Optical constants of restored and etched reduced graphene oxide: a spectroscopic ellipsometry study

Yuhong Cao; Ertao Hu; Jie Xing; Li Liu; Tong Gu; Jiajin Zheng; Kehan Yu; Wei Wei

doi:10.1364/OME.9.000234

1. Introduction

Graphene is a monolayer of carbon atoms arranged in a honey-comb lattice, characterized by linear dispersion of the Dirac electrons and absence of band gap, presenting unique optoelectronic properties: massless carriers with 1/300 of light velocity [1], strong interaction with light from microwave to ultraviolet [2], ultrafast carrier dynamics [3,4], and tunable infrared optical absorbance [5,6] with many practical applications: photo-conductive switching [7], photocatalysis [8] and biomedical imaging [9]. Owing to the atomic thickness, the optical properties of graphene are sensitive to its structure, doping, and environment.

Ellipsometry method is a sensitive way to explore optical constants of thin films in nanometer thickness in a nondestructive manner [10–12]. Many ellipsometric studies have been performed on mechanically exfoliated graphene (MEG) [13,14], graphene grown by chemical vapor deposition (CVD) [12], graphene oxide (GO) [10,15–17], and reduced graphene oxide (RGO) [10,11,16–18]. The dispersion of optical constants of MEG and graphene grown by CVD have been explored by B-splines model [19] and Lorentz-Drude model [20] through spectroscopic ellipsometry (SE). Particularly, the optical response and the band structure of GO and RGO affected by surroundings (confinement of water) [15,18] and decoration of functional groups (epoxide, hydroxyl, and carboxyl groups) [21,22] have also been investigated experimentally and theoretically based on the SE techniques. Jung et al. [18] and Ghosh et al. [15] described ellipsometry studies on removal of confined water molecules trapped between graphene oxide sheets upon thermal treatment. Using a parameterized oscillator model, Shen et al. compared observed absorption features with theoretically predicted inter-band transition energies for GO sheets with different coverage levels of the oxygen-containing functional groups [16], and clarified controllable band-gap tuning during reduction [10,11].

The RGO consists of a large amount of defects, making its electrical and optical properties inferior to MEG or graphene grown by CVD [23–26]. Many attempts have been made to convert RGO or GO to high quality graphene, including thermal annealing [27,28], plasma-enhanced CVD (PECVD) [29], pulsed microwave reduction [30], thermal reduction [31], and high-temperature graphitization [32,33]. Very recently, we elaborated on the effect of temperature on the balance between healing and etching during the restoration of RGO by PECVD [34]. Despite of these efforts, the quality of the restored RGO or GO can hardly reach or exceed that of MEG or graphene grown by CVD. During the conversion of RGO or GO to high-quality graphene, the evolution of structures and electrical properties have been usually focused on [29,35]; however, the optical properties, in particular, the optical constants during the structural restoration have rarely been discussed.

Here, we report on a study on optical constants of RGO restored with PECVD. Lorentz oscillator model is applied to investigate optical transition in graphene grown by CVD, RGO, restored RGO, and etched RGO. By fitting the ellipsometric parameters, we find increases in optical constants (effective index of refraction n and effective extinction coefficient k) after restoration while decreases after etching comparing with the RGO. The variation of optical constants reflects the different levels of vacancies in the treated RGO. Our investigation opens a new angle of view to probe the structural evolution during the restoration of RGO and thus favors the production of high-quality graphene.

2. Experimental

GO gel purchased from C6G6 Technology Co., Ltd, was diluted in a mixed solvent of ethanol and dimethylformamide (DMF) (vol. 1:20). Fused quartz and SiO₂/Si substrates (p-type heavily doped Si with 300-nm thermal SiO₂) were rinsed with acetone and isopropanol, then they were treated in oxygen plasma for 5 min at room temperature. Then, the diluted GO suspension was ultrasonically sprayed (Hainertec Co. Ltd, HNN-4AE-1560-TS) onto the substrates heated at 150 °C. After thermal annealing in Ar flow (10 standard cubic centimeters per minute, sccm) at 900 °C at 0.2 Torr for 30 min, RGO thin films were obtained.

