Doping schemes

The different chemical doping schemes of graphene devices are shown in Fig. 1b. Our devices include large (W = 5 mm × L = 5 mm) (Fig. 1a) and small (W = 2–100 μm × L = 10–180 μm) epitaxial graphene Hall bars fabricated by conventional electron beam lithography (see Methods section). When PMMA is used as a spacer between graphene and the molecular dopant layer, the carrier density decreases three orders of magnitude from its pristine value, n ≈ 1 × 1013 cm−2 to near charge neutrality, n ≈ 1 × 1010 cm−2 (Fig. 1c). Importantly, even at such low carrier densities the carrier mobility remains high, with the largest measured value exceeding μ ≈ 50 000 cm2 V−1 s−1 at T = 2 K. The effect of doping is homogeneous over millimeter scale and large samples display quantum Hall effect at magnetic fields B < 1 T (Fig. 1a), retaining their low carrier density over the course of 2 years, even under ambient conditions (Supplementary Fig. 1). To achieve this, a 200-nm-thick layer of the PMMA-F4TCNQ dopant blend is spin-coated onto a PMMA-protected sample, followed by thermal annealing above the PMMA glass transition temperature. The resulting carrier density could be fine-tuned by the total annealing time. For a concentration of 7% of F4TCNQ in PMMA by weight, charge-neutral graphene is achieved after annealing at T = 160 °C for 5 min. Shorter annealing times yield hole-doping and longer times yield electron-doping (Supplementary Fig. 1). Using the optimal time, we have consistently observed a decrease in electron density by three orders of magnitude together with a tenfold increase of carrier mobility at T = 2 K in more than 20 devices on 11 different chips (Supplementary Table 1 and Supplementary Fig. 2). Typical carrier concentrations in doped samples are of the order of 5 × 1011 cm−2 at room temperature. They decrease to values ∼1 × 1010 cm−2 at T = 2 K, due to freezing of thermally activated carriers13. The corresponding carrier mobilities are in the range of 30 000–50 000 cm2 V−1 s−1 (Fig. 1d). The PMMA spacer layer plays a crucial role in achieving high carrier mobilities. While both PMMA and the dopant blend act independently as moderate p-dopants when deposited directly on SiC/G, it is only when the PMMA spacer layer is added between graphene and the dopant blend that we observe the near to charge neutrality doping effect. Similarly, carrier mobilities exceed 10 000 cm2 V−1 s−1 only if the PMMA spacer and dopant blend operate in tandem (Supplementary Fig. 3).

Fig. 1 Magnetotransport characterization of chemically doped SiC/G. a Top: macroscopic graphene Hall bar device (white dotted outline, W = 5 mm × L = 5 mm). Bottom: low field magnetoresistance and fully developed quantum Hall effect indicating low charge disorder in chemically doped graphene, even over macroscopic areas. For this device, the measured carrier density p = 9 × 109 cm−2 and mobility μ = 67 000 cm2 V−1 s−1. b The different encapsulation schemes with a polymer stack consisting of PMMA-F4TCNQ dopant blend, which comprises of F4TCNQ molecules in a PMMA matrix (F4TCNQ 7 wt%). The three schemes are dopant blend separated from graphene by a PMMA spacer (top), only PMMA layer (middle), and the dopant blend directly on the surface of graphene (bottom). c Carrier density as a function of temperature extracted from Hall measurements on small epitaxial graphene devices (W = 2–50 μm × L = 4–180 μm). d The corresponding Hall carrier mobility showing the highest μ ~ 55 000 cm2 V−1 s−1 at T = 10 K for sample prepared with PMMA spacer and dopant layer. The downturn in mobility at lower temperatures is due to quantum corrections to the Drude resistance. Carrier concentration n and mobilities μ were extracted from Hall measurements as n = 1/eR H and μ = R H /ρ XX , with e the elementary charge, the Hall coefficient R H = dR XY /dB, the longitudinal sheet resistance ρ XX = R XX W/L, and R XY the transversal resistance Full size image

