Bridgman growth

Also called Bridgman–Stockbarger method

In plain words

A way to grow a large from a melt. The ingredients are melted in a sealed tube with a pointed bottom, and the tube is lowered slowly out of the hot part of a furnace. The melt freezes first in the tip, where one small crystal wins out, and the rest of the melt freezes onto it as the tube moves on. It gives the big crystals, a centimetre or more across, from which of InSe, Bi₂Se₃ or PbI₂ are peeled.

Going deeper

A sealed ampoule is lowered slowly from the hot zone of a furnace into the cool zone, so the melt freezes from its pointed tip upwards. Several grains start in the tip, but only one survives to fill the ampoule, giving a single crystal large enough to peel many flakes from.

How it works

The ingredients are sealed in an ampoule, usually of quartz under vacuum, whose bottom tapers to a point. The furnace has a hot zone above the melting point and a cooler zone below it. Lowering the ampoule through the gradient, or moving the furnace instead, freezes the melt from the tip upwards. Several small grains form in the tip, but the narrow cone lets only the best-placed one survive, and it seeds the rest of the crystal.

Percy Bridgman described the method in 1925 for metals such as bismuth and antimony; Donald Stockbarger added a second furnace zone with a baffle between the two in 1936, which keeps the gradient steep and flat. Vertical and horizontal versions are both used. The same Bridgman made black phosphorus in 1914, but by squeezing white phosphorus at high pressure, not by this method.

What it is good for

Bridgman growth is quick and simple and gives large crystals: boules a centimetre or more across, from which many flakes can be exfoliated. It is the usual route to bulk InSe, GaSe, Bi₂Se₃ and Bi₂Te₃, to SnSe and its relatives, to BiTeI and to PbI₂.

It works best for compounds that melt congruently, turning into a liquid of the same composition. Those that decompose on melting, InSe among them, have to be grown from a melt with a little more of one element, and their crystals vary in composition from one end to the other – one reason InSe samples from different sources behave differently.

Its weaknesses

A crystal frozen from a melt keeps what the melt held. Impurities and any excess of one element are pushed ahead of the growing crystal and pile up along the boule, so the composition drifts from the first end to freeze to the last. The high temperature drives off volatile elements, and the they leave behind dope the crystal; the stress of cooling a large crystal leaves and, in some materials, mixed .

For the cleanest layered crystals, and , which grow slowly at lower temperature from a solution or a gas, usually do better, at the price of smaller crystals and longer runs. Reporting the growth method and the measured composition alongside the results is what makes samples comparable.

For specialists

Directional solidification of a melt in a sealed ampoule, usually conical at the bottom, moved through a temperature gradient at about a millimetre per hour (Bridgman, 1925; Stockbarger’s two-zone furnace with a baffle that sharpens the gradient, 1936). Competitive growth in the tip selects one grain, which seeds the boule. It suits compounds that melt congruently, such as Bi₂Se₃, Bi₂Te₃, SnSe and PbI₂; incongruently melting ones such as InSe are grown from off- melts. It is fast and gives large crystals, but freezes in the segregation, stoichiometry drift, vacancies and stacking of growth from the melt, so its crystals are often less pure and less ordered than those from flux or vapour transport.

Where this comes from

Certain physical properties of single crystals of tungsten, antimony, bismuth, tellurium, cadmium, zinc, and tin Bridgman · Proceedings of the American Academy of Arts and Sciences 60, 305 (1925)
The production of large single crystals of lithium fluoride Stockbarger · Review of Scientific Instruments 7, 133 (1936)
High electron mobility, quantum Hall effect and anomalous optical response in atomically thin InSe Bandurin et al. · Nature Nanotechnology 12, 223 (2017) cited by 1,359

Single crystal

A piece of material in which the atoms are lined up in one unbroken pattern from one side to the other, with every row pointing the same way. Most solids are not like that: they are polycrystalline, made of many small crystals stuck together at random angles, like a pavement of tiles laid every which way. The boundaries between those grains scatter electrons, weaken the material and blur measurements, so physics experiments and the best devices want single crystals – a centimetre-sized block to peel flakes from, or a sheet grown across a whole wafer in one orientation.

A solid whose lattice is continuous and uniformly oriented throughout, without grain boundaries – unlike polycrystalline material, made of misoriented grains, or amorphous solids without long-range order. Bulk single crystals of layered compounds are grown by chemical vapour transport, flux or Bridgman methods and are the usual source of exfoliated flakes; their quality is judged by X-ray rocking-curve widths, the residual resistivity ratio and the absence of twins and stacking faults. Large single-crystal films grow either from one nucleus or from aligned nuclei that merge without boundaries, as for graphene on Cu(111) or Ge(110) and MoS₂ or hBN on vicinal sapphire or copper, where substrate steps fix one orientation and remove the twin boundaries that two antiparallel orientations would form.

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

Stacking fault

A mistake in the order in which a crystal’s layers are stacked – one layer shifted or turned from where the pattern says it should sit, like one misaligned sheet in a neatly squared stack of paper. Layered crystals get them easily, because the weak bonds between layers barely care. But the stacking can change a material’s magnetism, symmetry or electronic behaviour, so faults can make one crystal behave unlike the next.

A planar defect in which the stacking sequence is interrupted – for example …ABCABABC… in place of …ABCABCABC… – without a change in the layers themselves. In van der Waals crystals the energy cost is small, so faults form during growth, on cooling through structural transitions, and during cleaving and handling. They produce diffuse streaks along c* in diffraction and can alter interlayer exchange, symmetry-allowed responses and transition temperatures, as in α-RuCl₃, where faulted regions order near 14 K rather than 7 K.

Full explanation

Stoichiometry

The ratio in which the elements of a compound are combined – the numbers in its formula. MoS₂ should have two sulfur atoms for every molybdenum atom. Real crystals often deviate slightly, with a few atoms missing or a few extra squeezed in, and in 2D materials a deviation of a few percent can change how a crystal conducts, glows or behaves magnetically. That is why careful work measures the composition rather than assuming the formula.

The proportions of the elements in a compound, ideally the integer ratios of its formula. Real crystals are often non-stoichiometric, through vacancies, interstitials, antisites or intercalated atoms whose concentrations depend on the chemical potentials during growth and on the Fermi level, as point-defect thermodynamics describes. Deviations dope the material and can decide its ground state: chalcogen-deficient TMDCs are n-type, self-intercalated titanium makes TiS₂ metallic rather than semiconducting, the alkali content of AV₃Sb₅ and the europium content of EuSn₂As₂ shift their transitions, and melt-grown InSe varies along the boule. Composition is measured by X-ray photoelectron or energy-dispersive spectroscopy, Rutherford backscattering or electron-probe microanalysis, with accuracies of about a percent at best, so small deviations are often inferred from properties instead.

Full explanation

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.

Full explanation