The second and third harmonic generation of GaAs/Ga$$_{1-x}$$Al$$_{x}$$As spherical quantum dots under a confining potential

The objective of this study is to theoretically discuss the impact of additional tuning factors on the second and third harmonic generation (SHG and THG) of GaAs/Ga [Formula omitted]Al [Formula omitted]As quantum dots (QDs) with the inversely quadratic Hellmann-Kratzer (IQHK) potential by adjusting the depth of potential and radius of the QDs. Within the formula method, the energy levels and the corresponding wave-functions are calculated by solving the Schrödinger equation. Then, the SHG and THG coefficients are deduced using the density matrix formalism with an iterative procedure. Finally, the results indicate that the additional tuning factors and structural parameters have significant effects on the peak positions and magnitudes of the calculated SHG and THG coefficients. Graphic abstract