A calculation of the ground state energies of a trion (X−) and an off-center negatively charged donor (D−) in InyAl1–yAs/AlxGa1–xAs quantum disks of finite height and square-well potential are presented. The fractal dimension method is used to find the D− energy. The X− energy is calculated within the framework of the adiabatic approximation. (© 2005 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)