Layer-dependent nanoscale electrical properties of graphene studied by conductive scanning probe microscopy
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The nanoscale electrical properties of single-layer graphene (SLG), bilayer graphene (BLG) and multilayer graphene (MLG) are studied by scanning capacitance microscopy (SCM) and electrostatic force microscopy (EFM). The quantum capacitance of graphene deduced from SCM results is found to increase with the layer number (n) at the sample bias of 0 V but decreases with n at -3 V. Furthermore, the quantum capacitance increases very rapidly with the gate voltage for SLG, but this increase is much slowed down when n becomes greater. On the other hand, the magnitude of the EFM phase shift with respect to the SiO2 substrate increases with n at the sample bias of +2 V but decreases with n at -2 V. The difference in both quantum capacitance and EFM phase shift is significant between SLG and BLG but becomes much weaker between MLGs with a different n. The layer-dependent quantum capacitance behaviors of graphene could be attributed to their layer-dependent electronic structure as well as the layer-varied dependence on gate voltage, while the layer-dependent EFM phase shift is caused by not only the layer-dependent surface potential but also the layer-dependent capacitance derivation.
Keywordsgraphene scanning capacitance microscopy electrostatic force microscopy layer dependence quantum capacitance
Graphene is drawing an increasing interest nowadays since its debut in reality  as it is a promising material for future nanoelectronic applications [2, 3, 4]. While many transport property studies have been carried out by traditional techniques with nanoelectrodes fabricated on graphene [5, 6, 7, 8], conductive scanning probe microscopy has recently been applied for direct nanoscale electrical measurements on graphene [9, 10, 11, 12, 13]. For example, scanning capacitance microscopy (SCM) was used to study the capacitance of few layer graphene (FLG) [14, 15, 16], and the unusual capacitive behavior of graphene due to its quantum capacitance has been found. Electrostatic force microscopy (EFM) was employed to study the electrostatic environment of graphene or to obtain the layer-dependent surface potential of FLG [17, 18]. Scanning Kelvin microscopy [19, 20] was performed to investigate surface potentials of different graphene layers, and the surface potential was discovered to vary with the layer number. Despite these efforts, the layer-dependent electrical properties, especially the difference between single-layer graphene (SLG) and bilayer graphene (BLG), which is expected to be large due to their different electronic structures, have not been well investigated yet. In this letter, the nanoscale electrical properties of SLG, BLG, and multilayer graphene (MLG with layer number > 2) are investigated by EFM and SCM, and their layer dependences are studied in detail.
The graphene samples were prepared by the mechanical exfoliation method  and deposited onto p-type Si substrates coated with a 300 nm of SiO2 layer. Although many novel methods have been used to fabricate graphene [21, 22], mechanical exfoliation  is still a fast and convenient way to obtain high-quality graphene with SLG, BLG, and MLG simultaneously. With the help of optical microscopy to locate the graphene , tapping-mode atomic force microscopy (AFM) (MultiMode V, Bruker Nano Surfaces Division, Santa Barbara, CA, USA) has been used to measure the topography. To study the nanoscale electrical properties of graphene, EFM and SCM are performed to investigate the electrostatic force and capacitance behaviors on graphene with different layer numbers. EFM records both the sample topography and the phase shift that is directly linked to the electrical force gradient by using a two-pass method. By SCM, the capacitance variation ΔC between the tip and the underlying semiconductor in response to a change in the applied ac bias ΔV could be obtained. The detailed operational modes of EFM and SCM have been reported elsewhere . All these experiments were carried out in nitrogen atmosphere at room temperature with Pt-Ir coated Si tips.
Calculated values for different graphene layers
Increase ratio (ΔCq (3 V)/ΔCq(0 V)
MLG (n = 4)
MLG (n = 8)
From Table 1, it can be seen that at the sample bias of 0 V, the quantum capacitance variation of graphene increases with n. With +3 V bias applied, all quantum capacitance variations are much larger than their corresponding values at 0 V. The increase is mostly significant for SLG, which increased about 280 times. The increase magnitude, as shown in Table 1, drops down quickly with increasing n. Therefore, the change of graphene quantum capacitance with the DC biases is dependent on n, resulting in the different layer-dependent quantum capacitances of graphene at 0 V and +3 V. Since SCM has been performed in the contact mode where the tip contacts with the surface, the DC bias applied between the tip and sample backside acts as the gate voltage. So our results indicate that the capacitance variations increase with the gate voltage for different graphene layers, and the increase magnitude decreases as n increases. In previous studies, both the SCM measurements on FLG [14, 15, 16] and theoretical studies on SLG  showed that the quantum capacitance of graphene increases significantly with the gate voltage. Our results are consistent with those conclusions, but since A tip / A eff = 1 is used for different graphene layers, it may cause errors for the obtained Cq values, especially at a DC bias of +3 V. Nevertheless, the different quantum capacitance behaviors for graphene with different n are definite. As the quantum capacitance represents the density of states (DOS) at Fermi level [26, 27] and the DOS of graphene was found to vary with n, it is reasonable to obtain that the quantum capacitance of graphene is dependent on n, as shown in Table 1. On the other hand, it was reported by Yu et al. that the work function could be tuned by the gate voltage, where they found that SLG showed larger work function changes with gate voltage than BLG did . They explained the work function change as due to the change in Fermi level (EF) in graphene, which was different for SLG and BLG. Our results can be interpreted in the similar viewpoint. Different changes of EF with gate voltage for different graphene layers could result in different carrier density changes with gate voltage, so are the changes of the quantum capacitance with gate voltage.
where k is the stiffness of the cantilever, Q is the quality factor, z is the tip-sample distance and C is the tip-sample capacitance. VDC is the applied bias, and Vsurf is the surface potential correlated with the difference between the tip and sample work functions (V surf = ( W tip - W sample )/ e ). Hence, both surface potential and capacitance derivation (∂2C/∂z2) will contribute to the phase shift of electrostatic force. First let's estimate the surface potential contribution (Vdc - Vsurf)2 to the different phase shift between SLG and BLG. The work function different between SLG and BLG was reported by Yu et al. , which is 4.57 eV for SLG and 4.69 eV for BLG, respectively. As the work function of the SiO2 substrate is about 5.0 eV and the same tip is applied (PtIr, approximately 4.86 eV), SLG should have a larger phase shift difference with respect to the SiO2 substrate than that of BLG for both biases. In other words, the difference in phase shift behavior between SLG and BLG could not only be attributed to their different surface potentials. Thus, the capacitance derivation should be another contribution to the phase shift. Our SCM results aforementioned do indicate that the quantum capacitance of graphene varies with n, and it is significantly dependent on the sample biases, which could be expected to induce different EFM phase shifts for different graphene layers at different samples biases.
In conclusion, the nanoscale electrical properties of graphene with different number of layers have been studied by SCM and EFM, and the layer dependences of capacitance variation and EFM phase shift are obtained. SLG, BLG, and MLG exhibit obvious differences in electrostatic force and capacitance behaviors. The different electrical properties obtained on different number of graphene layers could be mainly attributed to their different electronic properties.
This work was supported by the National Natural Science Foundation of China (grant number 10874030) and the special funds for Major State Basic Research Project of China (no. 2011CB925601).
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