Low temperature electrical transport in microwave plasma fabricated free-standing graphene and N-graphene sheets

Graphene, being the most outstanding of the 2D carbon-based materials, attracts a vast research interest and an impressive amount of research is reported, e.g. [1, 2]. This is provoked by their extraordinary characteristics, including electrical transport properties such as high conductivity and charge mobility. However, the extreme conducting properties are inherent to а perfect single infinite 2D graphene lattice. Actually, most graphene materials being epitaxially grown or prepared by chemical methods comprise some degree of disorder affecting their transport properties revealing localization effects, electron-electron interactions, phenomena known to control the transport in disordered conductors [3–6].

Moreover, different methods are applied intentionally for controlling graphene properties such as surface functionalization by exposure to gases or plasmas, doping with heteroatoms, formation of nanoribbons, etc [7, 8]. Different doping agents are generally used to influence the physicochemical and electronic properties such as oxygen, nitrogen, boron, phosphorus, etc [9–11]. Nitrogen-doped graphene (N-graphene) shows enhanced characteristics as compared to the pristine graphene, because it adds novel electrochemical features to the unique properties of graphene [11]. Generally, nitrogen doping shifts the Fermi level towards the conduction or valence bands depending on the N-doping configuration [11]. Nitrogen dopant usually resembles into the graphene lattice three bonding configurations, including pyridinic N (N with two C atoms, bonded in a hexagon) at the edge or defects, pyrrolic N (N with two C atoms, bonded in a pentagon), and graphitic N (N substitutes a C atom in a hexagon). It is shown that not only the nitrogen concentration, but also the specific bonding configurations are essential for the different applications [12]. Due to the modifications in the structure and the morphology, N-graphene can offer significantly improved performance in various applications, such as energy storage, electrocatalytic activity, transport properties etc [11, 13, 14].

Self-standing graphene sheets are an alternative to surface-supported graphene material needed for specific applications. Production of free-standing graphene sheets consisting of a few atomic monolayers is important for a variety of applications such as batteries, supercapacitors, nanocomposites, etc [15]. However, besides the variety of production methods developed high quality free-standing material production on a large scale in a reproducible manner and at low cost is a great challenge [16]. In this respect microwave-driven plasma methods were recently applied for selective synthesis of high quality free-standing graphene sheets via a single step process [17]. The material is produced in a free standing form in the plasma volume. It is not deposited on a substrate nor is detached from one and transfer methods are not needed. As far as there is no substrate, the properties of graphene material are not influenced by the presence of substrate as is observed in, e.g. CVD deposited graphene.

Although being of high structural quality as previously shown [17], the electrical transport properties of the synthesised material are not thoroughly explored. Actually, the studies on electrical conductivity of other free-standing carbon materials are scarce. Mostly graphene powders used as fillers in composite matrices and compacts produced by compression are investigated [18]. Graphene-based composites and results on their electrical properties as well as conductivities studies as a function of fabrication method are reviewed [18, 19]. Various studies show that the intrinsic material properties determine the bulk conductivity but it is also strongly affected by the packing density of the particles and matrix composition as well as of the contacts between particles, [19–21]. However, the transport mechanisms in such composite media are not examined in detail and the problem is worth of further investigation.

In this paper, we present investigations on transport properties of free-standing graphene sheets as well as N-doped graphene material fabricated by microwave plasma-based method. We address the current flow mechanism of graphene and N-graphene sheet compacted in pellets. For this purpose, the temperature dependence of the resistivity/conductivity is studied in a temperature range (10–300 K). The room temperature conductivity values are high being on the order of 10³ S m⁻¹. However, the observed temperature dependence reveals insulating behaviour in the whole temperature range below 300 down to 10 K. The observed behaviour is attributed to the influence of a quasi-two dimensionality of ordered graphene sheets and the presence of disorder in the compacts.

High structural quality free-standing graphene/N-graphene sheets were the materials under investigation. Three samples were considered in this study, i.e., pristine graphene (PG), N-graphene obtained by in situ plasma method (NG), and N-graphene obtained by plasma post-doping of pristine graphene (NG_PD).

