Stabilized Jellium Model Research Articles

On the specific behavior of the work function and surface potential of an asymmetric metal-dielectric nanosandwich

We examine thin film on a dielectric substrate (vacuum/Al/SiO2) in the stabilized jellium model and the Kohn–Sham method. We investigate surface and size effects on the effective potential and the electron work function, and analyze the spatial distributions of electrons and potentials. It is found that a dielectric environment generally leads to a decrease in the work function. The effect of dielectric confinement for the electron work function of the asymmetric metal-dielectric nanosandwiches is reduced only by the surface area weighted average value of the dielectric constants. This conclusion follows from the application of the Gauss theorem for a conducting sphere with an inhomogeneous dielectric coating. The flow of electrons from the dielectric face to the vacuum one due to the contact potential difference manifests itself in the appearance of an additional dipole between the left and right face within the spatial distributions of ions. This leads to the fact that in a vacuum the electrostatic and effective potentials change sign twice, as a result of which a potential barrier appears above the vacuum level. We introduced the position of an electron conduction band in the dielectric as the input parameter in the self-consistency procedure for one of the sandwich approximations. As it turned out, the barrier height depends only on the used local or non-local approximation of the exchange-correlation energy. The nontrivial origin and behavior of the calculated effective potential on the vacuum side of the film, as well as the reasons for it, are discussed.

Quantum hydrodynamic model for noble metal nanoplasmonics

The quantum hydrodynamic model (QHDM) has become a versatile and efficient tool for plasmonics at nanometer and even subnanometer length scales, but the theory is principally applicable only to simple metals. For the most common plasmonic materials, i.e., noble metals, QHDM has not been duly justified to describe their optical responses. In particular, when noble metal structures interface with dielectric materials, electron spillover plays an important role. Although a background optical permittivity is usually invoked in Amp\`ere's law to encompass the $d$-band electrons' effect on optical responses in a direct manner, their indirect effects, e.g., acting via conduction electrons, still remain elusive. Here we identify these indirect effects and develop a near-field potential ${U}_{\mathrm{aff}}$ refined QHDM (U-QHDM), in which the $d$-band electrons' effects on the conduction electrons are recognized and the electrostatic properties of dielectric are incorporated. We report the detailed procedures of calibrating U-QHDM. Material-independent model parameters are fitted with density functional theory (DFT) calculations for simple metals. Last, the calibrated U-QHDM is benchmarked against DFT and time-dependent DFT within stabilized jellium model for Ag, Au, and Al nanostructures interfacing with dielectrics. We expect U-QHDM will be a valuable asset for the rapidly developing field of extreme nanophotonics.

First principles study of adsorption and simulation of desorption properties of [formula omitted] surface alloy

The FCC structure of Pd1−xAgx (x= 0.25, 0.50, 0.75) alloys is considered as a fuel cell component in this study. We have looked into its qualities as a component of a fuel cell to see whether it could be potentially used as an alternative replacement of the Pt catalyst. We used Density Functional Theory (DFT) to study H and CO interaction with the surface, and simulation of desorption process to study H and CO desorption from the surface. The bulk modulus and equilibrium crystal structures of Pd1−xAgx alloys were computed using the GPAW code within plane wave basis set & a PBE exchange correlation functional treatment. The best values of lattice constant for the system are obtained by total energy calculations versus lattice cell volumes as fitted to the stabilized jellium model. Surface energies, cohesive energies, and binding energy of Pd1−xAgx alloys were computed to analyze the stability properties of structures. Band structure calculations, density of states (DOS), and projected density of states (PDOS) reveal the electronic properties as well as the availability of the eigenstates for occupation. The desorption process is simulated based on the Arrhenius type desorption rate & a temperature programming. The effects of lateral interactions between adsorbed molecules is taken into account while analyzing first & second order desorption. The outcomes show good qualitative agreement with literature.

Probing the Solid Phase of Noble Metal Copper at Terapascal Conditions.

