Kinetics of the thermal reduction process in graphene oxide thin films from in-situ transport measurements

We investigate the influence of the thermal annealing process on the transport properties of thin films made of graphene oxide. Specially developed methodology allows us to demonstrate that the thermal annealing process of graphene oxide thin films can be described as a kinetic process with one activation energy, which equals 0.94 eV ± 0.12 eV. Moreover, we show that the electrical transport mechanism evolves with the annealing temperature (reduction level) of GO thin films. We have noticed that the Variable Range Hopping transport model change from 3D, 2D to Efros-Shklvoskii with a reduction level. Our findings contribute to further understanding of the role of kinetics in thermal reduction processes of thin films made of graphene oxide and could be useful in applications in which electrical parameters need to be tuned.


Introduction
Graphene oxide (GO) is a highly defected (oxidized) and nonconductive version of graphene [1,2]. It possesses a few interesting features such as: (a) well-established production method taking abundantly occurring graphite crystal as a substrate [3][4][5]; (b) presence of hydroxyl and carboxyl groups [6][7][8][9][10], which could act as reactive centers for a variety of surface-modification reactions enabling, e.g., polymer composite formation [11,12]; (c) excellent water solubility [13][14][15] and high adhesion between flakes allowing for efficient thin-film production [16]; (d) tunable photoluminescence [17], carrier recombination time ranging from approximately 1 ps to above 300 ps [18], and saturable absorption [19] , which make GO an interesting material for ultrafast photonic applications. Moreover, through the chemical [20,21] or thermal [22][23][24] treatment as well as through the irradiation by the electron beam [25,26] or by the UV light [27], graphene oxide can be easily transformed into another important version of graphene-reduced graphene oxide (rGO) [28]. Such an indirect route of graphene fabrication through the intermediate GO phase is considered very attractive because it combines advantages of GO related to facile production and processing, and unique properties of graphene received in the end material after reduction. Formally, the reduction process consists of removal of some amount of functional groups containing oxygen (e. g., hydroxyl, carboxyl, epoxy) from the honeycomb carbon lattice. The reduction process leads to partial restoration of the pristine graphene properties [29], like conductivity and hydrophobicity, despite still large amount of structural defects.
This directly paves way to these graphene-based applications in which outstanding electrical parameters are not crucial [30], like transparent electrodes [23,24] or print [31,32].
First works on transport properties of graphene oxide during thermal annealing were published by Jung et al [22,33,34], who examined individual single-layer and multi-layer GO platelets obtained through the wet exfoliation method. The analysis of the electrical resistivity versus time in temperatures led to the conclusion that below 180°C the thermal reduction process can be described as a kinetic process with the activation energy of 1.6 eV mol −1 .
Moreover, the analysis of results from temperature programmed desorption experiment provided information that decomposition of graphene oxide begins at temperature equaling approximately 70°C. Among desorbing gases, apart from expected O 2  undesirable carbon loss occurs during annealing. What is important, most of these results have been further confirmed by other groups using, e.g., differential scanning calorimeter technique [35,36].
In this study, we focus on further deepening of our understanding of the reduction mechanisms of thin films made of graphene oxide induced by elevated temperatures, and on their link to changes in transport properties during thermal annealing. We note that in contrary to previously published reports [22,33,34], here we examine thin film made of graphene oxide, thus we are not studying properties of individual platelets, but homogenous films with lateral dimensions of few mm and thickness of 200 nm. Such films are much more complicated physical systems than individual single-or multi-layered flakes. The macroscopic conductivity consists of conduction of individual flakes part and conduction between adjacent flakes, which is ruled by their arrangement.
Therefore, the possibility of formation of percolation paths, the conduction through the interfaces, and changes in both during annealing should be embraced. Moreover, gas desorption occurring at elevated temperatures might lead to changes in film morphology, having a great impact on the distribution of the conduction paths and properties of the interfaces, which directly result from the morphology. For example, part of the desorbed gases could form a 'bubble' within the thin film that will locally loosen the thigh arrangement of the flakes leading directly to a further decrease in electrical conduction.
