Graphene, a mono-layer of sp2 bonded carbon atoms arranged in a honeycomb pattern (Figure 1a), is a two-dimensional semi-metal where the valence and conduction bands touch in two independent points at the border of the Brillouin zone, named K and K' valleys 1 2 3 4 5 . This material has remarkable electronic, optical and mechanical properties which can be used in a new generation of devices 6 7 . For instance, the high mobility of charge carriers is attracting considerable interest in the realm of high-speed electronics 8 . Furthermore, thanks to the unique combination of high electrical conductivity 4 5 and optical transparency 9 , graphene is a promising material for optoelectronic applications such as displays, photovoltaic cells and light-emitting diodes. Few-layer graphene are yet unique materials 10 with unprecedented physical properties: bilayers are semiconductors with a gate-tuneable band gap 11 12 13 14 15 16 17 18 19 20 21 , whereas trilayers are semi-metals with a gate-tuneable overlap between the conduction and valence bands 22 23 . However, the use of graphene for applications in daily-life electronics suffers from a major drawback, i.e. the current in graphene cannot be simply pinched off by means of a gate voltage. A valuable solution to this problem is to engineer a band gap in the energy spectrum of graphene for example confining the physical dimensions of graphene into nanoribbons 24 25 26 27 28 or by chemical functionalisation 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 .

When chemical elements, e.g. oxygen, hydrogen or fluorine, are adsorbed on the surface of graphene, they form covalent bonds with the carbon atoms. As a result, the planar crystal structure of graphene characterised by sp2 bonds between the carbon atoms is transformed into a three-dimensional structure with sp3 bonds (see Figure 1b). The adsorbed elements can attach to graphene in a random way, as it is the case in graphene oxide 44 45 46 , or they can form ordered patterns as it has been found for hydrogen 33 34 35 and fluorine 36 37 38 39 40 41 42 43 adsorbates. Ab initio calculations performed within the density functional theory formalism predict that functionalisation with hydrogen and fluorine should lead, respectively, to a band gap of 3.8 and 4.2 eV for full functionalisation 29 30 31 32 .

Successful hydrogenation and fluorination of graphene have been recently achieved by several groups 33 34 35 36 37 38 39 40 41 42 43 . Hydrogenation is usually carried out in a remote plasma of H₂ 33 34 35 which makes it difficult to control the degree of induced atomic defects as well as the stoichiometry of the functionalisation. Furthermore, hydrogenated graphene can loose H at moderate temperatures 33 , which limits the use of this material in applications where high-temperature stability is required. On the other hand, fluorine has higher binding energy to carbon and higher desorption energy than hydrogen 29 30 31 32 . Opposed to hydrogenation, the process of fluorination is easy to control, e.g. via temperature and reactant gases, leading to reproducibly precise C/F stoichiometries.

Here, we explore the electronic transport properties of functionalised graphene with a fluorine content ranging from 7% (i.e. CF_0.07 or F/C atomic ratio of 0.07) to 100% (CF₁). We have fabricated transistor structures with fluorinated graphene mono-layers and multi-layers and studied their electrical transport properties in the temperature range from 4.2 to 300 K. We show that the electronic transport properties of fluorinated graphene can be tuned by adjusting the fluorine content, so that different transport regimes can be accessed, like Mott variable range hopping (VRH) in two dimensions 47 48 , Efros-Shklovskii VRH 49 and nearest neighbour hopping (NNH) transport.

Fluorinated graphene mono-layers and multi-layers were mechanically exfoliated from fluorinated graphite and deposited onto conventional Si/SiO₂ (275 nm) substrates. The fluorinated graphite was synthesised via two routes: graphite fluorides (using F₂ gas) and fluorine graphite intercalation compounds (FGIC) (using XeF₂ as fluorinating agent), see Section 6. The samples produced using F₂ gas that we investigate here are multi-layers and have the concentration of fluorine of 28 and 100%, whereas the samples synthesised using XeF₂ gas are all mono-layers and have the fluorine content of 7, 24 and 28%.

