**3. Defects in graphene for energy storage**

that in pristine sample despite higher dopant concentration (~2.5 %). These results are consistent with our observations in the XPS spectra shown in **Figure 3a**. When nitrogen atoms enter the graphene lattice in non-graphitic configuration, vacancies are needed and result in armchair-type edges. Previous reports showed that armchair edges in graphene allow intervalley scattering of *iTO* phonons in the Brillouin zone unlike zigzag edges [22] and thus

**Figure 3.** (a) XPS spectra for N1s line. The colored peaks represent the deconvolution of N1s peaks. The resolution of the spectrometer was 0.5 eV. The peak at 400.5 eV corresponds to graphitic configuration. Peaks at 398 and 400 eV correspond to non-graphitic. Raman spectra of pristine and N-graphene are shown in (b) and (c). As seen in (b), the D and D′ bands increase in intensity for non-graphitic samples S1 and S3. The deconvolution of 2D band in (c) suggests

From the line-shape analysis of Raman 2D band (**Figure 3c**), we confirmed that our CVD-grown graphene samples are predominantly bilayers. As seen in **Figure 3c**, maximum downshift in 2D band (25 cm−1) was observed for sample S3 with relatively large dopant percentage (~3.5 %). On the other hand, sample S2 (graphitic configuration) showed little downshift in 2D band compared to sample S1 in spite of having higher dopant concentration. 2D band in S1 showed a downshift of ~10–15 cm−1 even in the presence of low dopant concentrations (~0.2 %). These differences in the 2D band shift in the Raman spectra can also be attributed to the nature of the dopant environment. For example, in samples S1 and S3 that are non-graphitic in nature, due to lattice symmetry breaking, electronic structure of graphene is strongly perturbed leading to possible renormalization of electron and phonon energies. Such a renormalization in electron energies results in a concomitant downshift in phonon energies of 2D band [7].

We further explored the influence of defects on the carrier scattering rate using pump-probe (PP) spectroscopy [8]. The differential transmittance (Δ*T*/*T*) was obtained by taking the ratio of pump-induced change in the probe transmittance (Δ*T*) at a time *t* after the pump excitation

increase the intensity of the D band as in samples S1 and S3.

88 Two-dimensional Materials - Synthesis, Characterization and Potential Applications

that graphene samples are bilayer.

**2.3. Nonlinear optical studies of N-graphene**

The increasing global energy demands have spurred a rigorous search for new renewable energy sources. In recent times, fuel cells, photovoltaic devices/solar cells, and various other renewable energy sources have received much attention and are all promising candidates for clean energy production. However, today's batteries and capacitors, which are the main components for energy storage, cannot meet the world's demand for combined power and energy densities [24–27]. As an example, the plot in **Figure 5** shows the general performance metrics for commercially available formats of charge/energy storage devices. This plot depicts *electrical capacitors* (on the top left hand side) with a fast response time and high-power-density *batteries and fuel cells* (on the bottom right hand side), which exhibit a large energy density due to the chemical/ionic basis of their reactions. The drawback of electrical capacitors is their inability to store large amounts of energy, while the batteries are incapable of fast charge/ discharge cycles due to the slow nature of the ion diffusion processes. This gap between capacitors and battery performance has been a *major roadblock* in electrochemical energy storage. Electrochemical double-layer capacitors (EDLCs) or *supercapacitors* have been proposed to bridge the gap between these disparate devices by incorporating elements of both technologies [12, 28–33]. The charge is stored in the electric double layer, which forms at the electrode/electrolyte interfaces and leads to a double-layer capacitance (Cdl). The specific energy (E) of the EDLC may be expressed in terms of the total measured device capacitance (Cmeas) and the operating voltage (V) as E = (1/2)CmeasV2 . Unlike traditional Li-ion batteries, EDLCs can be reliably used for hundreds of thousands of cycles since their charge storage mechanism does not involve ion motion and the consequent chemical irreversibility. Although the EDLCs are superior (say, to batteries) in terms of long-term cyclability, they suffer from poor energy density in that energy (or charge) is only stored at the surface/interface rather than within the bulk of the material.

**Figure 5.** (a) Ragone plot showing specific power versus specific energy for common electrical energy storage devices. Supercapacitors are expected to bridge the gap between batteries and capacitors and impact nearly every area of elec‐ trical energy usage. For practical applications, the energy and power densities indicated by the star are needed. (b) Cyclic voltammetry (CV) characterization of plasma processed FLG samples (in 0.25 M TBAHFP dissolved in a 1 M acetonitrile). The area enclosed by the CV curves was used to parametrize the Cmeas which increases with plasma pow‐ er (indicated on the figure). (c) A close to threefold enhancement in the Cmeas (left axis) and the contributions of the computed Cq (right axis), i.e., 1/Cmeas = 1/Cdl + 1/Cq, as a function of the plasma power.

