Doping

Everyday term

In plain words

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 it can also be done with a nearby voltage, molecules on the surface, or the material underneath.

Going deeper

Four routes to adding carriers to a 2D semiconductor. Only the first changes the crystal itself; the other three act from outside, which is possible because every atom of a monolayer is at its surface – and which is why doping can also arrive uninvited from the air or the substrate.

Four ways to add carriers

Substitution puts a foreign atom on a lattice site: niobium on a molybdenum site in MoS₂ brings one electron fewer and makes it , rhenium one more and makes it n-type. uses something on the surface: alkali metals such as potassium donate electrons, while strongly electron-withdrawing molecules or NO₂ take them. adds carriers with a voltage across a thin , without changing the chemistry at all. The and the surroundings contribute whether anyone wants them to or not, through trapped charges, adsorbed water and the of neighbouring layers.

Native defects add their own share. As-grown MoS₂ is usually n-type, which is often attributed to , although impurities and the substrate are also suspected.

Why silicon’s recipe does not transfer

Silicon is doped by implanting ions and annealing the damage away. Each phosphorus atom then gives up its electron easily, because the surrounding crystal screens its charge well. An atomically thin layer changes all of this. Implantation sputters and damages a sheet that is only a few atoms thick; there is little material around a dopant to screen it, so its carrier is bound more tightly and fewer dopants are ionised at room temperature; and every dopant sits in the plane the current flows through, so it also scatters carriers. In very small devices the number of dopant atoms becomes small enough that device-to-device variation grows. For these reasons, electrostatic and surface doping are used far more in 2D devices than in silicon.

Doping where it counts

The place where doping matters most is often under the contacts. Heavily doping the beneath a metal thins the Schottky barrier until carriers tunnel through it, which lowers ; NO₂-doped contacts on WSe₂ were an early example. Split gates beneath one create p–n junctions electrostatically, with no chemistry at all.

Surface doping is reversible, which makes it easy to try and hard to keep: molecules desorb, react with air or migrate, unless the layer is sealed. Doping can be tracked optically. Graphene’s G peak stiffens when either electrons or holes are added, the out-of-plane A₁g mode of MoS₂ softens with electron doping, and in emission the , or trion, grows at the expense of the neutral as carriers are added.

For specialists

Control of carrier type and density by substitutional impurities, surface charge transfer, electrostatic gating or the . Stable, spatially localised substitutional doping remains difficult in 2D semiconductors, and surface-transfer doping is often unstable in air.

Where this comes from

High-performance single layered WSe₂ p-FETs with chemically doped contacts Fang et al. · Nano Letters 12, 3788 (2012) cited by 1,870

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.

Full explanation

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 Fe₃GeTe₂, 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.

Full explanation

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.

Full explanation

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.

Full explanation

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.

Full explanation