We propose a semiconductor heterostructure that allows an effective control of the shape of the carriers wavefunctions by varying just one main structural parameter. The structure is formed by a type II quantum dot and a type I quantum well. We present the results of calculations for a particular system consisting of an InP/GaAs quantum dot and an InGaAs/GaAs quantum well using a simple effective mass model that provides a good insight on our structure. We show that the wavefunction of the carrier that remains outside the dot changes from a spheroidal to a ring-like shape depending mainly on the separation between the well and the dot layers. This change has a significant impact on relevant excitonic properties such as its lifetime and electrical dipole, and it also determines the possibility of observing the optical Aharonov–Bohm effect.