Quantum Capacitance Of Graphene Research Articles

Impact of typology and density of point defects on capacitance of graphene-based electrodes

The influence of defects on graphene quantum capacitance has been widely studied using various modeling approaches and in particular the fixed-band approximation (FBA). However, computational models do not yield results in agreement with experiments and can rarely account for the effect of the metallic substrate. They typically predict capacitance values an order of magnitude higher than experiment. In this paper we assess the capacity of the recently developed interfacial capacitance model (ICM) based on density functional theory (DFT) calculations, to investigate the impact of three point-like defects on graphene capacitance. The modeled defects are single-vacancy, double-vacancy, and Stone-Wales; all defective graphene structures are modeled on Cu(111) substrate. The impact of the density of single-vacancy defects on the capacitance was carefully analyzed. The computations demonstrate that the ICM can predict capacitance of graphene on a metallic substrate in agreement with experiment even in the case of the existence of defect. This suggests that ICM can be generalized for assessing graphene capacitance and interfacial capacitance regardless of morphology of the surface. The results ranged from 1.692 μF cm−2 to 1.872 μF cm−2 for defective models, compared with 1.73 μF cm−2 of pristine model which is in agreement with experiment. Various defective cases were analyzed using density of states, projected density of states, electrons isosurfaces, and structural parameters. The charge separation triggered by defects can be correlated with the increase in capacitance as long as no chemical bonding is triggered by the defect between copper and graphene.

Electronic structures and quantum capacitance of twisted mixed-dimensional van der Waals heterostructures of graphene/C2H based on tight-binding model

Constructing twisted mixed dimensional graphene-based van der Waals heterostructure (vdWH) is an effective strategy to manipulate the electronic structures and improve the quantum capacitance (C q) of graphene. In this work, mixed dimensional vdWH of graphene/C2H has been proposed owing to similar Dirac semimetal character of one-dimensional C2H with that of graphene. Meanwhile, the influence of twisting angle (θ) and interlayer interaction strength on the electronic structures and the C q of the MD vdWH are systemically explored based on tight binding model. With the fitted hopping integral parameters, it is found that the linear dispersion of the graphene is basically preserved but the bandwidth is decreased with modulating twisting angle and interlayer interaction, and the C q of mixed dimensional vdWH is improved 5–19 times compared with graphene at zero bias. Moreover, the compressed strain could enhance the C q of mixed dimensional vdWH to 74.57 μF cm−2 at zero bias and broaden the low working voltage window of mixed-dimensional vdWH with considerable C q. Our results provide suitable tight-binding model parameters and theoretical guidance for exploring the twisted MD vdWH of graphene/C2H and offer an effective strategy to modulate the electronic structures and the C q of graphene through constructing the MD vdWH.

Modelling the Quantum Capacitance of Single-layer and Bilayer Graphene

In this paper, we report the modelling of quantum capacitance in both single-layer and bilayer graphene devices to investigate the temperature dependence. The model includes the existence of electron and hole puddles due to local fluctuations of the potential, which is taken into account with the possibility of finite lifetimes of electronic states to calculate the quantum capacitance using the Gaussian distribution. The results indicate that the simulations are in agreement with the experimental measurements, which proves the accuracy of the proposed model. On the other hand, temperature dependence around the charge neutrality point has been reported for both single and bilayer graphene.

Electronic structures and quantum capacitance of twisted bilayer graphene with defects based on three-band tight-binding model.

Twisted bilayer graphene (tBLG) with C vacancies would greatly improve the density of states (DOS) around the Fermi level (EF) and quantum capacitance; however, the single-band tight-binding model only considering pz orbitals cannot accurately capture the low-energy physics of tBLG with C vacancies. In this work, a three-band tight-binding model containing three p orbitals of C atoms is proposed to explore the modulation mechanism of C vacancies on the DOS and quantum capacitance of tBLG. We first obtain the hopping integral parameters of the three-band tight-binding model, and then explore the electronic structures and the quantum capacitance of tBLG at a twisting angle of θ = 1.47° under different C vacancy concentrations. The impurity states contributed by C atoms with dangling bonds located around the EF and the interlayer hopping interaction could induce band splitting of the impurity states. Therefore, compared with the quantum capacitance of pristine tBLG (∼18.82 μF cm-2) at zero bias, the quantum capacitance is improved to ∼172.76 μF cm-2 at zero bias, and the working window with relatively large quantum capacitance in the low-voltage range is broadened in tBLG with C vacancies due to the enhanced DOS around the EF. Moreover, the quantum capacitance of tBLG is further increased at zero bias with an increase of the C vacancy concentration induced by more impurity states. These findings not only provide a suitable multi-band tight-binding model to describe tBLG with C vacancies but also offer theoretical insight for designing electrode candidates for low-power consumption devices with improved quantum capacitance.

