Uniform doping of graphene close to the Dirac point by polymer-assisted assembly of molecular dopants

Tuning the charge carrier density of two-dimensional (2D) materials by incorporating dopants into the crystal lattice is a challenging task. An attractive alternative is the surface transfer doping by adsorption of molecules on 2D crystals, which can lead to ordered molecular arrays. However, such systems, demonstrated in ultra-high vacuum conditions (UHV), are often unstable in ambient conditions. Here we show that air-stable doping of epitaxial graphene on SiC—achieved by spin-coating deposition of 2,3,5,6-tetrafluoro-tetracyano-quino-dimethane (F4TCNQ) incorporated in poly(methyl-methacrylate)—proceeds via the spontaneous accumulation of dopants at the graphene-polymer interface and by the formation of a charge-transfer complex that yields low-disorder, charge-neutral, large-area graphene with carrier mobilities ~70 000 cm2 V−1 s−1 at cryogenic temperatures. The assembly of dopants on 2D materials assisted by a polymer matrix, demonstrated by spin-coating wafer-scale substrates in ambient conditions, opens up a scalable technological route toward expanding the functionality of 2D materials.

. Magnetotransport characterization of chemically doped SiC/G. (a) Top: macroscopic graphene Hall bar device (white dotted outline, W=5 mm x 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=9x10 9 cm -2 and mobility μ= 39,000 cm 2 /Vs (b) The different encapsulation schemes with a polymer stack consisting of polymer-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 m x L=10-100 m). (d) The corresponding Hall carrier mobility showing the highest ~55,000 cm 2 /Vs at T=10K for sample prepared with PMMA spacer and dopant layer. The downturn in mobility at lower temperatures is due to quantum corrections to Drude resistance. Carrier concentration n and mobilities  were extracted from Hall measurements as n=1/eRH and = RHXX, with e the elementary charge, the Hall coefficient RH=dRXY/dB, the longitudinal sheet resistance XX=RXXW/L, and RXY the transversal resistance.
Here we show a molecular approach to dope epitaxial graphene homogeneously, yielding graphene with low carrier density (n<10 10 cm -2 ), low charge fluctuations (at the level of n±6x10 9 cm -2 ), and carrier mobilities up to 70,000 cm 2 /Vs over macroscopic areas at low temperatures. So far, such electron transport properties have only been attained in microscopic single crystal graphene flakes encapsulated by hexagonal boron nitride (hBN) 12 or in suspended graphene 13 . The doping method described here was applied to samples over 5 x 5 mm 2 , resulting in graphene-based devices readily applicable to quantum resistance metrology, i.e. stable devices displaying quantum Hall effect at low magnetic fields (Fig. 1a).
We show that air-stable molecular doping of graphene is achieved when organic molecules embedded in a polymer matrix, diffuse through the matrix, and spontaneously accumulate at the graphene surface due to formation of a charge-transfer complex. High electron affinity F4TCNQ molecules are incorporated in PMMA spin coated at ambient conditions on SiC/G, with graphene being used both as the target substrate for molecular assembly and, simultaneously, as a charge sensor. The stability of the samples allows us to study the chemical composition as well as electronic transport properties of the F4TCNQ/graphene system. Our devices include large (W=5 mm x L=5 mm) and small (W=2-50 m x L=10-100 m) epitaxial graphene Hall bars fabricated by electron beam lithography as described elsewhere 14 . After fabrication, devices were encapsulated by a 200 nm-thick, dopant-free PMMA layer to prevent drift in carrier concentration from ambient exposure and characterized by magnetotransport measurements.
The different chemical doping schemes of graphene devices are shown in Fig. 1b.
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1x10 13 cm -2 to near charge neutrality, n1x10 10 cm -2 (Fig. 1c). Importantly, even at such low carrier densities the carrier mobility remains high, with the largest measured value exceeding 50,000 cm 2 /Vs at T=2 K in small devices. The effect of doping is homogeneous over millimeter scale and samples retain their low carrier density over the course of two years, even under ambient conditions (Supplementary S1). To achieve this, a 200 nm-thick layer of the polymer-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 wt.% of F4TCNQ in PMMA, charge neutral graphene is achieved after annealing at T=160 ˚C for 5 minutes.
