Classical Drude Model Research Articles

A Combinatorial Study Investigating the Growth of Ultrasmall Embedded Silver Nanoparticles upon Thermal Annealing.

Ultrasmall nanoparticles (NPs) with a high active surface area are essential for optoelectronic and photovoltaic applications. However, the structural stability and sustainability of these ultrasmall NPs at higher temperatures remain a critical problem. Here, we have synthesized the nanocomposites (NCs) of Ag NPs inside the silica matrix using the atom beam co-sputtering technique. The post-deposition growth of the embedded Ag NPs is systematically investigated at a wide range of annealing temperatures (ATs). A novel, fast, and effective procedure, correlating the experimental (UV-vis absorption results) and theoretical (quantum mechanical modeling, QMM) results, is used to estimate the size of NPs. The QMM-based simulation, employed for this work, is found to be more accurate in reproducing the absorption spectra over the classical/modified Drude model, which fails to predict the expected shift in the LSPR for ultrasmall NPs. Unlike the classical Drude model, the QMM incorporates the intraband transition of the conduction band electrons to calculate the effective dielectric function of metallic NCs, which is the major contribution of LSPR shifts for ultrasmall NPs. In this framework, a direct comparison is made between experimentally and theoretically observed LSPR peak positions, and it is observed that the size of NPs grows from 3 to 18 nm as AT increases from room temperature to 900 °C. Further, in situ grazing-incidence small- & wide-angle X-ray scattering and transmission electron microscopy measurements are employed to comprehend the growth of Ag NPs and validate the UV + QMM results. We demonstrate that, unlike chemically grown NPs, the embedded Ag NPs ensure greater stability in size and remain in an ultrasmall regime up to 800 °C, and beyond this temperature, the size of NPs increases exponentially due to dominant Ostwald ripening. Finally, a three-stage mechanism is discussed to understand the process of nucleation and growth of the silica-embedded Ag NPs.

Study of electrical properties and conduction mechanisms in La0.4Bi0.3Sr0.2Ba0.1MnO3 Ceramic elaborated by sol gel method

Using the sol gel method, we will incorporate Bi, Sr and Ba in site A into the LaMnO3 matrix to get La0.4Bi0.3Sr0.2Ba0.1MnO3 compound. Our aim is to explore the structural and the electrical properties of this compound. X-ray diffraction study indicates that the investigated compound exhibits a rhombohedral crystalline phase with R3̅c space symmetry. Temperature dependence of the electrical conductivity indicates that the investigated sample exhibits a semiconductor behavior in the explored temperature range [80–400 K]. Then a saturation region appears at ambient temperature. For ac-conductivity, the spectra obey to the double Jonscher response in the temperature range [80–135 K], the single Jonscher power law for [140–210 K] and to the classical Drude model for [220–400 K]. At elevated temperatures, the conduction is governed by the thermally activated hopping of small polaron (SPH). However, the most appropriate conduction mechanism at low temperatures is the Variable Range Hopping process (VRH). In the intermediate temperature range, the transport properties are described by Greaves variable range hopping model. Then, the correlated barrier hopping (CBH) and the Jump relaxation Model (JRM) were used to explain the dispersion region. Moreover, the value of the extracted activation energies is strongly dependent on frequency suggesting that the hopping mechanism is the dominant conduction process. Also, the disorder energy decreases with increasing frequency indicating that the separation path between jump centers is modified. Indeed, the contribution of various processes to the conductivity makes our system as good candidate in the solid oxide fuel cells (SOFCs) applications.

Limitations of Drude model in determining plasma properties for multivalley semiconductors: a case study with Ge1-xSnx alloy

Classical Drude model has long been employed to study the plasma behavior of metals. The model has also been used for semiconductors to obtain the expressions for plasma frequency and carrier-induced changes in refractive index and absorption in terms of effective mass, transport relaxation time, and mobility of the carriers. However, these expressions remain invalid for semiconductors in which carriers occupy different valleys, as in strained SiGe alloys, GeSn alloys, and even in GaAs or InP under high electric field. We modify Drude equations for occupancy of two valleys by electrons and show deviations from standard textbook expressions. The conditions for recovering known expressions are then established. To illustrate, we consider unstrained GeSn alloys over the range 0 < x < 0.2 in which L and Γ conduction band valleys cross positions at x = 0.08 resulting in a crossover from indirect to direct nature of the band gap. A comparison is made between the present values with values obtained previously.