Nanocarbons including carbon nanotubes and graphene have been widely used as an electrode in EDLCs due to their high surface area (~2000 m2 /g), modest electrical conductivity, electro‐ chemical stability, and open porosity [25, 27]. However, the performance of the carbon-based EDLCs (particularly, graphene) is fundamentally limited by the so-called quantum capacitance (Cq), which is defined as Cq = e2 DOS(EF) with *e* being the charge of an electron [6]. An intrins‐ ically small DOS (EF) in graphene results in a small serial Cq, which diminishes the total device capacitance value (1/Cmeas = 1/Cdl + 1/Cq) in EDLCs [6, 28]. Although graphene has high surface area and consequently high Cdl, the total EDLC energy is limited by small Cq. Defects can be advantageous for alleviating the limitation of Cq by increasing the DOS (discussed later in **Figures 5b** and **c**). In our previous work [6], we synthesized few-layer graphene (FLG) on Ni foil substrates through chemical vapor deposition and subsequently subjected to argon-based plasma processing to intentionally induce charged defects (see the inset in **Figure 6**). Argon was chosen because the constituent ionic species are limited to Ar+, implying relatively simple plasma chemistry.

energy densities [24–27]. As an example, the plot in **Figure 5** shows the general performance metrics for commercially available formats of charge/energy storage devices. This plot depicts *electrical capacitors* (on the top left hand side) with a fast response time and high-power-density *batteries and fuel cells* (on the bottom right hand side), which exhibit a large energy density due to the chemical/ionic basis of their reactions. The drawback of electrical capacitors is their inability to store large amounts of energy, while the batteries are incapable of fast charge/ discharge cycles due to the slow nature of the ion diffusion processes. This gap between capacitors and battery performance has been a *major roadblock* in electrochemical energy storage. Electrochemical double-layer capacitors (EDLCs) or *supercapacitors* have been proposed to bridge the gap between these disparate devices by incorporating elements of both technologies [12, 28–33]. The charge is stored in the electric double layer, which forms at the electrode/electrolyte interfaces and leads to a double-layer capacitance (Cdl). The specific energy (E) of the EDLC may be expressed in terms of the total measured device capacitance

EDLCs can be reliably used for hundreds of thousands of cycles since their charge storage mechanism does not involve ion motion and the consequent chemical irreversibility. Although the EDLCs are superior (say, to batteries) in terms of long-term cyclability, they suffer from poor energy density in that energy (or charge) is only stored at the surface/interface rather than

**Figure 5.** (a) Ragone plot showing specific power versus specific energy for common electrical energy storage devices. Supercapacitors are expected to bridge the gap between batteries and capacitors and impact nearly every area of elec‐ trical energy usage. For practical applications, the energy and power densities indicated by the star are needed. (b) Cyclic voltammetry (CV) characterization of plasma processed FLG samples (in 0.25 M TBAHFP dissolved in a 1 M acetonitrile). The area enclosed by the CV curves was used to parametrize the Cmeas which increases with plasma pow‐ er (indicated on the figure). (c) A close to threefold enhancement in the Cmeas (left axis) and the contributions of the

Nanocarbons including carbon nanotubes and graphene have been widely used as an electrode

chemical stability, and open porosity [25, 27]. However, the performance of the carbon-based EDLCs (particularly, graphene) is fundamentally limited by the so-called quantum capacitance

ically small DOS (EF) in graphene results in a small serial Cq, which diminishes the total device

computed Cq (right axis), i.e., 1/Cmeas = 1/Cdl + 1/Cq, as a function of the plasma power.

in EDLCs due to their high surface area (~2000 m2

(Cq), which is defined as Cq = e2

. Unlike traditional Li-ion batteries,

/g), modest electrical conductivity, electro‐

DOS(EF) with *e* being the charge of an electron [6]. An intrins‐

(Cmeas) and the operating voltage (V) as E = (1/2)CmeasV2

90 Two-dimensional Materials - Synthesis, Characterization and Potential Applications

within the bulk of the material.

**Figure 6.** Enhanced plasma processing applied to the pristine sample results in a substantial intensity enhancement of the D- and D′-peaks as seen in the Raman spectra (normalized to the G-peak). An increase in power, say to 50 W, may result in irreversible changes due to graphene removal. The inset schematic shows the difference between armchair and zigzag defects (created using plasma processing) in the graphene lattice.

As shown in **Figure 6**, we found that the D band in the Raman spectrum of graphene increased with increasing power of plasma etching due to the introduction of new structural defects such as pores, which contain both armchair and zigzag edges. An important attribute of zigzag defects is that they may be electrically active and could contribute to an enhanced DOS much more than the armchair-type edge defects (which contribute less due to the two constituent carbon atoms belonging to different sublattices). We observed that the increase in plasma power resulted in a high device capacitance due to higher Cq arising from defect-induced DOS (EF). Indeed, we used cyclic voltammetry to quantify the changes in Cq and Cmeas (**Figure 5b**). The more than doubling of the Cmeas from 1.9 μF/cm2 (for the pristine sample) to 4.7 μF/cm2 (for the sample subject to 20 W plasma) is remarkable and suggests a novel means of substan‐ tially enhancing capacitance through defects. However, at higher plasma power (>20 W), high defect concentration results in poor electrical conductivity leading to a drop in Cmeas suggesting the importance of defect concentration in determining 2D material properties.

Thus, as evidenced by our data in graphene, the presence of defects does not necessarily deteriorate the material performance. Though there is only one way for a given material to be defect-free, there are many possibilities for it to be imperfect. While defect configuration is important in determining the mobility through carrier scattering rate, controlling defect concentration is critical for electrochemical applications. Accordingly, future efforts must be focused on finding new approaches to identify and control the right defect configurations (e.g., N in graphitic configuration to increase carrier concentration without compromising carrier scattering rates or mobility) and concentrations, which could improve material properties instead of dismissing all defects as detrimental for carrier mobility.
