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Free electron model
About: Free electron model is a research topic. Over the lifetime, 4678 publications have been published within this topic receiving 103535 citations.
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TL;DR: In this paper, the structure of the electronic energy bands and Brillouin zones for graphite was developed using the "tight binding" approximation, and it was found that graphite is a semi-conductor with zero activation energy, but they are created at higher temperatures by excitation to a band contiguous to the highest one which is normally filled.
Abstract: The structure of the electronic energy bands and Brillouin zones for graphite is developed using the "tight binding" approximation. Graphite is found to be a semi-conductor with zero activation energy, i.e., there are no free electrons at zero temperature, but they are created at higher temperatures by excitation to a band contiguous to the highest one which is normally filled. The electrical conductivity is treated with assumptions about the mean free path. It is found to be about 100 times as great parallel to as across crystal planes. A large and anisotropic diamagnetic susceptibility is predicted for the conduction electrons; this is greatest for fields across the layers. The volume optical absorption is accounted for.
4,395 citations
TL;DR: In this paper, the interpenetrating network formed from a phase-segregated mixture of two semiconducting polymers is shown to provide both the spatially distributed interfaces necessary for efficient charge photo-generation, and the means for separately collecting the electrons and holes.
Abstract: THE photovoltaic effect involves the production of electrons and holes in a semiconductor device under illumination, and their subsequent collection at opposite electrodes. In many inorganic semiconductors, photon absorption produces free electrons and holes directly1. But in molecular semiconductors, absorption creates electrona¤-hole pairs (excitons) which are bound at room temperature2, so that charge collection requires their dissociation. Exciton dissociation is known to be efficient at interfaces between materials with different electron affinities and ionization potentials, where the electron is accepted by the material with larger electron affinity and the hole by the material with lower ionization potential3. A two-layer diode structure can thus be used, in which excitons generated in either layer diffuse towards the interface between the layers. However, the exciton diffusion range is typically at least a factor of 10 smaller than the optical absorption depth, thus limiting the efficiency of charge collection3. Here we show that the interpenetrating network formed from a phase-segregated mixture of two semiconducting polymers provides both the spatially distributed interfaces necessary for efficient charge photo-generation, and the means for separately collecting the electrons and holes. Devices using thin films of these polymer mixtures show promise for large-area photodetectors.
3,165 citations
TL;DR: In this paper, the wave-number-dependent dielectric function is derived for various models of a semiconductor and expressions for the wave number-dependent Dielectric functions are derived for different models of semiconductors.
Abstract: Expressions for the wave-number-dependent dielectric function are derived for various models of a semiconductor The calculation is carried out for the diagonal part of the dielectric function at zero frequency It is found that calculations based on plane wave models (such as the free electron model) give poor results for small values of the wave number due to neglect of both Bragg reflections and Umklapp processes We use instead an isotropic version of the nearly free electron model in which dielectric function depends on only one parameter ${E}_{g}$ representing an average energy gap that can be determined from optical data It is noted that for small wave numbers Umklapp processes give the major contribution to the dielectricfunction, where-as for large wave numbers normal processes dominate The dielectric function is evaluated numerically for a value of ${E}_{g}$ appropriate to Si
1,857 citations
TL;DR: In this article, the energy of interaction between free electrons in an electron gas is considered and the correlation energy is calculated by an approximation method which is, essentially, a development of the energy by means of the Rayleigh-Schrodinger perturbation theory in a power series of e2.
Abstract: The energy of interaction between free electrons in an electron gas is considered. The interaction energy of electrons with parallel spin is known to be that of the space charges plus the exchange integrals, and these terms modify the shape of the wave functions but slightly. The interaction of the electrons with antiparallel spin, contains, in addition to the interaction of uniformly distributed space charges, another term. This term is due to the fact that the electrons repell each other and try to keep as far apart as possible. The total energy of the system will be decreased through the corresponding modification of the wave function. In the present paper it is attempted to calculate this “correlation energy” by an approximation method which is, essentially, a development of the energy by means of the Rayleigh-Schrodinger perturbation theory in a power series of e2.
1,815 citations
TL;DR: In this article, the real and imaginary parts of the dielectric constant and the function describing the energy loss of fast electrons traversing the materials are deduced from the Kramers-Kronig relations.
Abstract: Reflectance data are presented for Si, Ge, GaP, GaAs, InAs, and InSb in the range of photon energies between 1.5 and 25 eV. The real and imaginary parts of the dielectric constant and the function describing the energy loss of fast electrons traversing the materials are deduced from the Kramers-Kronig relations. The results can be described in terms of interband transitions and plasma oscillations. A theory based on the frequency-dependent dielectric constant in the random phase approximation is presented and used to analyze these data above 12 eV, where the oscillator strengths coupling the valence and conduction bands are practically exhausted. The theory predicts and the experiments confirm essentially free electron-like behavior before the onset of $d$-band excitations and a plasma frequency modified from that of free electrons due to oscillator strength coupling between valence and $d$ bands and $d$-band screening effects. These complications are absent in Si. The energy loss functions obtained from optical and characteristic energy loss experiments are also found to be in good agreement. Arguments for interpreting structure in the reflectance curves above 16 eV in terms of $d$-band excitations are given.
1,749 citations