2.1.  In situ plasma synthesis of graphene/N-graphene structures

2.2. Post-doping plasma synthesis of N-graphene structures and material characterization

More commonly used doping procedure is post-treatment plasma approach, which relies on N₂ or ammonia plasma processing of previously synthesized graphene [24, S7]. The level of nitrogen doping can be controlled by tuning the plasma parameters and the exposure time. Moreover, by post plasma synthesis usually higher doping concentrations are achieved. One of the samples reported in this work, i.e., NG_PD was obtained by processing a pristine graphene in a low-pressure microwave N₂-Ar large-scale plasma reactor. The graphene sheets were treated in the afterglow region of slot-antenna-excited microwave plasma, described in [S13, S14]. The graphene sample was processed for 12 min at pressure and microwave power of 1 mbar and 600 W, respectively.

2.2.1. Structural and chemical characterization

The synthesized graphene/N-graphene was caracterized by Scanning Electron Microscopy (SEM), Raman and x-ray photoelectron spectroscopies (XPS) and Near Edge x-ray-absorption fine-structure (NEXAFS) spectroscopy. Details regarding the experimental techniques are given in the Supplementary data.

Results from the physico-chemical characterization of NG_PD sample, consisting of SEM, Raman spectroscopy, XPS and NEXAFS analyses are shown in figure 1. The morphology of the free-standing N-graphene sample shows 2D nature of the structures, i.e., randomly oriented sheets with curvatures can be clearly identified, see figure 1(a). The white areas on the image represent the zones of folded edges, as well as overlapped and wrinkled sheets. Raman spectroscopy is very often used to efficiently provide a quick and easy structural characterization of the sample. Amongst the several spectra, measured at different randomly selected areas of the N-graphene sample, two types of spectra were distinguished, and the average spectra are shown in figure 1(b). The spectra comprise three dominant peaks at ∼1332 cm⁻¹, 1585 cm⁻¹, and 2658 cm⁻¹ attributed to the D, G, and 2D bands, respectively. The presence of G and 2D bands in the spectra demonstrate graphene-like nature of the material. The G peak is typical for all sp² carbon systems, representing the in-plane vibrations, while 2D peak is related to the second order scattering process and it is intense, narrow and symmetrical only in graphene-like materials.

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The most prominent for graphene-like materials 2D peak is often used to estimate the number of graphene layers: full width at half maximum of 2D peak is ∼(48–50 cm⁻¹) suggesting that these structures are predominantly composed of several-layers [S3, S4]. The D peak and the small shoulder of the G peak (D') are typically activated by defects, presence of sp³ carbon, and/or edge effects, but also by doping effects. The intensity of D and D' peaks depend on the type of defects and their concentration in the graphene layer and the size of graphene flakes their folding. The presence of nitrogen atoms in the sample represents structural defects in graphene lattice, contributing to the D band intensity. The variation of the peak intensities of the two types of spectra $\left({I}_{D}/{I}_{G}\sim 0.4-1.08\right)$ imply that the sample is inhomogeneous, which is expected since the post-doping of graphene leads predominantly to surface doping. Contrary to the direct plasma N-graphene synthesis, here the post-plasma doping modifications are localized at the sample surface.

The XPS survey spectrum, taken in the binding energy range 0–600 eV, revealed presence of dominantly carbon, but also oxygen and nitrogen. The elemental composition, obtained from the intensities of the major photoelectron lines after removing the background of Shirley type, was estimated as follows: 96.9 at % of C, 1.54 ± 0.1 at % of N and 1.56 ± 0.1 at % of O. The most intense contribution at 284.4 eV readily attributed to the sp² C–C bond and accompanied by its shake-up π – π* satellite, figure 1(c), is an evidence of the graphene nature of the material. The contribution at 285.2 eV can be due to the sp³ carbon i.e., defects, while the contribution at 286.3 eV is related to the C–O–C and/or N bonds with sp² hybridized carbon [25, 26]. The N 1s photoionization, figure 1(d), was fitted to two contributions of equal intensity at 398.8 eV and 400.2 eV, attributed to pyridinic and pyrrolic nitrogen groups, respectively [26, 27].

Additionally, the NEXAFS spectra, presented in figures 1(e), (f), were obtained on the C K-edge and N K-edge. The characteristics sharp C 1s → π* resonance (A) at ∼285.3 eV [28, 29] and the σ* resonance (C) at ∼291.8 eV [28, 30] are detected. The moderate feature detected in between (B) gives indication that small amounts of N and O are present, which is verified also in the peak detected in N K-edge spectrum, figure 1(f). A narrow peak (A) at ∼399 eV is assigned to pyridine-like bonding that arises from transitions from the K-shell to the unoccupied π* orbital [31], while (B) at ∼400 eV is usually assigned to pyrrole/amino groups/substitutional graphite-like bonding . Other contributions (C, D) at ∼402–410 eV, are attributed to N–C/N–H bonding [32].

