Simple Drude Model Research Articles

Absolute photoabsorption measurements of Mg, Al, and Si in the soft-x-ray region below the L2,3 edges.

Absolute measurements of the photoabsorption coefficient of Mg, Al, and Si from 25 eV up to the ${\mathit{L}}_{3}$ absorption edge are presented. Transmission measurements were performed on free-standing thin films using a laser-produced plasma source. The surface oxide is corrected for by taking the ratio of the absorption for different film thicknesses. The values so obtained are, in general, lower than have been reported in the literature. Structure below the edge is observed for Al and Si. Despite the fact that the absorption below the ${\mathit{L}}_{3}$ edge is due to the valence or conduction electrons, the magnitude of the absorption coefficient for the solid is much higher than is predicted by a simple Drude model and is close to that expected from calculations for the free atom.

Optical properties of incommensurately modulated calaverite, AuTe2

The optical reflection spectrum of incommensurately modulated calaverite is presented. Using a Kramers-Kronig analysis the dielectric function is derived from the reflection spectrum. The results for the imaginary part of the dielectric function are qualitatively discussed in terms of absorption by phonon, free electron and interband scattering. The phonon contribution clearly shows the influence of the incommensurability by the activity of phonons with k not=0. The free electron scattering can be understood in terms of a simple Drude model. The interband scattering is found at a lower frequency than predicted from electronic band structure calculations.

Optical reflectivity of Si above the melting point

AbstractThe variation of the optical reflectivity of a Si single crystal during irradiation with two successive Nd:YAG laser pulses is investigated with ns resolution. The first pulse melts the surface and therefore the reflection coefficient increases up to the value of the metallic liquid at the melting temperature (1685 K). Upon further heating the surface with the second, time‐delayed pulse, a decrease of the reflection coefficient is observed, resulting from the temperature‐dependent dielectric function of the molten Si. The largest decrease in the reflectivity that could be reached before damaging the surface amounted to 9% for a probe wavelength of 633 nm. The application of a simple Drude model for the optical constants above the melting point is discussed.

Microwave reflection measurements on doped semiconductors with picosecond transient radiation

Broadband microwave reflection spectroscopy using the COMITS (coherent microwave transient spectroscopy) method is described. COMITS is particularly suited to reflection studies because the picosecond transient radiation emitted from planar antennas is strongly linearly polarized. The validity of the technique is verified by reflection measurements on isotropic and anisotropic dielectrics. Reflection studies on a series of doped silicon samples demonstrate that the carrier dynamics in the 15-140-GHz frequency range are well described by a simple Drude model. >

Electronic Structures of 2,7-Bis(methylthio)-1,6-dithiapyrene (MTDTPY) Charge Transfer Complexes

Abstract Polarized reflection spectra were measured on two charge-transfer complexes of 2,7-bis(methylthio)-1,6-dithiapyrene (MTDTPY) with chloranil and 7,7,8,8-tetracyanoquinodimethane (TCNQ), which showed metallic conductivity. In spite of short intercolumnar S–S contacts, the spectra showed a strong one-dimensional character. The optical conductivity spectra, σ(ω), and real part of the dielectric constant, ε′(ω), along the stack axis were obtained by means of Kramers–Kronig transformation. The conductivity spectra and the dielectric constant of both complexes substantially differ from the simple Drude model. These results were analyzed with a one-dimensional electron localization model in a disordered system with the optical parameters: ωp=13500 cm−1, τi=1.6×10−15s (τi−1=3300 cm−1) for chloranil complex and ωp=12000 cm−1, τi=2.5×10−15s (τi−1=2100 cm−1) for TCNQ complex.

Carrier dynamics of electrons and holes in moderately doped silicon.

A time-domain spectroscopic technique, based on the generation and detection of a collimated beam of subpicosecond broadband terahertz pulses, is used to measure the absorption and dispersion of n- and p-type silicon, with resistivities of 0.1, 1, and 10 \ensuremath{\Omega} cm in the submillimeter range of 0.1--2 THz. From the transmission measurements performed at room temperature and at 80 K, the absorption and dispersion, and concomitantly the full complex conductivity, of the doped silicon could be obtained. The results provide an accurate view on the dynamics of the electrons and the holes. Although the simple Drude model, with an energy-independent relaxation time, gives a surprisingly accurate description of the observed carrier dynamics, the measurements do show that some refinements are needed. An extended model, with an energy-dependent carrier-relaxation rate, can explain most of the observed deviations from the simple Drude model.

Intersubband transitions and subband-Landau-level coupling in a vicinally oriented Si n-type inversion layer.

