# Tuning of Graphene-Based Optical Devices Operating in the Near-Infrared
## 2 Graphene Optical Properties
### Graphene Electrode Configurations  
This paragraph focuses on the analysis of graphene electrode configurations considering the relationship between the applied voltage (\(V_{\mathrm{G}}\)) and the distance between graphene electrodes (\(D_{\mathrm{G}}\)). Figure 6 shows the cross sections of the GE configurations inside the optical devices. In particular, GE locations inside the optical devices can be categorized into two types: (1) Graphene-Insulator-Waveguide (GIW), Figure 6a, is a single GE above the Si waveguide [5,7,9,11,13,14,17,18,21,24,25]. (1a) Electrolyte/ion-gel-Graphene-Waveguide+PhC Cavity (EGWC), Figure 6c, is the PhC Nanocavity structure, which is located under the graphene electrode [65] and, in some cases, the capacitor insulator is located on top (electrolyte or ion-gel) [7,19,20] (partly a subgroup of GIW). (2) Graphene-Insulator-Graphene (GIG), Figure 6b, this is the case when two GEs are above the waveguide [8,10,12,15,16,21,64];  
(2a) Graphene-Electro-inside (GEin), Figure 6d, is the case when two GEs are located inside the waveguide [26,66] (partly a subgroup of GIG). We will use the abbreviation GIW/EGWC to describe the dielectric waveguide (e.g., Si or Si\({}_{3}\)N\({}_{4}\)) that is indicated by W. The EGWC case also implies a non-use of PhC cavities (Electrolyte/ion-gel-Graphene-Waveguide). In some configurations, e.g., EGWC, the insulator layer of the capacitor is located on the top in the form of an ion-gel or an electrolyte. In other cases, it is necessary to consider the thickness of the layers of the graphene-based capacitor. For example, a dielectric with a thickness of 90 nm [8] or 120 nm [65] between two layers of graphene causes a weak electrostatic bond, which is expressed in high applied voltages (from \(-40\) V to 40 V). In this regard, the boundary value of \(D_{\mathrm{G}}\) may be 90 nm, but the optimal value will be in the range <20 nm. However, for all configurations, the optical properties of the graphene are modulated by applying a voltage across the capacitor. For all cases, the large distance between the GE (or bottom GE) and the waveguide, which we denote as the insulator thickness (\(t_{\mathrm{I}}\)), leads to a relatively weak light interaction. Figure 6: Sketches of the location of graphene electrodes: (**a**) Graphene-Insulator-Waveguide (GIW), (**b**) Graphene-Insulator-Graphene (GIG), (**c**) Electrolyte/ion-gel-Graphene-Waveguide+PhC Cavity (EGWC) and (**d**) Graphene-Insulator-Graphene inside waveguide (GEin). (G–Graphene electrode and E-electrode). The Fermi level of graphene can be modulated by applying a voltage across the capacitor. In fact, the external voltage causes the accumulation of charges at the armatures of the capacitor, thus changing the carrier density on graphene and, consequently, the Fermi level as [21]  
\[\mu_{c}(n_{\mathrm{s}})=sgn(n_{\mathrm{s}})hv_{\mathrm{F}}\sqrt{\pi|n_{\mathrm{s}}|} \tag{6}\]  
where \(n_{\mathrm{s}}\) is the graphene surface carrier density. The voltage needed to charge a GIW capacitor is a sum of two contributions: the first is the actual potential across the insulator; the second is due to the shift of the Fermi potential induced by the accumulated carriers on the graphene layer. Using Equation (6), it is possible to obtain  
\[|V_{G}-V_{Dirac}|=\frac{qn_{s}}{C_{ox}}+\frac{|\mu_{c}|}{q}=\frac{q_{s}}{C_{ox} }\frac{\mu^{2}}{\pi(hv_{F})^{2}}+\frac{|\mu_{c}|}{q} \tag{7}\]  
where \(C_{ox}=\varepsilon\epsilon_{0}(W_{m}l/t_{I})\) is the oxide (insulator) capacitance per unit area (\(\sim\)20 mF/m\({}^{2}\) for ion-gel [19], \(\sim\)0.493 mF/m\({}^{2}\) for SiO\({}_{2}\)[15], \(\sim\)27 mF/m\({}^{2}\) for polyethilenoxide (PEO) + LiClO\({}_{4}\)[7]), and \(V_{Dirac}\) is the flat-band voltage corresponding to the charge-neutral Dirac point. \(V_{Dirac}\) depends on the intrinsic surface carrier density on the graphene electrode due to band alignment, lattice imperfections, charged defects or other impurities in the fabricated graphene sheet.