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# Band diagram

About: Band diagram is a research topic. Over the lifetime, 1750 publications have been published within this topic receiving 37382 citations.

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General Electric

^{1}TL;DR: The band structure of InSb is calculated using the k ·. p perturbation approach and assuming that the conduction and valence band extrema are at k = 0 as mentioned in this paper.

Abstract: The band structure of InSb is calculated using the k ·. p perturbation approach and assuming that the conduction and valence band extrema are at k = 0. The small band gap requires an accurate treatment of conduction and valence band interactions while higher bands are treated by perturbation theory. A highly nonparabolic conduction band is found. The valence band is quite similar to germanium. Energy terms linear in k which cannot exist in germanium are estimated and found to be small, though possibly of importance at liquid-helium temperature. An absolute calculation of the fundamental optical absorption is made using the cyclotron resonance mass for n-type InSb. The agreement with experimental data for the fundamental absorption and its dependence on n-type impurity concentration is quite good. This evidence supports the assumptions made concerning the band structure.

2,905 citations

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IBM

^{1}TL;DR: In this paper, a theoretical model is presented to predict the band offsets at both lattice-matched and pseudomorphic strained-layer interfaces, based on the local density functional pseudopotential formalism and the ''model solid approach'' of Van de Walle and Martin.

Abstract: Semiconductor heterojunctions and superlattices have recently shown tremendous potential for device applications because of their flexibility for tailoring the electronic band structure. A theoretical model is presented to predict the band offsets at both lattice-matched and pseudomorphic strained-layer interfaces. The theory is based on the local-density-functional pseudopotential formalism and the ``model-solid approach'' of Van de Walle and Martin. This paper is intended as a self-contained description of the model, suitable for practical application. The results can be most simply expressed in terms of an ``absolute'' energy level for each semiconductor and deformation potentials that describe the effects of strain on the electronic bands. The model predicts reliable values for the experimentally observed lineups in a wide variety of test cases and can be used to explore which combinations of materials and configurations of the strains will lead to the desired electronic properties.

1,807 citations

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TL;DR: In this paper, the authors derived the effective mass Hamiltonian for wurtzite semiconductors, including the strain effects, using the k-ensuremath{\cdot}p perturbation method, which is then checked with that derived using an invariant method based on the Pikus-Bir model.

Abstract: We derive the effective-mass Hamiltonian for wurtzite semiconductors, including the strain effects. This Hamiltonian provides a theoretical groundwork for calculating the electronic band structures and optical constants of bulk and quantum-well wurtzite semiconductors. We apply Kane's model to derive the band-edge energies and the optical momentum-matrix elements for strained wurtzite semiconductors. We then use the k\ensuremath{\cdot}p perturbation method to derive the effective-mass Hamiltonian, which is then checked with that derived using an invariant method based on the Pikus-Bir model. We obtain the band structure ${\mathit{A}}_{\mathit{i}}$ parameters in the group theoretical model explicitly in terms of the momentum-matrix elements. We also find the proper definitions of the important physical quantities used in both models and present analytical expressions for the valence-band dispersions, the effective masses, and the interband optical-transition momentum-matrix elements near the band edges, taking into account the strain effects. \textcopyright{} 1996 The American Physical Society.

924 citations

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Kyoto University

^{1}TL;DR: Polarization mode selection in a two-dimensional (2D) photonic crystal laser is demonstrated by controlling the geometry of the unit cell structure by observing coherent lasing action with a single wavelength and controlled polarization in good agreement with the predicted behavior.

Abstract: We demonstrate polarization mode selection in a two-dimensional (2D) photonic crystal laser by controlling the geometry of the unit cell structure. As the band diagram of the square-lattice photonic crystal is influenced by the unit cell structure, calculations reveal that changing the structure from a circular to an elliptical geometry should result in a strong modification of the electromagnetic field distributions at the band edges. Such a structural modification is expected to provide a mechanism for controlling the polarization modes of the emitted light. A square-lattice photonic crystal with the elliptical unit cell structure has been fabricated and integrated with a gain media. The observed coherent 2D lasing action with a single wavelength and controlled polarization is in good agreement with the predicted behavior.

605 citations

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PARC

^{1}TL;DR: A first-principles approach to deriving the relative energies of valence and conduction bands at semiconductor interfaces is presented, along with a model which permits a simple interpretation of these band offsets, and results are reported for a large number of lattice-matched interfaces.

Abstract: We present a first-principles approach to deriving the relative energies of valence and conduction bands at semiconductor interfaces, along with a model which permits a simple interpretation of these band offsets. Self-consistent density-functional calculations, using ab initio nonlocal pseudo-potentials, allow us to derive the minimum-energy structure and band offsets for specific interfaces. Here we report results for a large number of lattice-matched interfaces, which are in reasonable agreement with reported experimental values. In addition, our systematic analysis leads to the important conclusions that, for the cases considered, the offsets are independent of interface orientation and obey the transitivity rule, to within the accuracy of our calculations. These are necessary conditions for the offsets to be expressible as differences between quantities which are intrinsic to each of the materials. Based on the information obtained from the full interface calculations, we have developed a new and simple approach to derive such intrinsic band offsets. We define a reference energy for each material as the average (pseudo)potential in a “model solid,” in which the charge density is constructed as a superposition of neutral (pseudo)atomic densities. This reference depends on the density of each type of atom and the detailed form of the atomic charge density, which must be chosen consistently for the different materials. The bulk band structures of the two semiconductors are then aligned according to these average potential positions. For many cases, these model lineups yield results close to those obtained from full self-consistent interface calculations. We discuss the comparison with experiments and with other model theories.

508 citations