Flakes of fluorinated graphene are located using an optical microscope (see Figure 1d) and subsequently characterised by Raman spectroscopy. Mono-layer graphene flakes were identified by fitting the 2D peak of the Raman spectra by a single Lorentzian function (see Figure 2b), with a full width at half maximum (FWHM) of 30-45 cm^-1 which is typical for pristine mono-layer graphene 50 . The height of the studied multi-layer flakes is determined by Atomic Force Microscopy: 10-nm height for flakes exfoliated from the CF and 0.86-6.1 nm for flakes obtained from CF_0.28. In total, four mono-layer, five CF and five CF_0:28 multi-layer flakes were processed into four-terminal transistor devices, where the electrical contacts were defined by e-beam lithography, deposition of Cr/Au (5/50 nm) and lift-off procedure, see Figure 1e,f.

The typical optical contrast of fluorinated graphene is ~2-6%, which is systematically lower than what we observe on pristine graphene (~9%), see Figure 1c,d. The reduced contrast in fluorinated graphene has to be expected, since the opening of a large energygap in the energy dispersion of fluorinated graphene lowers the optical absorption transitions between conduction and valence bands.

Figure 2 shows the Raman spectra of a mechanically exfoliated pristine graphene flake, with the G and 2D (also known as G') bands at 1580 and 2700 cm^-1. The G band is associated with the double degenerate E2g phonon mode at the Brillouin zone center, while the 2D mode originates from a second-order process, involving two intervalley phonons near the K point, without the presence of any kind of disorder or defect 50 . In the fluorinated graphene, additional peaks are activated in the Raman spectra (see Figure 2), the D and D' peaks that appear at 1350 and 1620 cm^-1. These Raman peaks originate from double-resonance processes at the K point in the presence of defects, involving, respectively, intervalley (D) and intravalley (D') phonons 51 52 53 54 .

In exfoliated pristine graphene, the D peak can only be observed at the edges of the flakes where there is a large concentration of structural defects and its intensity is typically much lower than the intensity of the G peak 55 56 . In our studies performed on pristine graphene flakes with similar size as the fluorinated graphene flakes, the intensity of the D peak is typically well below the sensitivity of our Raman setup, i.e. we are usually not able to detect any D peak because of the edges of the flakes. Therefore, the observed D peak in our fluorinated graphene samples must originate from other defects than simply the edges of the samples. As all our samples contain networks of sp2 bonded carbon atom rings, we believe that the D peak is mainly activated by the F atoms which act as vacancies in these sp2 rings.

A better understanding of the level of disorder in our samples is reached when analysing the intensity ratio I_D/I_G for the D and G bands. It has recently been shown that in graphene I_D/I_G has a non-monotonic dependence on the average distance between defects L_D, increasing with increasing L_D up to L_D ~ 4 nm and decreasing for L_D > 4 nm 53 54 57 . Such behavior has been explained by the existence of two disorder-induced regions contributing to the D peak: a structurally disordered region of a radius ~1 nm around the defect and a larger defect-activated region which extends to ~3 nm around the defect. In the defect-activated region, the lattice structure is preserved, but the proximity to a defect causes a mixing of Bloch states near the K and K' valleys. Consequently, the breaking of the selection rules leads to an enhancement of the D peak. Furthermore, it was shown that in the structurally disordered region, the G and D' peaks overlap.

The Raman spectra of fluorinated mono-layer samples produced from graphite with fluorine content of 7 and 28% (see Figure 2a) systematically show that the G and D' peaks have a significant overlap. On the other hand, the samples exfoliated from CF_0.24 exhibit very distinct G and D' peaks. Based on the aforementioned phenomenological model 53 54 57 , we can state that the CF_0.07 and CF_0.28 samples are in the regime where the intensity ratio I_D/I_G increases with increasing L_D (i.e. decreasing the concentration of F) whereas the CF_0.24 samples are in the opposite regime. This scenario is confirmed when comparing the intensity ratio I_D/I_G for fluorinated mono-layers extracted from graphite with different fluorine content: I_D/I_G = 1.74 for CF_0:28 and I_D/I_G = 2.16 for CF_0.07. From the L_D dependence on I_D/I_G we estimate L_D ~ 1.5 nm for CF_0.28 and L_D ~2 nm for CF_0.07 53 54 57 . For the CF_0.24 samples, we estimate L_D ~ 5.3 nm for device 1 and L_D ~ 6.1 nm for device 2. These values of L_D are in agreement with the observed frequencies of the D, G, D' and 2D peaks as well as with the FWHM values of the 2D peaks 53 .

In the case of the fluorinated multi-layer flakes, see Figure 2c,d, it is difficult to perform a similar analysis, as the intensity of the G band depends on the number of graphene layers present in the sample 50 . For samples thicker than three to four layers, the structure of the 2D peak does not provide an accurate estimation for the number of layers because of the large number of fitting parameters.

