The issue of quantum mechanical coupling between a semiconductor quantum dot and a quantum well is studied in two families of GaAs- and InP- based structures at cryogenic temperatures. It is shown that by tuning the quantum well parameters one can strongly disturb the 0D-character of the coupled system ground state, initially located in a dot. The out-coupling of either an electron or a hole state from the quantum dot confining potential is viewed by a significant elongation of the photoluminescence decay time constant. Band structure calculations show that in the GaAs-based coupled system at its ground state a hole remains isolated in the dot, whereas an electron gets delocalized towards the quantum well. The opposite picture is built for the ground state of a coupled system based on InP.