahedron – six neighbours, three above and three below, turned against each other – or a trigonal prism, where the upper three sit right above the lower three. That one turn can make the same compound a semiconductor or a metal.
The polyhedron formed by an atom’s nearest neighbours; their number is its coordination number. In MX2 layers the metal is either trigonal prismatic (D3h, as in 2H-MoS2 ) or octahedral (D3d, as in 1T-TaS2 , and distorted in 1T′-WTe2 ), and the ligand-field splitting of the d levels in each geometry, together with the d-electron count, decides whether the layer is a semiconductor or a metal. Halides and many oxides build layers from MX6 octahedra sharing edges (CrI3 , RuCl3 ) or corners (layered perovskites), and that connectivity sets the lattice – honeycomb, triangular or square – that the metal ions form.
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Quasiparticle gap versus optical gap
Two answers to ‘how much energy does it take to excite this material?’. Adding a free electron and a free hole costs more; creating a bound electron–hole pair with light costs less, and in 2D materials the difference is large.
The quasiparticle gap is the energy to add an electron and a hole independently; the optical gap is smaller by the exciton binding energy.
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Nanosheet
A general word for a very thin sheet of material, often just a few atoms thick and up to a few micrometres – thousandths of a millimetre – across. It is used especially for flakes made in large quantities in liquids.
A particle whose lateral dimensions far exceed its nanometre-scale thickness; the term is used especially for liquid-exfoliated and chemically derived dispersions, whose lateral-size and thickness distributions must be specified rather than assumed. In transistor engineering ‘nanosheet’ also denotes the stacked silicon channel sheets of gate-all-around devices.
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MXene
A large family of 2D carbides and nitrides – thin sheets of metal atoms bonded to carbon or nitrogen. They are made by chemically etching one kind of atom out of a bulk crystal, and they conduct electricity well, which makes them useful for batteries, coatings and electromagnetic shielding.
Two-dimensional transition-metal carbides, nitrides and carbonitrides Mn+1 Xn Tx , obtained by selectively etching the A-element layers from MAX phases, commonly in fluoride-containing acids. Surface terminations Tx (–O, –OH, –F, –Cl) set their properties; Ti3 C2 Tx is the most studied, with metallic conductivity and hydrophilic surfaces that allow water-based processing.
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Etching
Removing material on purpose, with a chemical or a plasma. In chip-making it carves patterns: a stencil of light-sensitive polymer protects some areas while a plasma eats away the rest. For 2D materials etching has three jobs: cutting flakes into shaped devices, thinning a crystal one layer at a time, and – for MXenes – making the material in the first place, by dissolving one kind of atom out of a layered ceramic so that the remaining sheets come apart.
Material removal by chemical reaction in a liquid (wet etching) or by reactive and physical processes in a plasma (dry etching, including reactive ion etching with oxygen-, fluorine- or chlorine-based chemistries, and atomic layer etching). For 2D materials it patterns channels and Hall bars through resist masks – oxygen plasma for graphene, fluorine-based plasmas for hBN and TMDCs – exposes edges in encapsulated stacks for edge contacts, thins crystals layer by layer, and selectively removes the A element, usually aluminium, from MAX phases with hydrofluoric acid or fluoride-containing acids to make MXenes. Its side effects are edge roughness and damage, residues, doping and plasma-induced defects in neighbouring layers, so the etched edge and its electronic states have to be considered in narrow devices.
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Fermi-level pinning
When the junction between a metal and a semiconductor behaves the same whichever metal is used. The choice of metal ought to set the height of the energy step electrons must climb to get into the semiconductor, but stray electron states at the interface take up charge and hold the step at much the same height every time. It makes low-resistance contacts hard to engineer.
The fixing of the Fermi level at a metal–semiconductor interface by interface states, so the Schottky barrier barely depends on the metal work function.
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Semiconductor
A material whose ability to carry electricity can be switched on and off, for example by an applied voltage. That switching is what every transistor in a computer chip relies on. Silicon is the classic example; several 2D materials, such as MoS2 , are semiconductors too.
A material with a band gap of a few electronvolts or less, whose conductivity can be tuned over many orders of magnitude by doping, gating, temperature or light. 2D semiconductors attract interest because their sub-nanometre thickness preserves electrostatic gate control in very short channels.
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Topological phase
A state of matter told apart not by how its atoms are arranged but by a whole number that describes how its electrons’ waves twist across the crystal – the way a doughnut differs from a ball by its one hole. A whole number cannot change a little, so what it guarantees, such as current running along an edge without loss, survives defects and dirt until the band gap itself closes.
A gapped phase characterised by a topological invariant of its occupied bands – a Chern number, a Z2 index, a winding number – that cannot change under deformations that keep the gap open and any protecting symmetry intact. Where regions with different invariants meet, the gap must close, which forces boundary states: chiral edge channels in Chern insulators, helical ones in quantum spin Hall insulators, Fermi arcs in Weyl semimetals, Majorana modes in topological superconductors. Topological order in the strict sense – the long-range entanglement of fractional quantum Hall states and spin liquids – is a distinct, stronger notion.
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Bubbles and wrinkles
Flaws that appear when a thin layer is laid on a surface or on another layer. Water and dirt trapped underneath gather into small bubbles that push the layer up, and a layer with more length than the surface beneath it folds into wrinkles. Both stretch or bend the layer where they sit and change how it conducts and glows there, so careful stacking keeps them away from the part that is measured.
Blisters of trapped adsorbates – mainly hydrocarbons and water – between transferred or stacked layers, from nanometres to micrometres across, and ridges where compressive strain from transfer or thermal-expansion mismatch is relieved out of plane. Van der Waals adhesion squeezes contamination into bubbles, leaving atomically clean interfaces between them, and the bubbles take a universal shape set by adhesion and in-plane stiffness. Both strain the layer locally, shifting band edges, Raman modes and emission, and both scatter carriers.
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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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Raman spectroscopy
Shining a laser on a material and measuring the tiny fraction of light that comes back at slightly different colours. The shifts reveal how the atoms vibrate, which tells researchers how many layers a flake has and whether it is strained or damaged.
Inelastic light scattering that measures phonon energies. In 2D materials peak positions, widths and intensity ratios – graphene’s G and 2D bands, or the E′ and A′1 modes of TMDCs – report layer number, strain, doping and defect density; laser heating and substrate interference must be controlled.
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X-ray photoelectron spectroscopy (XPS)
X-rays knock electrons out of the atoms at a surface, and the energies those electrons carry say which elements are present and what they are bonded to. It is the standard check that a film really is the compound you wanted and has not oxidised.
Core-level photoemission giving elemental composition and chemical state from the top few nanometres. On 2D films it fixes stoichiometry, detects oxidation and substitutional impurities, and follows doping through rigid core-level shifts. Binding-energy referencing is the usual source of error – adventitious carbon at 284.8 eV is not a reliable standard on a semiconductor – and charging has to be controlled on insulating substrates.
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Charge carrier mobility
How easily electrons, or the gaps they leave behind (holes), move through a material when pushed by a voltage. Higher mobility means faster, more efficient electronics – but it is easily ruined by dirt, defects and a poor substrate.
Drift velocity per unit electric field, usually quoted in cm2 /V·s. In 2D materials it is limited intrinsically by phonon scattering and extrinsically by charged impurities, roughness, remote phonons and disorder; field-effect values extracted from two-terminal devices can be distorted by contact resistance.
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