A general phenomenological model for work function

Brodie, I.; Chou, Sharon H.; Yuan, Huan

doi:10.1016/j.susc.2014.03.002

Cited by 13 publications

(12 citation statements)

References 35 publications

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“…Brodie, not employing an ab initio method, has calculated the WF of the polycrystalline surface in terms of the conducting-sphere radius and the Fermi energy, obtained a good agreement with experimental data for several fcc and bcc metals [10], and has recently generalized his model of WF [11]. Using Brodie's concept as the starting point, Halas and Durakiewicz (H-D) have combined the polarization length of metal-lattice plasma (MLP) with the Fermi energy to calculate the polycrystalline WF of sixty elements [12].…”

Section: Introductionmentioning

confidence: 87%

“…There are also phenomenological approaches to the electron work function (WF) which is one of the most important characteristics of materials. In order to ensure a wide area of applicability to metals and alloys, such * E-mail: jacek.brona@ifd.uni.wroc.pl approaches use the classical electrostatic image or the unscreened Coulomb potential [9][10][11][12][13][14][15].…”

Section: Introductionmentioning

confidence: 99%

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Two-extremum electrostatic potential of metal-lattice plasma and the work function of an electron

Surma

Brona

Ciszewski

2015

Materials Science-Poland

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Metal-lattice plasma is treated as a neutral two-component two-phase system of 2D surface and 3D bulk. Free electron density and bulk chemical potential are used as intensive parameters of the system with the phase boundary position determined in the crystalline lattice. A semiempirical expression for the electron screened electrostatic potential is constructed using the lattice-plasma polarization concept. It comprises an image term and three repulsion/attraction terms of second and fourth orders. The novel curve has two extremes and agrees with certain theoretical forms of potential. A practical formula for the electron work function of metals and a simplified schema of electronic structure at the metal/vacuum interface are proposed. This yields 10.44 eV for the Fermi energy of free electron gas; −5.817 eV for the Fermi energy level; 4.509 eV for the average work function of bcc tungsten. Selected data are also given for fcc Cu and hcp Re. For harmonic frequencies ∼ 10E16 per s of the self-excited metal-lattice plasma, energy gaps of 14.54 and 8.02 eV are found, which correspond to the bulk and surface plasmons, respectively. Further extension of this thermodynamics and metal-lattice theory based approach may contribute to a better understanding of theoretical models which are employed in chemical physics, catalysis and materials science of nanostructures.

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Section: Introductionmentioning

confidence: 87%

Section: Introductionmentioning

confidence: 99%

Two-extremum electrostatic potential of metal-lattice plasma and the work function of an electron

Surma

Brona

Ciszewski

2015

Materials Science-Poland

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“…A crystal of several h-oriented grains, which are ended with atomically flat surfaces, has a curved surface with a finite radius. Brodie, in his original model [16], has shown in fact that the sphere-symmetry WF practically corresponds to that of a planar system. Consequently, the MLP physicochemical system can comprise m independent species, and m phases (here, m = 9) in accord with the commonly accepted picture of the two-dimensional MLP.…”

Section: Basicsmentioning

confidence: 99%

“…Wojciechowski et al [12], Kiejna [13] employed the local metal-lattice plasma (MLP) polarization concept of Halas and Durakiewicz [14,15] to calculate the face-dependent WF using the Kiejna selfconsistent electron density profiles of stabilized jellium. Brodie et al [16] proposed a general phenomenological model using the Maxwell classical image force and assuming Brodie minimum uncertainty distance [17] for the surface 2D plasma, to cover both clean and electropositive adsorbate covered surfaces. An LEED experimental and theoretical study of the 1D surfacepotential barrier for the W(1 1 0) and (1 0 0) surfaces was done by Baribeau et al [18].…”

Section: Introductionmentioning

confidence: 99%

Electron Work Functions of (H K L)-Surfaces of W, Re, and Cu Crystals

Surma

Brona

Ciszewski

2018

Materials Science-Poland

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Work function (WF) and some physicochemical data for several most prominent crystal planes of three metals of typical structures are calculated within the linear approximation employing the surface dipole and 2D gas models. "Composite" crystal of a homogeneous bulk phase and a thick surface composed of eight (h k l)-oriented facets with different unsaturated bonds is treated as a nine-phase nine-component system with two degrees of freedom. It contains the two-dimensional metal-lattice plasma of free electrons and the immobile atom-core network. For twenty four (h k l) surfaces, the WF and dipole barrier term, chemical and electrostatic potential levels, electron charge densities, surface dipole fields, and other parameters are calculated and tabularized. WF values obtained from the thermodynamics based formula are compared to the ones obtained from the quantum mechanics based formula, which shows good agreement with experiment and also reveals a specific deviation in the case of field emission method for the most packed plane. A set of accurate face dependent data can be of interest to electronics and materials science workers.

