Improving Terahertz Sheet Conductivity of Graphene Films

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Improving Terahertz Sheet Conductivity of Graphene Films Synthesized by Atmospheric Pressure Chemical Vapor Deposition with Acetylene Mei Qi, Yixuan Zhou, Fangrong Hu, Xin Long Xu, Weilong Li, Anran Li, Jintao Bai, and Zhao Yu Ren J. Phys. Chem. C, Just Accepted Manuscript • Publication Date (Web): 17 Jun 2014 Downloaded from http://pubs.acs.org on June 19, 2014

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The Journal of Physical Chemistry

Improving Terahertz Sheet Conductivity of Graphene Films Synthesized by Atmospheric Pressure Chemical Vapor Deposition with Acetylene Mei Qi1, Yixuan Zhou1, Fangrong Hu2, Xinlong Xu1,*, , Weilong Li1, Anran Li1, Jintao Bai1, and Zhaoyu Ren1,†, 1

State Key Lab Incubation Base of Photoelectric Technology and Functional Materials, International Collaborative Center on Photoelectric Technology and Nano Functional Materials, Institute of Photonics & Photon-Technology, Northwest University, Xi'an 710069, China 2 School of Electronic Engineering and Automation, Guilin University of Electronic Technology, Guilin 541004, China

ABSTRACT Graphene has shown great potential for terahertz (THz) applications in recent years. THz sheet conductivity of graphene is essential to assess the high performance of THz devices such as modulators based on graphene. In this work, THz sheet conductivity of graphene grown with different temperatures, along with the effects of chemical doping by HNO3, were studied in detail. Graphene films were synthesized on Cu surface by atmospheric pressure chemical vapor deposition with C2H2. Different samples with growth temperature from 850 to 1030 oC were characterized by Raman spectroscopy, transmission electron microscope, and UV-Vis spectroscopy. THz time-domain spectroscopy was used to study the THz sheet conductivity of the samples before and after HNO3 doping. The results show that graphene grown at 1000 oC has the highest THz sheet conductivity. Compared with the sample grown at 850 oC, the value enhances 600%. In addition, after HNO3 doping, the THz sheet conductivity of the sample grown at 1000 oC becomes 2.42 mS, which enhances 44%. These indicate that both the optimization of the growth temperature and chemical doping can improve the THz sheet conductivity of graphene significantly. Combining with the characterization of the material, we have attributed the effect of the growth temperature to the influence of carrier momentum scattering time in graphene, and the chemical doping to influence of the carrier concentration in graphene. This

*

Corresponding author: [email protected].

†

Corresponding author: [email protected].

ACS Paragon Plus Environment

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work advances the understanding of improving THz sheet conductivity by in-situ growth and post-growth and paves the way for efficient THz components with graphene. KEYWORDS graphene; growth temperature; chemical doping; terahertz sheet conductivity; acetylene.


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1. INTRODUCTION Terahertz (THz) technology, as an attractive research field, promises a lot of applications ranging from imaging, spectroscopy, to security check, communications, etc. 1. At present, efficient THz devices are urgent needed to advance this field 2. For example, one major bottleneck for the development of THz modulators based on conventional semiconductors, in which the THz conductivity can be tuned by the charge carrier injection, is hindered by the limitation on the change of free carrier density (the highest electron carrier density ~1×1012 cm-2) 3

. Graphene is a monolayer sp2-bonded carbon atoms in honeycomb lattices

4-5

. On the basis of

the symmetric conical band structure, the high carrier density of graphene can reach as high as 1×1014 cm-2 for both holes and electrons 6, which leads to a good tunability of the THz conductivity. This is based on the tuning of the Fermi level, which is related with the hole/electron carrier density in graphene. Therefore, graphene has attracted much attention in THz community for broadband and tunable THz devices 2, 7-8. The THz-wave spot size has the diameter in the scale of millimetre 9-11. Thus continuous large area and high quality samples are desirable for the THz devices based on graphene. There are ‘top-down’ approaches such as mechanical exfoliation chemical vapor deposition (CVD) method

13

4, 12

and ‘bottom-up’ approaches such as

to achieve the high quality graphene samples.

