Characterizing graphene

Six measurements tell you what a graphene flake is. Optical contrast on SiO₂/Si finds it, AFM and the Raman spectrum count its layers, the Raman D band gives the distance between its defects, electron diffraction tells one layer from two, and a field-effect device gives its carrier density and mobility.

1. Optical contrast: On oxidised silicon, thin-film interference makes a single layer visible; the colours here are computed for graphene with n = 2.6 − 1.3i and 0.34 nm per layer (Blake et al. 2007). 2. AFM height: Each layer adds graphite’s interlayer spacing, 0.335 nm; tapping-mode AFM can add as much as 1 nm to the measured height of thin flakes (Nemes-Incze et al. 2008). 3. Raman spectrum: At 532 nm a monolayer shows the G band at 1582 cm⁻¹ and one sharp 2D band at 2675 cm⁻¹, about 28 cm⁻¹ wide and 3.6 times as intense; the 2D band changes shape, width and position with the number of layers (Ferrari et al. 2006; Qiu et al. 2016). 4. Defect density: I(D)/I(G) against the mean distance between defects, L_D, rises to a maximum near 3 nm and depends on the laser; for L_D ≥ 10 nm, L_D² ≈ 4.3 × 10³ / (E_L⁴ · I(D)/I(G)), with L_D in nm and the laser energy E_L in eV (Cançado et al. 2011). 5. Electron diffraction: Six-fold spots from the periodicities of 2.13 and 1.23 Å (Meyer et al. 2007); a monolayer’s inner {101̅0} spots are brighter than its outer {112̅0} ones, while in thicker stacks the inner ones are weaker (Hernandez et al. 2008). 6. Field effect: The resistance peaks at the Dirac point; on 300 nm SiO₂ each volt on the gate adds 7.2 × 10¹⁰ carriers per cm², and the first devices reached about 10,000 cm²/V·s at room temperature (Novoselov et al. 2004); curve from the model of Kim et al. (2009).

Starting materials: Exfoliated or CVD graphene on SiO₂/Si (suspended over holes for TEM). Product: Layer number, defect density, crystal structure, carrier density and mobility.

Ferrari et al., “Raman spectrum of graphene and graphene layers”, Phys. Rev. Lett. 2006 (doi:10.1103/PhysRevLett.97.187401); Blake et al., “Making graphene visible”, Appl. Phys. Lett. 2007 (doi:10.1063/1.2768624); Cançado et al., “Quantifying defects in graphene via Raman spectroscopy at different excitation energies”, Nano Lett. 2011 (doi:10.1021/nl201432g); Meyer et al., “The structure of suspended graphene sheets”, Nature 2007 (doi:10.1038/nature05545); Novoselov et al., “Electric field effect in atomically thin carbon films”, Science 2004 (doi:10.1126/science.1102896); Nemes-Incze et al., “Anomalies in thickness measurements of graphene and few layer graphite crystals by tapping mode atomic force microscopy”, Carbon 2008 (doi:10.1016/j.carbon.2008.06.022); Qiu et al., “Raman and conductivity analysis of graphene for biomedical applications”, Materials 2016 (doi:10.3390/ma9110897); Hernandez et al., “High-yield production of graphene by liquid-phase exfoliation of graphite”, Nat. Nanotechnol. 2008 (doi:10.1038/nnano.2008.215); Kim et al., “Realization of a high mobility dual-gated graphene field-effect transistor with Al2O3 dielectric”, Appl. Phys. Lett. 2009 (doi:10.1063/1.3077021); Nair et al., “Fine structure constant defines visual transparency of graphene”, Science 2008 (doi:10.1126/science.1156965).

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