Variable-Angle Spectroscopic Ellipsometry of Graphene-Based Films

: A review of the authors’ research works on Variable-Angle Spectroscopy (VASE) of graphene-based ﬁlms is presented. The interaction of graphene oxide (GO) with magnetron-sputtered metals is a promising research area. VASE optical models of GO thin ﬁlms deposited on magnetron-sputtered titanium (Ti), silver (Ag) and gold (Au) are discussed. Moreover, the optical properties of graphene nanoplatelet (GNPS) ﬁlms and reduced graphene oxide (RGO) stabilized with Poly(Sodium 4-Styrenesulfonate) (PSS) ﬁlms, which are less studied graphene-related materials, are shown. Fi-nally, different optical behaviors of chemical vapor deposition (CVD)-grown monolayer, bilayer, and trilayer graphene ﬁlms on silicon and polyethylene terephthalate (PET) substrates are recapitulated.


Introduction
A transparent conductor is a relevant constituent in several photoelectronic appliances. Indium tin oxide (ITO) is principally used for fabricating transparent conductors due to its properties [1]. Nevertheless, ITO has many disadvantages; for instance, it is expensive and it does not find application in flexible devices because of its brittle nature [2]. Consequently, consideration in the semiconductor field has been drawn to graphene [3], which shows broadband light absorption, linear dispersion band structure and an ultrahigh chargecarrier mobility. Graphene-based materials are thus advantageous materials that can be produced in ultrathin sheet form and may be used in several applications [4][5][6][7][8][9][10][11].
Chemical vapor deposition (CVD) is a technique used for high-quality graphene production [12]. The employment of CVD technology in ultradense photonic, optoelectronic, and electronic instruments has been reported [13][14][15].
Graphene oxide (GO) is a graphene-based material that has more oxygen-containing groups and defects in comparison with mechanically exfoliated or CVD-grown graphene. These defects are advantageous to enhance the performance of photodetectors [16]. Additionally, GO thin films show high optical transmittance in the visible region that allows their use as protective coatings and optically transparent electrodes, crucial in solar cells and for optical applications [17].
GO reduction is a method for large scale graphene manufacturing [18]. Reduced graphene oxide (RGO) is achieved using chemical methods [19], which eliminate or diminish the oxygen-containing groups. Additional reduction methods are thermal annealing that should be carried out above 200 • C [20] and "green reducers" (for instance vitamin C) [21].
RGO can be functionalized with Poly(Sodium 4-Styrenesulfonate) (PSS), which is a polyelectrolyte that avoids RGO aggregation. PSS interacts with graphene by means of π-π interactions, is soluble in water and safe to use [22].
Presently graphene nanoplatelets (GNPs) have arisen as a new graphene-based material. GNPs show some of the beneficial properties of single layer graphene [23]. GNPs are composed of mono-to few-layer sheets of sp 2 bonded carbon atoms that overlap creating nanometers thick 2D particles [24]. They can be obtained by means of exfoliation of cheap graphite flakes and then through chemical oxidation and graphite oxide nanoplatelets reduction [24].
Graphene-based materials show notable optical properties such as highly transparency in visible spectrum, photo-response up to Terahertz frequency range and tunable infrared optical absorbance [25].
Spectroscopic Ellipsometry (SE) [26] is an highly precise optical method designed for studying the optical properties of materials.
SE has been extensively used to study graphene-based films. The complex refractive index of monolayer graphene has been investigated using SE [25,27,28]. In Ref. [29] the optical constants of graphene were studied by means of a phenomenological Fano model. The optical properties of thick as well as few-layer GO and RGO were studied using SE [30,31].
Despite the availability of literature on SE of graphene-based materials [40], there are not reviews about the optical interaction of GO with magnetron-sputtered metals studied using VASE, which is a promising research area. Moreover, we report about VASE optical model of less studied graphene-based materials such as GNPs and RGO stabilized with PSS films; particular attention to CVD-grown graphene on flexible substrates is given.
The "Results and discussion" part of this review is divided in three main sections. In Section 3.1: "Interaction of graphene oxide with magnetron-sputtered films" the optical properties of GO dip-coated on magnetron-sputtered titanium (Ti), gold (Au) and silver (Ag) thin films were discussed.
In Section 3.2: "Optical properties of graphene-based thin films" the optical properties of GO, thermally reduced graphene oxide, RGO stabilized with PSS and GNPs films were summarized.
Finally, in Section 3.3 "Optical properties of CVD-grown monolayer, bilayer, and trilayer graphene" the optical properties of CVD-grown monolayer graphene samples were reported. In addition, the optical study of CVD-grown bilayer and trilayer graphene samples on silicon and polyethylene terephthalate (PET) substrates was summarized.

