Nanoscale Charge Density and Dynamics in Graphene Oxide

Graphene oxide (GO) is widely used as a component in thin film optoelectronic device structures for practical reasons because its electronic and optical properties can be controlled. Progress critically depends on elucidating the nanoscale electronic structure of GO. However, direct experimental access is challenging because of its disordered and nonconductive character. Here, we quantitatively mapped the nanoscopic charge distribution and charge dynamics of an individual GO sheet by using Kelvin probe force microscopy (KPFM). Charge domains are identified, presenting important charge interactions below distances of 20 nm. Charge dynamics with very long relaxation times of at least several hours and a logarithmic decay of the time correlation function are in excellent agreement with Monte Carlo simulations, revealing an universal hopping transport mechanism best described by Efros–Shklovskii’s law.


SI.1. Experimental
In low conducting very thin materials such as GO, the intensity of the localized charge contribution to the VKPFM signal increases as the relative permittivity of underlying substrate decreases [1]. For that reason, we have used a thick 300nm SiO2 (εr≈4.3) on Si. In addition, all the measurements have been carried on under a dry nitrogen atmosphere to avoid waterscreening effects. To highlight the influence of these two parameters, in Figure SI.1 we show the KPFM images of a GO flake deposited between two gold stripes evaporated on a 300 nm SiO2/Si substrate at different relative humidity (RH). We note that the charge domains are detected only at low humidity and only on the SiO2 channel. In this case, the Vcharge contribution is large enough to be detected and superimposed on the VCP≈80mV contribution (that is essentially an offset). On the contrary, charge domains cannot be resolved on the Au substrate even at low humidity. Due to the high Au permittivity, the Vcharge contribution is so low, that GO flakes on Au shows a constant VKPFM, that correspond only to the VCP contribution.

SI.2. Two-pass measurements
In the two-pass acquisition mode, the tip scans each fast scan line twice before it moves to the next scanning line. In this way, two simultaneous images are obtained. Since the two lines are acquired very close in time, they can be directly compared neglecting artefacts due to drift, tip changes, etc. Typically, this mode is used to study the influence of one or several parameters on the measurements by changing them between the first and the second pass (tip-sample distance, illumination, oscillation amplitude, etc). Since our goal is to study the charge dynamics, in this work the same acquisition parameters (set-point, scan speed and feedback parameters) are used. Figure SI.2 shows the first and second pass images together with the line by line subtracted image. We clearly see that on the GO flake there is a larger fluctuation than on the SiO2 substrate. A line profile shows that these fluctuations are no larger than ±60mV but well above the substrate noise level σnoise≈10mV. To estimate how much charge has moved between two pass lines to produce such Vcharge change, we need to calculate the Vcharge signal that would produce one charge (Vpoint) in a GO flake deposited on a SiO2 substrate, and how it changes with the lateral distance.

SI.3. Calculation of the V point
To obtain the Vpoint signal ( Fig. SI.3) that would produce a single point charge on a monolayer of GO, we have used the image charge-based method proposed in ref [1]. This Vpoint, allows us to estimate the effective amount of charge that has moved at a point within the time scale of the two pass (2s in our case) to produce the observed change in VKPFM (less than ±60mV). We find that it corresponds to a charge redistribution in which effectively an electron has travel a distance no larger than 10 nm. For the calculation, we have used a tip radius R=15 nm, tip sample distance d=7 nm and a SiO2 relative permittivity εSiO2=4.3. As explained above, these parameters are obtained as proposed in ref.
[¡Error! Marcador no definido.]. In addition, we have used a GO thickness h=1.5 nm (obtained from topography images) and εGO=4.3, similar to the one of SiO2. The εGO of a single GO flake is not precisely known. From our measurements, we see no difference between the SiO2 and the GO flakes in the capacitance images obtained from the 2ωelec, signal while they show a clearly lower permittivity than silicon if the GO is deposited directly on it (not shown). We estimate that in the perpendicular direction, the εGO should be between 3.5 and6. Variation on the εGO in our calculations between these values results in a charge density variation less than 10%, since for a very thin film layer, the Vpoint is mainly determined by the εr of the substrate.

SI. 4. Charge density image from the V KPFM image.
To calculate the charge density image q(x,y) we use Fast Fourier Transform based algorithms (FFT) described in ref [2]. To do so, we first calculate the Vpoint image as explained above and we use it for the deconvolution of the VKPFM images (Fig.SI. 4). Due to experimental noise, in the deconvolution process a circular Gaussian filter in k-space to remove nonphysical artifacts is applied. In this work, we have selected the corresponding filter radius (kc) as such that ( )/ ( ) ≈ 1, as explained in ref [1]. The use of this filter limits the lateral resolution broadening the charge peaks and blurring the details smaller than a radius Rc=2π/kc. In Figure SI.5 we have added to the ideal noise-free Vpoint(x,y) image a random Gaussian noise (σ=10 mV) and we have obtained the corresponding qpoint(x,y) image using exactly the same kc filter radius used in our experimental VKPFM(x,y) images. In this way, we can estimate the charge distribution produced by one punctual electron in our system including the experimental noise. We notice that although the peak is broad (due to the filter), the charge is conserved under the integration of the peak.

SI.5 Mean and STD images from the movie.
We have calculated the mean and the STD images of a charge density movie (q(x,y,ti)) of N=292 frames (total time 17h and 20 min and  (3) Applying a mask analysis, we calculate the variance of the mean frame ( � 2 ( )) of the GO flake as a function of number of averaged frames. The STD image (Fig SI.6 (b)) presents different regions with large and small STD, but the mean and the STD images are very weakly correlated (Fig. SI. 8), except at the flake border where due to the applied mask the procedure is not fully reliable. We have analyzed the origin of such STD lateral structure finding that it is mainly due to the long-time fluctuations; while the short-time fluctuations are essentially homogeneous over the flake This fact confirms our expectation that there are no fixed net charges in the flake. If a region has a large probability to keep a charge of a given sign, the STD in that region should be smaller. However, we realize that the flake twists visible in the topography shows a lower STD signal. This means that the twists in the flake do not attract charges of any particular sign, but reduce the charge mobility.

SI.6 Complementary Characterization
Complementary spectroscopic studies were performed on powder samples of GO obtained by freeze-drying the purchased GO dispersion.

X-Ray Photoelectron Spectroscopy (XPS)
XPS analysis of GO powder was carried out using an ESCA Plus Omicron spectrometer using a monochromatized Mg X-ray source (1253.6 eV). Surface charging effects due to the insulating nature of GO needed to be compensated by a shift of the XPS spectrum by 3.3 eV.
A Shirley background was subtracted and the XPS peaks were fitted with a GL(70) function, whose line-shape accounts for 70% Gaussian and 30% Lorentzian character. The full width half maximum (FWHM) values were fixed to a maximum of 1.6 eV. Asymmetry for the sp 2 carbon peak was defined by a line-shape asymmetry function LF (1, 2, 57, 0). Figure    The peak at 1735 cm -1 can be assigned to C=O stretching modes, compatible with the presence of ester and lactone groups in GO. The peak at 1625 cm -1 corresponds to the scissor mode of water (deformation vibration), which overlaps the asymmetric stretch mode of sp 2 C=C vibrations commonly appearing at 1580-1600 cm -1 . The vibrations at 1230 cm -1 and 1050 cm -1 can be ascribed to alcohol (C-OH) and epoxy (C-O-C) groups, respectively.