Graphene films printable on flexible substrates for sensor applications

Figure 1 shows a scanning electron micrograph of the graphene deposit. It is apparent that the lateral dimensions of the flakes are in the micrometre range, although of course their thickness is three orders of magnitude smaller. Such materials pose challenges for this form of microscopy because the thickness of the flakes is massively smaller than the penetration depth of the electron beam used, and is even small compared to the range of secondary electrons used to form the image. As a result the three-dimensional structure of the whole near surface contributes to the image, rather than the normal situation when the image is dominated by the topography of the outermost surface. Additionally, the backscattered electron and secondary yields of graphene are both extremely low [18], and so ultimate resolution must be compromised in order to achieve sufficient signal to form an image.

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The XRD spectrum in figure 2 of the sample shows a strong and sharp [002] peak at 26.19° corresponding to an interlayer distance of ${{d}}_{002}=0.34\,{\rm{nm}}$ determined using Bragg's law, where the subscript (002) refers to the diffraction plane. These results are in good agreement with those obtained for exfoliated graphite oxide precursor after electrochemically reduction at 1.5 V, and are close to those for pristine graphite [19]. A value of 5.57 nm is estimated for the average crystallite size, ${D}_{002},$ from the Debye–Scherrer formula in the form:

$$\begin{eqnarray}&&{D}_{002}=\,\tfrac{0.94\,\lambda }{\beta \,\cos \,\theta },\end{eqnarray} \tag{ 1 }$$

where the value of the full width at half maximum (FWHM) ${\beta }={1.5}^{^\circ }$ is found from figure 2.

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The number of graphene layers ${{N}}_{{\rm{G}}{\rm{L}}}\,\,\,$ is estimated to be 15 from the expression ${{D}}_{002}=({{N}}_{{\rm{G}}{\rm{L}}}-1){{d}}_{002}$ assuming ${D}_{002}$ represents the thickness as measured from the centre of the sample. The stacking of these layers is responsible for the intensity and sharpness of the [002] peak [20]. The additional weak peak at 2θ = 13° due to the reflection from [010] plane implies the presence of residual oxygenated functional groups with interlayer spacing of 0.68 nm in the crystalline matrix of GI [21].

The Raman spectra in figure 3 for the GI sample were recorded for the wavenumbers ranging from 1000 to 3000 cm⁻¹. The characteristics peaks of D and G have been observed at 1345 cm⁻¹ and 1575 cm⁻¹ respectively in figure 3(a). These peak positions are in agreement with those observed for the annealed graphene layer ink-jet printed on a Si/SiO₂ substrate [22]. The D band is due to the breathing modes of sp² rings of six-atom rings. The intense G band arises from in-plane vibration of sp² carbon atoms present in the sample [23]. The intensity ratio of I_D/I_G is found to be 0.3, reflecting the defect concentration of carbonaceous materials [24]. A value of 20.6 nm is estimated for an average inter-defect distance L_D in nm using the relation [25]:

$$\begin{eqnarray}&&{{{L}}_{{\rm{D}}}}^{2}=\tfrac{4.3\times {10}^{3}}{{{{E}}_{{\rm{L}}}}^{4}}{\left[\tfrac{{{I}}_{{D}}}{{{I}}_{{G}}}\right]}^{-1},\end{eqnarray} \tag{ 2 }$$

where ${E}_{{\rm{L}}}\,=\,2.41\,{\rm{eV}}$ is the laser excitation energy. Although the spot size is nominally 2 μm, the laser beam is expected to penetrate into the depth of >50 nm encountering a large number of graphene flakes. Therefore, the estimated value of L_D is considered to be reasonable in the context of the scattering within a large volume [26]. The value of $74.9\times {10}^{5}\,{{\rm{cm}}}^{-2}$ is found for the defect density n_D from the knowledge that $\,{{{n}}_{{\rm{D}}}}^{2}=\tfrac{1}{(\pi {{L}_{{\rm{D}}}}^{2})}.$ These defects are believed to be located at the flake edges responsible for activation by double resonance giving rise to the D peak. Figure 3(b) shows that a broad 2D peak due to absorptions by second order zone-boundary phonons appears at 2690 cm⁻¹, representing a blue-shift by ~30 cm⁻¹ in relation to monolayer samples [27]. Also, a value of 80 cm⁻¹ for the FWHM of the 2D peak is approximately three times larger than that reported from single layer graphene. These observations are consistent with earlier XRD studies that the sample is multi-layered. This 2D peak, usually referred to as a second-order overtone of the D peak, is not assigned to the defects for their activation since its origin is attributed to the momentum conservation by two phonons with opposite wave vectors. However, the positions of both D and 2D peak are dispersive dependent on the laser excitation energy. Figure 3(b) also illustrates an analysis of the 2D peak envelope, assuming a Lorentzian peak shape. Three components are found to fit the envelope with their peaks to be located at 2675, 2700 and 2725 cm⁻¹.