Although graphene prepared by mechanical exfoliation has the highest quality 14, the maximum size on the scale of micron level limited its THz application. CVD on transition metals (especially Cu) is a cost-efficient method for high quality, large-scale graphene films. Moreover, CVD graphene films can be transferred to any substrate. As a result, CVD graphene shows the high potential for broadband THz applications. The THz conductivity of graphene is determined by the intraband transition and follows the Drude model 2, 15. Thus the THz conductivity can be assessed by the DC conductivity ( σ s ) 2. The variation range of the sheet resistance ( ρ s ) of CVD graphene is quite wide in different literatures, from ρ s =150 Ω/sq 16 to ρ s =2100 Ω/sq 17, corresponding to DC sheet conductivity from σ s =6.67 mS to 0.48 mS. However, the THz sheet conductivity of graphene still has the room to improve, which will be more satisfied to the sensitive THz applications. The study of THz sheet conductivity of graphene, particularly the influences from in-situ growth and post-processing,


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will greatly improve the quality of the THz response of graphene, thus lead to better THz devices based on graphene. In this work, the graphene films were synthesized on Cu surface by atmospheric pressure CVD (APCVD) with acetylene (C2H2). C2H2 served as the carbon precursor that can dramatically decrease the defects in synthesized graphene due to the healing mechanism of divacancy defects 18

. THz sheet conductivity of graphene grown with different temperature, along with the effects

of chemical doping by HNO3, was studied in detail. Different samples with growth temperature from 850 to 1030 oC were characterized by Raman spectroscopy, transmission electron microscope (TEM), and UV-Vis spectroscopy. THz time-domain spectroscopy (THz-TDS) system was used to study the THz sheet conductivity of the samples before and after HNO3 doping. It is worth noting that the THz sheet conductivity of the graphene grown at 1000 oC was the highest. Compared with the sample grown at 850 oC, it enhanced 600%. In addition, after HNO3 doping, the THz sheet conductivity of graphene grown at 1000 oC became 2.42 mS, which enhanced 44%. What is more, we have analyzed the reasons for these changes combined with the Raman and TEM results. These results indicate that by optimizing growth temperature, the THz sheet conductivity of graphene can be improved mainly from the better sample quality with higher carrier momentum scattering time. Meanwhile, by chemical doping, the THz sheet conductivity of graphene can be improved mainly from the control of the carrier concentration. This work offers useful insights into the understanding of improving THz sheet conductivity by in-situ growth and post-growth and paves the way for efficient THz components with graphene. 2. EXPERIMENT METHOD Graphene films were synthesized on 25 µm Cu foils (Alfa Aesar, 99.8% purity) by APCVD with C2H2. C2H2 served as the carbon precursor that can dramatically decrease the defects in synthesized graphene 18. First of all, the Cu foils of 6 cm2 were cleaned by ultrasonic for 15 min in alcohol and acetone, respectively. Then, the APCVD process was carried out as follows: the Cu foils were heated to the growth temperature (1030 oC, 1000 oC, 950 oC, or 850 oC, respectively) for 60 min and then annealed for 20 min under the 300 standard-state cubic centimeters per minute (sccm) H2 and 300 sccm Ar. During the growth process of graphene, the gas flow rates of H2, Ar, and C2H2 were set to 50, 950, and 1 sccm, respectively. The growth time was set to 10 min. Finally, the sample was naturally cooled down to room temperature under the same H2 and Ar flow rates as the growth condition.


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The Cu foils with as-grown graphene on top of it (1 cm × 1 cm) were etched out with the etchant [Ferric chloride (Sinopharm Chemical Reagent Co., Ltd, 1 g) and hydrochloric acid (Sinopharm Chemical Reagent Co., Ltd, 1 ml) in deionized water (25 ml)] for 5 hours and the graphene films were transferred onto a quartz substrate (2 cm × 2 cm × 1 mm). Chemical doping was achieved by dipping the graphene films on the quartz substrate into HNO3 (Sinopharm Chemical Reagent Co., Ltd, 68%) for 5 min. The graphene films were characterized by Raman spectrometer (Laboratory Ram HR800, excitation wavelength at 514 nm), TEM (Tecnai G2 F20 S-TWIN, point resolution: 0.24 nm, line resolution: 0.14 nm), UV-Vis spectroscopy (Lambda 950), and a commercial THz-TDS system (Zomega Z-3, femtosecond laser: FemtoFiber pro NIR, TOPTICA Photonics, repetition rate 80 MHz, pulse width 100-fs, central wavelength 790 nm). 3. RESULTS AND DISCUSSION

