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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Monolayer
One single layer of a layered material. Two stacked layers are a bilayer; a handful are called few-layer. Many properties change between one, two and several layers, so the exact count matters.
A single structural layer of a layered crystal – one atom thick for graphene and hBN, three atomic planes for a TMDC such as MoS2 . Band structure, screening and symmetry depend on layer number (monolayer 2H-MoS2 lacks the inversion symmetry of the bilayer), so monolayer, bilayer and few-layer samples are distinct systems.
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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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Dangling bond
A bond left with nothing on the other end, on an atom at a surface that has lost the neighbour it was bonded to inside the crystal. Such bonds grab stray molecules and trap electrons, which is why ordinary surfaces are messy – and why layered crystals, whose sheets keep every bond inside themselves, split into faces that stay clean down to a single layer.
An unsaturated valence orbital at a surface, edge or defect where a covalent bond has been cut. In a bulk semiconductor such as silicon these states lie in the gap, trap charge and pin the Fermi level unless passivated by hydrogen or a grown oxide. The basal plane of a layered crystal has none, which is what allows van der Waals stacking without lattice matching and interfaces with few traps – and also why atomic layer deposition nucleates poorly on it. Edges, grain boundaries and vacancies do carry them, and are where 2D materials are chemically active.
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Electron hole
Usually just called a hole: the empty place an electron leaves behind in an otherwise full band. It behaves like a particle of its own with a positive charge. When a neighbouring electron steps into the gap, the gap moves the other way – like the empty space in a queue of cars, which travels backwards as each car edges forward. Many materials conduct mainly with holes, and chips need both kinds of carrier.
An unoccupied state in an otherwise filled band, usually near the valence-band maximum, treated as a quasiparticle with positive charge and a positive effective mass set by the band curvature. Holes carry the current in p-type semiconductors and give a positive Hall coefficient. In 2D semiconductors good p-type transport is harder to obtain than n-type, largely because metal contacts pin the Fermi level nearer the conduction band.
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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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Phonon
A packet of vibration travelling through a crystal – the way its atoms jiggle together. Sound travelling through a solid is made of phonons. They also carry heat, slow electrons down by jostling them, and are what Raman spectroscopy measures.
A quantised collective lattice vibration. 2D materials host flexural (out-of-plane) acoustic modes with quadratic dispersion; electron–phonon scattering sets intrinsic mobility limits, and phonon frequencies measured by Raman spectroscopy report layer number, strain and doping.
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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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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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Wafer and wafer-scale growth
A wafer is the thin, round slice of ultra-pure silicon – today 300 millimetres across – on which computer chips are made, hundreds at a time. Wafer-scale growth means making a 2D material evenly over a whole wafer rather than as scattered flakes, which is what any factory needs. For the best 2D materials that is still hard: a sheet one atom thick has to have the same thickness, quality and orientation from one edge of a dinner-plate-sized disc to the other.
The substrate format of the semiconductor industry – 200 and 300 mm silicon wafers, with sapphire, SiC and glass for particular processes – and the scale at which a material must be grown, transferred and processed to enter manufacturing. Wafer-scale growth of 2D materials uses CVD and MOCVD of TMDCs, CVD of graphene and hBN, and MBE, with targets of uniform layer number, low defect and grain-boundary density and, increasingly, a single orientation on vicinal sapphire or Cu(111). The obstacles are the growth temperature against the thermal budget of a finished wafer (growth on the back end of line needs to stay below about 400 to 450 °C), the transfer from growth substrate to device wafer, and metrology that confirms thickness and quality across the wafer at production speed.
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Atomic layer deposition (ALD)
A way to coat a surface one layer of atoms at a time. Two chemicals take turns: the first sticks to every free spot on the surface but not to itself, the excess is pumped away, and the second reacts with what stuck, leaving one thin layer of, say, aluminium oxide. Repeating the pair builds the film with a precision of a fraction of a nanometre, even over deep, steep structures. It is how the gate insulators of modern computer chips are made – and on 2D materials it runs into a problem: their clean surfaces give the first chemical nothing to stick to.
