Free Electron Model Research Articles

Potential electron emission induced by multiply charged ions in thin film tunnel junctions

Thin film metal-insulator-metal tunnel junctions are used to investigate the electronic excitation process induced by the impact of multiply charged ions onto a metallic surface. Hot charge carriers (electrons and holes) generated by the dissipation of the kinetic and potential energies of the projectiles are detected as an ion induced internal emission current from the bombarded ``top'' metal film into the ``bottom'' substrate electrode. Results are presented for ${\text{Ar}}^{q+}$ ions with a kinetic impact energy of 1 keV and charge states $q=1--8$ impinging onto an ${\text{Ag-AlO}}_{x}\text{-Al}$ junction. It is shown that the internal emission yield exhibits an approximately linear dependence on the potential energy of the projectile. At low potential energy, a bias voltage applied between the two metal films is found to strongly influence the internal emission current, whereas this influence becomes much weaker with increasing projectile charge state. The results are shown to be qualitatively well described in the framework of a thermodynamical free-electron model.

Plasmonic-based Detection of NO2 in a Harsh Environment

The surface plasmon resonance (SPR) band response of Au nanoparticles embedded in yttria-stabilized zirconia (Au-YSZ) nanocomposite films are extremely sensitive to high-temperature catalysis processes. By varying the concentration of NO2 in air and O2 in N2, we show that Au-YSZ nanocomposite films are sensitive to changes in NO2 concentration in air, with a detection limit of 5 ppm. We also show a linear relation between the change in the equilibrium ratio, pO2−1/8pNO2−1/4, contributing to oxygen ion diffusion into and out of the YSZ matrix, and the change in the square of the SPR band peak position, confirming an interpretation of the experimental results using the free electron theory model for the optical properties of metal nanoparticles. Furthermore, we observe that there is a temperature dependence in the sensor response of the Au-YSZ nanocomposite film that has an inverse relation to concentrations of surface adsorbed O− species on the YSZ matrix.

A theoretical study of a spin polarized transport and giant magnetoresistance: The effect of the number of layers in a magnetic multilayer

This study presents a quantum-mechanical free electron model for analyzing a spin polarized transport and current-perpendicular-to-the-plane giant magnetoresistance (CPP-GMR) in a more realistic way. The CPP-GMR is evaluated by using three spin resolved conductance parameters based on the Landauer conductance formula. In a ballistic regime, a transfer-matrix method is used to calculate the spin dependent transmission probability as a function of the transverse mode. A spin dependent conduction band structure is constructed by extracting parameters of the free electron model, such as the atomic magnetic moments and the conduction electron densities, from the spin dependent layer-decomposed density of states of the Cu and Co interfacial layers in a Cu5/Co11 slab; these calculations are derived from the density functional theory. As a result, this study shows that the CPP-GMR in a [Cu(5ML)∕Co(11ML)]n magnetic multilayer (n=2–5) with a 35ML×35ML cross section is in the range of 60%–111%. It is qualitatively comparable to the calculation results of first principles. This study also uses transmission probability to explain the increase of spin dependent scattering and CPP-GMR as a function of the number of layers in the [Cu∕Co]n magnetic multilayer. Moreover, the study confirms that modification of the free electron model by quantum-mechanical methods can be applied to calculations of a spin polarized transport and CPP-GMR in a specific material system.

Direct Observations of Electrochemical Reactions within Au−YSZ Thin Films via Absorption Shifts in the Au Nanoparticle Surface Plasmon Resonance

The surface plasmon resonance (SPR) band of Au nanoparticles embedded in an YSZ matrix was monitored at 500 °C under varying gas exposure concentrations of H2 and O2 in N2. Because the peak position of the SPR band relies closely on the number of driven oscillating free electrons per gold nanoparticle, we were able to monitor electrochemical charge transfer from Au nanoparticles to diffusing oxygen ions by monitoring the optical properties of the Au−YSZ nanocomposite thin film, specifically the peak position of the SPR band. A direct relation was observed for the change in the equilibrium ratio, pH21/4/pO21/8, contributing to oxygen ion diffusion into and out of the YSZ matrix, and the change in the square of the SPR band peak position. Free electron theory states that this change in the square of the SPR band peak position is directly proportional to the change in conduction electrons available per Au nanoparticle; thus, our observations agree with the expected trend for charge transfer vs the redox gas ...

