Classical Drude Model Research Articles

Optical Absorption in Nano-Structures: Classical and Quantum Models

In the last decade, nano-structured materials have gained a significant interest for applications in solar cells and other optical and opto-electronic devices. Due to carrier confinement, the absorption characteristics in these structures are quite different from the absorption in bulk materials and thin films. Optical absorption coefficients of a silicon nano-wire are obtained based on a semi-classical model where the photon-electron interaction is described by the interaction of an electromagnetic wave with the electrons in the valence band of a semiconductor. The absorption characteristics showed enhanced optical absorption but no resonant peaks. In our modified model, we have identified optically active inter band transitions by performing electronic structure calculations on unit cells of nano-dimensions. The absorption spectrum obtained here shows explicit excitonic processes. This absorption is tunable from the visible region to near UV portion of the solar spectrum. In our previous work on thin films (100 nm) of ITO, we have used classical Drude model to describe free electron absorption. Using the imaginary part of the calculated complex dielectric function, we have plotted the absorption coefficient versus wavelength of the photon and compared with the experimental data showing good agreement between theory and experiment.

On the determination of the quasiparticle scattering rate in unconventional superconductors by microwave surface impedance

As found from numerous microwave experiments on the unconventional Fe-based superconductors, the temperature dependence of the quasiparticle scattering rate τ−1 cannot be accurately described within the framework of standard Drude module in the popular approximation of ωτ ≪ 1, where ω is the signal frequency. To account for the discrepancy, we have extended the classical Drude model for the case of arbitrary values of ωτ, and obtained the expression for τ−1 as a function of experimentally measurable quantities, namely the real and imaginary parts of the microwave surface impedance. We then show the temperature dependence of τ−1 in superconducting Ba(Fe1-xCox)2As2 single crystal pnictide derived from the Ka-band surface impedance measurements within the framework of the modified expression. The measurements indicate the extent to which assumption of ωτ ≪ 1 gives results different from those obtained without this restriction, i.e., incorrect results.

Plasmon Spectra of Cylindrical Nanostructures Including Nonlocal Effects

We investigate the nonlocal effects on plasmon spectra of cylindrical metallic nanostructures using a semiclassical nonlocal hydrodynamic description of the electron density. We obtain new dispersion relations for plasmon modes in nanowires, nanocavities, nanotubes, and parallel nanowires and compare the results with recent works based on the purely classical local-response Drude model. We find that the nonlocal effects lead to a significantly modified plasmon dispersion relations of the systems.

A polarizable force field of dipalmitoylphosphatidylcholine based on the classical Drude model for molecular dynamics simulations of lipids.

A polarizable force field of saturated phosphatidylcholine-containing lipids based on the classical Drude oscillator model is optimized and used in molecular dynamics simulations of bilayer and monolayer membranes. The hierarchical parametrization strategy involves the optimization of parameters for small molecules representative of lipid functional groups, followed by their application in larger model compounds and full lipids. The polar headgroup is based on molecular ions tetramethyl ammonium and dimethyl phosphate, the esterified glycerol backbone is based on methyl acetate, and the aliphatic lipid hydrocarbon tails are based on linear alkanes. Parameters, optimized to best represent a collection of gas and liquid properties for these compounds, are assembled into a complete model of dipalmitoylphosphatidylcholine (DPPC) lipids that is tested against the experimental properties of bilayer and monolayer membranes. The polarizable model yields average structural properties that are in broad accord with experimental data. The area per lipid of the model is 60 Å(2), slightly smaller than the experimental value of 63 Å(2). The order parameters from nuclear magnetic resonance deuterium quadrupolar splitting measures, the electron density profile, and the monolayer dipole potential are in reasonable agreement with experimental data, and with the nonpolarizable CHARMM C36 lipid force field.

