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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Photon
The smallest possible amount of light – one indivisible packet of it. The packets of a given colour all carry the same energy, and blue ones carry more than red: that is why ultraviolet light gives you sunburn and red light, however bright, does not. A semiconductor absorbs only photons with enough energy to cross its band gap and gives light back at about the gap’s energy – which is why LEDs of different colours are made from different semiconductors.
The quantum of the electromagnetic field, with energy E = hν and momentum h/λ but no mass or charge. Visible photons carry about 1.7–3.1 eV, comparable to the band gaps of semiconducting TMDCs, but a momentum far smaller than the crystal momenta across the Brillouin zone, so optical transitions are vertical and an indirect gap needs a phonon to make up the difference. Single-photon emission is established by antibunching in photon-correlation measurements.
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Band gap
The energy an electron needs to jump from a full band, where it is stuck, into an empty one where it can move and carry current – like a car in a packed car park, which can only drive off once it is lifted to the empty deck above. Metals have no gap and always conduct; insulators have a large gap and hardly conduct; semiconductors sit in between, which is what makes them switchable.
The energy range between the valence-band maximum and the conduction-band minimum in which a crystal has no electronic states. It is direct when both extrema lie at the same crystal momentum and indirect otherwise; monolayer MoS2 is direct while bulk MoS2 is indirect. In 2D the quasiparticle and optical gaps differ strongly because excitons are tightly bound.
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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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Exciton
An electron paired with the ‘hole’ it left behind – the empty place, which acts like a positive charge. The two attract each other and form something like a tiny atom. In very thin materials these pairs hold together unusually strongly, so they dominate how the material absorbs and emits light – even at room temperature.
A bound state of a conduction-band electron and a valence-band hole. In 2D semiconductors reduced dielectric screening raises binding energies to hundreds of meV in freestanding TMDC monolayers, so excitons dominate optical spectra at room temperature and follow a non-hydrogenic Rydberg series.
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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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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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Strain
Stretching or squeezing a material. Because 2D materials can be stretched much further than ordinary crystals before breaking, strain can be used as a knob to change their colour, conductivity or band gap.
Relative deformation of a lattice. 2D crystals sustain elastic strains of several percent, with graphene exceeding 10 % in nanoindentation, and strain shifts band edges, Raman modes and exciton energies. Unintended strain from substrates, bubbles and transfer is a common confounder in measurements.
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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 Bi2 SeO5 on Bi2 O2 Se, 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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Trion
An exciton that has picked up an extra electron or hole, which makes it electrically charged. It shows up as a separate, slightly lower-energy glow when a thin semiconductor carries extra charge.
A charged exciton (an exciton bound to an extra electron or hole), visible as a lower-energy PL peak in doped monolayers.
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Doping
Adding a small amount of extra electrons to a material, or taking some away to leave ‘holes’ that act as positive charges, to change how well it conducts. In silicon this is done by mixing in foreign atoms; in 2D materials it can also be done with a nearby voltage, molecules on the surface, or the material underneath.
Control of carrier type and density by substitutional impurities, surface charge transfer, electrostatic gating or the dielectric environment. Stable, spatially localised substitutional doping remains difficult in 2D semiconductors, and surface-transfer doping is often unstable in air.
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Gating
Changing a material by putting a voltage on a nearby electrode – a gate – separated from it by an insulator. The voltage pulls electrons into the material or pushes them out, as in every transistor. Because a 2D material is so thin, the gate reaches all of it, so the number of electrons can be dialled up and down continuously: a single device can be turned from insulator to metal, its magnetism strengthened, or superconductivity switched on. Two gates, above and below, can also apply an electric field across the layer.
Electrostatic control of carrier density and electric field through a gate coupled capacitively across a dielectric: the induced density equals the gate capacitance times the voltage beyond threshold, divided by the electron charge, reaching a few 1013 cm−2 with oxide or hBN gates before breakdown. Dual gating sets density and perpendicular displacement field independently, opening the gap of bilayer graphene and tuning moiré flat bands. Ionic-liquid and solid-electrolyte gating form an electric double layer about a nanometre thick and reach 1014 –1015 cm−2 , enough to induce superconductivity in MoS2 or raise the Curie temperature of Fe3 GeTe2 , but can intercalate or react electrochemically and work only while the ions are mobile. Hysteresis from traps, contact effects and quantum capacitance are the usual caveats.
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Charge transfer
Electrons moving from one material to its neighbour simply because they are more comfortable there. It is how a layer gets doped without adding a single impurity atom to it – the charge comes from the molecule, substrate or layer next door.
Equilibration of electrochemical potential across an interface, moving electrons to whichever side has the deeper states and leaving a dipole and band bending behind. It dopes 2D layers without substitutional disorder, from adsorbed molecules and substrate surface states to the partner layer in a type-II stack, where photoexcited carriers separate in tens of femtoseconds – faster than they recombine, which is what makes such stacks useful for light harvesting and detection.
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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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Encapsulation
Sealing a delicate 2D material between protective layers so that air, water and dirt cannot reach it. Wrapping it in boron nitride, itself a 2D material, is the standard way to get the cleanest results.
Enclosure of a 2D layer between barrier layers – most often hexagonal boron nitride for the highest quality, or deposited oxides and polymers for larger areas – to suppress oxidation, adsorbates, charge disorder and substrate roughness. It also seals in whatever contamination was present when it was applied.
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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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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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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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Dielectric screening
The way a material weakens the pull between two charges inside it: its own electrons shift slightly and partly cancel the field between them. A sheet one atom thick has almost nothing around it to do this, so charges in it attract each other far more strongly than in a thick crystal – which is why light makes tightly bound pairs in 2D materials, and why whatever a sheet rests on changes its properties.
The reduction of the Coulomb interaction by the polarisation of bound electrons and ions and, in metals and doped layers, by free carriers, described by a dielectric function ε(q, ω). In a monolayer the field lines between distant charges run through the surroundings, so ε(q) approaches 1 as q → 0 and the screening is non-local and set by the environment. Exciton binding energies reach hundreds of meV, and a change of substrate or encapsulation shifts the quasiparticle gap by 100 meV or more while the optical gap barely moves.
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