Materials and Methods
Ellipsometry measures two values ∆ and Ψ. The two quantities (∆ and ψ) are measured as a function of incident angle and wavelength and are defined in Equations (1) and (2) [26]: The tangent of the angle Ψ provides thus the ratio of the amplitude attenuation or magnification upon reflection for the p and s polarizations, its value can be from zero to 90 • . ∆, instead, provides the difference between the phase shifts experienced upon reflection by the p and s polarizations. The value of ∆ can be between zero and 360 • .
The terms p and s denote the incident plane and the perpendicular direction to the incident plane.
The complex quantity ρ, which is the complex ratio of the total reflection coefficients, is defined in Equation (3): where R p and R s include information on the properties of the materials that are investigated. The use of a capital R implies that the actual material structure can be multilayered and/or multicomponent. The ellipsometric angles ψ and ∆ spectra were obtained using a V-Vase (Woollam Co., Lincoln, NE, USA) ellipsometer (Rotating Analyzer Ellipsometer configuration with AutoRetarder) or a M2000 F (Woollam Co., Lincoln, NE, USA) ellipsometer (Rotating Compensator Ellipsometer).
The optical models were evaluated using WVASE32 application by means of the nonlinear Levenberg-Marquardt algorithm [41]. The minimum value of the Mean Square Error (MSE) [26] is defined in Equation (4): where N is the data points number, M is the fitting parameters number, (Ψ exp , ∆ exp ) and (Ψ mod , ∆ mod ) are the experimental and modeled ellipsometric angles, σ ψ and σ ∆ are the measured ellipsometric angles standard deviations. The modeled ellipsometric angles (Ψ mod , ∆ mod ) are functions of all fit parameters. GO and graphene-based dispersions, discussed in this review, were bought from "Sigma Aldrich (St. Louis, MO, USA)" and "Punto Quantico (Roma, Italy)".
CVD-grown monolayer, bilayer, and trilayer were bought from Graphenea Co. (San Sebastián, Spain). Additional details about the materials and the substrates discussed in this review can be found in Refs. [32][33][34][36][37][38][39]. Electrophoretic deposition (EPD) is extensively employed for GO thin films deposition [42][43][44]. The GO platelets are negatively charged because of the plentiful deprotonated carboxylate groups, hence they are electrophoretically drawn to the positive electrode and make a film when a direct current voltage is applied.

Results and Discussion
The optical study of the GO films electrophoretically deposited on Ti was carried out using VASE, before and after the annealing, and reported in Ref. [39].
The optical models of GO and RGO films are represented respectively by a combination of two and three Lorentz oscillators (Equation (5)): E is the incident photons energy, ε ∞ is the dielectric function real part with E → ∞ , A k is the contribution of each oscillator k to the system, Γ k is the broadening end E k is the central energy of the k-th oscillator. Figure 1a,b shows the optical constants dispersion curves in the (300-1000) nm wavelength range. shown previously that increased electron-hole (e-h) interactions in RGO implied an increased excitonic effect with a red-shift of the absorption peak of RGO [46,47]. This result is attributable to the Van Hove singularity in the density of states of graphene [48].
In comparison with other research works [31,45,49], using EPD we have obtained higher optical constants.    shown previously that increased electron-hole (e-h) interactions in RGO implied an increased excitonic effect with a red-shift of the absorption peak of RGO [46,47]. This result is attributable to the Van Hove singularity in the density of states of graphene [48].
In comparison with other research works [31,45,49], using EPD we have obtained higher optical constants.    Dip-coating [50] was employed for the deposition of GO films on magnetron-sputtered Au thin films [38]. Figure 4 shows the dispersion laws of the GO/Au samples in the (300-1000) nm wave-  After GO reduces to RGO, the amount of oxygen declines, a change from sp 3 to sp 2 hybridization happens and the main peak moves from 5.1 to 4.6 eV [31,45]. It has been shown previously that increased electron-hole (e-h) interactions in RGO implied an increased excitonic effect with a red-shift of the absorption peak of RGO [46,47]. This result is attributable to the Van Hove singularity in the density of states of graphene [48].
In comparison with other research works [31,45,49], using EPD we have obtained higher optical constants.

VASE Investigation of the Optical Properties of Graphene Oxide Dip-Coated on Magnetron-Sputtered Gold Thin Films
Dip-coating [50] was employed for the deposition of GO films on magnetron-sputtered Au thin films [38]. Figure 4 shows the dispersion laws of the GO/Au samples in the (300-1000) nm wavelength range. In Figure 5, SEM images of the GO thin film dip-coated on magnetronsputtered Au are shown.
The dispersion model of GO/Au samples was described using a combination of three Lorentz oscillators (Equation (5)).
The optical model for GO/Au samples is described by three oscillators at 3.1, 1.8 and 3.8 eV.
GO absorbs mostly in the UV region [1]; the oscillator at 3.8 eV is due to n − π * transition of C=O bond [51]. The oscillator at about 1.8 eV denotes different coverage of mixed hydroxyl groups and oxygen atoms [31]. By means of Au magnetron-sputtered thin films as substrates, GO absorbs also in the visible region and the peak of the extinction coefficient k is at~3.1 eV, which may be described in terms of strong metal-GO interactions.
As reported in Ref. [38], GO/Au thin films could improve GO optical properties, conserving the oxygen amount of GO without the reduction method [52].