Having characterised the level of disorder from Raman spectroscopy, we now proceed to address the role of disorder on the electrical transport properties of fluorinated graphene materials. Figure 3 shows the resistivity (ρ) as a function of gate voltage (V _g) for the fluorinated mono-layer samples for different temperatures. The resistivity exhibits a non-monotonous dependence on V _g with a maximum at V _g = +10 V, stemming for a doping level of n = 0.74 10¹² cm^-2 commonly seen also in pristine graphene devices and attributed to doping by atmospheric water. In all cases, the resistivity of fluorinated graphene shows a pronounced temperature dependence. Indeed, the maximum of resistivity changes over two orders of magnitude as T decreases from 300 to 4.2 K. Away from the maximum of resistivity region, the temperature dependence remains weak, with the mobility of carriers of 150 cm²/Vs. Furthermore, at low temperature the resistance shows strong mesoscopic fluctuations, as expected for samples of small size 58 . In the analysis of the maximum of resistivity, we smooth the ρ(V _g) curves using a moving average filter.

To examine the presence of the energy gap, we analyse the temperature dependence of the maximum of resistivity by an exponential law describing thermal activation of carriers across an energy gap Δε: ρ(T) = ρ ₀ exp(Δε/2k _BT), see Figure 4a. This analysis clearly shows that our data are not described by the thermal activation law over the whole temperature range. We note that the slope of lnρ (1/T) versus 1/T decreases with decreasing T, which is a signature of hopping conduction via localised states 48 . The fact that in the whole range of studied temperatures electron transport is not due to thermal activation across the gap but due to hopping becomes clear when re-analysing the temperature dependence in terms of the 2D Mott VRH (2D-VRH) 47 48 . In this model, the functional dependence of ρ on temperature is ρ(T) = ρ ₀ exp(T ₀/T)^1/3, where k _B T ₀ = 13.6/a ² g(ε_F ), g is the density of localised states at the Fermi level ε_F and a is the localisation length 47 48 . Experimentally we find that the measured ρ(T) for the samples produced from CF_0.07 and CF_0.24 graphite (see Figure 3b for CF_0.24) is described well by the 2D-VRH model.

Figure 4c shows the hopping parameter T ₀ as a function of carrier concentration for these three samples. The value of T ₀ approaches zero at a carrier concentration of ±1.2 10¹² cm^-2. This value gives the concentration of the localised electron states in the energy range from ε = 0 to the mobility edge, see Figure 4d. The mobility edge occurs at V _g ± 20V and indicates the transition from hopping to metallic conduction.

In order to relate the obtained concentration of the localised states to the energy gap Δε, one needs to know the exact energy dependence of the density of states in the gap. For estimations, we will use the linear relation for the density of extended states above the mobility edge g(ε) = 2ε/πħ ² v ² (v = 10⁶ m/s is the Fermi velocity), and a constant value for the density of localised states below the mobility edge, Figure 4d. This gives Δε = 60 meV and twice this value for the full mobility gap. In this approximation, the density of the localised states in the gap is ~10³⁶ J/m². Using the obtained value of the hopping parameter at the maximum of resistivity, we can then estimate the localisation length at ε = 0 as a = 40 nm for CF_0.24 (device 1), a = 81 nm for CF_0.24 (device 2) and a = 265 nm for CF_0.07.

Figure 4e shows the analysis of the temperature dependence of the resistivity for fluorinated mono-layer graphene exfoliated from CF_0.28 graphite. For this sample, characterised by the largest disorder L_D ~1.5 nm, the experimental data cannot be described by thermally activated law nor Mott VRH. In this case, the ln(ρ) follows a T ^-1/2 dependence characteristic of the Efros-Shklovskii VRH in the presence of Coulomb interaction between the localised states (ρ(T) = ρ ₀ exp(T ₀/T)^1/2) 49 . T ₀ is related to the localisation lengths through T ₀ = 2.8e² / 4 πε_rε ₀ k _B a and for our sample we estimate T ₀ = 52 K. Assuming that ε_r is the dielectric constant of SiO₂ we obtain the localisation length a = 282 nm.

