Lateral homogeneity of the electronic properties in pristine and ion-irradiated graphene probed by scanning capacitance spectroscopy
© Giannazzo et al; licensee Springer. 2011
Received: 30 September 2010
Accepted: 31 January 2011
Published: 31 January 2011
In this article, a scanning probe method based on nanoscale capacitance measurements was used to investigate the lateral homogeneity of the electron mean free path both in pristine and ion-irradiated graphene. The local variations in the electronic transport properties were explained taking into account the scattering of electrons by charged impurities and point defects (vacancies). Electron mean free path is mainly limited by charged impurities in unirradiated graphene, whereas an important role is played by lattice vacancies after irradiation. The local density of the charged impurities and vacancies were determined for different irradiated ion fluences.
Graphene, a two-dimensional (2D) sheet of carbon atoms in a honeycomb lattice, attracted the interest of the nanoelectronics scientific community for its remarkable carrier transport properties [1, 2]. Ideally, in a free-standing graphene sheet without lattice defects and adsorbed impurities, charge carriers can exhibit a giant intrinsic mobility  and can travel for micrometers without scattering at room temperature. As a matter of fact, very high values of mobility (>2 × 105 cm2 V-1s-1) and electron mean free path have been observed only in vacuum and at low temperature (5 K) in "suspended" graphene sheets obtained by mechanical exfoliation of highly oriented pyrolytic graphite (HOPG) . The mobility values measured at room temperature commonly reported in the literature range from approximately 2 to 2 × 104 cm2 V-1s-1, depending on the graphene synthesis methods [1, 4], on the kind of substrate on which it is deposited , and on the processing conditions used to fabricate the test patterns for electrical characterization. This large variability is a clear indication that the intrinsically outstanding transport properties of graphene are severely limited by extrinsic factors, like the presence of charged impurities, lattice defects and, more generally, by lattice disorder (including local strain). Single layers of graphene (SLG) obtained by mechanical exfoliation of HOPG  typically exhibit a very high crystalline order, whereas a high-defect density is present both in epitaxial graphene growth by thermal decomposition of SiC  and in graphene obtained by chemical reduction of graphene oxide .
Recently, the intentional production of defects in selected areas of a graphene sheet has also been proposed as a method to locally modulate the transport properties. Several methods, like plasma treatments , and electron  or ion irradiation , have been used for this aim. Recently, it has been reported that graphene hydrogenation by exposure to atomic hydrogen resulted in the conversion of graphene, a zero bandgap semiconductor, to graphane, a two-dimensional insulator . Among all these methods, ion irradiation allows a better control through a precise definition on the ion energy and fluence. Spectroscopic characterization methods, like micro Raman spectroscopy (μR), are the commonly used techniques to evaluate the density of defects in a graphene sheet. The characteristic D line at 1360 cm-1 in the Raman spectra is a fingerprint of defects/disorder in the crystalline lattice of graphitic materials. However, the lateral resolution of μR is limited by the laser spot size (typically in the order of 0.5-1 μm). In this article, we present a scanning probe method based on nanoscale capacitance measurements to determine locally (on 10-100 nm scale) the electron mean free path in pristine and in ion-irradiated graphene with different ion fluences. The impurity and vacancy densities on the probed area were extracted by fitting the experimental results with models of electron scattering by Coulomb impurities and lattice defects.
Graphene samples obtained by mechanical exfoliation of HOPG were deposited on a n+-Si substrate covered with 100 nm SiO2. Optical microscopy, tapping mode atomic force microscopy (AFM) and μR spectroscopy were used to identify SLG . Some of the as-deposited (pristine) samples were then irradiated with C+ ions at 500 keV. Irradiations of the samples with C+ ions were carried out under high vacuum conditions (10-6 Torr) to minimize surface contaminations. At 500 keV energy, the projected range of the C+ ions is approximately 1 μm, quite deep into the n+-Si substrate. This minimizes the damage both in the 100 nm SiO2 layer and at the interface between SiO2 and n+ Si. Infact, a quality of SiO2 and SiO2/Si interface comparable to that of non-irradiated samples is crucial for the capacitance measurements discussed later. Different C+ ion fluences, ranging from 1 × 1013 to 1 × 1014 ions/cm2, were used for irradiation .