Ramp compression along a low-temperature adiabat offers a unique avenue to explore the physical properties of materials at the highest densities of their solid form, a region inaccessible by single shock compression. Using the National Ignition Facility and OMEGA laser facilities, copper samples were ramp compressed to peak pressures of 2.30TPa and densities of nearly 30 g/cc, providing fundamental information regarding the compressibility and phase of copper at pressures more than 5 times greater than previously explored. Through x-ray diffraction measurements, we find that the ambient face-centered-cubic structure is preserved up to 1.15TPa. The ramp compression equation-of-state measurements shows that there are no discontinuities in sound velocities up to 2.30TPa, suggesting this phase is likely stable up to the peak pressures measured, as predicted by first-principal calculations. The high precision of these quasiabsolute measurements enables us to provide essential benchmarks for advanced computational studies on the behavior of dense monoatomic materials under extreme conditions that constitute a stringent test for solid-state quantum theory. We find that both density-functional theory and the stabilized jellium model, which assumes that the ionic structure can be replaced by an ionic charge distribution by constant positive-charge background, reproduces our data well. Further, our data could serve to establish new international secondary scales of pressure in the terapascal range that is becoming experimentally accessible with advanced static and dynamic compression techniques.

More on the Effect of Vacancies on Metal Characteristics. Work Function and Surface Energy

Within the density functional method, a simple method for determining the dependence of the work function of electrons and specific surface energy of the metal on the relative density of internal vacancies $${{c}_{{v}}}$$ is proposed. Preserving the style of the stabilized jellium model, the preliminarily calculated volume shift of the conductivity zone bottom e(0) ∝ $${{c}_{{v}}}$$ in a specific homogeneous metal is introduced into a one-dimensional functional as the zero-point energy. Using the quantity $${{c}_{{v}}}$$ as a small parameter, linear corrections to the abovementioned quantities are found. The expansion coefficients are expressed in terms of characteristics of a defectless metal. Calculations for Na and Al are carried out by the Kohn–Sham method. Temperature dependences of Al characteristics have been constructed in the thermodynamic limit.

К вопросу о влиянии вакансий на характеристики металла. Работа выхода и поверхностная энергия

AbstractWithin the density functional method, a simple method for determining the dependence of the work function of electrons and specific surface energy of the metal on the relative density of internal vacancies $${{c}_{{v}}}$$ is proposed. Preserving the style of the stabilized jellium model, the preliminarily calculated volume shift of the conductivity zone bottom ε^(0) ∝ $${{c}_{{v}}}$$ in a specific homogeneous metal is introduced into a one-dimensional functional as the zero-point energy. Using the quantity $${{c}_{{v}}}$$ as a small parameter, linear corrections to the abovementioned quantities are found. The expansion coefficients are expressed in terms of characteristics of a defectless metal. Calculations for Na and Al are carried out by the Kohn–Sham method. Temperature dependences of Al characteristics have been constructed in the thermodynamic limit.

Comparison of the stabilized jellium model and the model with fixed point ions

A numerical analysis of the electron density and the electrostatic potential distribution in spherically symmetric bubbles of ionized hydrogen of nanometer size was made using density functional theory (DFT). Two models are considered: the stabilized jellium model, which allows to carry out one-dimensional computations for the spherically symmetric case, and the model with fixed point ions, where calculations are carried out in 3D geometry. For calculation in the point ions model Octopus and CP2K codes were used. One-dimensional computations in the jellium model require much less computational resources that allows to carry out calculations for systems with large number of electrons (about 105). A conclusion about applicability of the stabilized jellium model for calculations of such systems. These calculations would be useful for studying inhomogeneities of the electric field, which affect ion motion during rapid compression of gas bubbles.

Energetics of charged metal clusters containing vacancies.

