Abstract
Investigating the charge transport behavior in one-dimensional quantum confined system such as the localized states and interference effects due to the nanoscale grain boundaries and merged domains in wide chemical vapor deposition graphene constriction is highly desirable since it would help to realize industrial graphene-based electronic device applications. Our data suggests a crossover from interference coherent transport to carriers flushing into grain boundaries and merged domains when increasing the current. Moreover, many-body fermionic carriers with disordered system in our case can be statistically described by mean-field Gross-Pitaevskii equation via a single wave function by means of the quantum hydrodynamic approximation. The novel numerical simulation method supports the experimental results and suggests that the extreme high barrier potential regions on graphene from the grain boundaries and merged domains can be strongly affected by additional hot charges. Such interesting results could pave the way for quantum transport device by supplying additional hot current to flood into the grain boundaries and merged domains in one-dimensional quantum confined CVD graphene, a great advantage for developing graphene-based coherent electronic devices.
1. Introduction
Graphene, a single layer of carbon atoms arranged in a hexagonal lattice, has demonstrated novel optoelectronic and electronic devices in information technology, such as photodetectors [1], solar cells [2, 3], and transistors [4]. Most importantly, the large-scale application of graphene is an urgent development for industrial developments and integrations. The chemical vapor deposition (CVD) growth of graphene has revealed great potential due to the large-area, cost-effective, and industrial-like schemes such as optical lithography to fabricate one-dimensional graphene quantum constrictions for electronic coherent devices [5–10]. Recent reports underscore the importance of interference effects due to the intrinsic nanoscale grain boundaries and merged domains within the CVD graphene [11, 12]. Such nanoscale grain boundaries and merged domains revealed different transport properties studied by low-temperature scanning gate microscopy (LT-SGM) for making current paths across that specific regions [13, 14] so as to strongly enhance the interference effect in comparison with homogenous exfoliated graphene, like backscattering suppression and Klein tunneling [15]. Such interesting CVD graphene-based electronic devices with its intrinsic grain boundaries and merged domains due to Aharonov-Bohm effect have recently revealed interesting interference effect [14] and could possibly finely control and tune the total conductance by gate voltages, magnetic fields, and source-drain currents so as to generate a high on/off ratio signal as a quantum coherent transistor for next generation information technology [16]. Consequently, the microscopic view of fermionic dynamic transport behaviors within wide CVD graphene constriction becomes a necessary study for realizing the applications of graphene-based electronic devices.
In this work, we used LT-SGM to study the interference behavior within a CVD graphene wide constriction region. With low current, we observed the enhanced and reduced conductance pattern outside the wide constriction region, indicative of the ring-structure current paths due to the nanoscale grain boundaries and merged domains within the wide constrictions. With additional hot current, the stimulations based on mean-field Gross-Pitaevskii equation revealed that the current charges were floored into the nanoscale grain boundaries and merged domains so as to reduce the interference effect that is consistent with our previous LT-SGM experimental results [14], which provide deep understanding of the one-dimensional CVD graphene transport and also provide a novel transport mechanism by tuning hot current into wide CVD graphene constrictions.
2. Experimental
High-quality and uniform commercial CVD graphene [17] on 285 nm thick SiO2/Si wafer was prepared, and the graphene films were known as different layer numbers and polycrystalline consisting of grains [18]. The CVD single layer graphene region, which can be confirmed by optical microscope image in green channel contract [19] as shown in Figure 1(a) inset and atomic force microscopy images as in our previous studies [13, 14], was particularly searched and it was etched to wide constriction with = 800 nm and = 1000 nm using oxygen plasma etching and deposited with two terminal Ti/Au contacts for source-drain electrodes. Especially, the single layer region reveals nanoscale ripples due to the grain boundaries and merged domains observed by scanning electron microscopy (SEM) as shown in Figure 1(a).
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Our home-built LT-SGM setup is mounted inside a He3 cryostat with a base temperature of = 0.3 K and superconducting magnet of = 9 T. In order to sensitively perturb the carrier transport interference effect, an AC driving current from lock-in amplifiers ejects through the single layer graphene wide constriction. Furthermore, the conductance is recorded when a LT-SGM tip scans in the square region (4.2 μm × 4.2 μm at 1.8 K) near the single layer graphene wide constriction with lift-mode operation at constant height ( nm) over the surface as previous studies [13, 14] and as shown in Figure 1(b).
3. Results and Discussion
As shown in Figure 2(a), negative magnetoresistance was observed at = 1 K in the case that the magnetoresistance decreased with increasing near zero magnetic field, which is the evidence for the weak localization (WL) effect [20–22]. We are able to calculate the phase coherence length by the following typical equation in disordered graphene system [23]:where , , , , , , and are the magnetoresistance, digamma function, the Planck constant, electron charge, phase coherence length, intervalley scattering length, and intravalley scattering length, respectively. The inset of Figure 2(a) reveals the normalized magnetoconductance (black curve) which could be fitted well by the theoretical equation (red curve) although there are some conductance oscillations near high magnetic field regime due to the mesoscopic wide constrictions and highly disordered conditions [13, 14]. Based on this fitting, the phase coherence length at = 1 K is = 80 nm, which indicated the highly disordered condition ( nm ≫ ) due to the atomically sharp disorder, like nanoscale grain boundaries within the CVD graphene [24].
