A Hamiltonian operator in assessing the energy levels and wavefunctions of quantum dots (QDs) was proposed. The finite element method was used to solve the numerical Schrödinger equation for envelope function in the effective mass approximation. Within this model, we have investigated QDs with different geometries (cone, lens and dome-shaped dot). While it is easy to attain stability for conical QDs, it is difficult with lens QDs. Strain and mole-fraction effects are also studied. Our results coincide with the experimental one.
Four wave mixing analysis is stated for quantum dot semiconductor optical amplifiers (QD SOAs) using the propagation equations (including nonlinear propagation contribution) coupled with the QD rate equations under the saturation assumption. Long wavelength III-nitride InN and AlInN QD SOAs are simulated. Asymmetric behavior due to linewidth enhancement factor is assigned. P-doping increases efficiency. Lossless efficiency for InAlN QDs for longer radii is obtained. Carrier heating is shown to have a considerable effect and a detuning dependence is expected at most cases. InN QD SOAs shown to have higher efficiency.
In corner areas of structures, high stress values and gradients occur, and lead to stress concentrations. Infinite stress and deformations are determined by a solution of the linear elasticity theory problem in the area with a wedge-shape boundary notch. Infinite solutions of the elasticity problem occur under impact of forced deformations, when a surge of the deformation value reaches beyond the area boundary. Relative values of stress concentrations for corner area zones make no more sense. At finite displacements, high deformation and stress values occur in the corner zones of the area. For a linear statement of the elasticity theory problem, at minor deflections, not only first-order, but also second-order derivatives of the displacements function are significant. To account for finite deformations of such corner zones of the area, correct formulations of elasticity problems are required. Study objective: influence determination of the infinitesimal order of the deformation on the appearance of equilibrium equations of an area with induced (temperature) deformations. This allows for the analysis of the influence of linear, shear deformations, and of the swing on the solution of the elasticity problem with induced deformations.
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