VASE Investigation of the Optical Properties of Graphene O Magnetron-Sputtered Gold Thin Films
Dip-coating [50] was employed for the deposition of GO film tered Au thin films [38]. Figure 4 shows the dispersion laws of the GO/Au samples in t length range. In Figure 5, SEM images of the GO thin film dip-coa tered Au are shown.   The dispersion model of GO/Au samples was described using a combination of three Lorentz oscillators (Equation (5)).
The optical model for GO/Au samples is described by three oscillators at 3.1, 1.8 and 3.8 eV.
GO absorbs mostly in the UV region [1]; the oscillator at 3.8 eV is due to − π * transition of C=O bond [51]. The oscillator at about 1.8 eV denotes different coverage of mixed hydroxyl groups and oxygen atoms [31]. By means of Au magnetron-sputtered thin films as substrates, GO absorbs also in the visible region and the peak of the extinction coefficient k is at ~3.1 eV, which may be described in terms of strong metal-GO interactions.
As reported in Ref. [38], GO/Au thin films could improve GO optical properties, conserving the oxygen amount of GO without the reduction method [52].

VASE Investigation of the Optical Properties of Graphene Oxide on Magnetron-Sputtered Silver Thin Films
The optical characterization was performed on GO deposited by dip-coating on magnetron-sputtered Ag as reported in Ref. [37].
The optical model of GO dip-coated on Ag is described using a combination of three Lorentz oscillators and a Drude-like oscillator (Equation (5)).
In Figure 6, the optical constants dispersion curves are reported in the (190-900) nm wavelength range. The optical characterization was performed on GO deposited by dip-coating on magnetron-sputtered Ag as reported in Ref. [37].
The optical model of GO dip-coated on Ag is described using a combination of three Lorentz oscillators and a Drude-like oscillator (Equation (5)).
In Figure 6, the optical constants dispersion curves are reported in the (190-900) nm wavelength range.  The optical model in the visible and in the ultraviolet region is represented by three Lorentz oscillators (Equation (5)). The Drude oscillator describes the free-carriers in the near-infrared and, consequently, the conductive properties of GO on magnetron-sputtered Ag. The oscillator at 3.8 eV is attributable to the silver volume plasmon [53], whereas the oscillator at 5.4 eV is due to the π plasmon above ~4 eV in graphene and graphite [54].
Remarkably, these films may be useful for hyperbolic metamaterials, as reported in the Effective medium Theory simulations in our work in Ref. [37].
It is worth noticing that VASE measurements were carried out also for Ag/GO/Au sandwich structures, as reported in Ref. [35].     The optical model in the visible and in the ultraviolet region is represented by three Lorentz oscillators (Equation (5)). The Drude oscillator describes the free-carriers in the near-infrared and, consequently, the conductive properties of GO on magnetron-sputtered Ag. The oscillator at 3.8 eV is attributable to the silver volume plasmon [53], whereas the oscillator at 5.4 eV is due to the π plasmon above ~4 eV in graphene and graphite [54].

1.0µm
Remarkably, these films may be useful for hyperbolic metamaterials, as reported in the Effective medium Theory simulations in our work in Ref. [37].
It is worth noticing that VASE measurements were carried out also for Ag/GO/Au sandwich structures, as reported in Ref. [35]. The optical model in the visible and in the ultraviolet region is represented by three Lorentz oscillators (Equation (5)). The Drude oscillator describes the free-carriers in the near-infrared and, consequently, the conductive properties of GO on magnetron-sputtered Ag. The oscillator at 3.8 eV is attributable to the silver volume plasmon [53], whereas the oscillator at 5.4 eV is due to the π plasmon above~4 eV in graphene and graphite [54].
Remarkably, these films may be useful for hyperbolic metamaterials, as reported in the Effective medium Theory simulations in our work in Ref. [37].
It is worth noticing that VASE measurements were carried out also for Ag/GO/Au sandwich structures, as reported in Ref. [35].

