Self-flux growth

In plain words

Growing crystals from a molten bath made mostly of one of the crystal’s own ingredients – extra selenium, for example – much as sugar crystals grow from a cooling syrup. Because the bath is part of the crystal already, no foreign solvent atoms get trapped inside.

Going deeper

Self-flux growth dissolves a compound in a melt of one of its own elements – here excess selenium for WSe₂ – and grows crystals by cooling very slowly. Because the solvent is part of the crystal, no foreign atoms can be taken up from it.

How it works

Flux growth dissolves the ingredients of a crystal in a molten solvent, the flux, well below the temperature at which the compound itself would melt. On slow cooling, the solubility falls and crystals nucleate and grow close to equilibrium, often with well-formed facets. fluxes such as tin, gallium or indium are common for intermetallic compounds.

Self-flux growth is the special case in which the flux is one of the crystal’s own elements: excess selenium for WSe₂, excess tellurium for tellurides. The components are sealed in a quartz ampoule, heated until they dissolve, held, and cooled over days or weeks. At the end, the remaining liquid is poured or spun off through a filter while still hot, or the leftover is removed afterwards by evaporation.

Why the crystals are cleaner

The most common alternative for crystals, , carries material through the gas phase with a transport agent such as iodine. It is faster, but the agent can end up inside the crystal, and growth happens further from equilibrium. A self-flux has no foreign solvent to incorporate, grows slowly, and keeps the crystal in chalcogen-rich conditions.

The difference is measurable. In a study of transition-metal diselenides combining scanning tunnelling and , the dominant intrinsic defects were metal and chalcogen antisites rather than , and controlling the synthesis cut their density from above 10¹³ to below 10¹¹ per cm², with emission efficiency rising about a hundred-fold.

Costs and pitfalls

The price is time and yield: a run can take weeks, and the crystals are usually millimetres across. Droplets of flux can stick to surfaces or be trapped inside, and they have to be removed before . Not every compound works: the must allow the wanted phase to crystallise first from a melt rich in one component.

Chalcogens have high vapour pressures at growth temperatures, so sealed ampoules are under pressure and can burst; thick-walled quartz, limited fill amounts and careful heating are part of the method. Crystal quality is judged by defect counts from , linewidths and, for metals, the ratio of room-temperature to low-temperature resistance.

For specialists

Crystal growth from a melt rich in one of the crystal’s own constituents, such as excess selenium for WSe₂.

Where this comes from

Growth of single crystals from metallic fluxes Canfield and Fisk · Philosophical Magazine B 65, 1117 (1992) cited by 794
Approaching the intrinsic limit in transition metal diselenides via point defect control Edelberg et al. · Nano Letters 19, 4371 (2019) cited by 246

Metal, semimetal and insulator

The three basic ways a solid treats electricity, set by how its electrons fill the energies open to them. In a metal they fill a band of energies only partly, so the smallest push sets them moving, and it conducts at any temperature. In an insulator they fill a band completely and a wide gap separates it from the next, so nothing can move. A semimetal sits in between: two bands just touch or overlap a little, leaving a small number of mobile electrons and holes. NbSe₂ is a metal, graphene a semimetal, hBN an insulator.

A classification by where the Fermi level falls in the band structure. In a metal it crosses a partly filled band, leaving a Fermi surface, a carrier density of order one per atom (about 10²² cm⁻³) and a resistivity that falls on cooling. In a band insulator it lies in a gap of several electronvolts; a semiconductor is an insulator whose gap is small enough to be doped or gated. A semimetal has a slight overlap between conduction and valence bands (graphite, bismuth, bulk WTe₂) or bands that touch at isolated points (graphene), giving low and nearly equal densities of electrons and holes. Interactions can open gaps that band theory does not predict: Mott insulators from half-filled bands, excitonic insulators from semimetals.

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

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

Phase transition

A sudden change in the state of a material when temperature, pressure or another control is varied – ice melting into water, a magnet losing its magnetism when heated, a metal becoming a superconductor when cooled. Each happens at a definite transition temperature. In quantum materials, transitions mark where new kinds of order appear: charge density waves, magnetism, superconductivity, ferroelectricity. A map of which state appears where, against temperature and a second knob such as doping or pressure, is a phase diagram.

A non-analytic change of thermodynamic state at a transition point, described by an order parameter that vanishes in the disordered phase and is finite in the ordered one – magnetisation, polarisation, charge-density-wave amplitude, superconducting gap. First-order transitions show latent heat, phase coexistence and hysteresis; continuous ones show a diverging correlation length and susceptibility and universal critical exponents set by dimension and symmetry (Landau theory, the renormalisation group). In two dimensions fluctuations are stronger: the Mermin–Wagner theorem forbids breaking a continuous symmetry at finite temperature, leaving anisotropic, Ising-like order or Berezinskii–Kosterlitz–Thouless quasi-order. Transition temperatures change with layer number, gating, strain and twist, which makes 2D materials tunable platforms for phase diagrams, including quantum phase transitions driven at zero temperature by non-thermal parameters.

Full explanation

Scanning tunnelling microscopy (STM)

A needle sharpened to a single atom is brought so close to a surface that electrons tunnel across the gap – a quantum effect by which they pass through a barrier they could never climb over. The current maps the surface atom by atom, and how it changes with voltage tells you which energies electrons are allowed to have at that exact spot.

Tunnelling between a sharp tip and a conducting surface, giving atomic-resolution topography and, in spectroscopy mode, the local density of states against energy. On 2D materials it resolves defect levels, moiré potentials, edge modes and quasiparticle gaps site by site. The sample has to be clean and conducting, so it is run on epitaxial films or on flakes placed on graphite, in vacuum and often at cryogenic temperature.

Full explanation