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Interestingly, we observed the periodic oscillations after eliminating from the WL peak and the average background of the resistance as shown in Figure 2(b) as previous studies [13, 14]. Consequently, the oscillation period in magnetic field is around = 0.49 T for the corresponding Fourier spectrum with the peak of Lorentz fitting as shown in the inset of Figure 2(b). Due to the result of = 0.49 T, we are able to calculate the ring radius ≈ 52 nm (A ) based on the Aharonov-Bohm effect within our CVD graphene wide constriction region according to the grain boundaries and merged domains as previous reports [13, 14, 25]. Consistently, the = 80 nm is at = 1 K in WL effect, in good accordance with the atomically sharp disorder () [25].
As shown in Figure 3(a), the conductance () is measured by sweeping the back gate voltage from 0 V to −10 V with = 3 nA and = 1.8 K. From the 285 nm thick SiO2 substrate, the field-effect mobility is below 100 cm2/Vs [26] and the Dirac point is far from zero voltage (>0 V), which is possibly due to the significant -type chemical doping. Besides, there are conductance oscillations at = 1.8 K, which also suggests that the evidence of ring structures within wide constrictions is due to the nanoscale grain boundaries and merged domains as our previous studies [13, 14].
In order to further confirm the ring structures within charge transport behavior of conductance oscillations with back gate voltage, we present LT-SGM images with = −6 V at = 1.8 K and zero magnetic field as shown in Figures 3(b) and 3(c). Figure 3(b) reveals electrostatic force microscopy (EFM) image for searching the graphene wide constriction region due to the charge screening effect on graphene [27]. Obviously, the graphene wide constriction region is revealed in bright color as shown in Figure 3(b). Interestingly, the enhancing and reducing conductance spots are not restricted to the wide constriction outline that was marked by white dashed line in Figure 3(c), and the hot current would suppress the conductance oscillations as previous reports [14, 25, 28]. Such LT-SGM conductance characteristics are typical evidences for quantum ring structures due to the lateral expanse of the tip perturbation as previous reports [13, 14, 29, 30]. From the SEM image of Figure 1(a), the single layer region was revealed to have few nanoscale ripples, which are strong evidences for the existence of nanoscale grain boundaries and merged domains so as to cause the ring-structure transport behaviors as previous studies [13, 14].
Most importantly, the charge quantum transport dynamic evolution with increase of the current so as to suppress the interference effect within the CVD graphene wide constriction has never been studied to date although some experimental results have observed the suppression of interference effect in ring structures devices [14, 25, 31]. We are interested in whether the additional carriers flushing would not follow the nanoscale ring-structure paths. Therefore, we performed numerical simulations based on the mean-field Gross-Pitaevskii equation [32–35] (see Supporting Information in Supplementary Material available online at http://dx.doi.org/10.1155/2016/1806871 for detail). The unit one normalized charge density () is defined by ideal charge distribution without any disordered potential fluctuations. Considering the disordered potential fluctuation that comes from the nanoscale grain boundaries and merged domains, we used autocorrelation function to set up the initial condition of the original disordered potential distribution in 800 nm (width) × 1000 nm (length) region from the variation of conductance fluctuation distribution as shown in Figure 3(c) so as to simulate the normalized charge density distribution in a tiny steady unit AC current without affecting the disordered condition that is intrinsic barrier potentials from nanoscale ring structures as shown in Figure 4(a) [29]. By increasing the current to , , , and as shown in Figures 4(b)–4(e), the normalized charge density fluctuation distribution in this region gradually becomes small and the normalized charge density gradually becomes unit one supported by the line profile (blue line shown in Figure 4(a)) as shown in Figure 4(f), which indicates that the increasing hot current would start to flush into the barrier potentials so as to suppress the interference effect, an excellent correspondence to previous experimental results [14, 25, 31]. From this point of view, the hot charges with spreading kinetic energy would flush into the barrier potentials that are equivalent to nanoscale ring structures within the wide constriction under supply of the additional hot charge, which interestingly implies that hot fermions in single layer graphene could flush into the barrier potentials formed from CVD graphene grain boundaries and merged domains that is a novel transport property in comparison with the serious scattering fermions in low current regime by grain boundaries and merged domains (see Electronic Supplementary Material for a movie of the evolution [36]). Our results obtained on CVD graphene in wide constriction show that the interference effect is sensitive in the low current regime due to the intrinsic nanoscale ring structures, and the interference effect is suppressed in high current regime. The LT-SGM experiments and simulation results reveal that the hot charges start to flush into the nanoscale grain boundaries and merged domains by supplying additional hot charges into the wide constriction region, which is a novel transport mechanism in comparison with conventional two-dimensional electron gas systems [37–41].
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4. Conclusions
In conclusion, we performed LT-SGM experiments on CVD-grown graphene wide constriction, which was further supported by numerical simulations. The LT-SGM images revealed the nanoscale ring structures existence so as to cause interference effect. Meanwhile, the numerical simulations suggested that the hot charges could flush into the grain boundaries and merged domains from the dynamical point of view. This work provides a subtle unified scope of current dependence charge transport behavior and pictures on CVD graphene in wide constriction, a great advance for realizing industrial graphene-based electronic device.
Competing Interests
The authors declare that they have no competing interests.
Acknowledgments
As an International Research Fellow of the Japan Society for the Promotion of Science (JSPS), Chiashain Chuang acknowledges the JSPS Postdoctoral Fellowship.
Supplementary Materials
The theoretical background and numerical method for mean-field Gross-Pitaevskii equation.