Topic
Gaussian surface
About: Gaussian surface is a research topic. Over the lifetime, 563 publications have been published within this topic receiving 12445 citations.
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Papers
IBM1
TL;DR: In this article, the authors generalized the energy-level calculation to include arbitrary orientations of the constant energy ellipsoids in the bulk, the surface or interface, and an external magnetic field.
Abstract: The strong surface electric field associated with a semiconductor inversion layer quantizes the motion normal to the surface. The bulk energy bands split into electric sub-bands near the surface, each of which is a two-dimensional continuum associated with one of the quantized levels. We treat the electric quantum limit, in which only the lowest electric sub-band is occupied. Within the effective-mass approximation, we have generalized the energy-level calculation to include arbitrary orientations of (1) the constant-energy ellipsoids in the bulk, (2) the surface or interface, and (3) an external magnetic field. The potential associated with a charged center located an arbitrary distance from the surface is calculated, taking into account screening by carriers in the inversion layer. The bound states in the inversion layer due to attractive Coulomb centers are calculated for a model potential which assumes the inversion layer to have zero thickness. The Born approximation is compared with a phase-shift calculation of the scattering cross section, and is found to be reasonably good for the range of carrier concentrations encountered in InAs surfaces. The low-temperature mobility associated with screened Coulomb scattering by known charges at the surface and in the semiconductor depletion layer is calculated for InAs and for Si (100) surfaces in the Born approximation, using a potential that takes the inversion-layer charge distribution into account. The InAs results are in good agreement with experiment. In Si, but not in InAs, freeze-out of carriers into inversion-layer bound states is expected at low temperatures and low inversion-layer charge densities, and the predicted behavior is in qualitative agreement with experiment. An Appendix gives the phase-shift method for two-dimensional scattering and the exact cross section for scattering by an unscreened Coulomb potential.
1,905 citations
TL;DR: In this paper, a theory for laser-induced periodic surface structure was developed by associating each Fourier component of induced structure with the corresponding Fourier components of inhomogeneous energy deposition just beneath the surface.
Abstract: We develop a theory for laser-induced periodic surface structure by associating each Fourier component of induced structure with the corresponding Fourier component of inhomogeneous energy deposition just beneath the surface. We assume that surface roughness, confined to a region of height much less than the wavelength of light, is responsible for the symmetry breaking leading to this inhomogeneous deposition; we find strong peaks in this deposition in Fourier space, which leads to predictions of induced fringe patterns with spacing and orientation dependent on the angle of incidence and polarization of the damaging beam. The nature of the generated electromagnetic field structures and their relation to the simple "surface-scattered wave" model for periodic surface damage are discussed. Our calculation, which is for arbitrary angle of incidence and polarization, applies a new approach to the electrodynamics of randomly rough surfaces, introducing a variational principle to deal with the longitudinal fields responsible for local field, or "depolarization," corrections. For a $p$-polarized damaging beam our results depend on shape and filling factors of the surface roughness, but for $s$-polarized light they are essentially independent of these generally unknown parameters; thus an unambiguous comparison of our theory with experiment is possible.
1,309 citations
TL;DR: In this paper, a theoretical model is used to investigate the geometrical self-shadowing of a surface described by Gaussian statistics, and expressions for various shadowing probabilities as functions of the parameter characterizing surface roughness and of the angle of incidence of the illuminating beam.
Abstract: In the context of the backscattering of waves from a random rough surface, a theoretical model is used to investigate the geometrical self-shadowing of a surface described by Gaussian statistics. Expressions are derived for various shadowing probabilities as functions of the parameter characterizing surface roughness and of the angle of incidence of the illuminating beam. The theoretical shadowing functions compare closely with those obtained experimentally from a recent computer simulation of a Gaussian surface.
520 citations
TL;DR: In this article, a solution of Poisson's equation utilizing Boltzmann statistics, the space charge, electric field, and change in free carrier concentration have been calculated for a semiconductor surface.
Abstract: In the study of the surface properties of semiconductors, it is valuable to know the relation between carrier density at the surface and the shift in electrostatic potential from the bulk to the surface. By a solution of Poisson's equation utilizing Boltzmann statistics, the space charge, electric field, and change in free carrier concentration have been calculated for a semiconductor surface. The results are expressed as a function of the deviations of the Fermi energy from its intrinsic value in the bulk and at the surface. The calculated curves may be used for any nondegenerate semiconductor at any temperature, provided that the donor and acceptor levels are completely ionized. Numerical values are given for germanium and silicon at room temperature.
362 citations
18 Sep 1998
TL;DR: In this paper, an illumination system with a prescribed output pattern consisting of a light source and an optical lens redirecting the light of the source into an output beam is considered, and the shape generated by the following method is defined: the Gaussian sphere establishes a first grid (100) of equal-flux zones of solid angle; a second grid (130) with the same number of equalflux zone of solid angles as the first grid, with a coordinate system topology congruent with that of the first, such that the zones of the second grid are in
Abstract: An illumination system with a prescribed output pattern comprising a light source and an optical lens redirecting the light of the source into an output beam, the lens with multiple surfaces (100, 130, 120) at least one of which has shape that is not a surface of revolution, the shape generated by the following method: the Gaussian sphere establishes a first grid (100) of equal-flux zones of solid angle; a second grid (130) with the same number of equal-flux zones of solid angles as the first grid, with a coordinate-system topology congruent with that of the first grid, such that the zones of the second grid are in one-to-one correspondence with the zones of the first grid (100), according to the local transmittance of the lens, with either of both of the grids being rotationally non-symmetric; by this correspondence define a flux-redistributing directional mapping function from the first Gaussian sphere to the second Gaussian sphere, whereby any light ray from the source can be assigned a direction in the output beam, according to the zone of the second grid (130) into which the ray falls, so that the redirected ray falls in corresponding zone of the first grid.
185 citations
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Performance Metrics
| Year | Papers |
|---|---|
| 2025 | 1 |
| 2024 | 3 |
| 2023 | 8 |
| 2022 | 7 |
| 2021 | 10 |
| 2020 | 9 |