Second and third-harmonic generation subjected to an external electric field in a strongly oblate ellipsoidal quantum dot have been studied in the framework of the present work. The adiabatic approximation has been used to divide the system into two subsystems and solve the problem analytically. The calculations have been applied for the strongly oblate ellipsoidal quantum dot made of GaAs. The influence of the external electric field on the matrix element change for the quantum transitions between energy levels of the electron have been discussed. As the obtained results show the increase of the electric field causes the peaks of the second and third-harmonic generation to rise and blueshifts their positions of the spectrum. However, the increase of the semi-minor axis of the strongly oblate ellipsoidal quantum dot leads to a redshift of the resonant peaks and a rise in their magnitudes.
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