Intersubband transitions on (118) Si $n$-type metal-oxide-semiconductor field-effect transistors have been observed with light propagation parallel to the magnetic field and field normal to the sample surface. In this geometry, coupling of the cyclotron motion to the intersubband transition dipole results from the anisotropic energy surfaces. Intersubband transition energies are unaffected by the magnetic field for subband transition energies much greater than cyclotron resonance. When the two transitions approach each other, large subband-Landau-level coupling is observed and is explained by a simple Drude model calculation.

Kinetics of high-density plasmas generated in Si by 1.06- and 0.53- microm picosecond laser pulses.

The dynamics of high-density (${10}^{19}$${10}^{21}$ ${\mathrm{cm}}^{\mathrm{\ensuremath{-}}3}$), high-temperature (300${T}_{e}$3000 K) plasmas, generated in silicon by single 1.06- and 0.53-\ensuremath{\mu}m picosecond laser pulses, is simulated with a self-consistent model based on the Boltzmann transport equation. Balance equations, which include possible plasma degeneracy effects, are used to obtain the spatial and temporal evolution of the lattice temperature as well as the carrier density and temperature. We compare predictions of the model, which employs parameters extracted from near-equilibrium experiments, with data from recent experiments which measured the melt threshold or time-dependent infrared reflectivity. The model is able to account quantitatively for the weak dependence of the melt threshold on pulse width at 0.53 \ensuremath{\mu}m as well as the strong dependence at 1.06 \ensuremath{\mu}m. In the former case, direct absorption and lattice parameters dominate energy evolution, but at 1.06 \ensuremath{\mu}m two-photon absorption and plasma dynamics dominate. The infrared reflectivity measurements are found to be consistent with a simple Drude model of the dielectric constant and the calculated plasma kinetics when one accounts for nonzero probe pulse widths and plasma spatial inhomogeneity. When this is done there is no need to introduce ultrashort momentum relaxation times or plasmon assisted recombination as speculated on in the recent literature. Finally, contrary to earlier suppositions, it is found that the carrier temperature can exceed the lattice temperature by more than ${10}^{3}$ K during pulses as long as 100 psec even for subpicosecond carrier-phonon relaxation times. It is also found that the carrier temperature exhibits two peaks as a function of time, one due to direct laser heating of the carriers and the other due to Auger heating.

Picosecond laser melting and evaporation of GaAs surfaces

Picosecond laser-induced melting and evaporation of GaAs surfaces are studied. The high reflectivities of molten GaAs observed at fluences above the melting threshold have a wavelength dependence inconsistent with a simple Drude model for a metallic molten GaAs surface. The observations at high laser fluences suggest that the liquid-vapor phase transition is initiated by a fast-expanding, high-density fluid.

Time-Resolved Optical Studies of Picosecond Laser Interactions With Gaas Surfaces

ABSTRACTThe interactions of picosecond laser pulses at 532 nm wavelength with GaAs surfaces have been studied with time-resolved reflectivity and transmission measurements at three probe wavelengths. At fluences below the melting threshold, the laser-generated electron-hole plasma is limited to a density below ≈1020cm−3. The high reflectivities of molten GaAs observed at fluences above the tlhreshold have a wavelength dependence inconsistent with a simple Drude model for a metallic GaAs molten layer. At high fluences, the evolution of a laser-induced vapor cloud is observed.

Nonreciprocity in the optical reflection of magnetoplasmas

We measured the reflectivity on a slab of $n$-type InSb with an incident angle of 45\ifmmode^\circ\else\textdegree\fi{} with different far-infrared laser frequencies of 337-, 311-, and 119-\ensuremath{\mu}m wavelengths as a function of applied magnetic field $B$ between 0 and 10 T. The field was applied in the plane of the surface perpendicular to the reflection plane. We observed clear evidence of nonreciprocal behavior in the reflectivity with respect to field reversal and light-propagation reversal. A simple Drude model accounts satisfactorily for this effect. The influence of damping, crucial for the existence of this effect, is discussed within the framework of electrodynamics as well as with thermodynamic arguments, generalizing Kirchhoff's law of radiation.

3d transition metal intercalates of the niobium and trantalum dichalcogenides

Abstract Optical reflectivity spectra of the first-row transition metal intercalation complexes, M1/3NbS2 and M1/3TaS2 (M = V, Cr, Mn, Fe, Co, Ni), Mn1/4 TaS2 and Fe1/4 NbSe2 have been measured at room temperature and compared with those for the host compounds, 2H NbS2, 2H TaS2 and 2H NbSe2. It is found that a simple rigid-band model is inconsistent with the data and that it is necessary to include both broadening of the valence and the lowest conduction band through increased interlayer interactions and broadening of the 3d energy levels on the intercalate ions through interaction with the Nb or Ta d-band conduction electrons. Quantitative analysis of the free-carrier reflectivity edge is performed by fitting to a simple Drude model from which the free-carrier effective mass and scattering time can be deduced.