Lifshitz Transition and Non-Fermi Liquid Behavior in Highly Doped Semimetals.

The classical Fermi liquid theory and Drude model have provided fundamental ways to understand the resistivity of most metals. The violation of the classical theory, known as non-Fermi liquid (NFL) transport, appears in certain metals, including topological semimetals, but quantitative understanding of the NFL behavior has not yet been established. In particular, the determination of the non-quadratic temperature exponent in the resistivity, a sign of NFL behavior, remains a puzzling issue. Here, a physical model to quantitatively explain the Lifshitz transition and NFL behavior in highly doped (a carrier density of ≈1022 cm-3 ) monoclinic Nb2 Se3 is reported. Hall and magnetoresistance measurements, the two-band Drude model, and first-principles calculations demonstrate an apparent chemical potential shift by temperature in monoclinic Nb2 Se3 , which induces a Lifshitz transition and NFL behavior in the material. Accordingly, the non-quadratic temperature exponent in the resistivity can be quantitatively determined by the chemical potential shift under the framework of Fermi liquid theory. This model provides a new experimental insight for nontrivial transport with NFL behavior or sign inversion of Seebeck coefficients in emerging materials.

Transport properties of La0.9Sr0.1MnO3 manganite

Impedance spectroscopy technique was used to characterize the electrical properties in a wide range of frequency [40–105 Hz] and temperature [80–700 K]. As a result, AC-conductivity spectrum follows the ‘double Jonscher Power Law’ in the temperature range [80–280 K], ‘Jonscher Power Law’ in [300–600 K] range and at 700 Kit is described by the classical Drude model. Moreover, the AC-conductivity analysis reveals the contribution of multiple mechanisms in conduction. In fact, the variation of the frequency exponent ‘s1’ with temperature shows that the correlated barrier hopping mechanism is the dominated model for conduction of charge carriers beyond T = 470 K. The previous model was observed again according to the temperature dependence of the frequency exponent ‘s2.’ Then, the deduced activation energy decreases with increasing frequency suggesting the availability of hopping conduction. The temperature dependence of AC-conductivity proves the existence of metal semi-conductor transition at 200 K. At high temperatures, the DC-conductivity analysis reveals that the conduction process is dominated by thermally activated hopping of small polaron. However, at low temperatures, it is confirmed that the most suitable mechanism for conduction is the Shklovskii–Efros-Variable Range Hopping process.

Temperature-dependent infrared ellipsometry of Mo-doped VO2 thin films across the insulator to metal transition

We present a spectroscopic ellipsometry study of Mo-doped VO2 thin films deposited on silicon substrates for the mid-infrared range. The dielectric functions and conductivity were extracted from analytical fittings of Ψ and Δ ellipsometric angles showing a strong dependence on the dopant concentration and the temperature. Insulator-to-metal transition (IMT) temperature is found to decrease linearly with increasing doping level. A correction to the classical Drude model (termed Drude-Smith) has been shown to provide excellent fits to the experimental measurements of dielectric constants of doped/undoped films and the extracted parameters offer an adequate explanation for the IMT based on the carriers backscattering across the percolation transition. The smoother IMT observed in the hysteresis loops as the doping concentration is increased, is explained by charge density accumulation, which we quantify through the integral of optical conductivity. In addition, we describe the physics behind a localized Fano resonance that has not yet been demonstrated and explained in the literature for doped/undoped VO2 films.

Normal spectral emissivity of liquid Al-Ti binary alloys

The normal spectral emissivity ε of four compositions in the Al-Ti binary liquid system was measured in dependence of the wavelength and temperature. It was found that all compositions show negligible temperature dependence. At a wavelength of 940 nm, the emissivity amounts to 0.37, 0.40, 0.32, and 0.31 for Ti, Al20Ti80, Al50Ti50, and Al70Ti30, respectively. The dependence of the emissivity on composition is in good agreement with literature data of binary and multi-component Al-Ti-based alloys. Using the classical Drude model, electrical resistivities are predicted for the Al-Ti system from the measured emissivities. Comparison with existing data from literature for Al show reasonable agreement.

