Considering the increasing number of experimental results in the manufacturing process of quantum dots (QDs) with different geometries, and the fact that most numerical methods that can be used to investigate quantum dots with nontrivial geometries require large computational capacities, the finite element method (FEM) becomes an incredibly attractive tool for modeling semiconductor QDs. In the current article, we used FEM to obtain the first twenty-six probability densities and energy values for the following GaAs structures: rectangular, spherical, cylindrical, ellipsoidal, spheroidal, and conical QDs, as well as quantum rings, nanotadpoles, and nanostars. The results of the numerical calculations were compared with the exact analytical solutions and a good deviation was obtained. The ground-state energy dependence on the element size was obtained to find the optimal parameter for the investigated structures. The abovementioned calculation results were used to obtain valuable insight into the effects of the size quantization’s dependence on the shape of the QDs. Additionally, the wavefunctions and energies of spherical CdSe/CdS quantum dots were obtained while taking into account the diffusion effects on the potential depth with the use of a piecewise Woods–Saxon potential. The diffusion of the effective mass and the dielectric permittivity was obtained with the use of a normal Woods–Saxon potential. A structure with a quasi-type-II band alignment was obtained at the core size of ≈2.2 nm This result is consistent with the experimental data.
Linear and nonlinear optical properties in colloidal CdSe/CdS core/shell quantum dots with different sizes have been theoretically investigated in the framework of effective mass approximation. The electron states in colloidal CdSe/CdS core/shell quantum dots have been calculated using the finite element method. The intraband linear and nonlinear absorption spectra have been calculated for colloidal CdSe/CdS core/shell quantum dots with different sizes. In addition, the dependences of the linear and nonlinear refractive index change on the incident light energy have been calculated. In the last section of the paper the second- and third-order harmonic generation spectra have been presented.
By using the numerical discretization method within the effective-mass approximation, we have theoretically investigated the exciton-related Raman scattering, interband absorption and photoluminescence in colloidal CdSe/CdS core/shell quantum dots ensemble. The interband optical absorption and photoluminescence spectra have been revealed for CdSe/CdS quantum dots, taking into account the size dispersion of the ensemble. Numerical calculation of the differential cross section has been presented for the exciton-related Stokes–Raman scattering in CdSe/CdS quantum dots ensemble with different mean sizes.
The current work used the effective mass approximation conjoined with the finite element method to study the exciton states in a conical GaAs quantum dot. In particular, the dependence of the exciton energy on the geometrical parameters of a conical quantum dot has been studied. Once the one-particle eigenvalue equations have been solved, both for electrons and holes, the available information on energies and wave functions is used as input to calculate exciton energy and the effective band gap of the system. The lifetime of an exciton in a conical quantum dot has been estimated and shown to be in the range of nanoseconds. In addition, exciton-related Raman scattering, interband light absorption and photoluminescence in conical GaAs quantum dots have been calculated. It has been shown that with a decrease in the size of the quantum dot, the absorption peak has a blue shift, which is more pronounced for quantum dots of smaller sizes. Furthermore, the interband optical absorption and photoluminescence spectra have been revealed for different sizes of GaAs quantum dot.
Talbot effect is a self-imaging or lensless imaging phenomenon of a periodic grating illuminated by a collimated light beam at regular distances from the grating. Research on the Talbot effect has recently made significant strides thanks to the quick development of optical superlattices. The emergence of various applications of this effect in fields such as optics, acoustics, X-ray, plasmonics, and information processing has led to the increasing importance of obtaining a Talbot carpet with the use of different structures. In this paper, we investigate the Talbot effect that originates from the tunneling effect between an ensemble of vertically coupled cylindrical quantum dots (QDs). The Talbot carpet can be manipulated by changing the parameters of the QD system. In the current paper, two modified Pöschl-Teller potentials were used to model the QDs ensemble. The exciton’s lifetime and tunneling time’s dependence on the first QD’s potential half-width is found for a fixed value of the external electric field. The nonlinear changes in the refractive index and absorption spectrum dependent on the tunneling effect are obtained. Afterward, the Talbot carpet formation is investigated, particularly the dependences of the formed periodic wavefront’s visibility on medium length, coupling field’s strength, and tunneling parameter. Finally, we have observed the intensity distribution of the diffraction field at Talbot half-distance.
Recently the interest in chalcopyrite semiconductor nanostructures has increased because of their non-toxicity and their wide direct bandgap. Likewise, structures with non-trivial geometry are particularly interesting because of their electronic, optical, and magnetic properties. In the current article, the finite element method was used in conjunction with the effective mass approximation to theoretically investigate the properties of a chalcopyrite AgInSe2 nanotadpole in the presence of an hydrogen like shallow off-center impurity. The morphology of the nanotadpole gives it excellent hydrodynamic properties and is ideal for a wide range of applications. The probability densities for various impurity positions and energy levels were obtained. The results suggested a strong dependence of the behavior of the electron on the impurity positions and the orientation of the wave function. The investigation of the nanotadpole’s energy spectra and their comparison with the cylindrical and spherical quantum dots suggest that the spectrum has degenerate states similar to the spherical case, however at some ranges, the levels behave similarly to the cylindrical case. The binding energy's dependence on the nanotadpole's size and the impurity position was obtained. The dependence of the diamagnetic susceptibility on the impurity position was calculated. An extensive investigation of the photoionization cross-section was carried out for the ground and the first two excited states as the initial states and the first twenty excited states as the final states.
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