Detailed studies of the luminescent properties of the Si-based 2D photonic crystal (PhC) slabs with air holes of various depths are reported. Ge self-assembled quantum dots served as an internal light source. It was obtained that changing the air hole depth is a powerful tool which allows tuning of the optical properties of the PhC. It was shown that increasing the depth of the holes in the PhC has complex influences on its overall photoluminescence (PL) response due to the simultaneous influences of counteracting factors. As a result, the maximal increase in the PL signal of more than two orders of magnitude was obtained for some intermediate, but not full, depth of the PhC’s air holes. It was demonstrated that it is possible to engineer the PhC band structure in such a way as to construct specific states, namely bound states in continuum (BIC), with specially designed dispersion curves being relatively flat. In this case, such states manifest themselves as sharp peaks in the PL spectra, and have high Q-factors which are larger than those of radiative modes and other BIC modes without such a flat dispersion characteristic.