The lateral homogeneity of the electronic transport properties both in pristine and ion-irradiated graphene was investigated by local capacitance measurements on the graphene/SiO2/n+Si stack, using scanning capacitance spectroscopy (SCS) [12, 15].
Results and discussion
where ρ is the graphene density (ρ = 7.6 × 10- 7 kg/m2) , D A is the acoustic deformation potential (D A = 18 eV) , v s is the sound velocity in graphene , k B is the Boltzmann constant, and T is the absolute temperature.
where ε = 2.4 is the average between ε ox and the vacuum relative dielectric constant, Z is the net charge of the impurity (it will be assumed Z = 1), and N ci is the density of impurities.
where N vac is the density of vacancies in graphene and R 0 is the vacancy radius, that we assumed to be coincident with the C-C distance in the graphene plane (approximately 0.14 nm).
The experimentally determined linear dependence of l on E F, far from the Dirac point, suggests that scattering with charged impurities and/or point defects, e.g., vacancies, can be assumed as the main mechanisms limiting electron mean free path.
In this pristine graphene sample, the density of defects is negligible, as confirmed by the absence of the characteristic D peak in micro-Raman spectra. Hence, charged impurities, either adsorbed on graphene surface, or located at the interface with SiO2 substrate, can be assumed as the main scattering source liming l. The density of charged impurities in the probed position can be estimated by fitting the experimental curves in Figure 3 with Equation 2. The best fit (red line) is obtained with N ci = 49 × 1010 cm-2 both for the holes and the electron branch.
For simplicity, an average value of the charged impurities density will be assumed in those positions (〈N ci〉 = 50 × 1010 cm-2), and the local vacancy density was determined from Equations 2-4 using N vac as the fitting parameter. The distributions of the vacancy densities in the probed positions are reported in Figure 5b,c, blue bar, for the two fluences. It is worth noting, that, while in graphene irradiated with the lowest fluence N vac is higher than 2.5 × 1010 cm-2 (i.e. more than one vacancy on the probed area at V g = 1V) on only 16% of the probed positions, in graphene irradiated with the highest fluence N vac > 2.5 × 1010 cm-2 on more than 75% of the probed positions.
where 〈N vac,0〉 is the extrapolation of the average vacancy density at Φ = 0, σ is the cross section for direct C-C collisions, N gr is the C density in a graphene sheet (N gr = 4 × 1015 cm-2), and ν is the vacancy generation efficiency. By linear fitting the data in Figure 6, 〈N vac,0〉 = (1.59 ± 0.04) × 1010 cm-2 and νσN gr = (8.55 ± 0.06) × 10-4 are obtained. For the calculated values of the C-C scattering cross section σ, ranging from 2 × 10-17 to 7 × 10-17 cm2, a very low vacancy generation efficiency (ranging approximately from 0.3 to 1.1%) is obtained for graphene irradiation with 500 keV C+ ions. It might be associated to a dynamical annealing, e.g. vacancy-interstitial recombination, during irradiation.
In summary, the authors propose an innovative method based on local capacitance measurements to probe the local changes in graphene electron mean free path, due to the presence of charged impurities or point defects, e.g., vacancies. Irradiation with 500 keV C+ ions at fluences ranging from 1 × 1013 to 1 × 1014 cm-2 was used to introduce defects in SLG deposited on a SiO2/n+Si substrate. The local charged impurity and vacancy density distributions were determined for the different irradiation fluences, and a low efficiency of vacancy generation (approximately from 0.3 to 1.1%) was demonstrated.
highly oriented pyrolytic graphite
scanning capacitance microscopy
scanning capacitance spectroscopy
single layers of graphene.
The authors want to acknowledge S. Di Franco and A. Marino from CNR-IMM, Catania, for their expert assistance in sample preparation and ion irradiation experiments. This study has been supported, in part, by the European Science Foundation (ESF) under the EUROCORE program EuroGRAPHENE, within GRAPHIC-RF coordinated project.
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