Figure 1. Raman spectra of graphene films synthesized with different temperatures on quartz substrates; it is 1030 °C (black line), 1000 °C (red line), 950 °C (green line) and 850 °C (blue line), respectively. Firstly, Raman spectroscopy has been used for characterizing the defects and layer numbers of the graphene films. As a noninvasive detecting method, Raman spectroscopy is a non-destructive method for graphene films and very sensitive to various kinds of defects. For instance, when the relative intensity ratio of D and G band (ID/IG) increases, it indicates the defects in graphene films increase 19. The FWHM of D band can be used to probe the crystallization degree of graphene. With the FWHM of D band becomes larger, the crystallization degree of graphene becomes


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lower

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. While the increasing of the relative intensity ratio of G and 2D band (IG/I2D) and the

FWHM of 2D band indicate the number of layers of graphene increases

19

. Fig. 1 shows the

Raman spectra of the graphene films synthesized with different temperature from 1030 °C to 850 °C. The Raman signal of graphene is consist of a D band at 1354 cm-1, a G band at 1581-1584 cm-1, and a 2D band at 2698-2704 cm-1.The full width at half-maximum (FWHM) of the G band of graphene grown with 850 °C , 950 °C, 1000 °C, and 1030 °C are 41.8 cm-1, 29.88 cm-1, 23.9 cm-1, and 26.9 cm-1, respectively. The results indicate the crystallization degree of graphene grown at 1000 °C is the highest

20

. Meanwhile, the ID/IG value of the graphene films grown at

850 °C, 950 °C, and 1000 °C are 0.56, 0.15, and 0.06, respectively. It indicates the quality of the graphene films are improved along with the increase of the growth temperature. In other words, the structural disorder of graphene synthesized with the lower temperature increases. The relationship of the effects of temperature on the sample quality is consistent well with the previous literature 21. At the same time, it is worth to note that when the growth temperature rises to 1030 °C, the value of ID/IG becomes 0.11. The Raman result indicates the quality of graphene films grown with higher temperature (1030 °C) that is closer to the melting point of Cu (1080 °C) is a little degradation. The in-plane crystallite sizes have a inverse relationship with ID/IG according to the TuinstraKoenig (TK) relation: La (nm) = (2.4 × 10−10 )λ 4 ( I D / I G )−1 , where λ is the excitation wavelength (514 nm)

22

. As a result, the crystallite sizes of the graphene grown with 850 °C, 950 °C, 1000

°C, and 1030 °C have been calculated to be 29.9 nm, 111.68 nm, 279.2 nm, and 152.3 nm, respectively. Next, we have calculated the IG/I2D value and the FWHM of 2D band of the graphene grown at 850 °C (IG/I2D=1.32, FWHM=59.46 cm-1), 950 °C (IG/I2D=1.26, FWHM=57.1 cm-1), 1000 °C (IG/I2D=0.84, FWHM=46.58 cm-1), and 1030 °C (IG/I2D=0.68, FWHM=43.98 cm-1). The Raman results indicate that the number of layers decreases with the growth temperature range from 850 °C up to 1030 °C. In order to further prove our conclusion, we show the TEM images and the light transmittance of the graphene films grown at 1000 °C and 850 °C in the following.


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Figure 2. (a) TEM image, (b) HR-TEM, and (c) SAED from the red circle area in part of the graphene synthesized at 1000 °C. (d) TEM image, (e) HRTEM, and (f) SAED from the red circle area in part d of the graphene synthesized at 850 °C. Fig. 2 shows the low resolution TEM image, high resolution TEM (HR-TEM), and the selected area electron diffraction (SAED) of the graphene films synthesized with 1000 °C (a-c) and 850 °C (d-f). The two samples grown at different temperature are both consecutive layers with some rumples on the edge of the films caused by the TEM sample preparation process, as shown in Fig. 2(a) and (d). We note that the graphene films grown with the lower temperature is continuous. The HR-TEM image (Fig. 2(b)) observations with corresponding SAED pattern (Fig. 2(c)) confirm the graphene films are bilayer and have a good crystallization degree when the growth temperature is 1000 °C

23

. The HR-TEM image (Fig. 2(e)) observations with

corresponding SAED pattern (Fig. 2(f)) confirm the graphene films are 5-layer with poor crystallization degree, but with no amorphous state.