Measurements of Terahertz Electrical Conductivity of Intense Laser-Heated Dense Aluminum Plasmas

We report the electrical conductivity of laser-produced warm dense aluminum plasmas measured using single-shot ultrafast terahertz (THz) frequency spectroscopy. In contrast with experiments performed at optical frequencies, measurements based upon THz probe reflectivity directly determine a quasi-dc electrical conductivity, and therefore the analysis does not require a free-electron Drude model based extrapolation to recover the near zero frequency conductivity. In fact, our experimental results indicate that the Drude model breaks down for warm (>0.6 eV), moderate-dense (<1.6 g/cm(3)) aluminum at THz frequencies. A calculation of THz reflectivity over a non-Fresnel boundary in dense plasmas is also presented.

Spectroscopic ellipsometry study of Co‐doped TiO2 films

AbstractCo‐doped TiO2 films were characterized by spectroscopic ellipsometry to determine their thickness, deposition rate and optical properties as function of substrate temperature and background gas composition. To fit the data we used a combination of a single Tauc–Lorentz oscillator with the Drude free electron model to take in account the free electrons present in the film. The Co doping and the addition of H2 to the gas phase during film growth cause the formation of a titanium oxide which containsfree electrons that absorb the energy of the red part of the spectrum, causing k to increase. The n of the films at 1.5 eV is about 2.3 eV. The fittings also show that the n of films decreases and k increases at the surface. This can be related to a segregation of Co to the surface, which in some cases, of high substrate temperature and high H2 flow during deposition, can lead to an even higher concentration of free electrons at the surface. (© 2008 WILEY‐VCH Verlag GmbH &amp; Co. KGaA, Weinheim)

Surface Plasmon Polaritons and Screened Plasma Absorption in Indium Tin Oxide Compared to Silver and Gold

This study addresses the ability of a conducting metal oxide to act as a material capable of supporting surface plasmon polaritons (SPPs). By use of a two-phase Fresnel model that provides insight into the difference between polariton-induced and absorptive decreases in reflectivity, indium tin oxide (ITO) is compared to the noble metals gold and silver, which are widely used as materials for surface plasmon resonance (SPR) detection of analytes. The study builds on application of the Drude free electron model that provides an explanation for the observed optical extinctions as a function of ITO film thickness, including the dependence of wavenumber on angle, by use of only two adjustable parameters, the plasma frequency ωp and the damping Γ. Herein, models of the dispersion and absorption include both the real and imaginary parts of the dielectric function to obtain the plasma absorption spectra and dispersion curves for ITO, Ag, and Au. ITO is found to have surface plasmon dispersion curves and plasma a...

One-dimensional combined field and thermionic emission model and comparison with experimental results

An integrated theoretical model has been developed to predict the entire range of emission from thermionic to field emission, including the mixed emission regime. The model assumes a Sommerfeld free electron model supply function, for which the Fermi-Dirac distribution applies with a nonzero temperature. The electron transmission coefficient is calculated in one dimension using a transfer matrix method (TMM) to solve the steady-state Schrödinger equation. Emission current densities have been measured for a periodic copper knife-edge cathode to compare with the TMM model result. It is shown that the computational result utilizing this model provides good agreement with the experimental data. Unambiguous and reliable estimates of the effective field enhancement factor βeff (βeff=Es∕Eg, where Es is the cathode surface electric field and Eg is the gap electric field between the cathode and anode) and the effective work function ϕeff are obtained from experimental measurements using this model by simultaneously fitting thermionic and field emission data for the cathode. Comparing the experimental and theoretical results reveals that finite temperature thermal contributions to the current emission can be significant in the operation of many field emission cathodes.

Free-electron model of current-induced spin-transfer torque in magnetic tunnel junctions

Spin and charge transport in a biased planar tunnel junction with two ferromagnetic electrodes are analyzed theoretically in the spin-polarized free-electron-like model. Tunneling current and both in-plane and out-of-plane components of the current-induced spin torque exerted on ferromagnetic components of the junction are determined as a function of the angle between magnetic moments of the electrodes, barrier height and thickness, and spin polarization of the electrodes. The out-of-plane component of the torque is found to be comparable in magnitude to the in-plane component. Numerical results for junctions with sufficiently high barriers show that the in-plane torque exerted on the sink electrode increases monotonically with increasing spin polarization (spin splitting) of the electron band in the source electrode, while the out-of-plane torque increases with increasing spin polarization of the electron bands in both electrodes. In junctions with thick and low barriers, the torque components can change their sign. The bias voltage dependence of the in-plane torque is not symmetric with respect to the bias reversal, even in symmetric junctions. When one of the ferromagnetic electrodes is replaced by a ferromagnetic layer of finite thickness (followed by a nonmagnetic electrode), both components of the spin torque depend significantly on the layer thickness due to the size effect and quantum well states formed in the thin magnetic layer.