Changes in transport properties of thin films made of GO during annealing have been barely studied, existing literature is limited to remarks about sudden decrease in the resistivity value and its further stabilization in time [37][38][39]. Here, on the contrary, we pay special attention to the first moments of the thermal annealing process. We demonstrate that analysis of temporal changes in resistivity while a set of thin films made of GO is exposed to different elevated temperatures allows us to conclude that, surprisingly, the thermal reduction can be described as the kinetic process with one activation energy, that equals 0.94 eV±0.12 eV. We note that we adopted a more strict methodology than in the works of Jung et al [22,33,34], that the unit of our result is eV not eV per mole or molecule, and that the value of the energy activation is in agreement with theoretical calculations on the GO reduction process [40][41][42]. We show that Variable Range Hopping (VRH) transport models are the predominant transport models in our thin films [43][44][45][46][47][48][49]. Moreover, we have noticed that the electrical transport model evolves with the reduction level of our GO thin films. Samples reduced in lower temperatures (450 K-475 K) shows 3D and 2D-VRH model, while samples with higher reduction level (490 K-500 K) are well described by the Efros-Shklovskii model (ES-VRH).

Experimental
Graphene oxide thin films were fabricated by the vacuum filtration method [50] from commercially available GO solution in water (concentration of 4 mg/ml, Graphenea Inc.). The lateral dimensions of all GO thin films are about 5 mm×5 mm, whereas their thicknesses are about 200 nm. Because all films are completely mechanically unstable, we deposited them on popular 10 mm×10 mm low resistivity silicon substrates with thermally grown silicon dioxide (SiO 2 ) . To make good/stable electrical contacts we evaporated 100 nm-thick palladium electrodes at the four edges of the GO films. Palladium film was deposited using a thermal evaporation system (Kurt J Lesker Nano 36) and mechanical mask. The mechanical mask approach has been chosen to ensure that we have got as clean samples as possible. The lithographic process for producing metal contacts requires using polymers, which should be annealed, and the additional chemical treatment in the developing process. Samples prepared this way were attached and bonded to an electrical adapter and placed inside Oxford MicrostatHe2 cryostat. One of the samples just before the measurements is shown in figure 1(a).
Before and after the thermal reduction process we made some structural investigations. SEM image shown in figure 1(b) illustrates a smooth and continuous GO surface. The optical images of the GO samples before and after the thermal reduction process are shown in figures 1(c) and (d). In figures 1(e) and (f) we present typical Raman spectra of our samples, which prove that we investigate a highly disordered form of carbon [51]. We can observe the D (defect-induced) and G (signature of the sp 2 carbon) modes, and no 2D (related to the quality of the sp 2 carbon lattice) mode. Statistical distributions of the ratio of the intensity of the D mode I D to the intensity of the G mode I G before and after the thermal reduction process are shown in figures 1(g) and (h). A significant increase in the I D /I G ratio that is seen, could be related to further damage of the hexagonal carbon lattice upon thermal treatment [50]. Figure 1(i) shows the intensity of the D mode I D versus the intensity of the G mode I G before and after the thermal reduction process. What can be concluded is the linear dependence between I D and I G and much lower Raman signal intensity after the thermal reduction process. The latter information means that carbon loss in the examined thin film is highly probable. Figure 1(j) shows a correlation analysis between the position of the D mode ω D and G mode ω G . Assuming that position of the D mode is approximately 2 times smaller than 2D mode [52], we can use the vector decomposition method [53] to conclude that thermal annealing results in an increase in doping whereas not affecting the strain.
