Distribution Of Excess Electrons Research Articles

Determination of diffusion coefficients in degenerate electron gas using Monte Carlo simulation

We propose a method for determining diffusion coefficients in degenerate semiconductors from an ensemble Monte Carlo simulation. The basic idea is that what is relevant for this problem is not the whole electron distribution function, but its perturbation in response to an addition of “excess carriers.” Starting from the Boltzmann transport equation, we derive the equation of evolution for this “excess electron distribution function.” We propose an interpretation in terms of scattering events suffered by particles, allowing one to solve the problem by Monte Carlo simulation. We simulate two sets of carriers, coupled by an “exchange scattering” mechanism which is properly defined. The first set represents the uniform background density in the semiconductor, whereas the second one represents the excess carriers. Only the latter is used for calculating diffusion coefficients. This method is applied to a highly degenerate two-dimensional electron gas in a doped GaAs quantum well. The diffusivity-field characteristics are calculated and discussed.

An electride with a large six-electron ring

ELECTRIDES are crystalline salts that contain complexed alkali metal cations whose charge is balanced by trapped electrons1. Theory2,3 and experiment4,5 indicate that the excess electron distribution is concentrated in cavities and channels formed by close-packing of the large complexed cations. Thus electrides might serve as models of a confined electron gas. Only three electrides have been structurally characterized previously6–8. Here we report the structure of a new electride, [Cs + (15C5) (18C6).e-]6.(18C6), where 15C5 and 18C6 represent crown ethers with five and six oxygen atoms respectively. The unit cell has threefold symmetry, with a central 18C6 molecule surrounded by six Cs+ cations, each sandwiched between a 15C5 and 18C6 molecule. The six electrons released from the Cs/crown ether interaction seem to be trapped in six cavities which form a puckered ring, three above and three below the plane of the central 18C6 molecule. The ground state is diamagnetic. This ring-like distribution of electrons contrasts with the chain-like connections between electron cavities observed in other electrides6–8. Polycrystalline samples of this new electride have an electrical conductivity about a million times greater than those of the electrides Cs+ (15C5)2.e- and Cs+ (18C6)2.e-. The size, shape and connectivity of the electron-containing cavities and channels evidently exert a critical influence on the properties of electrides.

Exchange and vibronic interactions in a tetrahedral, five-electron mixed-valence cluster

The distribution of an ‘‘excess’’ electron in a model mixed-valence tetranuclear metal cluster with open-shell ion cores is explored as a function of vibronic coupling, electron transfer, and electron exchange interactions. The system comprises five electrons, one ‘‘core electron’’ at each metal center, and one electron in a different local orbital which can delocalize among the sites. Vibronic coupling is introduced as the interaction of the electronic states with nontotally symmetric combinations of the subunit ligand vibrations. An extension of the Anderson–Hasegawa Hamiltonian is developed to describe the system, and adiabatic potential energy surfaces for the different spin states are obtained. From these, the excess electron distribution is deduced. The model is designed to be a prototype for understanding the excess electron distributions in tetranuclear iron–sulfur clusters. Examples of electron delocalization over three sites in an S=3/2 ground state and over two sites in an S=1/2 state are found. These distributions cannot arise in a tetranuclear cluster having closed-shell ion cores and are attributed to favorable double exchange interactions. The occurrence of pair delocalization in an S=1/2 ground state is consistent with experimental observations of (Fe4S4)3+ iron–sulfur clusters.

Electron localization in water clusters. II. Surface and internal states

Electron attachment and localization in small water clusters (H2O)n (n=8–128) is studied using path-integral molecular dynamics simulations. The electron-water molecule interaction is described via a pseudopotential which includes Coulomb, polarization, exclusion and exchange contributions. Different electron localization modes are found depending on cluster size. For small and intermediate size clusters (n=8–32), the energetically favored localization mode involves a surface state and the calculated excess electron binding energies are in agreement with experimentally measured values. In larger clusters, n=64, 128, internal localization (solvation) is energetically favored. In both cases the localization of the excess electron is accompanied by large cluster molecular reorganization. The cluster size dependence of the localization mode, the energetics, structure, and excess electron distributions in the negative molecular anions (H2O)−n, and the dependence on temperature are explored.

Small‐angle scattering from dense systems of non‐homogeneous particles, I

AbstractThe introduction of the effective integral quantities characterizing non‐homogeneous particles and their volume fraction leads to an expression for the distance distribution function analogous to that for homogeneous particles. This significantly simplifies the determination of the structure characteristics of particles. The procedure is outlined for obtaining the distribution of excess electrons and the total number of electrons within the particle from relative SAXSb) intensity data. The mode of the spatial arrangement of the partially ordered system of particles can be estimated by comparing the characteristic numbers calculated for different structure types with that characteristic number determined from relative intensities, namely from the effective quantities of the system and from the position of the maximum of interference function.

Optical indications of heterogeneous distribution of equilibrated solvated electrons in liquid and glassy ammonia-methanol solutions

Optical absorption spectra of solvated electrons, e − s, have been studied in methanol solutions of ammonia (12 and 16 m%) by pulse microsecond radiolysis. A jump of 0.7 eV has been found in the temperature dependencies of the energy of the optical absorption maximum, ( E − M), at the range 10–15°. The absorption bands showed a structured shape at the temperatures near the jump region. The enhanced photosensibility of the shape and the location of spectra of trapped electrons (e − t) has been discovered in these matrices at 77 K. The obtained results indicated that the equilibrated distribution of excess electrons over traps has common heterogeneous nature for the liquid and glassy ammonia-methanol mixture. Validity of the extension of this conclusion over other polar liquids is discussed.

Spectral Output of Semiconductor Lasers

This paper investigates problems associated with multimode oscillations in semiconductor lasers. In particular, even in semiconductors there can exist a spatially nonuniform distribution of excess electrons and holes because a given mode de-excites electrons most strongly at antinodes and not at all at nodes of the electric vector. This nonuniform distribution encourages the oscillation of other modes which have a different distribution of the electric field vector and which, in particular, have finite electric fields at nodes of the first oscillating mode. Diffusion of electrons and holes tends to wipe out nonuniform carrier distributions. For low temperatures, this diffusion is relatively slow, and for current densities only moderately above the threshold, several modes may oscillate simultaneously. At higher temperatures the suppression of additional modes is much more effective. Because of the complexity of the calculations, the present work had to be restricted to Fabry-Perot type modes and relatively low power levels. Comparisons are made between theory and experiments.