Analysis of the local Drude model involving the generalized fractional derivative

In this paper, newly proposed generalized fractional derivative has been used to study the classical Drude model. This model describe the motion of the electrons in a metal in the presence of an external electric field. We present the novel fractional operator and the general conditions for the existence and the uniqueness of the exact solutions for ordinary differential equations. Numerical simulations for several α values allows obtain new behaviors for the optical properties in metals. The applications of this new derivative open new doors for in-depth investigation in complex systems. The solutions of the corresponding classical model are recovered as particular cases, when α = 1.

The rain stick, a simple model for the dynamics of particles passing obstacles in a gravitational field

The problem of a light particle travelling through a field of obstacles or very massive particles in equilibrium pervades multiple fields in modern physics. We analyse such a problem by considering a toy rain-stick model, the mechanical analogue of the Drude model, for the motion of non-interacting electrons through a medium. We study the differences and similarities between a rain-stick model and the Drude model. Interestingly, we find that, when the only potential is gravitational, the system behaves very differently. Rather than finding a mechanical analogue to Ohm’s law, a different law is recovered. We further analyse the multi-particle case, and find the conditions under which the linear Ohm’s law might be restored. This might yield important tools to physicists’ arsenal, namely, the ability to look at bulk behaviour without the need for the microscopic model. Author summaryThe rain stick is a musical instrument, that at least on its face is a mechanical analogue to the classical Drude model. This model can and is used extensively to describe a directional interaction between two mediums, such as gaseous jets and other relatively localized interactions. Remarkably, we find the ’Ohm’s law’ analogue is essentially different, provided the thermal velocity is tightly coupled to the potential. This result might yield another tool in the physicist’s tool-box.

Analysis of the Drude model in view of the conformable derivative

In this paper, we use the fractional conformable derivative to analyze the classical Drude model with direct DC and alternating current AC. We apply the conformable Laplace transform to solve the corresponding equations and found that the electron current density in the DC case has a stretched exponential behavior, while in the AC case shows an exponential-like down-chirp response. It is shown that the conformable fractional Laplace transform is a powerful method to solve fractional linear differential equations with constant coefficients. The solutions of the corresponding classical model are recovered as particular cases, when γ = 1.

Investigation of structural, electrical and dielectric properties of sol-gel prepared La0.67-xEuxBa0.33Mn0.85Fe0.15O3 (x=0.0, 0.1) manganites

Polycrystalline samples of La0.67-xEuxBa0.33Mn0.85Fe0.15O3 (x = 0.0, 0.1) manganites have been prepared using sol-gel route. Structural characterizations of our materials were performed by powder X-ray diffraction, Scanning Electron Microscopy and by Energy Dispersive X-ray spectroscopy at room temperature. Our samples are single phase and crystallize in the orthorhombic structure with the Pbnm space group. Electrical and dielectric properties of La0.67-xEuxBa0.33Mn0.85Fe0.15O3 (x = 0.0, 0.1) compounds have been studied using impedance spectroscopy technique in the temperature range from 80 to 400 K and the frequency range from 40 to 107 Hz. DC measurements show that the studied structures exhibit semiconductor (SC) behaviour in all temperature range of study. AC data analysis show a transition from SC to metallic behaviour at 160<TSM<170 K and 220<TSM<240 K for x = 0 and 0.1 respectively. In the SC region, the conductivity σAC obeys to Jonsher power law at low temperatures while at high temperatures, the classical Drude model describes well the frequency dependence of the conductivity data. Nyquist plots allow us to propose an equivalent circuit involving the contribution of grains and grain boundary elements. Dielectric measurements show that the dielectric relaxation is governed by the DC conduction process. Dielectric results confirm the high values of the permittivity which approve the use of manganites in electronic applications. Besides, the relaxation process in the dielectric spectra is shown to be totally obscured by the DC-conductivity.