Dependence of the optical properties of UHV deposited silver thin films on the deposition parameters and their relation to the nanostructure of the films

Silver films were deposited on glass substrates under different deposition conditions, i.e. different film thicknesses, deposition rates and deposition angles. Their optical properties were measured by spectrophotometry in the spectral range of 185–3300 nm. The Kramers–Kronig method was used to analyze the reflectivity curves of the silver films to obtain their optical constants. The influence of substrate temperature on the microstructure of thin metallic films, the structure zone model (SZM), is well established, whereas there has been some previous work on the influence of film thickness and morphology, deposition rate and deposition angle on the microstructure and morphology of thin films. An effective medium approximation (EMA) analysis was used to establish the relationship between the atomic force microscopy results, SZM predictions and EMA results, and hence the optical properties of silver thin films. The predictions of the Drude free-electron theory are compared with experimental results for dielectric functions of Ag films produced under different deposition conditions. The real part of the dielectric constant increases with film thickness and decreases with increasing deposition rate and with increasing incidence angle, whereas the imaginary part of the dielectric constant decreases with increasing film thickness and deposition rate and with decreasing incidence angle over the whole energy range measured, including the interaband and interband regions.

Linear and nonlinear second-order polarizabilities of hemispherical and sector-shaped metal nanoparticles

In this paper, we present results of calculations of linear and second-order nonlinear polarizabilities of sector-shaped metallic nanoparticles hemisphere is a special case using free electron theory. The dependences of the ground state electron density distribution and polarizabilities on various shape parameters of sector are analyzed. The ground state electron densities near the corners and edges of sector-shaped nanoparticle are very low and do not contribute to the linear and second-order polarizabilities. The second-order polarizability is found to depend strongly on the angle of the sector and is shown to be proportional to the product of an appropriately defined asymmetric volume of the particle and the third power of the electron cloud length.

Stability of metallic thin films studied with a free electron model

The stability of metallic thin films is studied with a free electron model, which is popularly known as the model of ``particle in a box.'' A detailed theoretical framework is presented, along with discussion on typical metals, such as Pb, Al, Ag, Na, and Be. This simple model is found to be able to describe well the oscillation pattern of stability for continuous metallic films. In particular, it yields even-odd oscillations in the stability of Pb(111) film, consistent with both experimental observation and ab initio results. However, the free electron model is too crude to predict at what thickness a film is stable. Film stability is further examined with a model of ``particle in a corrugated box,'' where a lattice potential is added along the vertical direction of a film. The effect of lattice potential is found not substantial.

Quantum size effect of electron density in ultra-thin metal films and its influence on the interlayer relaxation

Further minimization of electronic devices and microelectromechanical systems (MEMS) requires the feature sizes of relevant materials to be shrunk significantly. In such a case, boundary effects, such as interfaces and surfaces, become remarkable, especially in nanometer scale, which must affect their microstructures and properties. In this work, we have analyzed the distribution of electron charge density in Cu and Al ultra-thin films using free electron model. The results show that an electrostatic field may come into being due to quantum size effect, and the interlayer separations must relax to decrease the Coulomb energy, the thinner the films, the larger the relaxation. More interestingly, two opposite deviating directions of the center of negative charges result in two absolutely distinct interlayer relaxations: inwards for Cu and outwards for Al.

A theoretical study of an amorphous aluminium oxide layer used as a tunnel barrier in a magnetic tunnel junction

AbstractAn amorphous aluminium oxide layer is assumed to be a condensed gas phase composed of (AlOx)N molecules. The total energy and the electron affinity of (AlOx)N molecules is calculated by using a DFT program. The effective tunnel barrier height in the MTJ is presumed from a difference between the work function of the ferromagnetic metal and the electron affinity of (AlOx)N molecules. By using a quantum‐mechanical free electron model the TMR and the R×A product are calculated as a function of the thickness of an amorphous aluminium oxide layer in the F/I/F tunnel junction. It is inferred that the tunnel barrier width determined by subtracting 6 Å from the thickness of an amorphous aluminium oxide layer is more suitable to explain an experimental report qualitatively than the tunnel barrier width equivalent to the thickness of an amorphous aluminium oxide layer. (© 2007 WILEY‐VCH Verlag GmbH &amp; Co. KGaA, Weinheim)

Sound-Wave-Like Collective Electronic Excitations in Au Atom Chains

Sound-wave-like collective excitation in Au atom chains on the Si(557) surface is investigated. Electron scattering spectroscopy using a highly collimated slow electron beam has detected a characteristic low-energy one-dimensional (1D) plasmon (wire plasmon) that is confined in the atom chains. Theoretical analysis adopting a quantum-mechanical scheme beyond the free-electron model indicates a significant dynamic exchange-correlation effect due to strong 1D confinement. By cooling to below 100 K, we have detected for the first time a significant change in the plasmon dispersion in a tiny momentum and energy region, which definitely reflects a gap opening due to a metal-to-insulator transition of the atom chains.