Plasmon resonances and plasmon‐induced charge transport in linear atomic chains

In linear hydrogen atomic chains, plasmon resonances and plasmon‐induced charge transport are studied by time‐dependent density functional theory. For the large linear chain, it is a general phenomenon that, in the longitudinal excitation, there are high‐energy resonances and a large low‐energy resonance. The energy of the large low‐energy resonance conforms to the results calculated by the classical Drude model. In order to explain the formation mechanism of the high‐energy resonances, we present a simple harmonic oscillator model. This model may reasonably account for the relationship between low‐energy and high‐energy resonances, and has a certain degree of universality. As the interatomic distance decreases, the current shows a gradual transition from insulator to metal. The current enhancement mainly depends on the local field enhancement associated with plasmon excitation, and the enhanced electron delocalization effect as a result of the decrease of the interatomic distance. © 2013 Wiley Periodicals, Inc.

Blueshift of the surface plasmon resonance in silver nanoparticles studied with EELS

Abstract We study the surface plasmon (SP) resonance energy of isolated spherical Ag nanoparticles dispersed on a silicon nitride substrate in the diameter range 3.5–26 nm with monochromated electron energy-loss spectroscopy. A significant blueshift of the SP resonance energy of 0.5 eV is measured when the particle size decreases from 26 down to 3.5 nm. We interpret the observed blueshift using three models for a metallic sphere embedded in homogeneous background material: a classical Drude model with a homogeneous electron density profile in the metal, a semiclassical model corrected for an inhomogeneous electron density associated with quantum confinement, and a semiclassical nonlocal hydrodynamic description of the electron density. We find that the latter two models provide a qualitative explanation for the observed blueshift, but the theoretical predictions show smaller blueshifts than observed experimentally.

Infrared absorption of n-type tensile-strained Ge-on-Si

We analyze the IR absorption of tensile-strained, n-type Ge for Si-compatible laser applications. A strong intervalley scattering from the indirect L valleys to the direct Γ valley in n+ Ge-on-Si is reported for the first time to our knowledge. The intervalley absorption edge is in good agreement with the theoretical value. On the other hand, we found that the classical λ2-dependent Drude model of intravalley free-carrier absorption (FCA) breaks down at λ<15 μm. A first-principle model has to be employed to reach a good agreement with the experimental data. The intravalley FCA loss is determined to be <20 cm(-1) for n=4×10(19) cm(-3) at λ=1.5-1.7 μm, an order lower than the results from Drude model. The strong L→Γ intervalley scattering favors electronic occupation of the direct Γ valley, thereby enhancing optical gain from the direct gap transition of Ge, while the low intravalley free-electron absorption at lasing wavelengths leads to low optical losses. These two factors explain why the first electrically pumped Ge-on-Si laser achieved a higher net gain than the theoretical prediction using λ2-dependent free-carrier losses of bulk Ge and indicate the great potential for further improvement of Ge-on-Si lasers.

Terahertz magneto-optical spectroscopy in HgTe thin films

Thin films of HgTe have been systematically investigated using continuous frequency terahertz spectroscopy in external magnetic fields. In these experiments, full control of the polarization state can be achieved including Faraday rotation and ellipticity. We present the details of the experimental procedure and of the data analysis. Besides the cyclotron resonance, an additional mode is observed in the zero-gap sample. The results at high temperatures can be well understood within the classical Drude model of the dynamic conductivity. Possible dimensionality of the charge dynamics at low temperatures is discussed.