The defect repairs were carried out in a 200-W remote radio- frequency (rf, 13.56 MHz) PECVD system (MTI, OTF-1200X-50S- PE-SL) at 900 °C. A mixture of methane (0.1 sccm), hydrogen (10 sccm), and Ar (50 sccm) was used as plasma gas. The pressures controlled by a metering valve were 1.4 Torr and 1.8 Torr for restoration and etching, respectively.

CVD graphene sample was obtained from 6Carbon Technology Inc. (Shenzhen), which was a mono-layer graphene grown on copper foil by CVD and then transferred onto SiO₂/Si wafer. According to the information provided by 6Carbon Technology Inc., the graphene grown by CVD has an optical transmittance of 97% in the visible wavelength range; its sheet resisntance and mobility is 1000 ohm/sqr and 1500 cm²V⁻¹s⁻¹, respectively.

Raman spectroscopy was carried out with an EZRaman-M Portable Raman System (EZM- 785-A2, $λ$ = 532 nm). Hall mobility and sheet resistance of graphene thin films were measured by a Hall effect measurement system (MMR K2500-RTSL, MK50). Optical transmittances of sample films were tested with a PerkinElmer Lambda 950 machine. The topography information was acquired by atomic force microscopy (AFM, NT-MDT Prima) in the tapping mode.

A variable-angle spectroscopic ellipsometer based the principle of synchronously rotating polarized and the relation of A = 2P (Shanghai Bright Enterprise Development Co., ELLP-SR-II) was used to acquire the ellipsometric parameters $Ψ$ and $Δ$ of the G, RGO, restored RGO, and etched RGO samples over the wavelength range of 250-1100 nm at three different incident angles of 65°, 70° and 75°, respectively.

3. Results and discussion

The as-prepared RGO thin film on SiO₂/Si wafer is illustrated in Fig. 1(A). The area in the white box is RGO thin film, the surrounding was etched away by oxygen plasma for easy observation. The RGO sample, together with restored and etched ones, and graphene grown by CVD (G), were characterized by Raman spectroscopy at room temperature with an excitation wavelength of 532 nm. As shown in Fig. 1(B), a typical Raman spectrum of G exhibits a symmetric 2D peak at 2685 cm⁻¹ with the intensity about 3 times of the G peak (1587 cm⁻¹) and no significant D peak (~1344 cm⁻¹), which confirms the high quality of the film [36] and the mono-layer feature [37].

Fig. 1 (A) A digital photograph of RGO thin film laying on a SiO₂/Si wafer. The area in the white box is RGO thin film, the surrounding was etched away by oxygen plasma for easy observation. (B) Comparison of the Raman spectra of G, RGO, restored RGO, and etched RGO. (C) Schematics of healing and etching of RGO.

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For RGO, restored RGO, and etched RGO, the G band (around 1585 cm⁻¹) and 2D band (around 2700 cm⁻¹) are characteristic of the sp²-hybridized carbon-carbon bonds in graphene [37,38]. It’s known that the restoration of RGO leads to filling of vacancies and enlargement of sp² domain [34,39]; in contrast, etching results in removal of sp³ carbon and enlarged vacancies [29,40], as demonstrated in Fig. 1(C). It has been shown that the ratio of the Raman peak intensities between the 2D and G bands, I(2D)/I(G), is related to the degree of recovery of sp² C = C bonds (graphitization) in graphitic structures [28]. The RGO has almost no detectable 2D peak while a pronounced 2D band width I(2D)/I(G) = 0.34 can be observed after restoration, because of the effective recovery of graphitic area. For the etched RGO, the removal of sp³ carbon leads to appearance of 2D peak, but enlarged vacancies make the 2D peak smaller than the restored one, which is consistent with our previous observation [34]. In addition, the G shows the highest mobility of 1302 cm²V⁻¹s⁻¹ which is three orders of magnitude higher than that of RGO. The mobility of RGO is higher than that of etched RGO, while it is lower than restored RGO, proving the defect level of RGO-related samples in the sequence of etched-RGO > RGO > restored-RGO. Hence, the content of vacancy should be in the sequence of G < restored RGO < RGO < etched RGO. The ratio of I(2D)/I(G) and mobility of all of the samples are listed in Table 1.

