Carbon-based layered structures have been attractive to physicists in the last two decades as a testing ground for the manifestation of intriguing optical, electronic, and mechanical properties that would revolutionize the nano-electronic industry via development next-generation quantum transport in opto-electronic devices, nanoelectromechanical actuators, and biomedical sensors [1-5]. Contrastingly, low-dimension and linearly vanishing density of states at Dirac point of graphene suggests that each and every carbon atom is located at the surface, making graphene an attractive material for studying surface physics. Through the years, a variety of authors reported surface potential distribution between the single-layer graphene (1LG), double layer graphene (2LG), multi-layer graphene (MLG), and/or few layer graphene (FLG) transferred onto different substrates [6-9]. This contact potential difference between 1LG, 2LG, MLG, and FLG is controlled by ambient atmosphere, NO2 environment, and substrate characteristics [10-11]. As a matter of fact, contact potential tuning is challenging in graphene, because electrostatic top-gate tends to degrade materials properties and the addition of chemical dopants or absorbents can cause unwanted disorder. To control these properties, electrostatic force microscopy (EFM) was used as a powerful tool to investigate graphene on different substrates, where accurate determination of flack height is less challenging, but the surface potential can be tuned by the electric-field effects without fabricating top-gate electrodes [9, 12]. Although contact potential between 1LG and 2LG has been extensively studied, the knowledge of surface potential value of individual graphene layers has been very limited and unexplored .
In this article, by combining both Kelvin Probe Force Microscopy (KPFM) and EFM techniques, the surface potential distribution of graphene layers deposited on SiO2 substrates has been demonstrated. AM-KPFM mapping showed the surface potential for the graphene as -0.33 V, whereas FM-KPFM imaging showed -0.54 V; the difference of 0.19 V could be attributed to the superior resolution of FM-KPFM and higher detection sensitivity of AM-KPFM. Significant monotonic increase of EFM phase is attributed to the contact potential of graphene caused by dc electric-field effect.
The used samples consist of mechanically exfoliated graphene/graphite transferred on to 300 nm thin SiO2/Si substrates, where the back electrode Si is doped with N at the concentration of 1018/cm2. A Solver Next commercial Atomic Force Microscope (AFM, NT-MDT, Russia) with cantilever having a conductive tip coated with Cr/Pt (resonant frequency 75 kHz and force constant 3 N/m) was used to characterize the graphene samples. In the first pass, the AFM tip traced the sample topography; subsequently, the surface potential mapping was performed in AM-KPFM mode (second pass mode). In FM-KPFM, the contact potential difference (CPD) was recorded along the same line scan in the second-pass mode while keeping the tip-surface distance of 10 nm. EFM is a two-pass mode, in which the electrostatic force between the charge on graphite and the tip is measured. The interatomic force is detected as a change in the resonant frequency with a corresponding phase shift as the cantilever experiences either attractive or repulsive force. In the present experiments, a lift height of h=50 nm is fixed above the surface to avoid topographic artifacts; the phase shift is imaged in the second-pass mode, while the dc bias applied to the probe. Schematic view of both KPFM and EFM is shown in Fig. 1.
Figure 1a-f shows the topography and surface potential distribution features of a graphene layer obtained via both AM-KPFM and FM-KPFM mappings. The topography image of graphite/SiO2 shows that the graphene layer is typically flat with small wrinkles and protrusions (Fig. 1a). The corresponding histogram profile indicates that the few layer graphene height is 10.19 nm, which is shown in Fig. 1b. Interestingly, both AM-KPFM and FM-KPFM images display slightly different contrast with much lower contact potential difference (ΔV C P D ) on the graphene layer in comparison with SiO2 substrate (Fig. 1c,e), suggesting a smaller work function of graphene. To evaluate the ΔV C P D of graphene, we plotted histogram profiles over the entire scanned area of Fig. 1d,f. The surface potential peak centered at 18 mV corresponds to the graphene layer, which is largely dark in contrast to the SiO2 substrate of 344 mV. The evaluated ΔV C P D between the SiO2 and graphite is -0.33 V in AM-KPFM mode. Accordingly, the Gaussian distribution of peak position of graphene surface potential is 35 mV and the SiO2 peak position is -570 mV, suggesting that the ΔV C P D between the SiO2 and FLG is about -0.54 V. The difference in the ΔV C P D of graphene in AM-KPFM and FM-KPFM mode will be interpreted in the next section.
To evaluate the work function of graphene, initially we estimate the work function of the Cr/Pt coated tip by surface potential mapping on calibrated Highly Oriented Pyrolytic Graphite (HOPG) sample. The AM-KPFM and FM-KPFM mappings revealed that the work function of Cr/Pt tip is 5.02 eV and 5.04 eV respectively. The contact potential difference is defined as follows:
(1) where ψ t i p is the work function of the SPM tip, ψ s a m p l e is the work function of the sample, e is the elementary charge, and ΔV C P D is the measured contract potential difference.
