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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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Journal ArticleDOI
TL;DR: In this article, a general solution for the motion of electrons in the potential field of the nuclei in a crystal lattice is developed for the energy interaction terms due to nuclear vibration and to the presence of other electrons; they are to be included later by approximation methods.
Abstract: A general solution is developed for the motion of electrons in the potential field of the nuclei in a crystal lattice. As usual the energy interaction terms due to nuclear vibration and to the presence of other electrons are neglected; they are to be included later by approximation methods.It is shown for low energies the wave function becomes a linear combination of the atomic wave functions, the allowed energies approximating the discrete atomic levels; and for high energies the wave function approaches that of the free electron, with the allowed energies a nearly continuous range. However, for electrons coming into the crystal from outside, the crystal becomes impenetrable for those electronic wave-lengths and directions analogous to the beams producing Bragg and Laue beams in x-rays.The solution is computed for a simple form of potential lattice, and the results are shown to be in quantitative agreement with the experimental results of Davisson and Germer. The phenomenon they call anomalous dispersion is shown to be a natural consequence of the characteristics of the wave function.

102 citations

Journal ArticleDOI
TL;DR: In this paper, the authors used intensity analysis and photo-ionization cross sections to confirm the nature of the band responsible for conducting properties and deduced number of free electrons in the valence band is used to correlate the asymmetry recorded for the core level lines.
Abstract: Valence band X-ray photoelectron spectra of the rutile oxides TiO2, RuO2, and IrO2 show a distinct evolution as a function of the increasing number of metal d-electrons. The observations are found to be in excellent agreement with recent theoretical models. Intensity analysis and photo-ionization cross sections are used to confirm the nature of the band responsible for conducting properties. The result is in accordance with a crystal field model proposed earlier. The deduced number of free electrons in the valence band is used to correlate the asymmetry recorded for the core level lines.

102 citations

Journal ArticleDOI
01 Apr 1939
TL;DR: In this article, the wave functions and energies of these states are calculated, on the nearly free electron approximation, in terms of the constants of the crystalline potential field, which is represented by a triple Fourier series having the periodicity of the lattice.
Abstract: It is shown that in a crystal there exist states in which the electron is bound to a surface of the crystal and has an energy lying within a forbidden band. The wave functions and energies of these states are calculated, on the nearly free electron approximation, in terms of the constants of the crystalline potential field, which is represented by a triple Fourier series having the periodicity of the lattice. The method is shown to be applicable to a general crystal having a surface parallel to any one of the crystal planes.

102 citations

Journal ArticleDOI
TL;DR: In this article, the Auger de-excitation mechanism was shown to be proportional to the number of free electrons in the Schottky barrier in the presence of trapped and free electrons.

102 citations

Journal ArticleDOI
TL;DR: In this article, a new model is proposed which greatly improves the accuracy in predicting the ablation depth and, for the first time, can predict the flat bottom crater shape for wide bandgap materials ablated by a femtosecond laser pulse.

101 citations


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Performance
Metrics
No. of papers in the topic in previous years
YearPapers
202340
202290
2021132
2020122
2019114
2018112