Graphene Electrical Properties: Measured Values and Conditions

Key takeaways

• Mobility depends on the surroundings more than on graphene. Devices on SiO2 usually sit near 10,000 cm²/Vs, suspended sheets passed 200,000 at 5 K, and graphene in boron nitride reached 140,000 at room temperature.
• Gated graphene in boron nitride has shown a sheet resistance below about 40 ohms per square at room temperature. Large-area CVD monolayer films sit near 125 ohms per square.
• Carriers move at about 10⁶ m/s and there is no band gap. Conductivity bottoms out near 4e²/h instead of zero, which kept transistor on/off ratios near 100 in 2007 reports.
• Graphene carried a few times 10⁸ A/cm² in a 2007 measurement, several orders of magnitude above present-day interconnects.
• Gaps can be opened, but small ones. About 200 meV in biased bilayers and in 15 nm ribbons, and roughly 16 to 28 meV on aligned boron nitride. Silicon has 1.12 eV.

What are the electrical properties of graphene, in numbers? Carriers move at about 10⁶ m/s and the band gap is zero. Room-temperature mobility runs from about 10,000 cm²/Vs on a common SiO2 chip to 140,000 cm²/Vs in boron nitride, and sheet resistance can fall below 40 ohms per square. Each figure below carries the substrate, temperature and carrier density it was measured at, because a mobility without them means little.

Mobility is the drift speed a carrier gains per unit of electric field. Sheet resistance is the resistance of a square of film, whatever its size. For carrier density n, mobility μ and electron charge e it equals 1/(n e μ). Our graphene versus silicon comparison covers the wider contest. This page is the reference table behind it.

Graphene electrical properties: the measured values

Read the conditions column before the number. A mobility of 200,000 cm²/Vs at 5 K in vacuum is a different claim from 100,000 at room temperature in a sealed stack. Temperatures are as the papers state them. The abbreviation hBN means hexagonal boron nitride.

Why the mobility numbers span a factor of 100

Graphene has little intrinsic scattering, so its surroundings set the mobility. On SiO2, charged impurities and substrate phonons dominate. Chen and colleagues found that SiO2 surface phonons alone cap the mobility near 40,000 cm²/Vs. Real devices sit well below that.

Removing the substrate helped. In Bolotin’s sample 1 the carriers travel a mean free path of about 1.2 µm at n = 2×10¹¹ cm^-2. A second suspended study held 120,000 cm²/Vs at 240 K. Its authors noted that this beats the best room-temperature semiconductor they cited, InSb at 77,000.

Suspension is fragile, so the practical route is hBN. Dean measured about 20,000 cm²/Vs on hBN and 2,000 on SiO2 in the same flake. Mayorov then sealed graphene between two hBN crystals and saw about 100,000 at room temperature, with ballistic transport over about 1 µm. Wang added edge contacts and reached 140,000.

One caution applies. These record mobilities are read at low density, near 10¹¹ cm^-2 in the encapsulated case. Wang’s figure at the high density that gives 40 ohms per square is about 40,000. Quote a mobility without its density and you have quoted the best case.

Sheet resistance and the minimum conductivity

Take n = 10¹² cm^-2. At 10,000 cm²/Vs the formula gives about 620 ohms per square. At 200,000 it gives about 31 ohms, which matches the phonon limit Chen reports. These are our calculations from the stated inputs.

Wang’s gated stack stayed below about 40 ohms per square. Multiply by 0.35 nm, the thickness Moser used, and the equivalent bulk resistivity is about 14 nΩm. Copper is 16.78 nΩm at 20 °C. Wang states that the stack beats every metal at room temperature. The comparison needs care, because the stack holds 4.5×10¹² cm^-2 carriers only under gate bias.

Large films tell a more modest story. Bae reported a monolayer at about 125 ohms per square with about 97% transmittance, against about 350 for the best earlier single-layer value they cite. A four-layer film doped with nitric acid reached about 30 ohms per square at about 90% transparency. They set that film against indium tin oxide at under 100 ohms per square.