Plasmon Ruler with Angstrom Length Resolution

We demonstrate a plasmon nanoruler using a coupled film nanoparticle (film-NP) format that is well-suited for investigating the sensitivity extremes of plasmonic coupling. Because it is relatively straightforward to functionalize bulk surface plasmon supporting films, such as gold, we are able to precisely control plasmonic gap dimensions by creating ultrathin molecular spacer layers on the gold films, on top of which we immobilize plasmon resonant nanoparticles (NPs). Each immobilized NP becomes coupled to the underlying film and functions as a plasmon nanoruler, exhibiting a distance-dependent resonance red shift in its peak plasmon wavelength as it approaches the film. Due to the uniformity of response from the film-NPs to separation distance, we are able to use extinction and scattering measurements from ensembles of film-NPs to characterize the coupling effect over a series of very short separation distances-ranging from 5 to 20 Å-and combine these measurements with similar data from larger separation distances extending out to 27 nm. We find that the film-NP plasmon nanoruler is extremely sensitive at very short film-NP separation distances, yielding spectral shifts as large as 5 nm for every 1 Å change in separation distance. The film-NP coupling at extremely small spacings is so uniform and reliable that we are able to usefully probe gap dimensions where the classical Drude model of the conducting electrons in the metals is no longer descriptive; for gap sizes smaller than a few nanometers, either quantum or semiclassical models of the carrier response must be employed to predict the observed wavelength shifts. We find that, despite the limitations, large field enhancements and extreme sensitivity persist down to even the smallest gap sizes.

Measurement of the dielectric constants of zinc metallic nanoparticles at various frequencies

The vacuum evaporated metallic nanoparticles mixed with a low loss tangent alumina powder dissolved in paraffin constructed in a cylindrical rod were inserted in the center of a cylindrical microwave cavity. The resonant frequencies and the quality factors measured from a resistance–inductance–capacitance (RLC) meter and a microwave network analyzer were exploited to compute the real and imaginary dielectric constants of zinc metallic nanoparticles at various frequencies from low radio frequency to microwave frequencies. The paraffin molecules are exploited to prevent the space from adsorbing moisture and air, which makes the measurement much accurately and stable. The magnitudes of the real part of the dielectric constants of zinc metallic nanoparticles decrease as the particle size decrease, which is satisfactorily consistent with the prescription of classical free electron Drude model.

Halothane Solvation in Water and Organic Solvents from Molecular Simulations with New Polarizable Potential Function

The partitioning of a substrate from one phase into another is a complex process with widespread applications: from chemical technology to the pharmaceutical industry. One particularly well-known and well-studied example is 2-bromo-2-chloro-1,1,1-trifluoroethane (halothane) trafficking through the lipid bilayer. Halothane is a model volatile anesthetic known to impact functions of model lipid bilayers, altering the structure and thickness upon its partitioning from the bulk phase. A number of theoretical and experimental investigations suggest the importance of electronic polarizability, determining a preference for halothane to partition in the interfacial systems as in lipid bilayers or binary solvents. The recently published protocol for the development of polarizable force fields based on the classical Drude model has provided fresh impetus to efforts directed at understanding the molecular principles governing complex thermodynamics of the hydrophobic hydration. Here, molecular simulations were combined with free energy simulations to study solvation of halothane in polarizable water and methanol. The absolute free energy of halothane solvation in different solvents (water, methanol, and n-hexane) has been evaluated for additive and polarizable models. It was found that both additive and polarizable models provide an adequate description of the halothane solvation in high-dielectric (polar) solvents such as water, but explicit accounting for electronic polarization is imperative for a correct description of the solvation thermodynamics in nonpolar systems. To study halothane dynamics in binary mixtures, all-atom molecular dynamics (MD) simulations for halothane-methanol mixtures in a wide range of concentrations were performed alongside an analysis of structural organization, dynamics, and thermodynamic properties to dissect the molecular determinants of the halothane solvation in polar and amphiphilic liquids such as methanol. Additionally, a theoretical test of the hypothesis on the weak hydrogen bonding of halothane and methanol in the condensed phase is provided, which was presented on the basis of spectroscopic analysis of the C-H vibrations in different gas-phase complexes. The simulations performed in the condensed phase suggest that hydrophobic interactions between halothane and methanol play a dominant role in preferential solvation.

