Figure 5.3 shows the measured optical transmission spectra of a bare silicon substrate, triazine-doped and undoped monolayer graphene prepared by CVD over a frequency range (1 – 10 THz) at 300 K. The substrate transmission is about 50% owing to reflection losses. Notably, the overall transmission intensity of the triazine-doped and undoped graphene is up to 30% lower than that of the silicon substrate, indicating strong absorption in the film. We model the transmission data using the classical Drude–Lorentz dispersion theory.
For the case of the graphene film thickness d << < , where is the skin or penetration depth and is the wavelength of the THz radiation, the transmission through the film into a non-absorbing substrate can be written as [94]:
ns 1A where Ts and Tg+s are the measured transmission spectra of a bare substrate and the graphene on the substrate; ns is the refractive index of the underlying silicon substrate; and A is frequency-dependent absorbance for a graphene film. The real part of optical conductivity σ1 for a graphene film relates to the absorbance by A
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Table 5.2: Parameters of a Drude-Lorentz fit for the room-temperature transmission data. All units are in cm-1.
CVD-undoped CVD-doped
ωpD 4528 4400
1/τpD 326 400
ωp1 － 2143
ω1 － 155
γ1 － 353
ωp2 15860 12479
ω2 1025 1022
γ2 1004 1000
ε∞ 4.1 4.3
Figure 5.4 displays the 300 K real part of optical conductivity for the triazine-doped monolayer graphene. There are three important features to the spectrum. First, it exhibits a coherent response of itinerant charge carriers at zero frequency. Our fits yield a Drude plasma frequency ωpD /2π ~ 21 THz and carrier relaxation time of 13 fs. This plasma frequency is close to that obtained in undoped monolayer graphene. In contrast, the carrier relaxation time is by a factor of 0.8 smaller than the value derived for undoped graphene. The decreased carrier relaxation time is attributable to the effects of impurities, defects, and disorders in the triazine-doped film. Second, a low-frequency resonance mode is observed at about 155 cm-1. One point that may be relevant for this mode is the likely presence of significant disorder induced by triazine doping. The behavior may thus reflect the localization of carriers in the graphene film
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initiated by triazine doping. Indeed, a peak in conductivity centered at finite frequency is a generic feature of disorder conductors and has been observed in disordered doped semiconductors [126-129] as well as conducting polymers [130]. Third, the mid-infrared absorption band near 1022 cm-1 can be associated with the interband transitions between the π bands near K and H points of the Brillouin zone [131].
When the sample is cooled from 300 to 10 K, transmission increases with decreasing temperature, corresponding to a decrease in conductivity. The temperature evolution of the Drude plasma frequency and the carrier relaxation time of the triazine-doped film are shown in Figure 5.5. With decreasing temperature, the Drude plasma frequency decreases, whereas the carrier relaxation time is almost temperature independent. The temperature dependence of Drude
conductivity can be calculated [ (thermally excited electron-hole pairs) and not in carrier relaxation time. Such behavior is typical of conventional semiconductors. The typical temperature dependence of conductivity may be expressed as: σ (T) = σ0 exp(-Ea/kBT) [132]. Here Ea is the thermal activation energy, kB is the Boltzmann constant and σ0 is the pre-exponential factor. The plot of log σ vs 1/T does not obey a single linear relationship; instead two different slops were obtained above and below a crossover point of 100 K. The activation energy at high temperature is about 3 meV whereas Ea is smaller at low temperature, probably due to the impurity effects [133,134]. Additionally, we notice that the position of the low-frequency peak monotonously decreases down to 10 K. In contrast, the mid-infrared band exhibits little temperature dependence.
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It is intriguing to compare our experimental results with predicted optical conductivity from both intra- and interband contributions for graphene. According to the transport mechanism proposed by Fritz et al, [135] the real part of conductivity in ideal monolayer graphene can be
In this theory, clean and undoped graphene is viewed as a nearly quantum critical system with weak Coulomb interactions. This implies that low-frequency conductivity is insensitive to phonons, impurities, and band structure effects when the energy of incident light is much smaller than the electronic bandwidth. Thus, low-frequency conductivity is simply a delta function at zero frequency with weight of order kBT. While at the high-frequency limit, conductivity
lower than the constant universal conductance. The deviation for the triazine-doped film becomes even larger, indicating that disorder might have a role to play.
Recently, we re-measurement low-frequency THz transmission spectra (0.5 – 3 THz) of the CVD-grown and ECE-grown graphene thin films using an Advantest TAS7500SU terahertz spectroscopic. Figure 5.8 shows the measured optical transmission spectra of a bare silicon
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substrate, CVD-undoped, CVD-doped, ECE-undoped, and ECE-doped graphene thin films over a frequency range (0.5 – 3 THz) at 300 K. The transmission intensity of CVD-grown and ECE-grown graphene thin films are up to 10% and 20% lower than that of the silicon substrate, respectively. Notably, the transmission intensity of the CVD-grown graphene thin films are higher than our previously studies by Bruker FTIR, which could be due to different light source or other optical components. We model the transmission data using the classical Drude dispersion theory. The parameters used to fit the measured optical data are listed in Table 5.3.
The fitting results are compared to the low-energy portion of the conductivity in Figure 5.9.
Figure 5.9 displays the 300 K real part of optical conductivity for four thin films. THz conductivity of all samples displays a coherent response of itinerant charge carriers at zero frequency. In addition, our fits yield a Drude plasma frequency ωpD /2π ~ 5 THz and carrier relaxation time of 84 fs for CVD-doped graphene thin films. This plasma frequency is close to that obtained in CVD-undoped ones. In contrast, the carrier relaxation time is by a factor of 0.6 smaller than the value derived for CVD-undoped graphene thin films. The decreased carrier relaxation time is attributable to the effects of impurities, defects, and disorders in the triazine-doped film. Additionally, the Drude plasma frequency of the ECE-grown graphene thin films is three times larger than that of CVD-grown ones. In contrast, the carrier relaxation time of the ECE-grown graphene thin films (~ 10 fs) is shorter than that of the CVD-grown samples. The behavior could be due to the changes of the charge distributions in the graphene thin films prepared by different growth methods.
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Table 5.3: Parameters of a Drude fit for the room-temperature transmission data. All units are in cm-1.
CVD-undoped CVD-doped ECE-undoped ECE-doped
ωpD 1031 1025 3538 3314
1/τpD 63 105 542 545
ε∞ 4.1 4.3 4.1 4.3