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Figure 3. Light transmittance of graphene films synthesized at 1000 °C (red line) and 850 °C (blue line). The insets show the photographs of the samples on quartz substrate. Fig. 3 shows the light transmittance of graphene films grown at 1000 °C (red line) and 850 °C (blue line). It is found that the light transmittance of the sample grown at 1000 °C at 550 nm is 95.2%. This value indicates that the sample is bilayer graphene films 24. The transmittance of the sample grown at 850 °C at 550 nm is 87.5% 24. It indicates that the sample is about five layers. The light transmittance results are consistent with the HR-TEM analysis results. The insets in Fig. 2 show the photographs of the bilayer and five-layer graphene films on quartz substrate. Xing et al. have studied the role of the growth temperature in CVD graphene with low concentration CH4 as carbon source

25

. When the growth temperature was low, the obtained

graphene films were discontinuous. It suggests that higher concentration CH4 is required to achieve the as-grown continuous and thicker graphene films. In our work, higher concentration C2H2 is used and continuous, few-layer graphene are synthesized. The results can be explained as follows. Combined with the thermodynamics of graphene growth on Cu surface with first-principles 26, an active atomic carbon is suggested to be unstable. Once the C concentration reaches the critical value ( Cnuc ), graphene nucleation occurs and the C concentration begins to drop until equilibrium. The C adatom concentration in equilibrium is expressed as Ceq

27-28

. When the

growth temperature decreases, both Cnuc and Ceq will drop. If C2H2 with enough concentration are used, multi-layer nucleation will be formed on the Cu surface with low growth temperature. That is to say, a high concentration of carbon source, and/or low growth temperature will break


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the self-limiting effect

25, 29

. And eventually multilayer nucleation grows into continuous

graphene films. The result is difference with H2 effect on the APCVD graphene. In our previous work 29, we have demonstrated that the nucleation of multilayer graphene could be deposited on top of a continuous bilayer graphene with high concentration H2 catalytic. Because of the weak catalytic ability of H2, the adjacent crystalline nuclei on top of a continuous bilayer graphene cannot join together completely and lead to the inhomogeneity of the graphene films. The above mentioned characterizations and discussions of the materials prove that the sample quality can be improved mainly by optimizing the growth temperature. Among these samples, graphene grown at 1000 °C has the best quality. In the following part, we will discuss the THz sheet conductivity of these samples.

Figure 4. (a) THz relative transmission and (b) THz sheet conductivity of the graphene films synthesized at 1030 °C (black line), 1000 °C (red line), 950 °C (green line), and 850 °C (blue line) transferred to quartz substrate. THz-TDS, as a non-destructive method for THz sheet conductivity measurement, is used to further analyze the graphene films grown at different temperature on quartz substrate (SiO2). As mentioned above, we have demonstrated that the graphene films are homogeneous. Thus, the THz sheet conductivity of the different points of graphene sample is almost the same. As the thickness of the quartz is ~1 mm. We only consider the first direct transmission pulse, and the THz time window is set to be 19 picoseconds without consideration of the multiple reflections from the front and back sides of the quartz substrate. We define the amplitudes for the first pulse of the THz wave transmitted through the SiO2 substrate and graphene/SiO2 as ASiO2 and Agrap − SiO2 . Thus, the THz transmittance of graphene can be expressed as:


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T =(

Agrap − SiO2 ASiO2

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)2 ,

(1)

Graphene can be regarded as a zero-thickness conducting film, thus the THz sheet conductivity can be calculated with 8: (

σ (ω ) = (n1 + n2 )

ASiO2 Agrap − SiO2

− 1)

Z0

,

(2)

( n1 = nair =1, nSiO2 =1.955, the impedance of free space: Z 0 =377 Ω). As shown in Fig. 4, THz transmission and sheet conductivity of graphene is flat and featureless from 0.3 to 1.0 THz. From Fig. 4(a) we can see that the relative transmission at 0.3 THz of the graphene grown at 850 °C, 950 °C, and 1000 °C are 0.92, 0.81 and 0.66, respectively. However, the relative transmission of the graphene grown with 1030 °C is up to 0.78. The calculated THz sheet conductivity of graphene grown at different temperature is shown in Fig. 4(b). As the change of the growth temperature, the THz sheet conductivity of the samples is much different ( σ 850°C =0.24 mS,