We study theoretically large metal clusters containing vacancies. We propose an approach, which combines the Kohn-Sham results for monovacancy in a bulk of metal and analytical expansions in small parameters cv (relative concentration of vacancies) and RN,v-1, RN,v being cluster radii. We obtain expressions of the ionization potential and electron affinity in the form of corrections to electron work function, which require only the characteristics of 3D defect-free metal. The Kohn-Sham method is used to calculate the electron profiles, ionization potential, electron affinity, electrical capacitance; dissociation, cohesion, and monovacancy-formation energies of the small perfect clusters NaN, MgN, AlN (N ≤ 270) and the clusters containing a monovacancy (N ≥ 12) in the stabilized-jellium model. The quantum-sized dependences for monovacancy-formation energies are calculated for the Schottky scenario and the "bubble blowing" scenario, and their asymptotic behavior is also determined. It is shown that the asymptotical behaviors of size dependences for these two mechanisms differ from each other and weakly depend on the number of atoms in the cluster. The contribution of monovacancy to energetics of charged clusters and the size dependences of their characteristics and asymptotics are discussed. It is shown that the difference between the characteristics for the neutral and charged clusters is entirely determined by size dependences of ionization potential and electron affinity. Obtained analytical dependences may be useful for the analysis of the results of photoionization experiments and for the estimation of the size dependences of the vacancy concentration including the vicinity of the melting point.

Density-functional theory study of ionic inhomogeneity in metal clusters using SC-ISJM

In this work we have applied the recently formulated self-compressed inhomogeneous stabilized jellium model [51] to describe the equilibrium electronic and geometric properties of atomic-closed-shell simple metal clusters of AlN (N = 13, 19, 43, 55, 79, 87, 135, 141), NaN, and CsN (N = 9, 15, 27, 51, 59, 65, 89, 113). To validate the results, we have also performed first-principles pseudo-potential calculations and used them as our reference. In the model, we have considered two regions consisting of “surface” and “inner” ones, the border separating them being sharp. This generalization makes possible to decouple the relaxations of different parts of the system. The results show that the present model correctly predicts the size reductions seen in most of the clusters. It also predicts increase in size of some clusters, as observed from first-principles results. Moreover, the changes in inter-layer distances, being as contractions or expansions, are in good agreement with the atomic simulation results. For a more realistic description of the properties, it is possible to improve the method of choosing the surface thicknesses or generalize the model to include more regions than just two.

On the localization of positrons in metal vacancies

The probability of localization of positrons in single vacancies of Al, Cu, and Zn as a function of temperature has been calculated. Vacancy has been simulated by a cavity with a radius of the Wigner–Seitz cell in the stabilized jellium model. A formula for the rate of trapping of a positron by a vacancy as a function of the positron energy has been obtained using the “golden” rule for transitions under the assumption that the positron energy is spent on excitation of electron–hole pairs. The temperature dependence of the localization rate has been calculated for thermalized positrons. It has been found that, in the vicinity of the triple point, the localization rate is close in order of magnitude to the annihilation rate. Based on the results reported in our previous publications devoted to the evaluation of the influence of vacancies on the work function of free positrons, it has been assumed that, near the surface of the metal, there are vacancies charged by positrons. In the approximation of a two-dimensional superlattice, the near-surface vacancy barrier has been estimated. The experimentally revealed shift of the energy distribution of re-emitted positrons has been assumed to be caused by the reflection of low-energy positrons from the vacancy barrier back into the bulk of the metal where they annihilate.

On the positron in a metal

The self-consistent calculations of the spatial distributions of electrons and potentials in vacancies of metals with a localized positron, the spatial distributions of positrons localized in surface states, and the binding energies of positrons and their lifetimes have been performed in terms of the Kohn-Sham method and the stabilized jellium model. The presence of a localized positron in a vacancy leads to the effect that the vacancy is weakly distinguishable for electron waves: the positron weakens the potential field in the vicinity of the vacancy and leads to a phase shift of the scattering electron wave functions. The calculation of the phase shifts of the wave functions for quasi-free positrons scattered by unperturbed vacancies and the representation of a system of vacancies as a “superlattice” in a metal have made it possible to find the shift of the positron work function and the vacancy contribution to the positron effective mass.