Chemical analysis of graphene-polymer hetero-structure

We demonstrate that the doping of graphene is the result of F4TCNQ molecules diffusing through the PMMA layer and accumulating at the graphene surface. Figure 2a, b shows the chemical depth profile of the polymer stack, obtained by using time-of-flight secondary ion mass spectrometry (ToF-SIMS), revealing both diffusion of F4TCNQ through the PMMA spacer and the accumulation of molecules at the graphene surface. From this we estimate the diffusion coefficient of F4TCNQ through PMMA to be of the order of 1014 cm2 s−1 and by integrating the areas under the ion current intensity curves, we estimate the density of F4TCNQ molecules near the graphene surface to be ~4.6 × 1014 cm−2 (Supplementary Fig. 4, Supplementary Note 1). Graphene and metallic surfaces promote the accumulation of F4TCNQ, while there are virtually no dopant molecules at the polymer/SiC interface. The surface density of F4TCNQ is roughly 50% greater on graphene (and sixfold higher on gold) compared to that in the dopant blend layer (Fig. 2c). We attribute the accumulation of F4TCNQ on the graphene surface and the measured p-doping effect to the formation of a charge transfer complex, with partially charged F4TCNQ remaining at the graphene interface to preserve overall charge neutrality. F4TCNQ is known to be mobile in thin polymer films14,15, with its diffusion depending on polarity and glass transition temperature of the polymer. When using an inert PMMA as a host matrix, F4TCNQ remains neutral both in the doping layer and as it diffuses through PMMA spacer layer16. The formation of a charge transfer complex takes place only when encountering an electron donor, such as graphene. Once charged, the F4TCNQ anion is bound to graphene, stabilized by Coulomb interaction17.

Fig. 2 Chemical profiling of the polymer layers using ToF-SIMS to detect fingerprints of the F4TCNQ molecule (F and CN ions) as one probes deeper into the polymer stack. a Samples were prepared with PMMA spacer, dopant blend, and PMMA encapsulation layer. Three distinct spots on the substrate have been investigated: (1) graphene, (2) gold, and (3) SiC surfaces. b When analyzing the polymer layers on spot 1, above the graphene surface, the ion intensity for F and CN ions (top inset shows a schematic representation of a F4TCNQ molecule) vs. sputter time reveals significant accumulation of F4TCNQ at the graphene/PMMA interface, as well as the spatial distribution of F4TCNQ molecules through the spacer and encapsulation PMMA layers. The onset of the silicon signal (Si) is the marker, which indicates that the SiC substrate has been reached. The shaded regions denote the extent of each layer, from top PMMA layer down to SiC substrate. c Here we focus only on the CN signal measured at all three different spots. This analysis shows accumulation of F4TCNQ on the conductive surfaces of graphene and gold, but virtually no accumulation on SiC Full size image

Low charge disorder in SiC/G doped close to Dirac point

We investigated further electron transport details of the F4TCNQ-graphene charge-transfer complex system by introducing a top electrostatic gate (Fig. 3a, inset) on top of a 30 μm × 180 μm Hall bar. The top gate enables additional fine tuning of the carrier concentration within Δn ~ 5 × 1011 cm−2 using gate voltages V G = −100 to +200 V. At V G = 0 V the carrier density is n = 5 × 1011 cm−2 at room temperature and graphene is in the metallic limit. In this case, ρ XX (T, V G = 0 V) decreases linearly with temperature from its room temperature value, due to suppression of acoustic phonon scattering. Quantum corrections to resistance result in a log(T) dependence below the Bloch-Grüneisen temperature \({{T}}_{{\mathrm{BG}}} = 2v_{{\mathrm{ph}}}{{E}}_{\mathrm{F}}/\left( {k_{\mathrm{B}}v_{\mathrm{F}}} \right) = 2v_{{\mathrm{ph}}}\hbar v_{\mathrm{F}}\sqrt {\pi n} /\left( {k_{\mathrm{B}}v_{\mathrm{F}}} \right) \approx 38\,{\mathrm{K}}\), with the phonon velocity ν ph = 2 × 104 m s−1 (\({{E}}_{\mathrm{F}} = \hbar v_{\mathrm{F}}\sqrt {\pi n}\) the Fermi level of graphene, ħ the reduced Planck’s constant, k B the Boltzmann constant, and ѵ F = 106 m s−1 the Fermi velocity in graphene18). In contrast, when graphene is gated to the Dirac point, the sheet resistance ρ XX (T, Vg = −50 V) monotonically increases as the temperature drops, though remains finite with no indication of a transport gap in the current voltage characteristics down to T = 2 K (Fig. 3a).

