The epilayer of vertically stacked, self-assembled InAs Quantum Dots (QDs) was grown by MBE with solid sources in non-cracking K-cells. An attractive feature of vertically stacked InAs^AlGaAs quantum dots, which were buriea in AlGaAs high potential barrier and spacer epilayer, exhibits an unknown macroscopic quantum phenomenoa In the vertically aligned QDs, due to many-body effect and quantum-mechanical renormalization, the electron ground state splits into series of peaks of wruch the intensity gradually, systematically decreases to redshift direction with a wavelength constant Photoluminescence (PL) of quantum dots embedded in high potential barriers is studied as functions of barrier thickness and temperature. With the increase of barrier thickness, both of strengthened two-dimensional electron gas (2DEG) structure and strongly localized electron wave functions can increase the carrier recombination-The PL recombination characteristic of the samples with the barriers adjacent to a Si-doping GaAs layer is different from that of samples with barrier ac^acent to an i-GaAs layer.