Ultrashort-pulse propagation through free-carrier plasmas

The past decade has seen frequent use of a modified nonlinear Schroedinger equation to describe ultrashort pulse propagation in materials where free-carrier plasmas are present. The optical contribution from the resulting free-current densities in this equation is often described using a classical Drude model. However, the ultimate form of this contribution in the modified nonlinear Schroedinger equation is somewhat inconsistent in the literature. We clarify this ambiguity by deriving the modified nonlinear Schroedinger equation from the classical wave equation containing a free-current density contribution. The Drude model is then used to obtain an expression for the complex free-carrier current density envelope with temporal dispersion corrections for ultrashort laser pulses. These temporal dispersion corrections to the current-density term differ, to our knowledge, from all other models in the literature in that they depend more sensitively on the value of the Drude free-carrier collision time. These corrections reduce to the current models in the literature for limiting cases. Theoretical analysis and computer simulations show that these differences can significantly affect the dynamic interactions of plasma absorption and plasma defocusing for materials with free-carrier collision times on the order of one optical cycle (or less) of the applied field.

Variable-wavelength frequency-domain terahertz ellipsometry

We report an experimental setup for wavelength-tunable frequency-domain ellipsometric measurements in the terahertz spectral range from 0.2 to 1.5 THz employing a desktop-based backward wave oscillator source. The instrument allows for variable angles of incidence between 30 degrees and 90 degrees and operates in a polarizer-sample-rotating analyzer scheme. The backward wave oscillator source has a tunable base frequency of 107-177 GHz and is augmented with a set of Schottky diode frequency multipliers in order to extend the spectral range to 1.5 THz. We use an odd-bounce image rotation system in combination with a wire grid polarizer to prepare the input polarization state. A highly phosphorous-doped Si substrate serves as a first sample model system. We show that the ellipsometric data obtained with our novel terahertz ellipsometer can be well described within the classical Drude model, which at the same time is in perfect agreement with midinfrared ellipsometry data obtained from the same sample for comparison. The analysis of the terahertz ellipsometric data of a low phosphorous-doped n-type Si substrate demonstrates that ellipsometry in the terahertz spectral range allows the determination of free charge-carrier properties for electron concentrations as low as 8x10(14) cm(-3).

Transient Electromagnetic Field of an Electric Line Source above a Plane Drude Model Plasmonic Half-space

The enhancement of the electromagnetic fleld at the surface of a Drude metal is classifled as the so called surface plasmon efiect. This surface plasmon efiect in a classical Drude model has been investigated extensively in the frequency domain. However, to understand what is actually happening to the electromagnetic fleld at the near vicinity of a Drude metal a thorough analysis in the space-time domain is needed. Once the space-time domain counterpart of the surface plasmon efiect is found, one is able to describe and classify the physical phenomena that are playing a role in the occurrence of this efiect. The phenomenon of surface plasmon resonance of metallic structures has been known and theoret- ically described for more than flfty years. Nowadays, the plasmonic nanostructures are used in a variety of applications, such as molecular sensing and imaging devices, optical devices and meta- materials. One of the materials in which plasmonic efiects are encountered are metals that have a frequency dependant conductivity described by the Drude model. Many researchers investigated Drude model metals in the frequency domain in order to determine the optical behaviour of metals within a certain frequency range. However, to understand what phenomena are at work when the electromagnetic fleld interacts in the near vicinity with a Drude model metal, a thorough analysis in the space-time domain is needed. Once the space-time domain counterpart of the surface plasmon efiect is identifled, a description and classiflcation of the physical phenomena that occur can be given. These results can be of great importance in the fleld of time-domain terahertz spectroscopy. The pulsed electromagnetic radiation from a line source above a plane plasmonic half-space, modeled by a classical Drude model, is investigated. In order to obtain closed-form expressions for the re∞ected electric fleld anywhere above the plasmonic half-space, the re∞ection factor RE that corresponds to the Drude metal half-space is mathematically written in the form of a Laplace transform integral, enabling the application of the Cagniard-de Hoop method. In the Cagniard-de Hoop method the Laplace transform with respect to time is used, in which the Laplace parameter s is kept real and positive in order to ensure causality in the space-time domain expressions for the electromagnetic fleld. Attention is paid to investigate which parts of the Laplace transform integral representation of RE give rise to the surface-plasmon efiect by means of enhancement of the re∞ected electromagnetic fleld at the near vicinity of the Drude metal interface. The derived space-time domain expressions for the re∞ected electric fleld explicitly show the special time and space dependence that exists in the re∞ection factor at the interface of the plasmonic half-space. Consequently, leading to a better understanding of the physical efiects, that occur at the interface of classical Drude metals in the space-time domain. Finally, a suitable source signature is proposed, which enables, without loss of generality, a suitable determination of analytical closed-form inverse Laplace transforms of the distinct source functions. Numerical results that support the conclusions made in this paper will be presented at the Symposium. 2. DESCRIPTION OF THE CONFIGURATION