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As shown in figure 4(a), in-plane dc conductivity measurements were made using the interdigitated electrode systems with dimensions of ${d}=0.5\,{\rm{mm}},$ $W\,=0.82\,{\rm{cm}}$ and ${N}=5,\,$where d, W and N are the distance between the fingers, the overlapping width and the number of fingers in the electrode system, respectively. Figure 4(b) shows the current I versus bias voltage V plots for the sample at $T\,=\,268\,{\rm{K}}$ and $T\,=\,330\,{\rm{K}}.$ These I(V) characteristics are linear within the bias voltage regime, implying the Ohmic nature of conduction. The dark Ohmic conductivity ${{\sigma }}_{{\rm{D}}}$ of the GI sample is estimated to be $1642\,\pm \,123\,{\rm{S}}\,{{\rm{m}}}^{-1}$ at $\,\,268\,{\rm{K}}$ from the relation:

$$\begin{eqnarray}&&{\sigma }_{{\rm{D}}}=\tfrac{1}{{R}_{{\rm{D}}}}\tfrac{d(N-1)}{t.w}.\end{eqnarray} \tag{ 3 }$$

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Values of dark Ohmic resistance ${{R}}_{{\rm{D}}}$ were determined from the slope of individual ${I}({V})$ plot in figure 4(a). This value of ${{\sigma }}_{{\rm{D}}}=\,1642\,{\rm{S}}\,{{\rm{m}}}^{-1}$ compares well with one observed for a printed $0.22\,\mu {\rm{m}}$ thick multi-layered graphene film which was annealed at 400 °C. The ink was produced from ultrasonicated ozone modification of aqueous dispersions containing exfoliated graphite [28]. Similarly a value of $1231\,\pm \,117\,{{\rm{S}}{\rm{m}}}^{-1}$ was obtained for ${{\sigma }}_{{\rm{D}}}$ at 330 K. A comparable value of $1100\,{\rm{S}}\,{{\rm{m}}}^{-1}$ for the room temperature conductivity is reported for a ~25 nm thick film spin-coated with dispersions of few layered graphene in N,N-dimethylformamide (0.7 mg ml⁻¹) solvent [29]. However, the resistivity of thin printed samples of UV-driven water-based graphene oxide/acrylic poly(ethylene glycol) diacrylate nanocomposite is reported to vary between ${10}^{4}\,\,$and ${10}^{6}\,{\rm{\Omega }}{\rm{m}}$ with the increase in the film thickness from 4 to 12 μm [30]. This shows the drop cast film of the present investigation is considerably more conducting than these nanocomposites.

Four further measurements were carried out at temperatures between $\,268$ and $\,330\,{\rm{K}}$ and the dependence of the dark resistivity ${\rho }_{{\rm{D}}}$ on T is shown in figure 5(a). This behaviour of ${\rho }_{{\rm{D}}}(T)$ can be described by a simple well-known relation in the form:

$$\begin{eqnarray}&&{\rho }_{{\rm{D}}}={\rho }_{{\rm{D}}0}[1\,+\,\propto T],\end{eqnarray} \tag{ 4 }$$