Fig. 3 Electrostatic gating of chemically doped graphene (30 μm × 180 μm Hall bar). a Temperature dependence of longitudinal resistance for graphene in the metallic limit (red) and gated to Dirac point (blue). (Inset) Schematic representation of a chemically doped graphene device with a metallic gate (the topmost Au layer). b ρ XX vs. carrier concentration shows the characteristic Dirac peak around the charge neutrality point (red dotted line serves as a guide to the eye). The Dirac point is crossed below Vg = −40 V, and the device has well-defined carrier densities within ±6 × 109 cm−2 at T = 2 K, which corresponds to a Fermi energy of ±9 meV. c Corresponding charge carrier mobilities, with values up to 70 000 cm2 V−1 s−1. Each point in b and c represents data of magnetic field scans where R XY is linear in the low magnetic field limit and the device shows fully developed quantum Hall effect at high magnetic fields (ρ XX = 0 and exactly quantized R XY plateaus). The gap in data around zero carrier concentration corresponds to omitted data points where graphene is in the charge puddle regime. For comparison, in c, red circles and blue triangles correspond to Hall measurements from two different Hall probe pairs on the same device. The gate voltage was applied at cryogenic temperatures; the measured leakage current did not exceed 50 pA, with the bias current on graphene of 100 nA Full size image

To characterize the magnitude of carrier density fluctuations (i.e. how precisely one can approach the Dirac point) we conducted low-temperature magnetotransport measurements on chemically and electrostatically gated devices and found these fluctuations to be on the level of Δn ~ ± 6 × 109 cm−2 (ΔE F ~ ± 9 meV). Figure 3b shows longitudinal resistance vs. carrier concentration in which every data point, extracted from individual measurements of ρ XX (B), R XY (B) at a fixed gate voltage, corresponds to devices behaving as a system with a single electronic band and spatially homogenous carrier density19,20,21,22,23. That is, data points in Fig. 3b fulfill simultaneously the criteria of linear R XY (B) at low fields19,20,21,22, and fully developed half-integer quantum Hall Effect at high fields23, i.e. ρ XX (B) = 0 Ω and strictly quantized R XY plateau over the entire available range of magnetic field (Supplementary Fig. 5). The gap in data around zero carrier concentration thus corresponds to data points where graphene is in the charge puddle regime. Under quantizing conditions, the residual disorder in the sample causes non-zero and oscillatory ρ XX (B) once the magnetic length approaches the average charge puddle size23,24. In our samples with low carrier density concentration ~1010 cm−2 we have observed no deviation from ρ XX (B) = 0 to the largest magnetic field available in our setup (B = 14 T) (Supplementary Fig. 5). Thus, we establish an upper limit for the puddle size of about \(l_{\mathrm{B}} = \sqrt {\hbar /{{eB}}} \approx 7\,{\mathrm{nm}}\). The charge puddle magnitude is directly connected to disorder introduced by, e.g., topography or inhomogeneous doping25. The small magnitude of charge puddles measured in our devices indicate that SiC/G doped with F4TCNQ molecules is homogenous also at the microscopic scale, with carrier density fluctuations comparable to those in high-quality, hBN-encapsulated single-crystal graphene flakes obtained by exfoliation11 or by chemical vapor deposition growth26 (Supplementary Fig. 6).

It is remarkable that epitaxial graphene displays such low disorder even at extreme dopant coverage, being decorated with a dense layer of molecules of about 3–4 molecules per nm2 (c ≈ 3 × 1014 cm−2, comparable to the molecular coverage of c ≈ 4.6 × 1014 cm−2 from SIMS). We estimated the molecular density at the graphene surface from the shift in carrier density measured in doped graphene with respect to its pristine concentration (Δn ≈ 1 × 1013 cm−2), and assuming that 0.3 electrons are withdrawn from epitaxial graphene per molecule27,28 with 1/10 gate efficiency10. The homogeneity in doping is in part enabled by the high degree of F4TCNQ dispersion inside the PMMA matrix, shown by room temperature grazing-incidence wide-angle X-ray scattering (GIWAXs). The diffractogram in Fig. 4a, b reveals a broad amorphous halo with a distinct diffraction peak at q = 9.6 nm−1 from PMMA (Supplementary Note 2). The absence of diffraction spots from F4TCNQ implies the lack of molecular aggregation (i.e. crystallites) inside the matrix. Given the size of the F4TCNQ molecule, we propose that at this packing density a feasible molecular orientation of F4TCNQ is close to that of molecules standing up on the graphene surface28. Yet, we do not rule out molecular re-orientation or thermally induced redistribution of charges in the dopant layer under the effect of electric field, even at low temperatures. Such charge redistribution in the dopants in close vicinity to graphene may be responsible for screening charge inhomogeneities that facilitate highly uniform doping1. Thermally activated motion of charges in the dopant layer is a plausible source of the hysteresis in ρ XX (T) when devices are subjected to thermal excursion from T = 2 to 230 K (Fig. 4c). This is also suggested by more accurate resistance measurements, which reveal that charges in the dopant layer are mobile down to T ≈ 113 K (Supplementary Fig. 7), in notable coincidence with the energy scale of the measured charge inhomogeneity in doped epitaxial graphene (ΔE F ~ ± 9 meV). The charge homogeneity of the samples is thus determined by the temperature at which the screening charges freeze.