VASE Characterization of GO and Thermally Reduced RGO Thin Films on Si/SiO 2 Substrates
The optical properties of GO and thermally reduced GO (RGO) films were investigated in Ref. [32].
GO and RGO optical properties were obtained using a Lorentz oscillator model (Equation (5)), in accordance with Kramers-Kronig relationships [55]. In GO optical model, the oscillator at ∼2.8 eV represents a coverage of mixed oxygen atoms and hydroxyl groups [31,56]. The oscillator at ∼3.2 eV denotes a transition that is close to the shoulder of GO absorbance spectrum and near the wavelength of RGO's blue luminescence [57]. The oscillator at ∼3.9 eV is attributable to the small shoulder of GO in the absorbance spectrum [57].
In RGO optical model, the oscillator at ∼2.1 eV represents coverage of mixed oxygen atoms and hydroxyl groups [31]. The oscillator at ∼3.17 eV could be attributable to the narrow photoluminescence peak of RGO [57]. In Ref. [58] excitonic features noticeable on RGO films between 4 and 4.4 eV are reported. The oscillator at ∼4 eV is included in that range. The optical properties of GO and thermally reduced GO (RGO) films were investigated in Ref. [32].
GO and RGO optical properties were obtained using a Lorentz oscillator model (Equation (5)), in accordance with Kramers-Kronig relationships [55].
In GO optical model, the oscillator at ~2.8 eV represents a coverage of mixed oxygen atoms and hydroxyl groups [31,56]. The oscillator at ~3.2 eV denotes a transition that is close to the shoulder of GO absorbance spectrum and near the wavelength of RGO's blue luminescence [57]. The oscillator at ~3.9 eV is attributable to the small shoulder of GO in the absorbance spectrum [57].
In RGO optical model, the oscillator at ~2.1 eV represents coverage of mixed oxygen atoms and hydroxyl groups [31]. The oscillator at ~3.17 eV could be attributable to the narrow photoluminescence peak of RGO [57]. In Ref. [58] excitonic features noticeable on RGO films between 4 and 4.4 eV are reported. The oscillator at ~4 eV is included in that range. Figure 8a,b show the dispersion laws of GO and RGO films on Si/SiO2 substrates in the (0.38-4.1) eV photon energy range. Figures 9 and 10 show SEM images of GO and RGO films on SiO2/Si.   The optical properties of GO and thermally reduced GO (RGO) films were invest gated in Ref. [32].
GO and RGO optical properties were obtained using a Lorentz oscillator mode (Equation (5)), in accordance with Kramers-Kronig relationships [55].
In GO optical model, the oscillator at ~2.8 eV represents a coverage of mixed oxyge atoms and hydroxyl groups [31,56]. The oscillator at ~3.2 eV denotes a transition that i close to the shoulder of GO absorbance spectrum and near the wavelength of RGO's blu luminescence [57]. The oscillator at ~3.9 eV is attributable to the small shoulder of GO i the absorbance spectrum [57].
In RGO optical model, the oscillator at ~2.1 eV represents coverage of mixed oxyge atoms and hydroxyl groups [31]. The oscillator at ~3.17 eV could be attributable to th narrow photoluminescence peak of RGO [57]. In Ref. [58] excitonic features noticeable o RGO films between 4 and 4.4 eV are reported. The oscillator at ~4 eV is included in tha range. Figure 8a,b show the dispersion laws of GO and RGO films on Si/SiO2 substrates i the (0.38-4.1) eV photon energy range. Figures 9 and 10 show SEM images of GO an RGO films on SiO2/Si.

VASE Characterization of Reduced Graphene Oxide Stabilized with Poly(Sodium 4-Styrenesulfonate)
The optical properties of PSS-functionalized RGO films were investigated in Ref. [32] and were described by a Lorentz model (Equation (5)).
In PSS-RGO optical model, the oscillator at ~2.8 eV is attributable to new states that are created by macro sp 2 carbon sheet formation throughout the reduction process [59]. Figure 11 shows the dispersion laws of PSS-functionalized RGO films on Si/SiO2 substrates in the (0.38-4.1) eV photon energy range. In Figure 12, SEM images of PSS-functionalized RGO films on SiO2/Si substrates are shown.

VASE Characterization of Reduced Graphene Oxide Stabilized with Poly(Sodium 4-Styrenesulfonate)
The optical properties of PSS-functionalized RGO films were investigated in Ref. [32] and were described by a Lorentz model (Equation (5)).
In PSS-RGO optical model, the oscillator at ∼2.8 eV is attributable to new states that are created by macro sp 2 carbon sheet formation throughout the reduction process [59]. Figure 11 shows the dispersion laws of PSS-functionalized RGO films on Si/SiO 2 substrates in the (0.38-4.1) eV photon energy range.

VASE Characterization of Reduced Graphene Oxide Stabilized 4-Styrenesulfonate)
The optical properties of PSS-functionalized RGO films were inv and were described by a Lorentz model (Equation (5)).
In PSS-RGO optical model, the oscillator at ~2.8 eV is attributab are created by macro sp 2 carbon sheet formation throughout the redu Figure 11 shows the dispersion laws of PSS-functionalized RGO strates in the (0.38-4.1) eV photon energy range.

