1, 2, 3, 4, 5 have studied the electronic structure for electrons confined in pyramidal and conical QDs. Using an analytical solution -valid for structures with apical angle less than π/6-, and contrasting and confirming the results with those obtained by means of numerical solutions using a finite element method (FEM), Bahramiyan et al., Gil et al., and Niculescu et al. The studies have considered effects of stationary electric and magnetic fields, hydrostatic pressure, temperature, non-resonant intense laser radiation, optical phonons, stresses on the surfaces, wetting layer (WL), presence of shallow impurities, and excitonic correlations, among others. There are reports of spherical, cubic, pyramidal, conical, core-shell, ellipsoidal, and truncated pyramidal QDs. Theoretical studies of the electronic and optical properties of carriers confined within QDs have included a wide variety of shapes and external effects on the system. Chemical synthesis is another technique, widely employed to produce, in this case, core-shell QDs and nanoparticles. This last technique has been implemented with highly reproducible results to obtain self-assembled pyramidal QDs in systems where the zero-dimensional system has been formed by the coupling between two materials with sufficiently different lattices constants to give rise to strain effects, which is finally the basis for the formation of QD. Several methods have been developed for obtaining the zero-dimensional QDs: Molecular Beam Epitaxy (MBE), Chemical Vapour Deposition (CVD), and Stranski Krastanov growth. The latter are widely referred in the literature as artificial atoms, due to the discrete nature of the electronic structure for the confined carriers. Among the more notorious we can cite: the two-dimensional quantum wells (QW), the one-dimensional quantum well-wires (QWW), and the zero-dimensional quantum dots (QD). Along these lines, the increasing use of low-dimensional semiconductor nanostructures has become a key element for the development of the most advanced devices. Applications in the construction of high resolution images in biomedicine, solid state lasers, and for photovoltaic generation in solar panels are known. These state-of-the-art systems allow to improve the operating capabilities of sensors, switches, emitters, filters, and optical and electronic transport systems, among others. Since the 1970s to date, the interest in the development and understanding of the physical bases that underline the operation of novel electronic and optoelectronic components has been growing. The calculation of the non-permanent electric polarization via the off-diagonal intraband dipole moment matrix elements allows to consider the related optical response by evaluating the coefficients of light absorption and relative refractive index changes, under different applied magnetic field configurations. A detailed study of the conduction band states wave functions and their associated energy levels is presented, with the analysis of the effect of the geometry and the external probes. For the numerical solution of the resulting three-dimensional partial differential equation we have used a finite element method. The research has been performed within the effective mass approximation taking into account position-dependent effective masses and the presence of external electric and magnetic fields. This system has a quite similar recent experimental realization through a cone/shell structure. We have theoretically investigated the electronic states in a core/shell pyramidal quantum dot with GaAs core embedded in AlGaAs matrix.
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