Effects of stacking layers and different doping elements on the electronic structures and quantum capacitance of graphene: A DFT study

The influence of boron (B), nitrogen (N), oxygen (O), and sulfur (S) doping on enhancing quantum capacitance were investigated through a series of the surface-doped trilayer graphene structures by using density functional theory (DFT) calculations. The quantum capacitance of monolayer models was enhanced through a single doping, a triple doping, and a vacancy defect. Our calculations suggested that the layer interactions within the trilayer models decreased the quantum capacitance but increased the stability of the doped structures. Interestingly, in the case of sulfur dopants with significantly larger atomic size than carbon, the stacking layers induced a surface distortion that could avoid the steric clashes with stacking layers and enhanced the stability. In conclusion, this work provided more realistic models of modified carbon-based electrodes for supercapacitors with more accurate information from the combined effects of doping and stacking layers.

An Exploration of Graphene-Water Interface Electrochemical Circuit Model

Graphene has been considered a good candidate for sensor material due to its large surface-to-volume ratio and high conductivity. For instance, high-sensitivity solvent sensors can be achieved through liquid-gated graphene field effect transistors (GFET). In such kind of sensors, ions and other molecules in the test solution will be chemically adsorbed by the graphene sheet. It results in changes of the channel surface potential and conductance. However, the measured potential difference are affected by electrical double-layer capacitance in solution, and quantum capacitance in graphene. Studies have reported the quantum capacitance of graphene in an ionic or aqueous liquid, while the interface between graphene and deionized (DI) water hasn’t been fully explored yet. To address this point, in this work, we measured the electrochemical impedance spectroscopy (EIS) of graphene electrodes in deionized water and proposed an electrical circuit model for the electrochemical cell. The meaning of each element of the circuit model was also discussed.In our experiment, single-layer graphene was grown by chemical vapor deposition (CVD) on copper foil and transferred to Si/SiO2 substrate with gold contacts. Our test solution, DI water, was confined on the graphene sensing layer by polydimethylsiloxane (PDMS). This electrochemical cell was measured with BioLogic SP-150 potentiostat by 2-probe EIS method, with graphene as working electrode (WE) and Ag/AgCl electrode placed in DI water as counter electrode (CE). Another electrochemical cell with gold pad WE was also prepared as the control group.The electrochemical impedance of the water-graphene cell was plotted in a Nyquist plot and showed two semicircles. This observation is different from a regular electrochemical cell, whose impedance shows a semicircle, corresponding to the interface RC impedance, and a low-frequency 45° straight line, corresponding to molecular mass transport limitation. The two semicircles in our water-graphene cell impedance indicate that the equivalent circuit model is based on two parallel RC circuits, corresponding to the interface and solution impedance. By modifying the biasing potential and adding supporting electrolyte, we observed the response of the impedance and identified that the high-frequency semicircle is related to solution impedance, and the low-frequency semicircle is related to interface impedance, which is consistent with the reaction rate of both parts. To make more precise fittings, an additional Warburg element was introduced into the circuit model for the effect of mass-transfer limitation. We proposed a model based on an RC parallel circuit in series with a Randles circuit. Comparing with the 2-RC model, the fitting residual of the proposed model improved by 13%. The RWC parallel circuit was fitted to the high-frequency semicircle, which corresponds to the solution impedance. This is different from the commonly used Randles model, where the Warburg element is included in interface impedance. This difference arises from the lack of supporting electrolytes. When there are supporting electrolytes in an electrochemical cell, the double-layer capacitor at the electrode-solution interface is mainly contributed by supporting electrolytes. While using DI water as the solution in our case, the charged species contributes to both faradic current and non-faradic current, which means that the mass-transport limitation affects both the charge transfer resistor and the double-layer capacitor. Hence, the Warburg element for mass-transport limitation can be extracted from the interface RC parallel circuit and put into the solution impedance when there is no supporting electrolyte.After the circuit model was decided and the elements were identified, we fit the electrochemical impedance curves of both the water-graphene cell and the control group, whose WE was replaced by a gold pad. The fitting result shows that the bulk resistor and capacitor, Rb and Cb, values are unrelated to the WE material, which again supports our circuit model. While the WE surface capacitance Cs of the graphene-water electrochemical cell is 0.0606 F/m2, which is 1/65 of that of the control group. To verify the reason for the capacitance difference, we considered the effect of the graphene quantum capacitance. The theoretic value of the quantum capacitance in single-layer graphene was found to be 0.0752 F/m2 under our setup, which is only 18.8% smaller than our experimental value. Hence, we concluded that SLG surface capacitance was dominated by quantum capacitance. Figure 1