VASE Study of Graphene Nanoplatelets Thin Films on Si/SiO2 Substrates
The optical study of GNPs films was carried out using VASE in Ref. [34] and the optical model is described using three Gaussian oscillators [60]. Each oscillator has three fit parameters (energetic position, amplitude, and broadening). Equation (6) describes the Gaussian oscillators: A is the amplitude, B is the broadening, ph is the light energy and is the oscillator energy [60].
The dispersion laws of GNPs dip-coated on Si/SiO2 substrates are reported in Figure 13 in the (300-1000) nm wavelength range. SEM images of GNP thin film dip-coated on Si/SiO2 substrates are reported in Figure 14.

VASE Study of Graphene Nanoplatelets Thin Films on Si/SiO 2 Substrates
The optical study of GNPs films was carried out using VASE in Ref. [34] and the optical model is described using three Gaussian oscillators [60]. Each oscillator has three fit parameters (energetic position, amplitude, and broadening). Equation (6) describes the Gaussian oscillators: A is the amplitude, B is the broadening, E ph is the light energy and E c is the oscillator energy [60].
The dispersion laws of GNPs dip-coated on Si/SiO 2 substrates are reported in Figure 13 in the (300-1000) nm wavelength range. SEM images of GNP thin film dip-coated on Si/SiO 2 substrates are reported in Figure 14.

VASE Study of Graphene Nanoplatelets Thin Films on Si/SiO2 Substrates
The optical study of GNPs films was carried out using VASE in Ref. [34] and th optical model is described using three Gaussian oscillators [60]. Each oscillator has thre fit parameters (energetic position, amplitude, and broadening). Equation (6) describes th Gaussian oscillators: A is the amplitude, B is the broadening, ph is the light energy and is the oscil lator energy [60].
The dispersion laws of GNPs dip-coated on Si/SiO2 substrates are reported in Figure 1 in the (300-1000) nm wavelength range. SEM images of GNP thin film dip-coated on Si/SiO substrates are reported in Figure 14.  The oscillator at 3.7 eV agrees with the bulk and surface interlayer state of graphite, whereas the oscillator at 2.7 eV is attributable to defects [61] and the oscillator at ~1.5 eV is in accordance with π* band of graphite [61].
In Ref. [62], it was stated that GNPs show an index of refraction n of 1.42 at 482 nm. Therefore, GNPs thin films display lower optical constants than GO [32] and graphene [36].

VASE Investigation of CVD-Grown Monolayer Graphene
The optical properties of CVD-grown graphene on Si/SiO2 were reported in Ref [36] and were described using four Lorentz oscillators (Equation (5)). The absorption peak at 4.5 eV is attributable to the effects of resonant excitons on the interband transition peak [63]. The oscillator at 2.36 eV is linked to the resonant excitonic effects attributable to the e-h interaction in the π and π * at the M point [63], whereas the oscillator at ∼2.8 eV is due to the hopping amplitude that gives rise to the Dirac nature of low lying excitations [64]. At ~0.5 eV a conducting layer with Drude-like electrons is observed. Figure 15 shows the estimated dispersion laws of CVD-grown monolayer graphene in the photon energy range between 0.38 and 6.2 eV. Figure 16 shows a 1 μm × 1 μm AFM image of the sample.  The oscillator at 3.7 eV agrees with the bulk and surface interlayer state of graphite, whereas the oscillator at 2.7 eV is attributable to defects [61] and the oscillator at ∼1.5 eV is in accordance with π* band of graphite [61].
In Ref. [62], it was stated that GNPs show an index of refraction n of 1.42 at 482 nm. Therefore, GNPs thin films display lower optical constants than GO [32] and graphene [36].

VASE Investigation of CVD-Grown Monolayer Graphene
The optical properties of CVD-grown graphene on Si/SiO 2 were reported in Ref [36] and were described using four Lorentz oscillators (Equation (5)). The absorption peak at 4.5 eV is attributable to the effects of resonant excitons on the interband transition peak [63]. The oscillator at 2.36 eV is linked to the resonant excitonic effects attributable to the e-h interaction in the π and π * at the M point [63], whereas the oscillator at ∼2.8 eV is due to the hopping amplitude that gives rise to the Dirac nature of low lying excitations [64]. At~0.5 eV a conducting layer with Drude-like electrons is observed. Figure 15 shows the estimated dispersion laws of CVD-grown monolayer graphene in the photon energy range between 0.38 and 6.2 eV. Figure 16 shows a 1 µm × 1 µm AFM image of the sample. The oscillator at 3.7 eV agrees with the bulk and surface interlayer state of graphite, whereas the oscillator at 2.7 eV is attributable to defects [61] and the oscillator at ~1.5 eV is in accordance with π* band of graphite [61].
In Ref. [62], it was stated that GNPs show an index of refraction n of 1.42 at 482 nm. Therefore, GNPs thin films display lower optical constants than GO [32] and graphene [36].