We turn now our discussion to multi-layer fluorinated graphene exfoliated from fully fluorinated graphite and from CF_0.28 prepared by exposure to fluorine gas. The fully fluorinated multi-layer show systematically a very large resistance (more than 100 GΩ) independently of the specific thickness and no gate-voltage control of the resistivity. To achieve gate modulation in these samples, we reduced the fluorine content by annealing the samples at 300°C, in a 10 % atmosphere of H₂/Ar for 2 h. This annealing process restores a partial gate-voltage control of the resistance (Figure 5a) while leaving unchanged the Raman spectrum in Figure 2d.

Resistance measurements of CF _n flakes after annealing show a strong temperature dependence, Figure 5a. Analysis of the temperature dependence of the resistance in terms of the activation law at the highest gate voltage V _g = 50 V (which is still far from the Dirac point) gives a gap of only 25 meV, which is significantly smaller than the expected energy gap for fully fluorinated graphene. Similarly to the fluorinated mono-layer graphene, the resistivity dependence on temperature is fitted well by VRH with the value of T ₀ = 20000 K. This confirms that the previously found activation energy of 25 meV is not the activation energy Δε that separates the localised states from extended states at the mobility edge, but is an activation energy δε of hopping between localised states within the mobility gap, see Figure 4d.

Figure 5c,d shows the transport data for the multi-layer fluorinated graphene CF_0.28 prepared by exposure to fluorine gas. The I-V characteristics of these samples are strongly non-linear (see Figure 5c) with resistances of more than 1 GΩ. In this case, the dependence of the resistivity on temperature cannot be described neither by 2D-VRH nor by Efros-Shklovskii VRH (see Figure 5d). The ln(ρ)(T) dependence is rather well described by a thermally activated law at elevated temperatures (regime A), with a Δε = 0.25 eV, followed by a temperature regime where the resistivity decreases with lowering the temperature (regime B). A 1/T dependence of ln(ρ) could be the consequence of either intrinsic transport through thermally excited carriers above the bandgap or conduction through NNH via localised states within the gap. Since the I-V characteristics of our devices show a non-linearity on a V _sd range much larger than the estimated Δε = 0.25 eV (see Figure 5c), we conclude that transport occurs via NNH.

Finally, for the same degree of fluorination (i.e. CF_0.28) the graphene multi-layers exhibit a stronger temperature dependence and a larger transport gap than what is observed in mono-layers. This difference could originate from the different fluorination processes used for the multi-layers (direct fluorination with F₂ gas at high temperature to produce graphite fluorides) and for the monolayers (FGIC synthesised at lower temperatures), see Section 6. Indeed, different fluorination processes may lead to different concentrations of localised states. Even though in both materials, F-GIC and graphite fluorides, the nature of the bonding between fluorine and carbon atoms is covalent, the C-F bond order is slightly lower in F-GIC 59 . The lower C-F bond order in F-GIC is due to the hyper-conjugation which occurs between the C-F and the C-C single bonds around the C-F bonds. In particular, the C-F and C-C single bond lengths are, respectively, longer and shorter in F-GIC than those in graphite fluorides. As a result, the electrons involved in the covalent C-F bonds in F-GIC are slightly delocalised by this hyperconjugation, which may result in a smaller transport gap.

In conclusion, we have demonstrated the possibility to tune the band structure and therefore the electronic transport properties of graphene through functionalisation with fluorine. In particular, depending on the fluorine concentration different transport regimes can be accessed. For mono-layer samples, we observe a transition from 2D Mott VRH to Efros-Shklovskii VRH with increasing the fluorine content. Multi-layer fluorinated graphene with high concentration of fluorine shows 2D Mott VRH, whereas CF_0:28 multi-layer flakes exhibit NNH transport. Our experimental findings demonstrate that the ability to control the degree of functionalisation of graphene is instrumental to engineer different electronic properties in graphene materials. In all cases, fluorinated graphene transistors exhibit a large on/off ratio of the current, making this material of interest for future applications in transparent and bendable electronics.

2D-VRH: two-dimensional Mott variable range hopping; AFM: atomic force microscopy; F-GIC: fluorine graphite intercalation compounds; FWHM: full width at half maximum; NMR: nuclear magnetic resonance; NNH: nearest neighbour hopping; VRH: variable range hopping.

The authors declare that they have no competing interests.

FW fabricated the fluorinated graphene devices and carried out the measurements. MD synthesised the fluorinated graphite. FW and MFC performed the data analysis. FW, SR and MFC wrote the manuscript. All authors discussed the results, read and approved the final manuscript.