σ 950°C =0.85 mS, σ 1000°C =1.68 mS, σ 1030°C =1.01 mS). The THz sheet conductivity increases as the growth temperature increased from 850 °C to 1000 °C, but the THz sheet conductivity decrease with the growth temperature continue to increase to 1030 °C. The changes in the sheet conductivity before and after optimum growth temperature can be calculated with the equation

∆σ = (σ 1000°C − σ 850°C ) / σ 850°C . We obtain ∆σ to be 600%, indicates an enhancement of the sheet conductivity of 600%. The result demonstrates that the THz sheet conductivity of graphene can be improved by optimize the growth temperature and the THz sheet conductivity of graphene grown at 1000 °C is highest. Thus, graphene grown with 1000 °C is more suitable for applications in the sensitive THz devices. The THz sheet conductivity can be expressed as σ sheet = σ THz × d N − layer , where σ THz is the THz conductivity of graphene and d N −layer is the thickness of N-layer (N = 1,2,3...) graphene. σ THz is related to the crystal quality of the graphene and d N − layer is related to the number of graphene layers. According to our TEM results, the graphene grown with 850 and 1000 oC are 5-layer and 2-layer, respectively. Thus the THz conductivity of graphene grown with 850 and 1000 oC can be calculated to be 1.41 × 106 and 2.47 × 107 mS/cm. The change in the THz conductivity before and


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after optimum growth temperature is about 1652%. This further confirms the conclusion that the improvement in THz conductivity from 850 to 1000 oC can be attribute to the quality of graphene crystal. In THz range where intraband transitions dominate, the relationship of THz conductivity ( σ THz ) and DC conductivity ( σ s ) of graphene is given by the Drude model 2:

σ THz =

σ dc ( EF ) , 1 + ω 2τ 2

(3)

( ω is the angular frequency, τ is carrier momentum scattering time, EF is the Fermi energy). Because ωτ

1 , the relationship of σ (ω ) and σ dc can be simplified to be: σ (ω ) ≈ σ dc ( EF ) .

The DC conductivity of graphene has been proved to be 30:

σ dc

2vFτ e2 π n, = h

(4)

where e , h , and ν F are elementary charge, Planck constant, and Fermi velocity, respectively. Therefore, the THz conductivity of graphene is mainly dependent by the carrier momentum scattering time τ and carrier concentration n . The former mainly depends on the quality of graphene and the later on the post-processing. Vlassiouk et al. have proved the crystallite sizes are related with the sheet conductivity of graphene 31. It is clear that the decreasing of the disorder degree (large crystallite sizes) will lead to higher THz conductivity. That is to say, the quality of graphene play a leading role on the trend of the THz sheet conductivity. Thus, the changes of the THz sheet conductivity can be related to the quality of graphene. From Fig. 4b, the THz sheet conductivity of the sample grown at 1000 °C is the highest. That is because, when the growth temperature is below or above 1000 °C, especially below 1000 °C, the structural disorder degree of graphene increases, which leads to a reduction of the carrier momentum scattering time. As shown in Eq. (4), sheet conductivity decreases in a linear manner with the carrier momentum scattering time. These results indicate that by optimizing growth temperature, the THz sheet conductivity of graphene can be improved because of the better sample quality with higher carrier momentum scattering time.


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Figure 5. (a) THz relative transmission and (b) THz sheet conductivity of the graphene films synthesized at 1000 °C (red line), 950 °C (green line), and 850 °C (blue line) transferred to quartz substrate after doping HNO3. Besides the influence of the growth temperature, chemical doping by HNO3 can also be pursued to increase the THz sheet conductivity of the graphene. Fig. 5 shows the THz relative transmission and sheet conductivity of the same graphene films synthesized at 850 °C, 950 °C, and 1000 °C on quartz substrate after chemical doping by HNO3. The relative transmission at 0.3 THz of the graphene grown with 850 °C, 950 °C, and 1000 °C after doping HNO3 is 0.78, 0.69 and 0.58, respectively. The THz sheet conductivity of graphene grown at 850 °C, 950 °C, and 1000 °C after doping HNO3 is 1.03 mS, 1.57 mS, and 2.42 mS. Through the formula:

∆σ = (σ H − grap − σ grap ) / σ grap ( where σ grap and σ H − grap are the THz sheet conductivity before and after doping HNO3, respectively) to calculate the changes in the sheet conductivity before and after doping HNO3, ∆σ 850°C , ∆σ 950°C , and ∆σ 1000°C is about 329%, 84.7%, and 44.0%. After doping by HNO3, the THz sheet conductivity of graphene synthesized at low temperature enhances significantly, but the maximum value is still lower than the conductivity of graphene grown at 1000 °C before HNO3 doping. After HNO3 doping, the THz conductivity of graphene grown at 1000 °C is still the strongest.