2.3. Electrical conductivity experiment

The measured longitudinal conductivity (σ_||) values are an order of magnitude higher than the transversal (σ_⊥) electrical conductivity measured on the compacted PG and N-graphene sheets, table 1. The observed dependence on the current flow geometry implies that the graphene sheets in the pellets have preferential orientation ordering probably induced during the compaction process. The observed electrical conductivity dependence on the current flow geometry is consistent with the predominant orientation of the graphene sheets in the pellets observed by SEM imaging. Actually, SEM imaging of the pellet's cross section (figure 2) shows the compacted primary graphene sheets forming agglomerates, mostly oriented parallel to the pellet's plane, figure 1(a).

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Тhе treatment of graphene-based free standing sheets is a complicated problem because the sheets are known to react during their processing. The observed near parallel orientation of the sheets can be induced by the compaction process during pellets' formation. As a result a network of connected graphene sheets could be formed. Graphene sheets are known to agglomerate in a composite due to their strong van der Waals attraction. Our observations support a process of self-organization of the graphene sheets according to their orientation with respect to the plane of the specimen. Further, the ordered graphene sheets form electrically percolated paths and the electric response of the composite as a whole is affected by such stacking. This arrangement yields a highly anisotropic conductive system.

The high longitudinal electrical conductivities measured could be due to the excellent properties of the individual graphene sheets. Because of the highly preferred in-plane orientation of the large surface area graphene sheets induced by the compaction process, the measured longitudinal conductivity yields mainly the intrinsic conductivity of primary single sheet for the in-plane direction. From another point of view, the application of pressure during the pallets´ preparation modifies the bulk density and influences the conductivity, as observed earlier [33], by enlarging the contact area between the graphene sheets and leads to increased conductivity. The electrical conductivities of the pellets were studied previously as a function of the bulk density and were found to depend on it. The study suggested bi-linear relationship observed for powder compacts around the percolation threshold [19]. All samples chosen for the present study are of similar density 0.4 ± 0.01 g cm⁻³ and show electrical conductivity just above the percolation threshold thus ensuring stable current flow.

Further, with the aim to establish the dominant conduction mechanism, temperature dependences of the resistivity ρ(T) are recorded in the temperature interval 10 K < T < 300 K. The current is limited to 10 mA, and measured voltage values are typically about 100–150 mV. The samples are mounted in the cryostat under vacuum conditions and cooled slowly to 10 K at average rate of about 2 K min⁻¹ and at every measurement point the temperature is set constant during the resistivity measurements.

The temperature dependences of resistivity of the samples prepared using the described different N doping procedures are presented in figure 3. Pristine graphene characteristics are also depicted for comparison. Figure 3(b) shows typical linear current-voltage characteristics confirming the Ohmic contact character for current values ranging from 1 to 10 mA. The room temperature conductivity values σ(300 K) reveal explicit influence of the N doping content, the higher at% sample being higher in conductivity (table 1).

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Further, the temperature dependences of the resistivity/conductivity for all samples show thermally activated transport. An increase of resistivity with decreasing temperature $(d\rho /dT\lt 0)$ is observed, being opposite to the typically metallic behaviour $(d\rho /dT\gt 0)$ that could be expected for highly conducting media. On the contrary, the $d\rho /dT\lt 0$ is characteristic for an insulating state or a localized system [5].

Measured temperature dependences ρ(T) from figure 3 besides showing non-metallic behaviour in the whole temperature range, reveal also change of the slope at a certain temperature T*. As seen from figure 3, no single law can fit the entire curve of the conductivity. Actually, two distinct behaviours at low and high temperatures are distinguished in the thermally excited transport. The characteristic temperature T* indicates a manifested transition between two competing physical processes.

Such anomalous temperature dependent transport in graphene is reported for CVD grown material [34], nano ribbons [35] and rGO [36]. Indeed, it is known that a variety of independent contributions to electron mobility in graphene are possible, depending on carrier density and temperature range, which could influence nontrivially the conductivity. The anomalous temperature dependence of graphene conductivity has been theoretically approached by accounting for the competition of thermal activation, screened impurity scattering, and phonon scattering [5, 37]. It was shown that graphene could exhibit $d\rho /dT\lt 0$ behavior or the expected 'metallic' behaviour $d\rho /dT\gt 0$ depending on carrier density and temperature ranges [4, 5]. Moreover, previous works reported that graphene transport properties are sensitive to the presence of disorder within the graphene matrix, i.e. [34].