Table 1. Raman peak intensity ratios of 2D/G, mobility, and average roughness of G, restored RGO, etched RGO, and RGO.

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The surface morphology of each sample was measured by AFM in the tapping mode with a scanning area of 10 × 10 μm². The results are presented in Fig. 2. The average roughnesses of all of the four samples are listed in Table 1. The G sample has some dust particles on it, resulting in a relatively large average roughness comparing with other samples. Clean and smooth surfaces were observed for the RGO, the restored RGO, and the etched RGO.

Fig. 2 AFM characterization of G (A), restored RGO (B), RGO (C) and etched RGO (D).

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The optical absorption of RGO, restored RGO, and etched RGO samples prepared directly on fused quartz were tested in the range of ultraviolet (UV) to mid-infrared (IR) (0.5 – 5 eV), displayed in Fig. 3. The prominent peaks centered at approximately at 4.5 – 4.7 eV are attributed to excitonic effect [41,42]. High-temperature annealing and plasma treatment of the RGO samples will lead to lower content of oxygen containing functional groups compared with those in GO [11,21]. The remaining defects are mostly vacancies, varying samples’ optical absorption by their content [43,44]. The variation in the optical absorption implies the changes in optical constants, i.e. refractive index n and extinction coefficient k, which can be qualitively discussed as following.

Fig. 3 Optical absorption spectra of restored RGO, etched RGO and RGO from the UV to mid-IR.

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All of the RGO-based samples, considered as a mix of pure graphene and void, can be treated by the effective medium approximation theory (EMA) to characterize the optical dispersion relation [45–47]. Either Bruggeman model or Maxwell-Garnet model has been proved to be suitable for the EMA theory, depending on the volume fraction of the pure graphene. Combined with the Raman spectra and the electrical measurement, the sample with the lowest defect content (G) should have the highest refractive index n and extinction coefficient k and vice versa (etched RGO). This can be further validated with SE investigation.

The thickness of the graphene film can be estimated by the formulae:

T = {(1 + \frac{1.13 π α N}{2})}^{- 2},

d = 0.334 N .

where T is the optical transmittance at 550 nm, N is the number of layer, d is the thickness, and

α

represents the fine structure constant (1/137) [48]. Note that the d obtained here is just an estimate where assuming 0.334 nm for each graphene layer. The real thickness must be larger since the defect induced curvature and oxygen-containing functional groups. But it could still be a good start point in the following fitting procedure.

The samples prepared on SiO₂/Si substrates were further examined with SE for different incident angles at 65°, 70°, 75° from UV to near IR (250 – 1100 nm). Lorentz oscillator model is adopted to fit the ellipsometric parameters $Ψ$ and $Δ$ [10,11,42]. Ellipsometric parameters, $Ψ$ and $Δ$ , are defined in

ρ = \frac{r_{p}}{r_{s}} = \tan Ψ e x p (i Δ)

where r_p and r_s represent the complex reflection coefficients of polarized light parallel and perpendicular to the incidence plane, respectively [49].

A four-phase model of Si substrate/SiO₂/RGO/ambient was used to analyze the SE spectra. In this model, unknown parameters, such as film thickness (d) and dielectric constant ( $ε$ ) for graphene thin films, are fitting variables. The optical constants for the SiO₂ layer atop of Si were obtained in advance. Then, in the fitting process, the optical constants for SiO₂ were fixed, while its thickness was varied in consideration of the thickness variation of SiO₂ in the real SiO₂/Si substrate. For G, RGO, restored RGO, and etched RGO samples, the intra-band transition region is in the far-IR range [50] with incident photon energy lower than 0.43 eV [42,51]. In consideration of the incident wavelength range of 250-1100 nm of the ellipsometric measurements, which is in the inter-band transition region, the Lorentz model [10,11,52] was employed to describe the optical dispersion relation of graphene and RGO-related samples.