VASE Investigation of CVD-Grown Monolayer Graphene
The optical properties of CVD-grown graphene on Si/SiO2 were reported in Ref [36] and were described using four Lorentz oscillators (Equation (5)). The absorption peak at 4.5 eV is attributable to the effects of resonant excitons on the interband transition peak [63]. The oscillator at 2.36 eV is linked to the resonant excitonic effects attributable to the e-h interaction in the π and π * at the M point [63], whereas the oscillator at ∼2.8 eV is due to the hopping amplitude that gives rise to the Dirac nature of low lying excitations [64]. At ~0.5 eV a conducting layer with Drude-like electrons is observed. Figure 15 shows the estimated dispersion laws of CVD-grown monolayer graphene in the photon energy range between 0.38 and 6.2 eV. Figure 16 shows a 1 μm × 1 μm AFM image of the sample.   The doping concentration, whose extracted value is 13 2 7.8 10 cm n − ≈ × , was obtained from the optical conductivity data.

VASE Characterization of Turbostratic CVD-Grown Bilayer and Trilayer Graphene on Si/SiO2
The VASE study of bilayer and trilayer graphene with random stacking orientation obtained by CVD synthesis on Si/SiO2 is reported in Ref. [33].
The optical models of bilayer and trilayer graphene on silicon are composed of two Lorentz oscillators (Equation (5)) and a pole.
The oscillator energy at ~4.4 eV for CVD-grown bilayer graphene is due to the peak due to the Van Hove singularity in the density of states [65], with a red-shift from 4.6 eV in single layer graphene to 4.4 eV for bilayer graphene [66]. Hence, such peak shift happens also in non-AB stacked graphene samples, as discussed in Ref. [25].
The oscillator energy at ~4.56 eV for trilayer graphene is linked to the above-mentioned peak that is visible in the absorbance pattern of trilayer graphene at ~4.6 eV [67].
The extinction coefficient peaks in the optical spectra of bilayer and trilayer graphene on silicon at ~3 eV are due to the nearest neighbor term ≈ 3 eV [65].
In Figure 17a,b, the dispersion laws of CVD-grown bilayer and trilayer graphene samples on silicon in the (0.38-5.2) eV photon energy range are reported.
In Figures 18 and 19, SEM images of CVD-grown bilayer and trilayer graphene on SiO2/Si are reported.  The doping concentration, whose extracted value is n ≈ 7.8 × 10 13 cm −2 , was obtained from the optical conductivity data.

VASE Characterization of Turbostratic CVD-Grown Bilayer and Trilayer Graphene on Si/SiO 2
The VASE study of bilayer and trilayer graphene with random stacking orientation obtained by CVD synthesis on Si/SiO 2 is reported in Ref. [33].
The optical models of bilayer and trilayer graphene on silicon are composed of two Lorentz oscillators (Equation (5)) and a pole.
The oscillator energy at ∼4.4 eV for CVD-grown bilayer graphene is due to the peak due to the Van Hove singularity in the density of states [65], with a red-shift from 4.6 eV in single layer graphene to 4.4 eV for bilayer graphene [66]. Hence, such peak shift happens also in non-AB stacked graphene samples, as discussed in Ref. [25].
The oscillator energy at ∼4.56 eV for trilayer graphene is linked to the above-mentioned peak that is visible in the absorbance pattern of trilayer graphene at~4.6 eV [67].
The extinction coefficient peaks in the optical spectra of bilayer and trilayer graphene on silicon at ∼3 eV are due to the nearest neighbor term t ≈ 3 eV [65].
In Figure 17a,b, the dispersion laws of CVD-grown bilayer and trilayer graphene samples on silicon in the (0.38-5.2) eV photon energy range are reported. Figure 16. AFM image of a CVD-grown monolayer graphene. Reprinted from Ref. [36] with permission from Elsevier. Copyright Elsevier.
The doping concentration, whose extracted value is 13 2 7.8 10 cm n − ≈ × , was obtained from the optical conductivity data.

