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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.

Theoretical investigation of the intraband transition in a cylindrical quantum dot with the Kratzer confining potential is considered in the presence of external electric and magnetic fields. The intraband linear absorption spectra have been calculated for GaAs cylindrical quantum dots with different sizes. Moreover, the behavior of the linear absorption spectra is observed for various regimes of magnetic quantization and depending on the strength of the electric field. The density probability of the electro has been presented depending on the value of the external electric field. It has been shown that the shift of electron localization area is asymmetric depending on the external electric field direction.

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