At the other end, conductivity does not vanish when the carrier density does. Geim and Novoselov show values clustering near 4e²/h across nearly 50 devices. That corresponds to about 6.45 kilohms per square by our arithmetic. The theoretical 4e²/(πh) would be about 20.3 kilohms. The disagreement has become known as the “mystery of a missing pie”, and their review leaves its cause open.

Dirac cone and Fermi velocity

Near the K points of the lattice, graphene’s energy rises linearly with momentum. The two bands form a cone with its tip at zero energy. Carriers behave like massless particles with an effective speed of light of about 10⁶ m/s. Castro Neto and colleagues put it near 1/300 of the real speed of light.

Chen explains a consequence. Because of the linear dispersion, resistivity from isotropic scatterers such as acoustic phonons does not depend on carrier density. That is why the phonon limit in the table above is a single number.

Why graphene has no off state, and how gaps are opened

A transistor channel must switch to near zero current. Graphene has no gap, so it keeps conducting at the neutrality point. Geim and Novoselov note on/off ratios of only about 100 and call the metallic neutrality point a major problem for mainstream logic.

Three routes open a gap. None reaches the 1.12 eV of silicon.

Every route trades something. A biased bilayer needs a strong field. A ribbon needs edges cut to about 10 nm, which is the width Geim and Novoselov say room-temperature operation requires. Aligned boron nitride gives a gap near thermal energy, which is about 25.9 meV at 300 K by our calculation.

Graphene against silicon, GaAs and copper

These comparisons mix devices and conditions, so use them for orientation only. The silicon and GaAs values come from a general reference. The two band gaps and the GaAs mobility are listed at 300 K. The silicon mobility has no stated temperature or doping.

Silicon and GaAs mobilities are from Wikipedia’s electron mobility page and its GaAs page. Band gaps are from the silicon and GaAs pages. All are secondary sources. For another device built on silicon charge transport, see our CCD article.

What these numbers do not tell you

Record values come from small flakes made in research labs. Wafer-scale CVD material sits far lower, as the 7,350 cm²/Vs Hall mobility Bae measured at about 6 K shows. Temperatures and densities differ between rows, so no two rows are a like-for-like comparison.

The sources here date from 2007 to 2013. We did not review later work on gaps, so the gap table may understate what newer devices achieve.

Sources

• Geim and Novoselov, The rise of graphene, Nature Materials 6, 183 (2007)
• Castro Neto et al., The electronic properties of graphene, Reviews of Modern Physics 81, 109 (2009)
• Bolotin et al., Ultrahigh electron mobility in suspended graphene, Solid State Communications 146, 351 (2008)
• Bolotin et al., Temperature dependent transport in suspended graphene (2008)
• Chen et al., Intrinsic and extrinsic performance limits of graphene devices on SiO2, Nature Nanotechnology 3, 206 (2008)
• Dean et al., Boron nitride substrates for high-quality graphene electronics, Nature Nanotechnology 5, 722 (2010)
• Mayorov et al., Micrometer-scale ballistic transport in encapsulated graphene at room temperature, Nano Letters 11, 2396 (2011)
• Wang et al., One-dimensional electrical contact to a two-dimensional material, Science 342, 614 (2013)
• Moser, Barreiro and Bachtold, Current-induced cleaning of graphene, Applied Physics Letters 91, 163513 (2007)
• Bae et al., 30 inch roll-based production of high-quality graphene films for flexible transparent electrodes (preprint of the 2010 Nature Nanotechnology paper)
• Mak et al., Observation of an electric-field induced band gap in bilayer graphene by infrared spectroscopy (2009)
• Han et al., Energy band-gap engineering of graphene nanoribbons, Physical Review Letters 98, 206805 (2007)
• Hunt et al., Massive Dirac fermions and Hofstadter butterfly in a van der Waals heterostructure, Science (2013)
• Wikipedia, Electron mobility (silicon and GaAs values, secondary source)
• Wikipedia, Gallium arsenide (band gap and electron mobility, secondary source)
• Wikipedia, Silicon (band gap, secondary source)
• Wikipedia, Copper (resistivity at 20 °C, secondary source)