We have theoretically investigated the electronic states in a core/shell pyramidal quantum dot with GaAs core embedded in AlGaAs matrix. This system has a quite similar recent experimental realization through a cone/shell structure [Phys. Status Solidi-RRL 13, 1800245 (2018)]. 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. For the numerical solution of the resulting three-dimensional partial differential equation we have used a finite element method. 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. 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.

Following the chronological stages of calculations imposed by the WIEN2K code, we have performed a series of density functional theory calculations, from which we were able to study the effect of strain on the kesterite structures for two quaternary semiconductor compounds Cu${}_2$ZnGeS${}_4$ and Cu${}_2$ZnGeSe${}_4$. Remarkable changes were found in the electronic and optical properties of these two materials during the application of biaxial strain. Indeed, the band gap energy of both materials decreases from the equilibrium state, and the applied strain is more pronounced. The main optical features are also related to the applied strain. Notably, we found that the energies of the peaks present in the dielectric function spectra are slightly shifted towards low energies with strain, leading to significant refraction and extinction index responses. The obtained results can be used to reinforce the candidature of Cu${}_2$ZnGeX${}_4$(X = S, Se) in the field of photovoltaic devices.