Investigation of electrical behavior and dielectric properties in polycristalline Pr0.8Sr0.2MnO3 manganite perovskite

The electrical and dielectric properties of Pr0.8Sr0.2MnO3 perovskite prepared by the solid-state method were investigated. The complex impedance results showed the contribution of grain and grain boundaries in the conduction mechanism. The dielectric data have confirmed the presence of interfacial polarization in the structure. Moreover, a dielectric transition fitted by Curie-Weiss law was observed. Besides, the observed relaxation diffuse phase transition is attributed to a strong heterogeneity introduced by the substitution of Pr by Sr ions. DC electrical measurements indicate that the structure exhibits a semiconductor behavior and the conductivity is governed by hopping process. The AC conductivity measurements show a clear semiconductor-metallic transition at high temperatures. The AC conductivity data can be divided into two parts, the first of which is a semiconductor one, described by the NSPT model, at low temperatures and the second is a metallic regime, fitted by the classical Drude model, at high temperatures.

Broadband optical properties of aluminium zinc oxide thin films prepared by spatial atomic layer deposition

In this work, a broadband ellipsometric investigation of aluminium zinc oxide (AZO) from the infrared to the ultraviolet spectral range is presented. Aluminium zinc oxide samples were fabricated using spatial atomic layer deposition (SALD) having a range of percent aluminium incorporation. The AZO was deposited using a coflow of diethyl zinc (DEZ) and dimethyl aluminium isopropoxide (DMAI), where the amount of aluminium incorporation was controlled by varying the DMAI partial pressure. The broadband permittivity is reported as a function of the aluminium content of these aluminium zinc oxide thin films. A model dielectric function, which includes the contribution of recently predicted broad shallow donor states, is presented and discussed. We find that an increase in the aluminium content of the aluminium zinc oxide thin films results in a monotonically decreasing scattering time while the carrier density increases with diminishing efficiency. To demonstrate the necessity of broadband ellipsometric measurements for the accurate determination of the dielectric function of aluminium zinc oxide, a comparison with the classical Drude model and a semi-empirical extended Drude dispersion model, which are frequently employed in the literature to describe the optical response of aluminium zinc oxide, is given.

Plasma Mirrors for Cleaning Laser Pulses from the Infrared to the Ultraviolet

Ultrashort laser pulses are generally preceded by prepulses which - in case of high main pulse intensities - may generate preplasmas on solid surfaces, thus making the initial conditions for the interactions ambiguous. Infrared laser systems applied successfully, with high efficiency self-induced plasma mirrors for improving the contrast of the beam. Short wavelength laser beams however have a larger critical density in the plasma, and due to their deeper penetration the absorption is higher, the reflectivity, and the corresponding plasma mirror efficiency is lower. We show herewith that with carefully planned boundary conditions plasma mirrors can reach up to 70% efficiency even for KrF laser radiation. Our observations can be qualitatively explained by the classical Drude model. The high reflectivity allows the use of plasma mirrors even after the final amplification or before the last amplifier. Different arrangement proposals for its integration to our high power KrF laser system are given as well.

Structural, electrical and dielectric properties of Bi-doped Pr0.8-xBixSr0.2MnO3 manganite oxides prepared by sol-gel process

The aim of this paper is to investigate the structural, electrical and dielectric properties of Pr0.8-xBixSr0.2MnO3 (x = 0, 0.05 and 0.1) perovskite materials. Our samples were synthesized by sol-gel route and characterized by X-ray powder diffraction at room temperature. It has been demonstrated that they crystallize in the orthorhombic perovskite system with Pnma space group. As x varies from 0 to 0.1, the MnO bond length and the unit cell volume increases. Consequently, the bandwidth describing the overlap between the Mn3d and O2p orbital is reduced and this affects physical properties. The studied samples were also characterized by complex impedance spectroscopy in a wide range of temperature and frequency. DC conductance results show that doping by Bi suppresses the metal behavior observed at low temperatures in the parent compound. The conductivity decreases when increasing the concentration of Bi due to the reduction of the specific free volume. AC conductivity measurements were split in two parts: The metallic region is well described by the classical Drude model and the semiconductor one was well fitted by the universal Jonscher power law. Results show that the conduction mechanism is described by non-overlapping small polaron tunneling (NSPT) model. Besides, the Cole-Cole plots which are fitted by adequate equivalent circuits show the contributions of grain and grain boundaries in the conduction mechanism. At high temperatures, the total conductivity tends to be governed by grains. Dielectric results show that the Pr0.75Bi0.05Sr0.2MnO3 sample has better dielectric properties than Pr0.7Bi0.1Sr0.2MnO3. Dielectric loss is analyzed by Giuntini theory and correlated with conduction losses. The energy required for carriers to jump over the potential barriers is determined.