where ${{\rho }}_{{\rm{D}}0}$ and α denote the resistance at 0 K and the temperature coefficient of resistivity of the GI sample. The ratio of the slope to the intercept at ${T}=0\,{\rm{K}}$ gives $(3.07\,\pm \,0.12)\times {10}^{-3}\,{{\rm{K}}}^{-1}$ for the temperature coefficient α. This value is larger than one reported for graphene nanowalls by an order of magnitude [31]. It is, however, within the same order of magnitude as other highly conducting materials such as copper and silver [32]. The existence of positive temperature coefficient may be attributed to an increase in the interlayer distance with the rise of temperature, thereby reducing the tunnelling current between the layers [33]. The contributions of both optical phonons and intervalley scattering by transverse and longitudinal modes become increasingly significant with rising temperature [34]. The value of the activation energy ΔE is estimated to be 12 meV from the slope of Arrenhius plot in figure 5(b) of $\mathrm{ln}({\sigma }_{{\rm{D}}})$ as the inverse of temperature ${{T}}^{-1}.$ ${\rm{\Delta }}{E}=12\,\mathrm{\pm }\,1.5\,{\rm{meV}}$ represents a non-zero band gap between the conduction and valence band and it is smaller than room temperature thermal energy. The small value of ${\rm{\Delta }}{E}=12\,{\rm{meV}}$ in the present work implies the possible break up of lattice symmetry at the Dirac points (K) of the graphene films due to the presence of defects [35]. This observation is consistent with our earlier observations from Raman and SEM studies. ΔE is generally sensitive to the measurement environment such as the presence of moisture, local humidity and the hydrophobicity of the binder resin. A value of ${\rm{\Delta }}{E}=29\,{\rm{meV}}$ which is almost equal to thermal energy is reported for CVD deposited graphene films from Van Der Pauw conductivity measurement in vacuum for the comparable temperature range [36]. Both temperature coefficient and activation energy have been measured for graphene flake- and solar exfoliated reduced graphene within a similar temperature range with a view to developing wearable temperature sensors. The temperature coefficient is negative with the value of the same order magnitude as obtained in the present investigation, implying the potential applications of the present GI in the development wearable temperature sensors. Also, values of 24.19 and 90.7 meV for activation energies of graphene flake- and solar exfoliated reduced graphene respectively are higher than one obtained in the present drop-cast graphene film, indicating non-metallic characteristics of these graphene [37].

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The bending is commonly applied as strain for uniaxial tensile stress. As shown in figure 6(a), the strain was applied parallel to the length of the film so that the electrodes were not subjected to any strain. The strain is estimated in percentage from the knowledge of the substrate thickness and radius of curvature. Three radii of curvature of 2, 7 and 12 nm were used. Figure 6(b) shows the results of the bending test in terms of percentage change of resistances, $\left(\tfrac{{\rm{\Delta }}{{R}}_{{\rm{BS}}}}{{{R}}_{{\rm{B}}0}}\right)$ due to stretching. ${{R}}_{{\rm{B}}0}$ is the fresh film resistance prior to application of any stretching and compression stress and ${\rm{\Delta }}{{R}}_{{\rm{BS}}}=\,{{R}}_{{\rm{BS}}}-{{R}}_{{\rm{B}}0}\,$ where R_BS is the resistance of the strained film. $\tfrac{{\rm{\Delta }}{{R}}_{{\rm{BS}}}}{{{R}}_{{\rm{B}}0}}$ is found to increase with increasing strain, implying an increase in the resistance (R_BS) on stretching. Similar behaviour was reported for CVD grown graphene layers [38]. Phenomenologically, the stretching causes the increase in length of the film with simultaneous decrease in its thickness and both these dimensional changes contribute to the increase in Ohmic resistance on stretching. The Dirac points in the strained graphene are believed to have undergone displacement from the K points, possibly opening up the energy gap. The GI film surface may be not completely flat because of imperfect adhesion to the PET substrate. The scattering of charges due to the non-flat nature of the strained GI surface may also contribute to the increase in resistance [39]. The measurements were repeated on the same film under compression over the same strain range and the results are also illustrated in figure 6(b) in the terms of the dependence of $\left(\tfrac{{\rm{\Delta }}{{R}}_{{\rm{BC}}}}{{{R}}_{{\rm{B}}0}}\right)$ on the compressing strain where ${\rm{\Delta }}{{R}}_{{\rm{BC}}}=\,{{R}}_{{\rm{BC}}}-{{R}}_{{\rm{B}}0}$ in which R_BC is the resistance of the compressed film. As expected, the resistance is found to decrease with the increase in the strain. The opposite dimensional changes of the films occur on compression, reducing the Ohmic film resistances. In order to investigate the repeatability of the gauge performance, the resistance of the film (R_Bw) was measured after the withdrawal of bending stresses and the magnitude of recovery was estimated as the ratio $\left(\tfrac{{R}_{{\rm{B}}{\rm{w}}}}{{R}_{{\rm{B}}0}}\right)$ and it is evident from figure 6(c), values of this ratio lie between 97% and 92% as the strain is reduced from 0.71% to 0.41% and the recovery is consistent between both stretched and compressed films. These results indicate a very good degree of the flexibility of the GI films, leading to possible application of these flexible GI films in resistance strain gauges for measuring strain within the range from 0.41% to 0.71%.