On the vacancy in a metal

The self-consistent calculations of spatial distributions of electrons and potentials in an isolated spherical cavity (with atomic radius RWS) of the Wigner-Seitz cell, the energy of the vacancy formation, and the vacancy contribution to the electrical resistance have been performed in terms of the modified Kohn-Sham method and the stabilized jellium model. The energy shift of the ground state of electrons in the Wigner-Seitz cell with radius Rv ≫ RWS (where Rv is the average distance between vacancies), the contribution of vacancies to the electron work function, and the effective mass of electrons have been found using the calculated phase shifts of the scattering wave functions and the representation of a system of vacancies as a “superlattice” in a metal.

On the Work Function and Schottky Barrier Heights of Metal Nanofilms in a Dielectric Environment

We suggest a method for self-consistent calculations of the characteristics of metal films in a dielectric environment. Within a modified Kohn–Sham method and the stabilized jellium model, the most interesting case of asymmetric metal-dielectric sandwiches is considered, for which the dielectric media are different on the two sides of the film. We calculate the spectrum, electron work function, and surface energy of polycrystalline and crystalline films of Na, Al, and Pb placed into passive isolators. It is found that a dielectric environment generally leads to a decrease of both the electron work function and the surface energy. It is revealed that the change of the work function is determined only by the average of dielectric constants on both sides of the film. We introduced the position of a conduction band in the dielectric as a parameter in the self-consistency procedure. The calculations with the use of the image potential for an aluminum film with ideal interfaces vacuum/Al(111)/SiO2 and vacuum/Al(111)/Al2O3 and the sandwich SiO2/Al(111)/Al2O3 are performed. As a result, the effective potential profiles and the Schottky barrier heights are calculated.

SELF-CONSISTENT CALCULATIONS OF WORK FUNCTION, SHOTTKY BARRIER HEIGHTS AND SURFACE ENERGY OF METAL NANOFILMS IN DIELECTRIC CONFINEMENT

We suggest a method for the self-consistent calculations of characteristics of metal films indielectric environment. Within a modified Kohn-Sham method and stabilized jellium model, themost interesting case of asymmetric metal-dielectric sandwiches is considered, for which dielectricmedia are different from the two sides of the film. As an example, we focus on Na, Aland Pb. We calculate the spectrum, electron work function, and surface energy of polycrystallineand crystalline films placed into passive isolators. We find that a dielectric environmentgenerally leads to the decrease of both the electron work function and surface energy. It isrevealed that the change of the work function is determined only by the average of dielectricconstants from both sides of the film. We introduced the position of a conductivity band in thedielectric as a parameter in the self-consistency procedure and performed calculations, usingimage potential, for the aluminum film with ideal interfaces vacuum/Al(111)/SiO 2 ,vacuum/Al(111)/AlO and sandwiches SiO/Al(111)/AlO. As a result, effective potential profilesand the Schottky barrier heights were calculated.

Quantum metal film in the dielectric environment

A method has been proposed for self-consistent calculations of characteristics of a metal film in dielectrics. The most interesting (asymmetric) case of metal-dielectric sandwiches, where the dielectrics are different on both sides of the film, has been considered in terms of the modified Kohn-Sham method and the stabilized jellium model. The spectrum, electron work function, and surface energy of polycrystalline films placed in passive insulators have been calculated for the first time using Al and Na as an example. It has been found that the dielectric environment generally leads to a negative change in both the electron work function and the surface energy. In addition to the size changes, the shift of the work function is determined by the arithmetic mean of the dielectric constants of the surrounding media.

Comparison of Calculated Work Function of Metals Using Metallic Plasma Model with Stabilized Jellium, Ab-Initio Approach and Experimental Values

The work function of metals was calculated using the metallic plasma model (MPM). The results obtained were compared with the available results of the stabilized jellium model (SJM), Ab -initio model and the experimental values. Result shows that the stabilized jellium model was in good agreement with experimental values for the simple metals, the transition, inner transition and rare-earth metals. The metallic plasma model gave results that are agreeable with experimental values for most of the metals especially the polycrystalline metals. The ab -initio results were higher than experimental values except for Ba, Ca and Sr, this shows that the metallic plasma model is more reliable in predicting the work function of metals.

