  Germanium self-assembled nanoislands and quantum dots are very prospective
for CMOS-compatible optoelectronic integrated circuits but their luminescence
intensity is still insufficient for many practical applications. Here, we
demonstrate experimentally that photoluminescence of Ge nanoislands in silicon
photonic crystal slab with hexagonal lattice can be dramatically enhanced due
to the involvement in the emission process of the bounds states in the
continuum. We experimentally demonstrate more than two orders of magnitude peak
photoluminescence enhancement and more than one order of magnitude integrated
PL enhancement in a photonic crystal slab compared with the non-structured
sample area. We theoretically study this effect by the Fourier modal method in
the scattering matrix form and demonstrate the appearance of quasi-normal
guided modes in our photonic crystal slab. We also describe their symmetry in
terms of group theory. Our work paves the way towards a new class of
optoelectronic components compatible with silicon technology.