Thin-film growth by alternating, self-limiting surface reactions of two precursors separated by purges – for Al2 O3 trimethylaluminium and water, for HfO2 a hafnium amide or chloride with water or ozone – typically at 100 to 300 °C, giving about 0.1 nm per cycle with sub-nanometre control and conformal coverage. It is the standard route to high-κ gate dielectrics in silicon CMOS. On the dangling-bond-free basal planes of graphene, TMDCs and hBN the first precursor finds no reactive sites, so nucleation starts only at steps, defects and residues, giving islands and pinholes. Seed layers (evaporated and oxidised Al, molecular layers), ozone or plasma functionalisation, low-temperature physisorption, or transferred and native-oxide dielectrics are used instead, each at a cost in thickness, interface traps or channel damage.
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Chemical vapour deposition (CVD)
A way of growing thin films from gases. The ingredients arrive as vapour, react on a hot surface and leave a solid layer behind. It is how large sheets of graphene and other 2D materials are made for industry.
Growth of films from gas-phase precursors that react or decompose on a heated substrate. For 2D materials this includes graphene on copper foil, powder-source CVD of TMDCs from metal oxides and chalcogens, and metal-organic CVD (MOCVD) for wafer-scale TMDC films; grain size, nucleation density and residues are the usual quality limits.
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Disorder and localisation
Every real crystal has some disorder: missing or misplaced atoms, impurities, stray charges in the substrate, a random mixture of elements in an alloy. Electrons moving through it scatter off these imperfections, which raises the resistance. If the disorder is strong enough, electron waves become trapped in small regions – localised – and the material stops conducting, even if it would be a metal when perfect. In a sheet one atom thick, disorder in its surroundings matters especially.
Deviations from perfect periodicity – point defects, substitutional or alloy disorder, interface roughness, charged impurities and strain variations in the substrate – that scatter carriers and, beyond a threshold, localise their wavefunctions through interference (Anderson localisation). Scaling theory predicts that non-interacting electrons in two dimensions without spin–orbit coupling are localised by any disorder; its precursor, weak localisation, appears as a logarithmic rise of resistance at low temperature that a magnetic field suppresses, while strong spin–orbit coupling gives weak antilocalisation. In graphene on SiO2 , charged impurities break the sheet near charge neutrality into electron–hole puddles, which hBN encapsulation reduces. Strong disorder leads to hopping conduction, broadens optical lines and smears phase transitions; in frustrated magnets and correlated oxides, structural or cation disorder can mimic exotic states.
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Layer transfer
Moving an atomically thin layer from where it was made to where it is needed – from the copper foil it grew on to a silicon wafer, or from a flake on tape onto another flake. The layer is too thin to pick up on its own, so it is carried on a polymer film or a soft stamp, put down, and the carrier removed. Each step risks tears, wrinkles, trapped bubbles and a film of leftover polymer, which is why transfer is often the dirtiest step in making a 2D device.
The step that moves a 2D layer from its growth substrate or exfoliation source to a target substrate or stack. Wet transfer coats the layer with a supporting polymer, usually PMMA, detaches it by etching the growth substrate or by electrochemical bubbling, and floats it onto the target before the polymer is dissolved. Dry transfer picks layers up with a viscoelastic PDMS stamp or a polymer film such as polycarbonate, often using the van der Waals adhesion of a top flake, and releases them by heating. The costs are cracks and wrinkles, trapped water, hydrocarbons and polymer residue, strain and doping, and – at wafer scale – yield that compounds with every transfer, which is why growth directly on the target and transfer-free routes are pursued.
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Air stability
How long a material survives in ordinary air. Some 2D crystals keep for years on a shelf; others change within hours as oxygen, water and light attack them – and a measurement on a degraded sample says little about the real material.
Resistance to reaction with oxygen, water and light under ambient conditions, which often decides what can be measured at all. Few-layer black phosphorus takes up water and degrades visibly within hours; CVD-grown TMDC monolayers age over months, oxidising along grain boundaries and collecting organic contamination. Report exposure time and handling with any result, and move to glovebox transfer and encapsulation when a material’s stability is short.
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