Electrical measurements of the sheet resistance R S value were performed in the van der Pauw configuration [54] with Keithley SMU 2450, National Instruments PCI-6281 acquisition card, and Keithley 7001 switch equipped with Keithley 7065 hall card. We carefully verified that our transport measurements do not lead to structural changes in an object under investigations, like, e.g., in the case of Raman spectroscopy [55]. The temperature of the samples was controlled through the Oxford Instruments Mercury iTC controller. Using the Pt1000 sensor we carefully verified that the temperature set on the controller is equal to the temperature of the silicon substrate surface in the whole 300 K-500 K temperature range.

Results and discussion
The main results of this paper are shown in figure 2(a), which illustrates the time evolution of the sheet resistance R S of five thin films made of GO exposed to five elevated temperatures (450 K, 460 K, 475 K, 490 K, and 500 K) at ambient atmosphere. Before we provide physical interpretation, we want to clarify a few unobvious issues. First, we note that for each of the prepared samples we applied only one selected temperature that was constant during the whole experiment (instead of stepwise temperature change like in works of Jung [22,33,34]). The main advantage of such an approach is the same (or very similar) 'starting point' for the reduction process in all cases because all the samples were fabricated from the same 'batch'. The main drawback is the requirement of having a set of very similar samples (the number of samples should be equal to the number of selected temperatures) and a longer duration of the whole experiment. Secondly, for all samples value of the sheet resistance decreases in time up to some level, afterwards it is approximately constant. Initial changes in R S depend on the temperature of the annealing (the lower temperature the slower changes meaning slower reduction process), which is an expected effect. The final value of sheet resistance does not follow the temperature trend, where we observed that samples reduced in 460 K and 490 K do not fit into the pattern. This effect could be described as a difference in the morphologies of the samples, which proves that it is a highly disordered material, especially when it is reduced. We would like to remind that all samples are from the same filtration process, which should ensure that morphologies are as similar as possible. Despite that, the conductivity distribution is no longer similar after the reduction process.
Third comment is related to the time scale which is limited and different for each of the temperatures. In the performed experiment the acquisition of voltage and current values were continuous from the very beginning up to the time the resistivity value has stabilized but no longer than 10 h. However, it can be seen that for each trace there is no experimental data even at the beginning of the measurements. It is because all samples were insulating after the fabrication process (a measurement of their resistance was beyond the technical possibility of used instruments). During the reduction process, the current value systematically increased and in consequence, at some point, the measured resistance value started to reflect the true sheet resistance of the sample. This effect is nicely rendered as the shift of the first plotted experimental point versus the temperature of the annealing. Selection of the moments from which we consider data reliable was made arbitrary. We also remark that in all cases the elevated temperature was applied at the 'zero' time. Analysis of the reduction process reflected in changes in resistance requires some justified assumptions: (1) we fabricated a set of very similar samples having very similar 'starting point'; (2) energy of desorption of all functional groups can be expressed as one averaged energy-we call it E a ; (3) Boltzmann statistic describes the energy distribution among functional groups, which implies that probability of desorption of one 'averaged' functional group equals p 1 =exp(−E a /k B T), where k B is Boltzmann constant and T means temperature; this probability p 1 is related to the time constant τ at which we observe the decrease in resistivity ρ; (4) number of functional groups dN that is desorbing in unit time t is proportional to the current number of functional groups N(t), i.e., dN=−N(t)·exp (−E a /k B T); (5) resistivity of the GO flake ρ(t) is related to number of functional groups N(t), i.e., N(t)-N f ∼lnρ(t)-lnρ f , where N f and ρ f are residual values of the number of functional groups and resistivity, after reduction [34,56,57]. Finally, we obtained the R(t) formula given by: where R 0 means the residual sheet resistance resulting for example from wires and contacts, β is the constant value of proportionality factors and final concentration, R f is the final value of resistance, τ is the time constant of the thermal reduction