The electrical conductivity and optical reflectance of graphite-SbF 5 compounds

Graphite intercalation compounds were prepared from pyrolytic graphite and SbF 5 or SbF 5-HF mixtures. The compounds were characterized by c-axis thickness increase, gravimetric and X-ray analysis, and in some cases by elemental analysis. Measurements were made of the room temperature, basal-plane, electrical conductivity and the optical reflectance from 0.07 to 2.0 eV. The results of these measurements show clearly that the optical reflectance data for these materials is not amenable to analysis by a simple Drude model and that the maximum a-axis conductivity is approx. 1 3 that of copper.

Optical and Electrical Properties of Graphite Intercalated withHNO3

Drude edges are observed in reflectance spectra and compared with the dc transport measurements in the lamellar compounds ${\mathrm{C}}_{6n}\mathrm{H}{\mathrm{NO}}_{3}$ with $n=1, 2, \mathrm{and} 3$. Both measurements confirm the general metallic character of these materials, but the optical data are inconsistent with a simple Drude model. We suggest that this is due either to a complex background dielectric constant or to a multiple-carrier Fermi surface.

Optical reflectivity of (SN) x-single crystals

The optical reflectivity of (SN) x single crystals was measured in the visible region and the near infrared with light polarized parallel and perpendicular to the polymer chain axis. Whereas the reflectivity for light polarized perpendicular to the chain axis is approximately constant in this region, the reflectance for light polarized parallel to the chain axis exhibits a pronounced plasma edge at 2.72 eV. A simple Drude model was used to analyse the data. Differences between these results and those of previous film measurements are discussed.

Optical properties of V, Ta, and Mo from 0.1 to 35 eV

The absorptivity or reflectivity of crystals of V, Ta, and Mo was measured from 0.1 to 35 eV. The data were Kramers-Kronig analyzed to determine the dielectric functions. The inadequacy of a simple Drude model to describe absorption at low energy is discussed. Structure in the dielectric functions is discussed in terms of direct interband transitions which extend to about 18 eV. Features below 6 eV are attributed to transitions near $\ensuremath{\Sigma}$, $G$, and perhaps along $P(D)N$ for V, Ta, and Mo, with additional transitions in Mo from the $\ensuremath{\Delta}$ portion of the Brillouin zone. High-lying energy bands are identified as giving rise to high-energy structure in the dielectric functions. Results obtained previously for Nb are reviewed and compared. The electron-energy-loss functions were calculated and are discussed in terms of volume and surface plasmons. These metals all exhibit two volume and two surface plasmons.

Equations for the Theory of Response and Transport in Statistical Mechanics

Taking the viewpoint that a complete solution of the Liouville equation contains much more information than is necessary in response theory (wherein one is concerned with a particular response), projection techniques are employed to introduce a shortcut in the problem. The treatment supplements and completes the formalism initiated in a previous publication and yields a general equation which is more relevant to response theory in the usual sense. The most natural application is to the theory of transport. The general transport equation is analyzed in the context of electrical conduction. Meaningful similarities to the simple classical Drude model of conduction are exhibited; the relationship of this exact formalism to the Kubo theory of linear response is shown, an exact solution for a step-function stimulus and approximation procedures which go beyond the linear regime are presented, and an expression for the electrical resistivity is explicitly calculated thus making contact with an earlier paper by Kenkre and Dresden. The response equation is also analyzed in the context of electric and magnetic polarization.

Determination of electrical conductivity parameters of metals from infrared measurements

Values for collision lifetime in silver, platinum and nickel deduced from Hagen and Rubens' observations on infrared emissivity differ from those deduced from the temperature coefficient of emissivity obtained from these data. Assuming the temperature coefficient of emissivity gives the true collision lifetime, the assumption of a single lifetime is invalid for platinum and nickel and it is concluded that the simple Drude model for optical constants is invalid for multivalent metals. It is claimed that, providing a detailed description of conductivity is used, Drude theory may be applicable to all metals. Metals may be divided into three categories according to whether the conductivity and Fermi surface are isotropic or the conductivity is isotropic but the Fermi surfaces are anisotropic (termed quasi isotropic), or the conductivity and Fermi surfaces are anisotropic and the metals are birefringent. Measurements on optical behaviour of metals may enable a description of the anisotropies in effective mass and collision lifetime of multivalent metals to be given. A similar proposal has been given by Roberts. (1) This proposal differs from Roberts' in several particulars. It is intended to show that the Hagen and Rubens' data may be interpreted to prove their law invalid for their experimental conditions, and to imply that by following the advice of Kronig (2) increasingly rational interpretations of electrical conductivity in metals may be attainable.