Terahertz conductivity of thin gold films at the metal-insulator percolation transition

Terahertz time-domain spectroscopy is used to measure the complex conductivity of nanometer-thick gold films evaporated on silicon substrates in the far-infrared spectral region from $0.2\phantom{\rule{0.3em}{0ex}}\text{to}\phantom{\rule{0.3em}{0ex}}2.7\phantom{\rule{0.3em}{0ex}}\mathrm{THz}$. With increasing film thickness a characteristic crossover from an insulating to a conducting state via a percolation transition is observed. Of particular interest is the characteristic non-Drude behavior close to the transition. Whereas effective medium theory is inconsistent with our measurements in this regime, the Drude-Smith model, a generalization of the classical Drude model which incorporates carrier localization through backscattering, provides excellent fits to the observed complex conductivity. Applying this model we observe extreme values for the carrier scattering time at the percolation threshold.

Optical Properties of Li Doped KTaO3 Using Spectroscopic Ellipsometer

Measurements of complex refractive indices n* = n - iκ are performed on pure KTaO 3 and K 0.93 Li 0.07 TaO 3 single crystals by using a spectroscopic ellipsometer in temperature range from room temperature to 10 K. At room temperature, experimentally obtained complex dielectric constants ϵ* = ϵ1−iϵ2 of both crystals are analyzed by the classical Drude model. Temperature dependence of the imaginary part ϵ 2 of K 0.93 Li 0.07 TaO 3 shows a small but distinct change around 70 K. The origin of the anomalous behavior is discussed.

Polarizable empirical force field for the primary and secondary alcohol series based on the classical Drude model.

A polarizable empirical force field based on the classical Drude oscillator has been developed for the aliphatic alcohol series. The model is optimized with emphasis on condensed-phase properties and is validated against a variety of experimental data. Transferability of the developed parameters is emphasized by the use of a single electrostatic model for the hydroxyl group throughout the alcohol series. Aliphatic moiety parameters were transferred from the polarizable alkane parameter set, with only the Lennard-Jones parameters on the carbon in methanol optimized. The developed model yields good agreement with pure solvent properties with the exception of the heats of vaporization of 1-propanol and 1-butanol, which are underestimated by approximately 6%; special LJ parameters for the oxygen in these two molecules that correct for this limitation are presented. Accurate treatment of the free energies of aqueous solvation required the use of atom-type specific O(alcohol)-O(water) LJ interaction terms, with specific terms used for the primary and secondary alcohols. With respect to gas phase properties the polarizable model overestimates experimental dipole moments and quantum mechanical interaction energies with water by approximately 10 and 8 %, respectively, a significant improvement over 44 and 46 % overestimations of the corresponding properties in the CHARMM22 fixed-charge additive model. Comparison of structural properties of the polarizable and additive models for the pure solvents and in aqueous solution shows significant differences indicating atomic details of intermolecular interactions to be sensitive to the applied force field. The polarizable model predicts pure solvent and aqueous phase dipole moment distributions for ethanol centered at 2.4 and 2.7 D, respectively, a significant increase over the gas phase value of 1.8 D, whereas in a solvent of lower polarity, benzene, a value of 1.9 is obtained. The ability of the polarizable model to yield changes in dipole moment as well as the reproduction of a range of condensed phase properties indicates its utility in the study of the properties of alcohols in a variety of condensed phase environments as well as representing an important step in the development of a comprehensive force field for biological molecules.