Modelling and Optimization of the Differential Surface Capacitance in Electrolyte-Gated Graphene Field-Effect Transistors

Graphene field-effect transistors (GFETs) are a promising avenue for the detection of biomarkers, allowing to envision improvements in diagnostic approaches for different types of cancer and other diseases. To enable such applications, the detection metrics of the devices must be optimized, including their sensitivity, selectivity, and stability. In particular, the capacitance of the device is one of the key determinants of the sensitivity of the electrical current of graphene to nearby changes in electrical potentials. In this presentation, we present our approach to optimize the surface capacitance of electrolyte-gated GFETs, by investigating theoretically and/or experimentally the effect of specific design parameters, including the graphene area, the removal of the backgate, and the passivation of electrodes. On the theoretical side, a mathematical representation of the device capacitance was established as an equivalent circuit of capacitors modelling for the quantum capacitance of graphene, the backgate capacitance, and the capacitance of electrical double layers in the electrolyte. On the experimental side, microchips of GFET arrays were assembled using microfabrication techniques on two types of substrates: a standard Si++/SiO2 wafer in which the doped silicon layer is used as a backgate, and a pure non-conducting borosilicate glass wafer in comparison. The capacitance of the devices was then measured using a custom parallel electrical prober by stepping the applied voltage in the solution and analyzing the resulting current response through a standard RC direct current model. We will present our analyses by comparing the relative impact of electrode passivation, backgate usage, and graphene area on the capacitance of devices. These results will enable a rational design of GFET devices with improved sensitivity for their use in applications such as biological, chemical, and gas sensing.

Modeling of charging dynamics in electrochemical systems with a graphene electrode

A classical electrochemistry problem related to the polarization of a graphene electrode immersed in an aqueous solution and subjected to a small external ac voltage is revisited. The Poisson-Nernst-Planck equations with proper boundary conditions are linearized and normalized, leading to an analytical formula for the impedance of the electrochemical system containing a graphene-metal electrode pair. Electrochemical impedance spectroscopy is utilized to compare the impedance behavior of the graphene-metal electrode pair with the standard metal-metal electrode pair for a range of ion concentrations in the electrolyte. Also studied is the electrochemical capacitive spectroscopy to provide a detailed analysis related to the effects of the quantum capacitance of graphene on the total capacitive properties of the system.

Enhanced quantum capacitance of MX4 (M = Fe, Co, Ni, Cu, and Zn; X = N, P) moieties embedded graphene: a DFT study

In this work, density functional theory calculations are performed to study the impact of embedding transition metal-(N/P)4 moieties in graphene on its geometric structure, electronic properties, and quantum capacitance. Enhancement of quantum capacitance of transition metal doped nitrogen/phosphorus pyridinic graphenes is observed, which is directly related to the availability of states near the Fermi level. The findings show that electronic properties and hence quantum capacitance of graphene can be tuned by varying transition metal dopants and/or their coordination environment. Modified graphenes can suitably be chosen as positive or negative electrodes of asymmetric supercapacitors depending upon the values of quantum capacitance and stored charges. Furthermore, quantum capacitance can be enhanced by widening the working voltage window. The results can serve as guidelines for the design of graphene-based electrodes in supercapacitor applications.