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The UV–vis absorption spectrum in figure 7(a) for the graphene film is due to for these interband transitions showing a pronounced and asymmetric peak at 270 nm [40]. This peak position is in close agreement with that observed for films deposited from n-methyl-2-pyrrolidone and ethanol/water based dispersions [11]. The peak is due to a van Hove singularity in the density of states, which occurs close to the hopping energy [41, 42]. The considerable red-shift with respect to the absorption peak of graphene oxide at 226 nm implies reduced disruption of the π-conjugation in the multi-layered graphene film [43]. The flat absorption band over the visible region results from the linear dispersion of Dirac electrons in graphene. The weak broad absorption band (shoulder) around 353 nm corresponds to residual graphitic sp² domains in the samples. However, other structural parameters like the number of graphitic layers, curvature of aromatic layers, crystallite size and so on, also affect the shifting of (π–π*) bond position. The action spectrum in figure 7(b) shows the dependence of photocurrent on the incident wavelength, at a fixed bias of $\,50\,{\rm{mV}}.$ As expected, it shows close similarities to the UV–vis absorption spectrum, with a sharp peak occurring at 270 nm. The minor differences may be attributed to scattering and recombination of charges in the GI film.

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Figure 8(a) shows I(V) characteristics from a GI sample recorded between $\pm 10\,\mathrm{mV}\,$were recorded at $T\,=\,268\,{\rm{K}}$ and ${T}=330\,{\rm{K}}$ under illumination of a constant light intensity ${{P}}_{{\rm{i}}}=10\,{\rm{m}}\,{{\rm{Wm}}}^{2}$ corresponding to the absorption peak at $\,270\,{\rm{nm}}.$ The resulting plots were found to be linear for both temperatures. Values of photoconductivity ${\sigma }_{{\rm{p}}{\rm{h}}}$ are estimated to be $8.05\,\pm \,0.67\,{{\rm{S}}{\rm{m}}}^{-1}$ and $2.8\,\pm \,0.16\,{{\rm{S}}{\rm{m}}}^{-1}$ at 268 K and 330 K, respectively using the following relation:

$$\begin{eqnarray}&&{\sigma }_{{\rm{p}}{\rm{h}}}=\,\tfrac{{R}_{{\rm{D}}}-\,{R}_{{\rm{i}}{\rm{l}}}\,}{{R}_{{\rm{D}}}{R}_{{\rm{i}}{\rm{l}}}}\tfrac{d(N-1)}{t.w}\,,\end{eqnarray} \tag{ 5 }$$

where ${{R}}_{{\rm{il}}}$ is the resistance for the GI sample under illumination.

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This decrease in ${\sigma }_{{\rm{p}}{\rm{h}}}$ by a factor of nearly 3 with an increase in temperature of 62 K from 268 to 330 K may be interpreted by the photo-thermoelectric effect due to a temperature gradient that is possibly produced between the graphene layers under illumination. The photocurrent in ordinary semiconductors is primarily due to separation of excited electron–hole pairs by a built-in electric field. A photoexcited e–h pair leads to ultrafast heating of the carriers in graphene because of strong e–e interactions [44, 45].

