Piezoelectricity

Everyday term

In plain words

Squeeze the crystal and it produces a voltage; apply a voltage and it changes shape. It makes the spark in a push-button lighter and keeps time in a quartz watch. It only works in crystals with no centre of symmetry, which is why a of MoS₂ is piezoelectric and two stacked layers are not.

Going deeper

Piezoelectricity – strain producing charge – is only allowed without a centre of symmetry. A 2H TMDC monolayer qualifies and its bilayer does not, so the effect alternates with layer number and disappears in the bulk. At a contact, the same charge shifts the barrier, which is the basis of piezotronics.

Why symmetry allows it at all

Piezoelectricity couples to polarisation linearly. Under inversion, strain is unchanged while polarisation reverses, so in a crystal the coupling must vanish. Only crystals without a centre of symmetry can be piezoelectric – 20 of the 32 crystal classes.

In layered materials this makes the effect depend on layer count. A monolayer lacks inversion symmetry and is piezoelectric; stacking a second layer in the natural, rotated way restores the centre and cancels it; a trilayer is piezoelectric again, though weaker. Bulk 2H crystals are therefore not piezoelectric at all, while 3R-stacked crystals, which never regain a centre, are.

Measuring it in one layer

calculations predicted the coefficients of monolayer BN, MoS₂ and related compounds in 2012, and measurements on monolayer MoS₂ followed: a suspended or clamped and strained produces an oscillating charge, with the sign reversing when the crystal is rotated by 60° and the response vanishing for an even number of layers – exactly the symmetry argument in action.

Numbers are usually given as a piezoelectric coefficient per unit strain for a sheet rather than per unit volume, because the thickness of a monolayer is ambiguous. That makes comparison with bulk piezoelectrics awkward, and it is one reason published values differ: they are not always the same quantity.

Piezotronics, and the practical limits

The charge produced by strain sits at the surface of a material that is all surface, so it modifies whatever is next to it. At a metal contact it shifts the , changing the current the contact passes – strain becomes a gate. This piezotronic effect has been used for strain , for tuning and for mechanical energy harvesting on the smallest scales.

The practical output is tiny: a single layer produces very little charge, so devices harvest microwatts at best, and the layer must be strained without slipping, which is why clamping and adhesion dominate the engineering. As with all these symmetry-driven effects, an even-layer control sample is the cleanest evidence that what was measured is really piezoelectricity and not a contact artefact.

For specialists

Linear coupling between strain and polarisation, allowed only in non-centrosymmetric crystals. Odd-layer 2H TMDCs lack inversion symmetry and are piezoelectric while even-layer stacks are not, so the response alternates with layer number and disappears in the bulk. Measurements on monolayer MoS₂ agree with the first-principles coefficients, and the same coupling gives piezotronic control of a contact by strain.

Where this comes from

Intrinsic piezoelectricity in two-dimensional materials Duerloo et al. · Journal of Physical Chemistry Letters 3, 2871 (2012) cited by 1,194
Piezoelectricity of single-atomic-layer MoS₂ for energy conversion and piezotronics Wu et al. · Nature 514, 470 (2014) cited by 2,293

Density functional theory (DFT)

The workhorse calculation of materials physics. Rather than following every electron, it works with the electron density and a recipe for how electrons avoid one another – which makes a whole crystal cheap enough to compute, and makes the accuracy depend entirely on that recipe.

Ground-state electronic structure from the density, exact in principle by Hohenberg–Kohn and made practical by the Kohn–Sham equations with an approximate exchange–correlation functional. Two dimensions need care: a vacuum gap wide enough that periodic images stop interacting or a truncated Coulomb interaction, a dispersion correction for interlayer binding, and the knowledge that semi-local functionals underestimate gaps – hybrid functionals narrow that error at far higher cost, and quantitative gaps and optical spectra need GW and Bethe–Salpeter on top.

Full explanation

Sensor

A device that turns something in its surroundings – a gas, a magnetic field, a pressure, a molecule in blood – into an electrical signal. 2D materials make unusually sensitive sensors because every atom is on the surface: a few molecules landing on a single layer change how well it conducts. Graphene also makes very good magnetic-field sensors. The hard part is not sensitivity but selectivity – responding to one thing and ignoring everything else – and staying stable for years.

Transducers in which a stimulus changes an electrical property of a 2D layer: chemiresistive and field-effect gas and humidity sensors, in which adsorbates transfer charge and shift the conductance (graphene registered single NO₂ molecules in 2007); Hall sensors, in which graphene’s low carrier density and high mobility give a large, temperature-stable Hall voltage; biosensors with receptors on a graphene or MoS₂ channel that bind target molecules; and strain, pressure and light sensors. Sensitivity comes from the all-surface geometry and the low density of states; the limits are selectivity, drift and hysteresis from humidity and contamination, recovery time, device-to-device variation and calibration, addressed by functionalisation, encapsulation and arrays read by pattern recognition.

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