Water in the Electrical Double Layer of Ionic Liquids on Graphene

The performance of electrochemical devices using ionic liquids (ILs) as electrolytes can be impaired by water uptake. This work investigates the influence of water on the behavior of hydrophilic and hydrophobic ILs─with ethylsulfate and tris(perfluoroalkyl)trifluorophosphate or bis(trifluoromethyl sulfonyl)imide (TFSI) anions, respectively─on electrified graphene, a promising electrode material. The results show that water uptake slightly reduces the IL electrochemical stability and significantly influences graphene's potential of zero charge, which is justified by the extent of anion depletion from the surface. Experiments confirm the dominant contribution of graphene's quantum capacitance (CQ) to the total interfacial capacitance (Cint) near the PZC, as expected from theory. Combining theory and experiments reveals that the hydrophilic IL efficiently screens surface charge and exhibits the largest double layer capacitance (CIL ∼ 80 μF cm-2), so that CQ governs the charge stored. The hydrophobic ILs are less efficient in charge screening and thus exhibit a smaller capacitance (CIL ∼ 6-9 μF cm-2), which governs Cint already at small potentials. An increase in the total interfacial capacitance is observed at positive voltages for humid TFSI-ILs relative to dry ones, consistent with the presence of a satellite peak. Short-range surface forces reveal the change of the interfacial layering with potential and water uptake owing to reorientation of counterions, counterion binding, co-ion repulsion, and water enrichment. These results are consistent with the charge being mainly stored in a ∼2 nm-thick double layer, which implies that ILs behave as highly concentrated electrolytes. This knowledge will advance the design of IL-graphene-based electrochemical devices.

Quantum Capacitance and Fermi Level Change in Graphene nanoribbons due to Gas Sensing

Here we used semiempirical computations to examine the property of nanoribbon of Graphene as a gas sensor with interaction of H2O gas molecule for both pure and defective GNRs which has been generated in Atomistix Toolkit (ATK) software. Density of States GNR before and after the interaction is shown in a (DOS) diagram with gas particles was discovered to be different which has been observed in MATLAB software. It's vital to look at the quantum capacitance when examining Graphene’s electrical properties. So, this study looked at change in quantum capacitance and Fermi Level of Graphene before and after gas sensing and the results were produced with necessary equations. Using a three-electrode electrochemical setup, we are able to directly quantify Graphene's quantum capacitance as a function of gate potential. If Graphene is used in a highly sensitive capacitive circuit, the change in Fermi energy was determined from experimental data of changed Density of States (DOS). Although this research has some limitations and future scopes, we can propose that the change in Fermi Energy level can be approximately 9.5 eV with respect to the quantum capacitance of fabricated Graphene interacting with H2O which is used as a MOSFET in this work.

Quantum Capacitance and Fermi Level Change in Graphene nanoribbons due to Gas Sensing

Here we used semiempirical computations to examine the property of nanoribbon of Graphene as a gas sensor with interaction of H2O gas molecule for both pure and defective GNRs which has been generated in Atomistix Toolkit (ATK) software. Density of States GNR before and after the interaction is shown in a (DOS) diagram with gas particles was discovered to be different which has been observed in MATLAB software. It's vital to look at the quantum capacitance when examining Graphene’s electrical properties. So, this study looked at change in quantum capacitance and Fermi Level of Graphene before and after gas sensing and the results were produced with necessary equations. Using a three-electrode electrochemical setup, we are able to directly quantify Graphene's quantum capacitance as a function of gate potential. If Graphene is used in a highly sensitive capacitive circuit, the change in Fermi energy was determined from experimental data of changed Density of States (DOS). Although this research has some limitations and future scopes, we can propose that the change in Fermi Energy level can be approximately 9.5 eV with respect to the quantum capacitance of fabricated Graphene interacting with H2O which is used as a MOSFET in this work.