process. Solid lines in figure 2(a) represent the theoretical dependence of the time function of resistivity fitted to experimental data for five annealing temperatures. Excellent correspondence between experiment and theory proves that the thermal reduction process of the thin film made of graphene oxide can be described as a kinetic process with one activation energy. Moreover, this conclusion consists with theoretical predictions, which underline the role of kinetics [41]. To calculate the value of the 'averaged' activation energy we plotted in figure 2(b) logarithm of the time constant τ (obtained from fitting procedure to data from figure 2(a)) versus (k B T) −1 . The slope of the fitted straight line equals the 'averaged' activation energy 0.93 eV±0.12 eV, which results directly from the third assumption. This value is comparable with the value reported by other authors. For example, Larciprete et al [40], who 'identifies a dual path mechanism in the thermal reduction of graphene oxide driven by the oxygen coverage' report activation energies of 1.13 eV (DFT) The last question we analyze in this work is the conduction mechanism of thermally reduced thin films made of GO. For this purpose we make measurements as a function of temperature, i.e., we measured R S for temperature ranging from room temperature (RT) up to the temperature the sample was annealing at (AT). Such temperature sweep was performed six times one after the other (AT→RT→AT→RT→AT→RT) just after annealing, which is illustrated in figure 3(a), and once again the whole sequence a few hours later, which is illustrated in figure 3(b). As can be seen, for all samples traces acquired just after annealing are repeatable despite small hysteresis (the difference between results obtained when heating and when cooling). This means that samples are stable at temperatures up to the temperature of the annealing; however, the temperature changes were too fast. On the other hand, traces acquired a few hours after annealing are almost reversible. The most visible discrepancy occurs for the first temperature sweep, but a smaller shift can be observed even for further sweeps. It is difficult to establish the origin of this effect; however, we suspect that it could be the effect of water absorption. We note that water is often observed compound during thermal desorption from graphene oxide.
For the analysis of the conduction mechanism we used averaged data from the first tarce ( figure 3(a)) and fit the variable range hopping model (figure 3(c)) expressed as: where R S means sheet resistance, R S,0 means the residual sheet resistance resulting from example from wires and contacts, T 0 is the Mott temperature, and m=1/(d+1), where d is the dimensionality of the conduction. The electronic transport determination has been done by two methods described in the supplementary information. We found out that the conduction transport model in our GO thin films evolves with reduction temperature, which is related to the reduction level of our materials. The general trend could be described as a reduction of dimensionality d with an increase of the annealing temperature. The samples reduced in temperatures 450 K, 460 K, and 475 K are well described by the 3D (m=1/4) and 2D-VRH (m=1/3). We note that the sample reduced 475 K were characterized by higher fluctuations, figure S1 (available online at stacks.iop.org/MRX/8/015601/ mmedia), which could be the reason of the m=1/4. Next, the samples reduced in higher temperatures are greatly described by the Efros-Shklovskii VRH model (m=1/2). The lower fraction of the sp 2 /sp 3 in GO thin-film network causes the electrical charges to hop between localized states in 3 dimensions as expected for low reduced GO films [46]. When sp 2 /sp 3 fraction is increasing, the transport is mostly realized within the rGO flakes area, changing the transport model from 3D to 2D. Further reduction leads to Efros-Shklovskii VRH model which take into account the Coulomb interactions between charges hopping between localized states [43,44].

Conclusions
We demonstrated that methodology proposed by us, i.e., transport measurements on a set of very similar samples during annealing at different but constant temperatures, may justify that thermal annealing process of thin films made of graphene oxide can be described as a kinetic process with one activation energy 0.93 eV± 0.12 eV. Moreover, we have noticed that the electrical transport model evolves with the annealing temperature (reduction level) of GO thin films. The samples reduced in temperatures 450 K, 460 K ,and 475 K are described by the 3D-and 2D-VRH models, while the reduction in higher temperatures (490 K and 500 K) resulted in the Efros-Shklovskii VRH model. Our results are consisted with results obtained by other authors from other experimental techniques or calculations, and further complements on the physics of graphene oxide compound and thin films made of 2D materials.