VASE Characterization of Turbostratic CVD-Grown Bilayer and Trilayer Graphene on Si/SiO2
The VASE study of bilayer and trilayer graphene with random stacking orientation obtained by CVD synthesis on Si/SiO2 is reported in Ref. [33].
The optical models of bilayer and trilayer graphene on silicon are composed of two Lorentz oscillators (Equation (5)) and a pole.
The oscillator energy at ~4.4 eV for CVD-grown bilayer graphene is due to the peak due to the Van Hove singularity in the density of states [65], with a red-shift from 4.6 eV in single layer graphene to 4.4 eV for bilayer graphene [66]. Hence, such peak shift happens also in non-AB stacked graphene samples, as discussed in Ref. [25].
The oscillator energy at ~4.56 eV for trilayer graphene is linked to the above-mentioned peak that is visible in the absorbance pattern of trilayer graphene at ~4.6 eV [67].
The extinction coefficient peaks in the optical spectra of bilayer and trilayer graphene on silicon at ~3 eV are due to the nearest neighbor term ≈ 3 eV [65].
In Figure 17a,b, the dispersion laws of CVD-grown bilayer and trilayer graphene samples on silicon in the (0.38-5.2) eV photon energy range are reported.
In Figures 18 and 19, SEM images of CVD-grown bilayer and trilayer graphene on SiO2/Si are reported. Figure 17. Estimated index of refraction (a) and extinction coefficient (b) of CVD-grown bilayer (black lines) and trilayer (red lines) graphene samples on silicon by VASE characterization. Reprinted from Ref. [33] with permission from Elsevier. Copyright 2020 Elsevier. 6.00 nm 0.00 nm 200nm Figure 17. Estimated index of refraction (a) and extinction coefficient (b) of CVD-grown bilayer (black lines) and trilayer (red lines) graphene samples on silicon by VASE characterization. Reprinted from Ref. [33] with permission from Elsevier. Copyright 2020 Elsevier.
In Figures 18 and 19, SEM images of CVD-grown bilayer and trilayer graphene on SiO 2 /Si are reported.  The optical models of monolayer, bilayer, and trilayer graphene samples on PET were represented using two Lorentz oscillators (Equation (5)) and were reported in Ref. [33]. The oscillators at 4.6 eV are due to the Van Hove singularity in the graphene's density of states. Remarkably, the red-shift of this peak is not reported, while it was visible on bilayer graphene on silicon. Consequently, the red-shift of the absorption peak is dependent on the substrate. Oscillators at ~4 eV are attributable to transitions between π and π* in graphite [68].
In Figure 20a,b, the dispersion laws of CVD-grown monolayer graphene, bilayer and trilayer on PET substrates in the (4-5.2) eV photon energy range are reported.  The optical models of monolayer, bilayer, and trilayer graphene samples on PET were represented using two Lorentz oscillators (Equation (5)) and were reported in Ref. [33]. The oscillators at 4.6 eV are due to the Van Hove singularity in the graphene's density of states. Remarkably, the red-shift of this peak is not reported, while it was visible on bilayer graphene on silicon. Consequently, the red-shift of the absorption peak is dependent on the substrate. Oscillators at ~4 eV are attributable to transitions between π and π* in graphite [68].
In Figure 20a,b, the dispersion laws of CVD-grown monolayer graphene, bilayer and trilayer on PET substrates in the (4-5.2) eV photon energy range are reported. Figure 19. SEM image of CVD-grown trilayer graphene transferred to SiO 2 /Si substrate (a) and related magnification (b). Reprinted from Supplementary material of Ref. [33] with permission from Elsevier. Copyright 2020 Elsevier.

VASE Characterization of Turbostratic CVD-Grown Monolayer, Bilayer and Trilayer Graphene on PET
The optical models of monolayer, bilayer, and trilayer graphene samples on PET were represented using two Lorentz oscillators (Equation (5)) and were reported in Ref. [33]. The oscillators at 4.6 eV are due to the Van Hove singularity in the graphene's density of states. Remarkably, the red-shift of this peak is not reported, while it was visible on bilayer graphene on silicon. Consequently, the red-shift of the absorption peak is dependent on the substrate. Oscillators at ∼4 eV are attributable to transitions between π and π* in graphite [68].
In Figure 20a,b, the dispersion laws of CVD-grown monolayer graphene, bilayer and trilayer on PET substrates in the (4-5.2) eV photon energy range are reported.

Conclusions and Outlook
This article presents a review of the authors' research works on VASE of graphenebased films.
In the section "Interaction of graphene oxide with magnetron-sputtered films" the optical properties of GO dip-coated on magnetron-sputtered Ti, Au, and Ag thin films are reported.
GO and RGO thin films deposited on Ti substrates were obtained by EPD. The thermal annealing changes the optical properties because some sp 3 bonds initially existing in GO were eliminated during this process. In comparison with other investigations, using EPD we obtained higher optical constants.
In addition, the optical properties of GO dip-coated on magnetron-sputtered Au are reported and three Lorentz oscillators were used for the model. Due to the strong interaction Au-GO, GO thin films dip-coated on Au absorbed in the visible region, with a peak of the extinction coefficient k at 3.1 eV. The improved optical properties of GO-Au thin films may be useful in many applications.
The optical properties of GO layers dip-coated on magnetron-sputtered Ag substrates are summarized in the same section. The optical constants were described with a set of Drude-like and Lorentz oscillators. An oscillator at 3.8 eV is attributable to the volume plasmon of silver, whereas another at 5.4 eV is due to the π plasmon above ~4 eV in graphene and graphite. Remarkably, these composite structures of GO on magnetronsputtered Ag thin films may find use in the field of multilayer hyperbolic metamaterials.
In the section "Optical properties of graphene-based thin films" the optical properties of GO, RGO, and RGO stabilized with PSS on SiO2 substrates are reported. The optical models of GO and RGO films are described using three Lorentz oscillators, while the model of PSS-functionalized RGO films is composed of a Lorentz oscillator and a pole.
In addition, the VASE optical model of GNPs thin films on silicon substrates is discussed. The optical model of GNPs was described with three Gaussian oscillators: the oscillator at 3.7 eV agrees with the surface and bulk interlayer state of graphite, whereas another at 2.7 eV is attributable to defects and the oscillator near 1.5 eV is linked to the π* band of graphite.
In the section "Optical properties of CVD-grown monolayer, bilayer, and trilayer graphene" the broadband optical properties of commercial monolayer CVD-grown monolayer graphene samples are reviewed. The CVD-grown monolayer graphene was modeled with four Lorentz oscillators and the carrier density extracted from optical conductivity data is 13 2 7.8 10 cm n − ≈ × . In the same section, VASE measurements on random stacked oriented CVD-grown bilayer and trilayer graphene on silicon are recapitulated. Furthermore, VASE optical

