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Terahertz Spectroscopy for Nanomaterial Characterization
Published in Klaus D. Sattler, st Century Nanoscience – A Handbook, 2020
Xinlong Xu, Lipeng Zhu, Yanping Jin, Yuanyuan Huang, Zehan Yao, Chuan He, Longhui Zhang, Changji Liu
Usually the measured optical constants can be described well by several models such as Drude, Drude–Smith, and Lorentz models for the carrier dynamics in a view of classical physics. Drude model is a free-electron gas model, which can be used to describe electrons in metals or in highly doped semiconductors or photoexcited free carriers (Hodgson 2012). The complex dielectric constants can be written as: ε(ω)=1−ωp2ω2+iΓω
Metal Plasmonics
Published in Myeongkyu Lee, Optics for Materials Scientists, 2019
Here ωp is the bulk plasma frequency and γ is the damping factor. The Drude model is a purely classical model of electron transport in conductors and describes the collision between freely moving electrons and heavy, stationary ion cores. It provides a good approximation of the conductivity of noble metals. For visible and near-infrared frequencies (ω ≫ γ), eq 10.34 can be simplified to () ε1(ω)≈1−ωp2ω2.
Charge Transport in Conducting Polymers
Published in Sam-Shajing Sun, Larry R. Dalton, Introduction to Organic Electronic and Optoelectronic Materials and Devices, 2016
Vladimir N. Prigodin, Arthur J. Epstein
A puzzling feature of the metallic phase in polymers is that ε is similar to that of dielectric samples with decreasing frequency, also changing sign from negative to positive at approximately the same frequency ~0.1 eV. However, for metallic samples ε changes again to negative at yet lower frequencies, ω ~ 0.01 eV, indicating that free electronic motion is presented [8,12]. The parameters of this low-frequency coherent phase are quite anomalous. From the Drude model, the relaxation time is found to be very long τ ~ 10−13 s; also, the new plasma frequency below which ε is again negative is very small ~0.01 eV [8,12].
The broadband absorber based on plasma metastructure with spiral resonators
Published in Waves in Random and Complex Media, 2023
Haining Ye, Li Zeng, Baofei Wan, Haifeng Zhang
The structure diagram of the single spiral narrowband MSA consisting of a three-layer structure is drawn in Figure 1. Aimed to ensure that EMW rarely reflects, the bottom layer is a metal plate made of copper with a conductivity σ of 5.8 × 107 S/m [26]. And the top layer is a solid plasma Archimedes spiral. Describing with the Drude model, the dielectric constant of the solid plasma is expressed as εp(ω) = ε∞– ωp2 / (ω2 + jωωc), where the ε∞ is 12.4, the solid plasma frequency ωp is 2.9 × 1014 rad/s, and the solid plasma collision frequency is 1.65 × 1013 rad/s [27].
Revisiting the experimental dielectric function datasets of gold in accordance with the Brendel-Bormann model
Published in Journal of Modern Optics, 2023
Farzad Firouzi, Sayed Khatiboleslam Sadrnezhaad
The classical Drude model is the most fundamental theory for expressing the complex dielectric function of materials based on free-electron effects [33,34]. Despite the simplicity and wide usage, it is not an accurate model; specifically for higher energies, the impact of bound electrons becomes more significant. Modified versions of the Drude model (e.g. the Lorentz-Drude modification) have been gradually developed by considering the bound-electron effects to overcome the shortcoming [35,36]. Accordingly, Brendel and Bormann (1931) [37] have developed one of the most accurate modified models for expressing the complex dielectric function of materials. Although the model was originally developed for amorphous solids, its validity for crystalline materials and metals, including gold, has also been confirmed [38–41]. Despite excellent accuracy, the Brendel-Bormann model has not been widely employed for practical usage, mainly due to its complicated formulation and calculation procedure which imposes specific computational skills and requirements. In this context, developing a fast and accessible approach for simplifying the model's computational procedure would be of great significance.
Theoretical and experimental investigations of plasmonic properties of Ag nanosphere and SiO2/Ag core-shell nanostructure
Published in Journal of Modern Optics, 2020
Mohammad Saeid Parvin, Maryam Saliminasab, Rostam Moradian
The optical properties of metals can be explained by a plasma model, where a free electron gas, having n carriers per unit volume, effective optical mass m and charge –ne, moves against a uniform background of positive ion cores. The complex dielectric function of the free electron gas comes from the so-called Drude theory and can be written as [32]: where ω=2πc/λ is the angular frequency of the incident field, λ is the wavelength, ωp and γbulk are the plasma frequency and electron collision damping in the bulk silver which are equal to 1.38 × 1016 Hz and 3.23 × 1013 Hz, respectively [33]. ε1(ω) and ε2(ω) are the real and imaginary parts of ε(ω), respectively. For alkali metals, a plasma frequency range extends up to the ultraviolet, while for noble metals, the interband transitions which occur at visible frequencies limit the validity of this model. The validity limits of the dielectric function of the free electron model in silver metal are shown in Figure 1. At the energy of ∼4 eV or more, the applicability of the Drude model breaks down due to the occurrence of the interband transitions which lead to an increase in ϵ2 (Figure 1). In fact, the Drude model is not in accordance with the experimental data at higher energies. In other words, the Drude model is not satisfactory for explaining either ϵ1 or ϵ2 at high frequencies (Figure 1).