Effective carrier doping and quantum capacitance manipulation of graphene through two-dimensional solid electrolytes of ScI3 and YBr3

Effective carrier doping would be expected to enhance the electrical conductivity and further improve the quantum capacitance (Cq) of graphene. In this work, two-dimensional solid electrolytes of ScI3 and YBr3 as buffer layers have been proposed to modulate the carrier density and improve the Cq. By using first-principles calculations, the effective carrier doping has been examined by building heterostructures of graphene/ScI3 and graphene/YBr3 combined with Li, Na, K, Ca, F dopants. The n-type doping with electron density and p-type doping with hole density of graphene reach up to 1.14 × 1014 cm−2 and 6.66 × 1013 cm−2, respectively. Remarkably, the linear band dispersions of graphene are maintained near the Dirac point. Moreover, the Cq is significantly increased around the zero bias due to the increased density of states near the Fermi level. For Li-, Na-, K-, and Ca-doped systems, the Cq in the negative bias region is effectively enhanced while the Cq is improved in the positive bias region for F-doped system. These results provide an ideal route to implement the effective carrier doping and the Cq manipulation of graphene, facilitating the applications of graphene as electrodes in high-performance optoelectronics and energy storage devices, such as light-emitting diodes, solar cells and supercapacitors.

Capacitive NO2 Detection Using CVD Graphene-Based Device.

A graphene-based capacitive NO2 sensing device was developed by utilizing the quantum capacitance effect. We have used a graphene field-effect transistor (G-FET) device whose geometrical capacitance is enhanced by incorporating an aluminum back-gate electrode with a naturally oxidized aluminum surface as an insulating layer. When the graphene, the top-side of the device, is exposed to NO2, the quantum capacitance of graphene and, thus, the measured capacitance of the device, changed in accordance with NO2 concentrations ranging from 1-100 parts per million (ppm). The operational principle of the proposed system is also explained with the changes in gate voltage-dependent capacitance of the G-FET exposed to various concentrations of NO2. Further analyses regarding carrier density changes and potential variances under various concentrations of NO2 are also presented to strengthen the argument. The results demonstrate the feasibility of capacitive NO2 sensing using graphene and the operational principle of capacitive NO2 sensing.

Density functional theory studies on graphene/h-boron nitride hybrid nanosheets for supercapacitor electrode applications.

Pristine graphene (C32), hexagonal boron nitride (h-BN), and graphene/h-BN hybrid nanosheets were examined using density functional theory calculations in order to find their suitability as an electrode material for supercapacitor applications. The stability of the structure, charge density, electronic properties, and quantum capacitance of pristine graphene and graphene/h-BN hybrid nanosheets were studied. The structural optimization results reveal that all the nanosheets are stable with zero transverse displacement of atoms along the z-direction. Further, replacing the C-C pair with B-N altered the average bond length and angle, thereby maintaining structural stability. The interaction between graphene and h-BN is higher for C16B8N8 compared to other hybrid nanosheets because of the delocalized distribution of the electron density cloud. The doping of the B-N pair into the graphene nanosheet shifts the Fermi level into either the valence band or the conduction band based on the concentration of the B-N pair. Meanwhile, the effective mass is increased and is relatively high for the hybrid nanosheets with a localized state. The pristine B16N16 nanosheet exhibits a quantum capacitance of 31.539 μF cm-2, while among the hybrid nanosheets, the C4B14N14 nanosheet exhibits a maximum quantum capacitance of 22.518 μF cm-2, and from the outcomes, they are suitable as an electrode for asymmetric supercapacitors.

Density functional theory study of the enhancement of quantum capacitance of graphene by phosphorous doping

AbstractCalculations based on density functional theory are performed to explore the effect of the phosphorus dopants and their oxygenation on the quantum capacitance of single‐ and double‐vacancy graphene in the voltage range from −1.5 to +1.5 V. It is found that these modified graphenes have improved quantum capacitance, and can store more charges compared to the pristine graphene. The findings can be used as a guidance for the rational design of P‐doped graphene as an electrode material of asymmetric supercapacitors with high energy density.