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“…15,34 Lastly, analytical models have been invoked to explain the origin of low work function via formation of a two-dimensional electron gas on the emitting surface. 35,36 In this study we explore the hypothesis that Sc 2 O 3 with Ba-O surface complexes provide a low work function electron emitter. This hypothesis is reasonable to consider because of the general agreement that a Ba-O dipole mechanism produces low work functions in B-type cathodes, 20 experimental data on scandate cathodes which indicate the inclusion of Sc 2 O 3 is critical for maximum work function reduction of the cathode, [9][10][11][12] and previous computational work which demonstrated that Sc 2 O 3 itself can supply the magnitude of emitted current densities observed in experiment and thus may function as the electron emissive material in scandate cathodes.…”

Section: Introductionmentioning

confidence: 99%

Electron Emission Energy Barriers and Stability of Sc₂O₃ with Adsorbed Ba and Ba–O

2014

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In this study we employ Density Functional Theory (DFT) methods to investigate the surface energy barrier for electron emission (surface barrier) and thermodynamic stability of Ba and Ba-O species adsorption (relative to formation of bulk BaO) under conditions of high temperature (approximately 1200 K) and low pressure (approximately 10 -10 Torr) on the low index surfaces of bixbyite Sc 2 O 3 . We employ both the standard Generalized Gradient Approximation (GGA) and the hybrid HSE functional to calculate accurate surface barriers from relaxed GGA structures. The role of Ba in lowering the cathode surface barrier is investigated via adsorption of atomic Ba and Ba-O dimers, where the highest simulated dimer coverage corresponds to a single monolayer film of rocksalt BaO. The change of the surface barrier of a semiconductor due to adsorption of surface species is decomposed into two parts: a surface dipole component and doping 2 component. The dipole component is the result of charge rearrangement at the surface and is described by the electrostatic Helmholtz equation. The doping component is due to charge transfer from the surface species, which changes the Fermi level and thereby changes the surface barrier. Different initial geometries, adsorption sites, and coverages were tested for the most stable low index Sc 2 O 3 surfaces ((011) and (111)) for both atomic Ba and Ba-O dimers. The lowest surface barrier with atomic Ba on Sc 2 O 3 was found to be 2.12 eV and 2.04 eV for the (011) and (111) surfaces at 3 and 1 Ba atoms per surface unit cell (0.250 and 0.083 Ba per surface O), respectively. The lowest surface barrier for Ba-O on Sc 2 O 3 was found to be 1.21 eV on (011) for a 7 Ba-O dimer-per-unit-cell coverage (0.583 dimers per surface O). Generally, we found that Ba in its atomic form on Sc 2 O 3 surfaces is not stable relative to bulk BaO, while Ba-O dimer coverages between 3 to 7 Ba-O dimers per (011) surface unit cell (0.250 to 0.583 dimers per surface O) produce stable structures relative to bulk BaO. Ba-O dimer adsorption on Sc 2 O 3 ( 111) surfaces was found to be unstable versus BaO over the full range of coverages studied. Investigation of combined n-type doping and surface dipole modification showed that their effects interact to yield a reduction less than the two contributions would yield separately.

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A general phenomenological model for work function

Cited by 13 publications

References 35 publications

Two-extremum electrostatic potential of metal-lattice plasma and the work function of an electron

Two-extremum electrostatic potential of metal-lattice plasma and the work function of an electron

Electron Work Functions of (H K L)-Surfaces of W, Re, and Cu Crystals

Electron Emission Energy Barriers and Stability of Sc₂O₃ with Adsorbed Ba and Ba–O

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A general phenomenological model for work function

Cited by 13 publications

References 35 publications

Two-extremum electrostatic potential of metal-lattice plasma and the work function of an electron

Two-extremum electrostatic potential of metal-lattice plasma and the work function of an electron

Electron Work Functions of (H K L)-Surfaces of W, Re, and Cu Crystals

Electron Emission Energy Barriers and Stability of Sc2O3 with Adsorbed Ba and Ba–O

Contact Info

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Electron Emission Energy Barriers and Stability of Sc₂O₃ with Adsorbed Ba and Ba–O