Single crystal

Everyday term

In plain words

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 , 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 from, or a sheet grown across a whole in one orientation.

Going deeper

In a single crystal one pattern runs unbroken through the whole piece; a polycrystal is a patchwork of grains at random angles whose boundaries scatter electrons. Single-crystal films are grown from islands that all point the same way and merge seamlessly; islands of two orientations meet in twin walls.

One crystal, or many

When a melt freezes or a film grows, crystals usually start at many points at once. Each grows with its own orientation until it meets its neighbours, and the result is polycrystalline: many grains joined at boundaries where the rows of atoms do not match. A single crystal results when only one of them is allowed to grow – by seeding with a small crystal, by letting a narrow tip select one grain as in , or by growing so slowly from a vapour or a solution that only a few crystals form.

For layered materials, single crystals are where most experiments begin. A crystal of MoS₂, CrI₃ or Bi₂Se₃ a few millimetres or centimetres across, grown by or from a flux, is peeled into flakes, and each flake is a single crystal too, as long as its parent was.

Why it matters

Grain boundaries scatter electrons and , trap charge, let chemicals in and can carry electronic states of their own, so a polycrystalline film usually has a lower and more variation from device to device than a single crystal. For delicate effects – quantum oscillations, unconventional , fragile – the difference decides whether anything is seen at all. Only a single crystal lets a property be measured along a chosen crystal direction, which layered materials need.

A crystal can be single and still imperfect. Twins, and mixed hide inside crystals that look flawless, so with narrow rocking curves, the of metals and microscopy across the sample are the usual checks.

Single-crystal films

Growing one crystal across a whole wafer from a single nucleus would be far too slow, so large single-crystal films are grown from many nuclei that all point the same way and merge without boundaries. The supplies the alignment. A copper (111) or germanium (110) surface aligns graphene; sapphire or copper cut at a slight angle, so that its surface carries regular atomic steps, aligns MoS₂ and hBN in a single direction, removing the mirror-image orientation whose domains would otherwise meet in twin boundaries. Films of this kind have reached wafer size in research laboratories.

For specialists

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.

Where this comes from

Epitaxial growth of a 100-square-centimetre single-crystal hexagonal boron nitride monolayer on copper Wang et al. · Nature 570, 91 (2019)
Epitaxial growth of wafer-scale molybdenum disulfide semiconductor single crystals on sapphire Li et al. · Nature Nanotechnology 16, 1201 (2021)

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.

Full explanation

Bridgman growth

A way to grow a large single crystal 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 flakes of InSe, Bi₂Se₃ or PbI₂ are peeled.

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-stoichiometric melts. It is fast and gives large crystals, but freezes in the segregation, stoichiometry drift, vacancies and stacking disorder of growth from the melt, so its crystals are often less pure and less ordered than those from flux or vapour transport.

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

Residual resistivity ratio (RRR)

A quick score for how clean a metal crystal is: its electrical resistance at room temperature divided by its resistance when cooled close to absolute zero. Cooling stops the atoms jiggling, so the resistance that remains comes from impurities and defects. A pure crystal loses almost all of its resistance and scores in the hundreds or thousands; a dirty one keeps most of it and scores near one.

The ratio R(300 K)/R(T → 0) of a metallic sample, where the low-temperature value is the residual resistivity from static disorder once phonon scattering has frozen out (Matthiessen’s rule). It is a standard, geometry-independent proxy for crystal quality and mean free path, from order one in disordered films to 10³–10⁵ in the purest metals. Its low-temperature reference is ambiguous in superconductors, where the normal-state value just above T_c is used, and in materials whose resistivity turns up at low temperature.

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