The photoresponsivity, S, is defined as the ratio of the photocurrent to the incident optical power P_i. Therefore S can explicitly be written for the interdigitated electrode system in the form:

$$\begin{eqnarray}&&S=\,\tfrac{\,t.w}{{d}^{2}\,N(N-1)}\tfrac{V{\sigma }_{{\rm{p}}{\rm{h}}}}{{P}_{{\rm{i}}}}.\end{eqnarray} \tag{ 6 }$$

The value of photosensitivity S at 268 K is estimated to be $161\,{\rm{A}}\,{{\rm{W}}}^{-1}$ from equation (6). As the temperature is raised to $330\,{\rm{K}},$ S is found to decrease to $56\,{\rm{A}}\,{{\rm{W}}}^{-1}.$ This value is of the same order of magnitude as one obtained for the hybrid films containing graphene quantum dots in the reduced graphene oxide matrix [46]. The specific detectivity D, can be estimated from the knowledge of S using the expression

$$\begin{eqnarray}&&D=\tfrac{{S}}{\sqrt{(2{q}{{\sigma }}_{{\rm{D}}}{\rm{tw}}/(d(N-1)))}}\,,\end{eqnarray} \tag{ 7 }$$

where $q\,=1.6\times {10}^{-19}\,{\rm{C}}$ is the absolute value of electronic charge. Using the expression above, values of $4.9\times {10}^{12}$ Jones and $1.9\times {10}^{12}$ Jones were estimated from equation (7) at 268 K and $330\,{\rm{K}},$ respectively. These values of the specific detectivity represent the capability of the devices to detect a small photo signal.

Values of the short circuit current ${{I}}_{{\rm{sc}}}$ at zero bias, V = 0, are found to be $2.0\,{\mu }{\rm{A}}\,\,$ and $0.4\,{\mu }{\rm{A}}$ at 268 K and 300 K, respectively, indicating that the number of photo-generated charges are smaller at higher temperatures for a given illumination strength [47]. Similarly, values of $6.7\,{\rm{mV}}$ and $\,1.6\,{\rm{mV}}$ are estimated for open circuit voltage ${V}_{{\rm{o}}{\rm{c}}}$ using I = 0 for 268 K and 300 K, respectively. Figure 8(b) shows a typical current versus time cycle for a fixed bias of 1 V as the light was turned on and off. Two conducting states, high and low, of the GI films are found to exist under illumination and the recovery to nearly low conducting occurs when the illumination is switched off. The response time ${\tau }_{{\rm{R}}}$ is estimated to be 42 s from fitting the exponential function $i={i}_{0}\left[1-{\rm{e}}{\rm{x}}{\rm{p}}\left(-\tfrac{t}{{\tau }_{{\rm{R}}}}\right)\,\right]$ to experimental rise curve in figure 8(b), where ${i}_{0}$ is the saturation photocurrent for $t=0$ at which instant light illumination was switched on at 150 s. This value is found to be comparable with those obtained for the UV sensors based upon reduced graphene oxide decorated ZnO nanostructures [48]. Figure 8(c) presents the results of the analysis of the time-dependent decay of the photocurrent current in terms of the Kohlrauch equation in the form:

$$\begin{eqnarray}&&i(t)=\,{i}_{0}\,{\rm{e}}{\rm{x}}{\rm{p}}\left(-{\left(\tfrac{t}{{\tau }_{{\rm{D}}}}\right)}^{\gamma }\right),\end{eqnarray} \tag{ 8 }$$

where ${i}_{0}$ is the saturation photocurrent for $t=0$ at which instant light illumination is switched off. The stretching parameter $\gamma \,\,$ normally varies between values of 0 and 1. For $\gamma \,=1,$ the function in equation (6) approaches classical single-exponential behaviour and differences in energy transfer processes become indistinguishable under this condition [49]. It is obvious that the decay curve in the present work is characterised by two regimes corresponding to (i) fast and (ii) slow relaxation processes. Values of the relaxation time constant, ${\tau }_{{\rm{D}}},$ were found to be $8.9\times {10}^{3}\,{\rm{s}}\,$ and $4.3\times {10}^{4}\,{\rm{s}}\,$ for the time scale regime (i) from 371 s to 463 s and (ii) from 463 s to 482 s respectively by fitting equation (8) to the experimental data. The present ${\gamma }=0.82$ may be ascribed to the combined effect of both defects and potential barriers between the edges of the single sheets within the overall assemblies [50].