Conclusions and Outlook
This article presents a review of the authors' research works on VASE of graphenebased films.
In the section "Interaction of graphene oxide with magnetron-sputtered films" the optical properties of GO dip-coated on magnetron-sputtered Ti, Au, and Ag thin films are reported.
GO and RGO thin films deposited on Ti substrates were obtained by EPD. The thermal annealing changes the optical properties because some sp 3 bonds initially existing in GO were eliminated during this process. In comparison with other investigations, using EPD we obtained higher optical constants.
In addition, the optical properties of GO dip-coated on magnetron-sputtered Au are reported and three Lorentz oscillators were used for the model. Due to the strong interaction Au-GO, GO thin films dip-coated on Au absorbed in the visible region, with a peak of the extinction coefficient k at 3.1 eV. The improved optical properties of GO-Au thin films may be useful in many applications.
The optical properties of GO layers dip-coated on magnetron-sputtered Ag substrates are summarized in the same section. The optical constants were described with a set of Drude-like and Lorentz oscillators. An oscillator at 3.8 eV is attributable to the volume plasmon of silver, whereas another at 5.4 eV is due to the π plasmon above~4 eV in graphene and graphite. Remarkably, these composite structures of GO on magnetronsputtered Ag thin films may find use in the field of multilayer hyperbolic metamaterials.
In the section "Optical properties of graphene-based thin films" the optical properties of GO, RGO, and RGO stabilized with PSS on SiO 2 substrates are reported. The optical models of GO and RGO films are described using three Lorentz oscillators, while the model of PSS-functionalized RGO films is composed of a Lorentz oscillator and a pole.
In addition, the VASE optical model of GNPs thin films on silicon substrates is discussed. The optical model of GNPs was described with three Gaussian oscillators: the oscillator at 3.7 eV agrees with the surface and bulk interlayer state of graphite, whereas another at 2.7 eV is attributable to defects and the oscillator near 1.5 eV is linked to the π* band of graphite.
In the section "Optical properties of CVD-grown monolayer, bilayer, and trilayer graphene" the broadband optical properties of commercial monolayer CVD-grown monolayer graphene samples are reviewed. The CVD-grown monolayer graphene was modeled with four Lorentz oscillators and the carrier density extracted from optical conductivity data is n ≈ 7.8 × 10 13 cm −2 .
In the same section, VASE measurements on random stacked oriented CVD-grown bilayer and trilayer graphene on silicon are recapitulated. Furthermore, VASE optical models of random stacked oriented CVD-grown monolayer, bilayer, and trilayer graphene samples on PET substrates are discussed. An absorption peak red-shift is observed from 4.6 to 4.4 eV on bilayer graphene on silicon, while this peak shift is not detected on PET substrates. An absorption peak at~3 eV is evident on CVD-grown bilayer and trilayer graphene on silicon samples due to e-h interactions.
It is no doubt that VASE is among the most valuable tools for studying graphene-based films and it is well-suited for many industrial applications.
As in other fields, research on graphene-based applications using VASE has seen dramatic development and it is expanding fast. The advances made in this area are stimulating and hopeful; nevertheless, the challenges are also enormous and should be overcome.
Future investigation on VASE of GO films should mainly focus on a much deeper understanding of the reduction mechanism. In fact, further studies on the controllable oxidation and reduction of GO could improve its use as semiconductor for transistor and photoelectronic devices.
Moreover, there are several ways that graphene-based films can be functionalized for use in different applications. For instance, VASE could be used to study the optical properties of compounds made by combining graphene-based material with other 2D materials. For instance, multilayers made alternating GO and Molybdenum disulfide (MoS 2 ) could be used for metamaterials with application in energy storage.
Another possible application of VASE may be the research on mixing graphenebased materials with matrix polymers, such as polyvinyl alcohol (PVA), to provide an original synthesis route to make graphene-polymers nanocomposites. It would be also interesting studying functional hybrid material composed of CVD-grown graphene on PET substrates and magnetron-sputtered Au and/or Ag for flexible high-performance graphene photodetectors.