The Lorentz oscillator model can be expressed as:

ε = ε_{1} + i ε_{2} = ε_{\infty} (1 + \sum_{i} \frac{A_{i}^{2}}{C_{i}^{2} - E^{2} - j v_{i} E})

where

ε_{\infty}

is the high-frequency dielectric constant, and A_i , C_i, and ν_i are the amplitude, center energy, and damping coefficient of each oscillator, respectively.

The global modified Levenberg-Marquardt method was adopted to minimize the difference between the measurements and the fitting results which is defined by the root mean square error (RMSE) [53]:

RMSE = \sqrt{\frac{1}{2 N - M} \sum_{i = 1}^{N} [{(\frac{Ψ_{i}^{mod} - Ψ_{i}^{exp}}{σ_{Ψ, i}^{exp}})}^{2} + {(\frac{Δ_{i}^{mod} - Δ_{i}^{exp}}{σ_{Δ, i}^{exp}})}^{2}]}

where N is the number of the experimental points, M is the number of parameters, σ is the standard deviation, and the superscripts mod and exp refer to the modeled and measured data, respectively.

Good agreement between the experimental and fitted ellipsometric parameters $Ψ$ and $Δ$ of RGO, restored RGO, and etched RGO from UV to near IR visible range can be obtained with the Lorentz oscillator model, as shown in Fig. 4. Key parameters obtained from the fitting are listed in Table 2.

Fig. 4 The experimental and calculated elllipsometric parameters (A-D) $Ψ$ and (E-I) $Δ$ of G, RGO, restored RGO, and etched RGO with the incidence angles of 65°, 70°, 75°, respectively.

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Table 2. Calculated oscillators energies (C_i) and their amplitudes (A_i) representing intra-band transition and combined resonance excitons and π*plasma resonance along with calculated thicknesses used in the Lorentz oscillator model for graphene grown by CVD, RGO, restored RGO, and etched RGO samples.

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The fitted thickness of monolayer graphene (G) is slightly thicker than 0.334 nm. That may be the chemical nature and thickness of residual debris formed after the transfer process [20]. From the fitting, the thicknesses d of RGO, restored RGO, and etched RGO are 5.55, 3.15, and 1.97 nm, respectively.

Lorentz parameters for G, RGO, restored RGO, and etched RGO are compared in Table 2. Note that oxygen and hydroxyl groups do not contribute to any oscillator since low coverage after high-temperature annealing and plasma treatment [11,21]. In Table 2, the first oscillators (C₁) can be attributed to intra-band transition, since an absorption energy above 0.43 eV is usually recognized as inter-band transition [42,51]. Two other oscillators (C₂, C₃) represent the excitonic effect and π* plasmon peak, respectively. In fact, it has been shown previously by electron energy loss spectroscopy that increased electron–hole interactions result in an enhanced excitonic effect in RGO compared with that in GO [19,42,54]. This effect is due to van Hove singularity in graphene’s density of states [55]. The Lorentz oscillator model provides a reasonable energy level distribution for graphene grown by CVD, RGO, restored RGO, and etched RGO.

The refractive index and the extinction coefficient are calculated from the dielectric function:

n = {[\frac{1}{2} \sqrt{ε_{1}^{2} + ε_{2}^{2}} + ε_{1}]}^{1 / 2},

k = {[\frac{1}{2} \sqrt{ε_{1}^{2} + ε_{2}^{2}} - ε_{1}]}^{1 / 2} .

Figure 5(A) and 5(B) show the calculated refractive index (n) and extinction coefficient (k), respectively. The n is largest for the G, then restored RGO > RGO > etched RGO, and the same sequence for the k. The results are consistent with the aforementioned EMA analysis, but in a more quantitive way. As reflected by Raman spectra, defects are scarce in G and are abundant in other samples. The restoration fills vacancies with carbon atoms while the etching results in enlarged vacancies. Thus, the content of vacancies should be in the sequence of etched RGO > RGO > restored RGO > G.

Fig. 5 (A) and (B) The calculated refractive index (n) and extinction coefficient (k) of G, RGO, restored RGO, and etched RGO.