Conduction mechanisms are frequently investigated in the presence of disorder in intrinsically conducting media. For metals or nanocrystalline semiconductors, the effects of disorder are manifested as an increase of the low temperature resistivity because of effects of weak-localization and electron-electron interactions. The transport is described by variable range hopping (VRH) mechanism [38]. The compacted graphene sheets under investigation here indeed form such a partially disordered system composed of stacked up together otherwise conducting individuals. Thus, the conductivity could be governed by hopping and tunnelling between separate graphene sheets within the pellet.

It is known that hopping conduction can be in the form of two main mechanisms: nearest neighbour hopping (NNH) and VRH. The two mechanisms usually proceed simultaneously while one of them is dominant depending on the specific experimental conditions. At low temperatures the dominant mechanism is variable range hopping. VRH has been observed in disordered systems, including amorphous carbon and involves consecutive inelastic tunnelling processes between available localized states [39, 40]

The typical expression for VRH conductivity σ considered according to Mott [38] is:

$$\begin{eqnarray}&&\sigma \propto exp\left(-{T}_{0}/{T}^{\gamma }\right)\end{eqnarray} \tag{ 1 }$$

Here, the exponent γ differs for different hopping mechanisms, being $\gamma =1/(d+1)$ where d denotes the dimensionality, with d = 2 for 2D and 3 for 3D case. Mott-VRH assumes density of states (DOS) near Fermi level N(E_F ) constant. An exponent γ of 1/2 corresponds to Efros and Shklovskii (ES) VRH, and 1 for NNH, respectively. Efros and Shklovskii [40] showed that Coulomb interactions between different hopping charged sites result in DOS depletion near the Fermi level and formation of Coulomb gap. The exponent in this case is independent of dimensionality and equals ½.

Further, the analysis of the temperature dependences of the conductivity from figure 3 in the high temperature range T > T* shows that all curves fit a simple temperature activated form:

$$\begin{eqnarray}&&\sigma \sim exp\left(-{E}_{a}/{k}_{B}T\right)\end{eqnarray} \tag{ 2 }$$

where E_a is hopping activation energy. The temperature dependences of the conductivity are depicted in figure 4(a) for all samples showing linear dependence on T⁻¹ in this temperature range (Arrhenius plot) which is consistent with NNH mechanism. The activation energy values E_a (table 2) are of the order of 3 to 10 meV which is consistent with the typical energy scales for NNH thermaly activated transport [41] in graphene films and graphene nanoribbons [35, 42]. Assuming ${E}_{a}=\tfrac{{k}_{B}T\alpha }{8d}$ [38] and the graphene nearest neighbour distance d = 1.42 Å, the localization length of the electronic wave function α values could be deduced.

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On the contrary, a change to a steeper functional dependence when the temperature is decreased (T < T*) suggests the onset of different temperature activated transport process that is best explained by transport via Mott hopping mechanism. All curves fit behaviour similar to Mott's approach to 2D VRH in disordered systems:

$$\begin{eqnarray}&&\mathrm{log}\,\sigma \propto {T}_{0}/{T}^{1/3}\end{eqnarray} \tag{ 3 }$$

Here T₀ is a characteristic coefficient which depends on the 2D DOS N(E_F ) as follows:

$$\begin{eqnarray}&&{T}_{0}={\left[\displaystyle \frac{3}{{k}_{B}N\left({E}_{F}\right){\alpha }^{2}}\right]}^{1/3},\end{eqnarray} \tag{ 4 }$$

where ${k}_{B}$ is the Boltzmann constant. Figure 4(b) presents the conductivities versus T^−1/3 for the three samples. The linear fits clearly show that the temperature dependence is consistent with the 2D VRH model (γ = 1/3). Satisfactory fits were obtained with correlation coefficients ${R}^{2}=0.98-0.99.$ From fitting analysis and using equations (1) to (4) values of the characteristic parameters for the two transport regimes, i.e. T₀ (being the slope in the high temperature limit), T*, N(E_F ), are deduced and listed in table 2. The average hopping distance R_h between the localized states is estimated at the crossover temperature T* (table 2) using equation 4 and the following expression [38]:

$$\begin{eqnarray}&&{R}_{h}={\left\{\left(8\pi /9\right)\,{k}_{B}TN\left({E}_{F}\right)/\alpha \right\}}^{-1/3}.\end{eqnarray} \tag{ 5 }$$

The N induces in the VRH system an increase in the hopping probability and hopping distance, and decrease in the resistance. It should be noted that the condition ${R}_{h}/\alpha \geqslant 1\,$which is required from Mott VHR strongly localized conditions is satisfied at the transition temperature.