Estimation of the density of localized electronic states for multiwalled carbon nanotubes

We estimate the density of localized electronic states in a multiwalled carbon nanotube with defects within the framework of disordered systems in the light of free-electron theory. In this context, we start from previous results concerning electrical conductance which is quantized and fractional with respect to the values taken on by the corresponding quantum number.

Ab initio calculation of the lifetime of quasiparticle excitations in transition metals within the framework of the GW approximation

This paper reports on the results of ab initio calculations of the lifetimes τ of quasiparticle excitations in cubic d transition metals (V, Nb, Ta, Mo, W, Rh, Ir) within the GW approximation, which represents the self-energy of quasiparticles by the product of the Green’s function and the dynamically screened Coulomb potential. A comparative analysis of the dependences of the lifetime τ(ω) on the excitation energy ω is performed, and the specific features of the dependences τ(ω) in going from metal to metal within a particular group and along the d periods are revealed. It is found that the dependence τ(ω) on the excitation energy differs from the dependence τ ∼ ω−2 obtained within the free-electron model and is primarily determined by the density of d states localized in the vicinity of the Fermi level and by the electron interaction screened by the d electrons.

Probing e–e interactions in a periodic array of GaAs quantum wires

We present the results of nonlinear tunnelling spectroscopy between an array of independent quantum wires and an adjacent two-dimensional electron gas (2DEG) in a double-quantum-well structure. The two layers are separately contacted using a surface-gate scheme, and the wires are all very regular, with dimensions chosen carefully so that there is minimal modulation of the 2DEG by the gates defining the wires. We have mapped the dispersion spectrum of the one-dimensional (1D) wires down to the depletion of the last 1D subband by measuring the conductance G as a function of the in-plane magnetic field B, the interlayer bias V dc and the wire-gate voltage V wg . There is a strong suppression of tunnelling at zero bias, with temperature and dc-bias dependences consistent with power laws, as expected for a Tomonaga–Luttinger liquid caused by electron–electron interactions in the wires. In addition, the current peaks fit the free-electron model quite well, but with just one 1D subband there is extra structure that may indicate interactions.

Spin-mixing conductances of thin magnetic films from first principles

We present a first-principles theory of the spin-mixing conductance for a thin ferromagnetic film embedded epitaxially between two nonmagnetic metallic electrodes. The complex spin-mixing conductance is formulated as a linear response of the spin torque experienced by the film due to the spin accumulation in one of the electrodes. The derivation is based on nonequilibrium Green's functions; the obtained result for the torque response is in agreement with the response of spin fluxes on both sides of the ferromagnet as well as with expressions derived within the Landauer-B\"uttiker scattering theory. Numerical implementation of the developed formalism employs the tight-binding linear muffin-tin orbital method and calculations are performed for selected metallic and half-metallic ferromagnetic films relevant for spintronics applications. The spin-mixing conductance of the $\mathrm{Cu}∕\mathrm{Ni}∕\mathrm{Cu}(100)$ system is found to exhibit pronounced oscillations as a function of Ni thickness; their period is explained by spin-resolved Fermi-surface properties of nickel. Investigated half-metallic films include the full-Heusler ${\mathrm{Co}}_{2}\mathrm{Mn}\mathrm{Si}$ compound and the diluted (Ga,Mn)As magnetic semiconductors attached to nonmagnetic Cr(100) leads; the imaginary part of their spin-mixing conductance has a magnitude comparable to the real part. This unusual feature has been qualitatively explained in terms of a free-electron model.

Front propagation into unstable metal nanowires

Long, cylindrical metal nanowires have recently been observed to form and be stable for seconds at a time at room temperature. Their stability and structural dynamics is well described by a continuum model, the nanoscale free-electron model, which predicts cylinders in certain intervals of radius to be linearly unstable. In this paper, I study how a small, localized perturbation of such an unstable wire grows exponentially and propagates along the wire with a well-defined front. The front is found to be pulled and forms a coherent pattern behind it. It is well described by a linear marginal stability analysis of front propagation into an unstable state. In some cases, nonlinearities of the wire dynamics are found to trigger an invasive mode that pushes the front. Experimental procedures that could lead to the observation of this phenomenon are suggested.