Self-compressed inhomogeneous stabilized jellium model and surface relaxation of simple metal thin films

The interlayer spacing near the surface of a crystal is different from that of the bulk. As a result, the value of the ionic density in the normal direction and near to the surface shows some variation from the bulk value, which is oscillatory in shape. To describe this behavior simply, we have formulated the self-compressed inhomogeneous stabilized jellium model and have applied it to simple metal thin films. In this model, for a ν-layered slab, each ionic layer is replaced by a jellium slice of constant density. The equilibrium densities of the slices are determined by minimizing the total energy per electron of the slab with respect to the slice densities. However, to avoid the complications that arise because of the increasing number of independent slice-density parameters for large-ν slabs, we consider a simplified version of the model that consists of only three jellium slices: one inner bulk slice with density [Formula: see text] and two similar surface slices, each of density [Formula: see text]. In this simplified model, each slice may contain more than one ionic layer. Application of this model to ν-layered slabs (3 ≤ ν ≤ 10) of Al, Na, and Cs shows that, in the equilibrium state, [Formula: see text] differs from [Formula: see text]. The difference is significant in the Al case, and the slab is more stable than that predicted by the homogeneous model with only one density parameter for the whole jellium background. In addition, we have calculated the overall relaxations, the work functions, and the surface energies and compared them with the results of earlier works.

Correlation energy functional from jellium surface analysis

Using the wave-vector analysis of the jellium exchange-correlation surface energy, we show that the PBEint generalized gradient approximation (GGA) of Fabiano et al. [Phys. Rev. B 82, 113104 (2010)] is one of the most accurate density functionals for jellium surfaces, being able to describe both exchange and correlation parts of the surface energy, without error compensations. We show that the stabilized jellium model allows us to achieve a realistic description of the correlation surface energy of simple metals at any wave vector $k$. The PBEint correlation is then used to construct a meta-GGA correlation functional, modifying the one-electron self-correlation-free Tao-Perdew-Staroverov-Scuseria (TPSS) one. We find that this new functional (named JS) performs in agreement with fixed-node diffusion Monte Carlo estimates of the jellium surfaces, and is accurate for spherical atoms and ions of different spin-polarization and for Hooke's atom for any value of the spring constant.

Shell structure and phase relations in electronic properties of metal nanowires from an electron-gas model

The electronic and dynamic properties of metal nanowires are analyzed by using a minimal electron-gas model (EGM), in which the nanowire is treated as a close system with variable Fermi energy as a function of nanowire radius. We show that the planar surface energy and the curvature energy from the EGM are reasonably consistent with those from previous stabilized-jellium-model calculations, especially for metals with low electron densities. The EGM shell structure due to the fillings of quantum-well subbands is similar to that from the stabilized jellium model. The crossings between subbands and Fermi energy level for the metal nanowire correspond to cusps on the chemical-potential curve versus nanowire radius, but inflection points on the surface-free-energy curve versus the radius, as in the case of metal nanofilms. We also find an oscillatory variation in electron density versus radius at the nanowire center with a global oscillation period which approximately equals half Fermi wavelength. Wire string tension, average binding energy, and thermodynamic stability from the EGM are in good agreement with the data from previous first-principles density-functional theory calculations. We also compare our model with those from previous reported free-electron models, in which the nanowire is treated as an open system with a constant Fermi energy. We demonstrate that the fundamental thermodynamic properties depend sensitively on the way that the potential wall is constructed in the models.

Effect of dielectric coating on the electron work function and the surface stress of a metal

The electron work function, contact potential difference, and surface stress of the elastically deformed faces of the metal covered by a dielectric are calculated by using the Kohn–Sham method and stabilized jellium model. Our calculations demonstrate the opposite deformation dependencies of the work function and contact potential difference. Dielectric coating leads to a negative change in the work function and a positive change in the contact potential difference. It is shown that the measurements of the contact potential difference of a deformed face by the Kelvin method give only the change in the value of the one-electron effective potential in the plane of a virtual image behind the surface, rather than the value of the electron work function. The obtained values of the electron work function and surface stress for Al, Au, Cu, and Zn are in agreement with the results of experiments for polycrystals.