In order to check the possibility for Efros-Shklovskii (ES-VRH) mechanism to be valid at low temperatures, the critical temperature T_c under which ES is applicable was determined using the expression [40]:

$$\begin{eqnarray}&&{T}_{c}=\frac{{e}^{4}\alpha N({E}_{F})}{{k}_{B}{(4\pi \varepsilon {\varepsilon }_{0})}^{2}}\end{eqnarray} \tag{ 6 }$$

where ε₀ and ε are the vacuum permittivity and the dielectric constant of the material. Assuming ε = 6 [43] the calculated T_c values were found to be lower than 1 K which is out of the temperature range of our measurements. Thus, the Coulomb interaction can be neglected, the used assumption for N(E_F ) being constant is applicable and Mott-VRH is concluded as the dominant conductance mechanism at temperatures T < T* here studied. It should be noted that the graphene samples under investigation are composed of compacted graphene sheets in a pellet and the stacks of individual sheets form 3D structure [38, 44]. Obviously, the two-dimensional (2D) character reflected by the observed ∼T^−1/3 dependence is consistent with the 2D structure of the sheets. Hopping events might occur between the distinct graphene stacks by consecutive inelastic tunneling processes.

We should point out that the conductivity σ(300 K) of the samples is high because of the highly conductive individual graphene sheets while the insulating temperature behaviour demonstrated is due to the disorder induced during the stacking of the material sheets.

Summarizing our results, the incorporation of N pronouncedly influences the transport mechanism consistent with other observations [45]. The conductivity of the N doped material increases, and accordingly, the estimated density of states show an increase with N-doping compared to the pristine material as the inclusion of N donates an extra electron per added N atom and to the electron conduction paths. The transition point from NNH to Mott-VRH moves to lower temperatures and higher conductivity with increasing N doping. After the transition to VRH is reached the influence of N doping is not much pronounced and the disorder is dominating the localization.

In this work the electrical conductivity mechanism of pristine graphene and N-graphene sheets compressed into pellets is reported for the first time. Orientation dependence of the conductivity is due to the preferential orientation of the free standing graphene sheets parallel to the pellets' plain. The synthesised material conductivity displays a highest measured value of (3500 ± 350) S/m, which is comparable or exceeds other reported values for graphene sheet powders obtained by different methods [46, 47]. It could be ascribed to obviously highly conductive primary sheets forming a conductive network with numerous interfaces between them. The observed overall insulating behaviour at temperatures lower than 300 K is disorder induced due to the structural configuration of the graphene sheets agglomerates. The charge transport indicates a transition from thermally activated near–neighbour hoping at relatively higher temperatures to variable range hopping via 2D localization at lower temperatures. The observed charge transport mechanism is typical for partially disordered systems like nanocrystal arrays. This investigation provides insight on the conductance properties of self-standing graphene sheets widely needed for application purposes as an alternative to surface-supported graphene. The investigated material, produced by microwave plasma-based method is of a high quality and fabricated on a large scale in a reproducible manner and at low cost.

This work was performed under the framework of the PEGASUS (Plasma Enabled and Graphene Allowed Synthesis of Unique nano-Structures) project, funded by the European Union's Horizon research and innovation program under grant agreement No 766894. Work partially funded by Portuguese FCT - Fundação para a Ciência e a Tecnologia, through EAGER project (PTDC/NAN-MAT/30565/2017) and under projects UIDB/50010/2020 and UIDP/50010/2020. The authors would like to thank S. Russev for the SEM images. M A, E V, K K and Zh K thank the European Regional Development Fund within the Operational Programme 'Science and Education for Smart Growth 2014–2020' under the Project CoE 'National center of mechatronics and clean technologies 'BG05M2OP001-1.001-0008'.

The data that support the findings of this study are available upon reasonable request from the authors.

The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.

E V and N B wrote the paper. E V formulated the research idea and analysis of the data. K K performed the conductivity experiments and analysis of the data. N B, A D, E F fabricated of the samples and analysis of the data. M A performed Raman spectroscopy measurements. N B, O M N D T performed XPS measuremants and analysis. T S performed NAXAFS measurements. Zh K, L L A and E T analysis of the data.