Using this relation, we evaluated the graphene work function as 4.69±0.02 eV in AM-KPFM, whereas FM-KPFM revealed 4.50±0.02 eV. This work function value of 4.69 eV is in a good agreement with previously reported work function of 4.68 eV; hence, we suggest that this graphene is p-type band gap semiconductor [7, 11]. In addition, the work function value (4.50 ± 0.02 eV) of obtained in FM-SKPM is consistent with the value of 4.57±0.05 eV . The difference of 0.19 eV in the work function is accounted by the fact that AM-KPFM has lower spatial resolution than FM-KPFM. In addition to that, slightly lower V C P D value obtained from FM-KPFM is possibly due to a faintly larger tip-surface separation due to the additional ac bias and also of higher resolution capacity [13-14]. Higher sensitivity is important for the detection of the smallest changes in ΔV C P D of very thin graphene layers; hence, AM-KPFM is better option to study work function of graphene.
Figure 3a,c shows the EFM phase images while applying the dc biases field of ± 4V to the probe; corresponding histogram profiles are shown in Fig. 3b,d. The phase contrast of graphene relative to SiO2 substrate is always positive, indicating that our graphene is doped with holes in the ambient conditions. At V t i p = 4 V, the EFM phase for graphite is 5.48∘ and this phase is enhanced to 15.61∘, while applying dc bias voltage of -4 V (Fig. 3b,d). We observed that the relative contrast between graphene is not reversed, even if the applied tip voltage has opposite polarity. But the relative phase contrast of graphene has improved much while applying negative dc bias fields, indicating that the EFM phase of graphene is more sensitive to negative dc field effects. Figure 3e shows the thickness dependence of EFM-phase of graphene layers, while the dc bias was applied to the tip (V t i p ). Each EFM phase plot was obtained by performing 21 scans with different dc fields. Notably, the experimental plots of different thicknesses of graphite layers reveal a characteristic parabolic shape, which is in a good agreement with a conventional model of capacitive coupling between the EFM probe and the sample is defined as:
(2) where Δ Φ(x, y) is the phase shift, Q and k are the quality factor and the spring constant of the cantilever, respectively, C(h) is the second derivative of the vertical distance between the tip-sample capacitance and the tip-bare substrate capacitance as a function of h, and V s (x,y) is the local electrostatic potential on the sample surface.
The phase shift in Eq. 2 is zero, when V t i p equals to the value of V s . Generally, V s is determined by the spatial distribution of charge carriers that are transferred to graphene from a thin buried layer of traps or defects in the SiO2 substrate. From the relation, it is clear that the EFM phase shift corresponding to the surface potential distribution (V s ); hence, the monotonic increases of EFM phase ascribed to the increases of surface potential of graphite with the dc field effect up to ± 5 V. In contrast, external contributions to the surface potential (e.g., such p-type adsorbates as water, oxygen, and hydrocarbons) lead to a uniform shift in the surface potential independent of the number of layers . From our experimental data, the intrinsic modification of V s corresponds to a steeper phase change originating from the shift of C 1s core level toward lower binding energies as the number of mono-atomic layers increases in graphene, assisted by the dc bias field effects applied to the probe .
In conclusion, we have demonstrated the local surface potential distribution of single-layer graphene deposited on SiO2/Si substrate by employing Kelvin Probe Force Microscopy (KPFM), and Electric Force Microscopy (EFM). The AM-KPFM offers a straightforward identification of graphene layer work function of 4.74 eV whereas FM-KPFM revealed 4.59 eV, the difference of 0.19 eV in work function being attributed to the superior resolution of FM-KPFM and higher detection sensitivity of AM-KPFM. In contrast, we observed that the parabolic dependence of EFM phase with increase of dc electric field applied to the probe from 0 to ± 5 V. This phase shift of EFM phase is attributed to the variations of the surface electronic structure due to surface potential induced by the interatomic interaction between the electronic states of Cr/Pt tip and the graphene surface electrons.
R.V. thanks Foundation of Science and Technology of Portugal for the postdoctoral grant SFRH/BPD/104887/2014. E.P., K.R and A.L.K. are grateful to the Russian Foundation for Basic Research (grant No 16-29-14050-ofr-m) and Government of the Russian Federation (Act 211, Agreement 02.A03.21.0006) for the financial support. Part of this work was developed in the scope of Project CICECO-Aveiro Institute of Materials (ref. FCT UID/CTM/50011/2013), financed by national funds through the FCT/MEC and, when applicable, cofinanced by FEDER under the PT2020 Partnership Agreement.