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4. Conclusion

In summary, we make graphene with different defect level by healing and etching RGO using plasma treatment. SE method cooperated with Lorentz oscillator model analysis reveals intra-band transition, excitonic effect, and π* plasma resonance in G, RGO, restored RGO, and etched RGO. By fitting the ellipsometric parameters, the optical constants, n and k, are calculated with the sequence of G > restored RGO > RGO > etched RGO. Correlated with the Raman spectra, it is concluded that fewer defects lead to higher density and thus higher optical constants in graphene.

Funding

National Natural Science Foundation of China (Nos. 61504064, 61605089), Natural Science Foundation of Jiangsu Province, China (No. BK20150847), NUPTSF (NY218107).

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	G	Restored RGO	Etched RGO	RGO
I(2D)/I(G)	3.23	0.34	0.29	0
Mobility [cm²V⁻¹s⁻¹]	1302	18.128	0.853	2.053
Average Roughness [12]	3.350	1.324	2.655	1.470

Oscillator parameters center energy C_n (eV), and oscillator amplitude A_n (no units)
Sample		G	Restored RGO	Etched RGO	RGO
intra-band transition	A₁	18.592 ± 0.005	11.001 ± 0.006	5.019 ± 0.003	1.958 ± 0.003
intra-band transition	C₁	0.024 ± 0.004	0.044 ± 0.001	0.057 ± 0.001	0.021 ± 0.005
resonance excitons	A₂	29.998 ± 0.007	0.983 ± 0.001	1.239 ± 0.005	0.383 ± 0.003
resonance excitons	C₂	4.458 ± 0.003	4.639 ± 0.004	4.640 ± 0.007	4.615 ± 0.008
π* plasma resonance	A₃	0.017 ± 0.001	6.478 ± 0.005	9.173 ± 0.008	3.018 ± 0.005
π* plasma resonance	C₃	4.696 ± 0.003	4.726 ± 0.005	4.984 ± 0.004	4.789 ± 0.006
ε_∞		0.094 ± 0.002	1.235 ± 0.004	0.909 ± 0.006	2.811 ± 0.005
RMSE		3.038	1.597	1.773	3.579
Thickness (nm)		0.71 ± 0.01	3.15 ± 0.01	1.97 ± 0.01	5.55 ± 0.01
Thickness (nm) obtained from the optical transmittance		0.334	1.864	0.574	1.215

	G	Restored RGO	Etched RGO	RGO
I(2D)/I(G)	3.23	0.34	0.29	0
Mobility [cm²V⁻¹s⁻¹]	1302	18.128	0.853	2.053
Average Roughness [12]	3.350	1.324	2.655	1.470

Oscillator parameters center energy C_n (eV), and oscillator amplitude A_n (no units)
Sample		G	Restored RGO	Etched RGO	RGO
intra-band transition	A₁	18.592 ± 0.005	11.001 ± 0.006	5.019 ± 0.003	1.958 ± 0.003
intra-band transition	C₁	0.024 ± 0.004	0.044 ± 0.001	0.057 ± 0.001	0.021 ± 0.005
resonance excitons	A₂	29.998 ± 0.007	0.983 ± 0.001	1.239 ± 0.005	0.383 ± 0.003
resonance excitons	C₂	4.458 ± 0.003	4.639 ± 0.004	4.640 ± 0.007	4.615 ± 0.008
π* plasma resonance	A₃	0.017 ± 0.001	6.478 ± 0.005	9.173 ± 0.008	3.018 ± 0.005
π* plasma resonance	C₃	4.696 ± 0.003	4.726 ± 0.005	4.984 ± 0.004	4.789 ± 0.006
ε_∞		0.094 ± 0.002	1.235 ± 0.004	0.909 ± 0.006	2.811 ± 0.005
RMSE		3.038	1.597	1.773	3.579
Thickness (nm)		0.71 ± 0.01	3.15 ± 0.01	1.97 ± 0.01	5.55 ± 0.01
Thickness (nm) obtained from the optical transmittance		0.334	1.864	0.574	1.215

Optical constants of restored and etched reduced graphene oxide: a spectroscopic ellipsometry study

Abstract

1. Introduction

2. Experimental

3. Results and discussion

4. Conclusion

Funding

References

Cited By

Figures (5)

Tables (2)

Equations (7)

Optical Materials Express