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Thermal conductivity

Everyday term

In plain words

How well a material carries heat from a hot place to a cold one. Graphene and boron nitride carry heat along their sheets better than copper, which is why they are used to spread heat away from hot spots – but across the sheets, and across every interface, heat moves far less easily.

Going deeper

Left: a block of stacked layers with a long arrow running along the layers labelled along the sheets, and a short arrow crossing them labelled across. Right: a bar chart on a logarithmic scale of thermal conductivity in watts per metre-kelvin: suspended graphene a few thousand, graphene on silicon dioxide about 600, copper about 400, silicon about 150, graphite across its layers about 6 and SnSe below 1. heat in a layered crystal along the layers: easy across strong bonds carry heat along the layers; the weak gaps between them block it room temperature, roughly graphene, free1000sgraphene on SiO₂~600copper~400silicon~150graphite, across~6SnSe<1 1101001000 W/m·K, log scale graphene on a substrate still beats copper; across layers heat barely moves
Left: heat moves easily along the strongly bonded layers of a layered crystal and poorly across the weak gaps between them. Right: approximate room-temperature values on a logarithmic scale – graphene along its sheet beats copper even when it rests on a substrate, while across the layers of graphite, or in SnSe, heat barely moves.

Heat carried by vibrations

In a metal, electrons carry most of the heat; in insulators and semiconductors the carriers are phonons, packets of lattice vibration. The conductivity is roughly the product of how much heat the phonons hold, how fast they travel and how far they get before scattering. Light atoms joined by stiff bonds make fast phonons and high conductivity – diamond, graphene and boron nitride are the champions – while heavy atoms and soft, anharmonic bonds make slow phonons that scatter often. SnSe, with a lattice conductivity below 1 W/m·K along some directions, is the classic low-conductivity layered crystal and one of the best thermoelectrics.

Anything that scatters phonons lowers the conductivity: boundaries and grain boundaries, point defects, isotopes – natural carbon’s 1% of carbon-13 is enough to measurably reduce graphene’s – and other phonons, which is why conductivity falls as temperature rises above the range where boundaries dominate.

Along the sheets and across them

In a layered crystal the strong bonds lie within the layers and the weak ones between them, so heat flows hundreds of times more easily along the layers than across them. Balandin and colleagues measured suspended single-layer graphene at several thousand W/m·K by heating it with a laser and reading its temperature from a Raman peak. Resting on silicon dioxide it still reaches about 600 W/m·K, more than copper, but the substrate scatters the flexural phonons that carry much of the heat in a free sheet. Black phosphorus conducts differently along its two in-plane directions, as it does electricity.

For devices, the bottleneck is usually not the sheet but the way out of it. Heat generated in a 2D transistor channel has to cross van der Waals gaps into the substrate, and each interface adds a thermal boundary resistance. A monolayer with superb in-plane conductivity can still run hot if nothing below it takes the heat away.

Uses, and reading a number

One of the largest commercial uses of graphene-type materials today is heat spreading: films of graphite, graphene or reduced graphene oxide in phones and batteries spread heat sideways from hot components. Such films conduct far less than a perfect monolayer, because they are made of many small, imperfect flakes – the headline figures belong to suspended single crystals, not to the product. At the other extreme, thermoelectric materials want the lowest possible conductivity combined with good electrical conduction.

Measured values vary with the method as much as with the material. Raman thermometry depends on knowing how much laser power the flake absorbs; suspended micro-bridge devices measure a flake between two tiny heaters; time-domain thermoreflectance measures heat flow across layers and interfaces. A reported conductivity means little without its method, sample size, support and temperature.

For specialists

The coefficient κ relating heat flux to temperature gradient, q = −κ∇T, carried in insulators and semiconductors almost entirely by phonons. Layered crystals are extremely anisotropic: graphite conducts about 2000 W/m·K along its layers and a few W/m·K across them; suspended graphene reaches several thousand, graphene on silicon dioxide about 600. Low κ – from heavy atoms, anharmonic bonding and interfaces, as in SnSe – is the goal for thermoelectrics, while the thermal boundary resistance at each interface often limits how fast heat leaves a 2D device.

Where this comes from

  1. Superior thermal conductivity of single-layer graphene Balandin et al. · Nano Letters 8, 902 (2008) cited by 13,873
  2. Two-dimensional phonon transport in supported graphene Seol et al. · Science 328, 213 (2010) cited by 1,932