On the emission of radiation by an isolated vibrating metallic mirror

Quantum electrodynamics predicts the appearance of radiation in an empty cavity in which one of the mirrors is vibrating. It also predicts the appearance of radiation from an isolated vibrating mirror. Such effects can be described within the framework of classical electrodynamics. We present the qualitative explanation of the effect, along with the results of numerical simulation of the emission of radiation by an isolated vibrating metallic mirror, which can be induced by mirror illumination by an ultrashort pulse of light. The dynamics of conduction electrons in the metallic mirror is described by the classical Drude model. Simulation was performed for the cases of mirror illumination by either a bipolar or a unipolar pulse.

An Analytical Quantum Model to Calculate Fluorescence Enhancement of a Molecule in Vicinity of a Sub-10 nm Metal Nanoparticle.

An analytical quantum model is used to calculate electrical permittivity of a metal nanoparticle located in an adjacent molecule. Different parameters, such as radiative and non-radiative decay rates, quantum yield, electrical field enhancement factor, and fluorescence enhancement are calculated by such a model and they are compared with those obtained by using the classical Drude model. It is observed that using an analytical quantum model presents a higher enhancement factor, up to 30%, as compared to classical model for nanoparticles smaller than 10 nm. Furthermore, the results are in better agreement with those experimentally realized.

Universal Faraday Rotation in HgTe Wells with Critical Thickness.

The universal value of the Faraday rotation angle close to the fine structure constant (α≈1/137) is experimentally observed in thin HgTe quantum wells with a thickness on the border between trivial insulating and the topologically nontrivial Dirac phases. The quantized value of the Faraday angle remains robust in the broad range of magnetic fields and gate voltages. Dynamic Hall conductivity of the holelike carriers extracted from the analysis of the transmission data shows a theoretically predicted universal value of σ_{xy}=e^{2}/h, which is consistent with the doubly degenerate Dirac state. On shifting the Fermi level by the gate voltage, the effective sign of the charge carriers changes from positive (holes) to negative (electrons). The electronlike part of the dynamic response does not show quantum plateaus and is well described within the classical Drude model.

Quantum Effects of Nonlocal Plasmons in Epsilon-Near-Zero Properties of a Thin Gold Film Slab

Dispersion properties of metals and propagation of quantum plasmons in the high photon energy range are studied. The nonlocal dielectric permittivity of a metal is determined by the quantum plasma effects and is calculated by taking into account collisions between free charge carriers and the lattice. The properties of epsilon-near-zero material are investigated in a thin gold film slab. The spectrum and the damping rate of the quantum plasmons are obtained for a wide range of energies, and the electron’s wave function is calculated in both classical and quantum limits. It is shown that the quantum plasmons exist with a propagation length of 1–10 nm, which strongly depends on the electron energy. The propagation length is found to be much larger than the propagation length in the classical regime, where the former is comparable to the atomic radius and the average inter-particle distance. It is found that the spatial localization of the electron wave function is extended due to the quantum effects. It is also shown that the damping of electromagnetic waves in the high photon energy range decreases when the photon energy decreases which is opposite to the conclusions obtained from the classical Drude model in this range.

Charge-Tunable Quantum Plasmons in Colloidal Semiconductor Nanocrystals

Nanomaterials exhibiting plasmonic optical responses are impacting sensing, information processing, catalysis, solar, and photonics technologies. Recent advances have expanded the portfolio of plasmonic nanostructures into doped semiconductor nanocrystals, which allow dynamic manipulation of carrier densities. Once interpreted as intraband single-electron transitions, the infrared absorption of doped semiconductor nanocrystals is now commonly attributed to localized surface plasmon resonances and analyzed using the classical Drude model to determine carrier densities. Here, we show that the experimental plasmon resonance energies of photodoped ZnO nanocrystals with controlled sizes and carrier densities diverge from classical Drude model predictions at small sizes, revealing quantum plasmons in these nanocrystals. A Lorentz oscillator model more adequately describes the data and illustrates a closer link between plasmon resonances and single-electron transitions in semiconductors than in metals, highlighting a fundamental contrast between these two classes of plasmonic materials.