Composition dependence of the infrared dielectric functions in Si-doped hexagonalAlxGa1−xNfilms onc-plane sapphire substrates

The optical properties of hexagonal ${\mathrm{Al}}_{x}{\mathrm{Ga}}_{1\ensuremath{-}x}\mathrm{N}$ ($x$ from 0.05 to 0.42) epitaxial films with Si doping concentrations up to ${10}^{18}\phantom{\rule{0.3em}{0ex}}{\mathrm{cm}}^{\ensuremath{-}3}$ grown on $c$-plane sapphire substrates by metal-organic chemical vapor deposition have been investigated using infrared reflectance spectra. The dielectric functions $(\ensuremath{\epsilon}={\ensuremath{\epsilon}}_{1}+i{\ensuremath{\epsilon}}_{2})$ of the ${\mathrm{Al}}_{x}{\mathrm{Ga}}_{1\ensuremath{-}x}\mathrm{N}$ films are determined in the wavelength region of $1.54--50\phantom{\rule{0.3em}{0ex}}\ensuremath{\mu}\mathrm{m}$ at room temperature. The experimental reflectance spectra are analyzed using classical harmonic Lorentz oscillators and Drude model in the transparent, reststrahlen, and free carrier absorption regions. GaN-like ${E}_{1}$ transverse-optical (TO) phonon frequency linearly decreases and its strength increases with decreasing Al composition. However, AlN-like ${E}_{1}(\mathrm{TO})$ phonon frequency shows a relatively weak composition dependence and its strength increases with increasing composition. At a wavelength of $1.54\phantom{\rule{0.3em}{0ex}}\ensuremath{\mu}\mathrm{m}$, ${\ensuremath{\epsilon}}_{1}$ varies between 4.86 and 5.2 when the composition $x$ changes from 0.05 to 0.42 and ${\ensuremath{\epsilon}}_{2}$ is close to zero. The longitudinal-optical phonon plasmon (LPP) coupled modes of $n$-type hexagonal ${\mathrm{Al}}_{x}{\mathrm{Ga}}_{1\ensuremath{-}x}\mathrm{N}$ films are also discussed. For samples with higher concentrations beyond ${10}^{18}\phantom{\rule{0.3em}{0ex}}{\mathrm{cm}}^{\ensuremath{-}3}$ the upper LPP coupled mode frequencies increase with increasing carrier concentration indicating the transition from phononlike to plasmonlike behavior.

Influence of plasmons on terahertz conductivity measurements

Time-domain terahertz spectroscopy allows measuring the complex conductivity spectrum of materials at frequencies on the order of 1 THz. Typically, terahertz (THz) studies produce conductivity spectra that are different from those predicted by the classical Drude model, especially in nanostructured materials. We claim that plasmon resonances in particles that are small compared to the THz wavelength cause these deviations. This is supported by measurements on photoexcited silicon, in bulk as well as in micron-sized particles. In the latter, the behavior is vastly different and strongly dependent on charge carrier concentration.

Anisotropy of infrared absorption in (110) porous silicon layers

In-plane birefringent porous Si (PSi) layers formed from heavily boron-doped (110) Si wafers are investigated by using polarization-resolved infrared absorption (IR) spectroscopy. The absorption by free charge carriers and by Si-Hx (x = 1, 2, 3) surface bond vibrations are found to exhibit strong anisotropy (dichroism), which originates from the form anisotropy of Si nanocrystals assembling (110) PSi layers. The free carrier absorption dichroism is explained by using the effective medium approximation and classical Drude model and considering additional carrier scattering in anisotropically shaped Si nanocrystals. (© 2005 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)