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Figure 6. The G and 2D band of the graphene films synthesized at 1000 °C before and after doping HNO3. In order to make a further explanation, the Raman spectra of the G and 2D band of graphene synthesized at 1000 °C before and after doping HNO3 are shown in Fig. 6. Before doping HNO3, the Raman shift of the G-band and 2D-band is 1586 cm-1 and 2698 cm-1. After doping HNO3, the Raman shift of the G-band and 2D-band is 1597 cm-1 and 2709 cm-1. The Raman spectra show about 11 cm-1 blueshift both for G and 2D band, indicating the graphene films after doping HNO3 are strongly p-doped

16

. The chemical reaction of between graphene and HNO3 can be

written as 32-34: 6HNO3 + 25C → C 25+ NO3- 4HNO3 + NO 2 + H 2 O. The chemical doping mechanism shown in the above reaction has been studied by Das et. al. 33-34

. HNO3 molecules are randomly doped in the graphene lattice. Then, the protonation process

occurs and C(O)OH, C-H, and NO3- are introduced in the graphene lattice through sp2-sp3 hybridization. The increase of the THz sheet conductivity can be attributed to the electron transfer from graphene to HNO3, which results in an increase of the hole carrier concentration of graphene (p-doped) and the Fermi level shift to a lower value 32. The carrier concentration n has a relation with the Fermi energy ( EF ): EF = ±hvF π n , where h is reduced Planck constant. Combined with Eq. (3-4), the THz sheet conductivity will become larger with the carrier concentration increasing. In Eq. (3), the carrier scattering time of graphene before and after doping HNO3 is changeless. Assuming that the scattering time of graphene grown with 1000 oC is 50 fs

35

, the carrier concentration of before and after doping is approximate 4.96 × 1012 and


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8.8 × 1012 cm-2. These results indicate the THz sheet conductivity of graphene can be tuned by controlling of the carrier concentration, thus lead to better THz devices based on graphene.

4. CONCLUSION The graphene films were synthesized on Cu surface by APCVD with C2H2. We have studied the THz sheet conductivity of these samples grown at different temperature before and after chemical doping of HNO3. It is worth noting that THz sheet conductivity of the graphene grown at 1000 oC is highest. And compared with the graphene grown at 850 oC, it enhances 600%. In addition, after HNO3 doping of the sample grown at 1000 oC, THz sheet conductivity enhances 44%. These results indicate that by optimizing growth temperature, the THz sheet conductivity of graphene can be improved mainly from the better sample quality with higher carrier momentum scattering time. Meanwhile, by chemical doping, the THz sheet conductivity of graphene can be improved mainly from the control of the carrier concentration. These results offer useful insights into the understanding of improving THz sheet conductivity by in-situ growth and post-growth and pave the way for efficient THz components with graphene.

AUTHOR INFORMATION Corresponding Author *Telephone: +86-29-88303336. Fax: +86-29-88303336. E-mail: [email protected]. †Telephone: +86-29-88303336. Fax: +86-29-88303336. E-mail: [email protected].

ACKNOWLEDGMENTS This work was supported by National Natural Science Foundation of China (No. 61275105, 11374240, 61177059), Natural Science Basic Research Plan in Shaanxi Province of China (No. 2012KJXX-27, 12JK0990), and Ph.D. Programs Foundation of Ministry of Education of China (No. 20136101110007, 20126101120029), Key Laboratory Science Research Plan of Shaanxi Education Department (13JS101).


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ABBREVIATIONS CVD, chemical vapor deposition; APCVD, atmospheric pressure CVD; TEM, transmission electron microscope; HR-TEM, high resolution TEM; THz-TDS, THz time-domain spectroscopy; sccm, standard-state cubic centimeters per minute; FWHM, full width at half-maximum.

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TOC for the manuscript


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Improving Terahertz Sheet Conductivity of Graphene Films

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