Non‐Local Electrostatic Gating Effect in Graphene Revealed by Infrared Nano‐Imaging

AbstractElectrostatic gating lies in the heart of field effect transistor (FET) devices and modern integrated circuits. To achieve efficient gate tunability, the gate electrode has to be placed very close to the conduction channel, typically a few nanometers. Remote control of a FET device through a gate electrode located far away is highly desirable, because it not only reduces the complexity of device fabrication, but also enables the design of novel devices with new functionalities. Here, a non‐local electrostatic gating effect in graphene devices using scanning near‐field optical microscopy (SNOM)—a technique that can probe local charge density in graphene—is reported. Remarkably, the charge density of the graphene region tens of micrometers away from a local gate can be efficiently tuned. The observed non‐local gating effect is initially driven by an in‐plane electric field induced by the quantum capacitance of graphene, and further largely enhanced by adsorbed polarized water molecules. This study reveals a non‐local phenomenon of Dirac electrons, provides a deep understanding of in‐plane screening from Dirac electrons, and paves the way for designing novel electronic devices with remote gate control.

An approach for quantum capacitance of graphene, carbon nanotube, silicene and hexagonal boron nitride nanoscale supercapacitors by non-equilibrium Green’s function method

We introduce a comprehensive approach to calculate quantum capacitance of nanoscale capacitors as a function of applied potential difference to have resemblance to actual device operating conditions. Ab initio analysis based on the non-equilibrium Green’s functions combined with density functional theory was applied for different elementary materials and geometries for the soundness of the approach. The results of planar single layer graphene, silicene, and hexagonal boron nitride and for tubular carbon nanotube supercapacitor symmetric model systems on the quantum capacitance are presented together with widely utilized fixed band approximation at planar systems for comparison purposes. The proposed procedure not only successfully reproduced the results for planar systems in a qualitative manner but is also consistently applicable for non-planar (tubular) systems by remarking the robustness of the procedure. Our work highlights the importance of the separation spacing (such as contact distance) search in obtaining quantum capacitance for electric double layer supercapacitors. In that search procedure, it is basically aimed to minimize the charge on the leads/plates for eliminating quantum effects. Induced charge sites under the applied bias could be indicative in some degree for the possible ion adsorption/desorption from the electrolyte or redox reactions at electrode/electrolyte interface to create a double layer. So that the proposed approach on the presented study could also be treated as a qualitative measure on the quantum capacitance for realistic systems with dopants, defects, and functional groups for supercapacitor understanding.

Contact spacing controls the on-current for all-carbon field effect transistors

All-carbon field-effect transistors, which combine carbon nanotubes and graphene hold great promise for many applications such as digital logic devices and single-photon emitters. However, the understanding of the physical properties of carbon nanotube (CNT)/graphene hybrid systems in such devices remained limited. In this combined experimental and theoretical study, we use a quantum transport model for field-effect transistors based on graphene electrodes and CNT channels to explain the experimentally observed low on currents. We find that large graphene/CNT spacing and short contact lengths limit the device performance. We have also elucidated in this work the experimentally observed ambipolar transport behavior caused by the flat conduction- and valence-bands and describe non-ideal gate-control of the contacts and channel region by the quantum capacitance of graphene and the carbon nanotube. We hope that our insights will accelerate the design of efficient all-carbon field-effect transistors.

Measuring quantum conductance and capacitance of graphene using impedance-derived capacitance spectroscopy

Here, we demonstrate that impedance-derived capacitance spectroscopy is a useful method for measuring and analyzing the quantum of conductance and capacitance of a single-layer graphene sheet. Both quantum conductance and capacitance exhibit the expected traditional V-shape when measured as a function of bias potential (with the minima of both parameters being at the Dirac point) in a 1-Butyl-3-methylimidazolium tetrafluoroborate ionic liquid environment. Measurements were conducted at a specific low-frequency limit in which the conductance and capacitance were scanned as a function of bias potential to attain the quantum conductive and capacitive V-shapes. The V-shapes agree in terms of magnitude and profile with those reported in the literature using different methodologies and/or techniques. This validates impedance-derived capacitance spectroscopy as a suitable method to acquire key information of graphene and its derivatives. This method represents an alternative for rapid construction of both conductive and capacitive V-shapes of graphene in a single, simple experimental run.