Shorter annealing times yield hole-doping and longer times yield electron-doping (Supplementary S1). Using the optimal time, we have consistently observed a decrease in electron density by three orders of magnitude together with a ten-fold increase of carrier is roughly 50% greater on graphene (and 6-fold 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 films 15,16 , 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 layer 17 . 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 interaction 18 . We investigated further electron transport details of the F4TCNQ-graphene chargetransfer complex system by introducing a top electrostatic gate (Fig. 3a, inset). The top gate enables additional fine tuning of the carrier concentration within n~5x10 11 cm -2 using gate voltages VG=-100 V to +200 V. At VG=0 V the carrier density is n=5x10 11 cm -2 at room temperature and graphene is in the metallic limit. In this case, XX(T, VG=0 V) decreases linearly with temperature from its room temperature value, due to suppression of acoustic indication of a transport gap in the current voltage characteristics down to T=2 K (Fig 3a).
To characterize the magnitude of carrier density fluctuations (so-called charge puddles) we conducted low-temperature magnetotransport measurements on chemically and electrostatically gated devices and found these fluctuations to be on the level of n~±6x10 9 cm -2 (EF~±9 meV).  and (c) represents data of magnetic field scans where RXY is linear in the low magnetic field limit and the device shows fully developed Quantum Hall Effect at high magnetic fields (XX=0 and exactly quantized RXY plateaus). The gap in data around zero carrier concentration corresponds to omitted data points where graphene is in the charge-puddle regime.
It is remarkable that epitaxial graphene displays such high carrier mobilities and low disorder even at extreme dopant coverage, being decorated with a dense layer of molecules of about 3-4 molecules nm -2 (c3x10 14 molecules/cm 2 , comparable to the molecular coverage of c4.6x10 14 molecules/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1x10 13 cm -2 ), and assuming that 0.3 electrons are withdrawn from epitaxial graphene per molecule 27,28 with 1/10 gate efficiency 11 . 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 S5). 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 surface 28 . 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 doping 29   The reference sample, without F4TCNQ in the dopant blend displays a clear peak diffraction ring with radius q=9.6 nm -1 ; the addition of F4TCNQ molecules enhances the signal twofold. (c) Stability of doping at low temperature in a device that has been cooled down from room temperature. Starting at T=300 K we applied a gate voltage VG=+50 V and kept down during cool down Once we reached T = 2 K, the gate terminal is set to VG=0 V and sample sheet resistance acquires a value of XX=4 kΩ (point A). Thermal excursions to T=50 K (B), 100 K (C), 150 K (D) result in reversible XX(T) along the black curve. Once temperature exceeds T=150 K (E), XX(T) irreversibly changes to a higher resistive value (red curve), and on cooling down back to T=2 K, the sample resistance takes a value of XX =5 k (F) In the absence of the gate voltage, the sample resistance remains in the higher resistance XX(T) branch.
A possible explanation for the observed high charge carrier mobility of SiC/G at large molecular coverage is a high degree of spatial correlation between adsorbed F4TCNQ and impurities present on bare graphene. Together with the low charge carrier density fluctuations, increasing impurity (e.g. F4TCNQ) density can lead to suppression of charge scattering in graphene if there is sufficient inter-impurity correlation present in the system 30,31 . The actual organization and conformation of charged molecules on graphene is the result of delicate balance between molecule-graphene interactions as well as the intermolecular many body dispersion forces 32,33 in the presence of polymer. While the exact arrangement of molecules on graphene is difficult to probe through the thick polymer layers with surface science techniques, the graphene itself utilized as detector allows to gain an insight of such molecular reorganization at the polymer-graphene interface.
In summary, we presented a method of guiding the assembly of molecular dopants onto the surface of graphene by using an organic polymer matrix. With the doping stability observed in our samples, the tuneability of molecular coverage, and given the vast catalogue of polymers and organic/organo-metallic molecules, we expect this method to open up a scalable route towards expanding the properties and functionality of graphene and other 2D materials well beyond doping control. Moreover, the presented analysis of chemical and electron transport properties of doped graphene sheds light on the complex processes that molecular dopants undergo when embedded in polymers. This is relevant to the understanding of performance, materials, and interfaces in organic electronic devices, especially when combined with 2D materials. This method can be explored in the future to create and study electron transport properties of novel twodimensional systems of ordered molecular arrays templated by 2D crystals 34,35 .