  Light trapping is a constant pursuit in photonics because of its importance
in science and technology. Many mechanisms have been explored, including the
use of mirrors made of materials or structures that forbid outgoing waves, and
bound states in the continuum that are mirror-less but based on topology. Here
we report a compound method, combing mirrors and bound states in the continuum
in an optimized way, to achieve a class of on-chip optical cavities that have
high quality factors and small modal volumes. Specifically, light is trapped in
the transverse direction by the photonic band gap of the lateral
hetero-structure and confined in the vertical direction by the constellation of
multiple bound states in the continuum. As a result, unlike most bound states
in the continuum found in photonic crystal slabs that are de-localized Bloch
modes, we achieve light-trapping in all three dimensions and experimentally
demonstrate quality factors as high as $Q = 1.09 \times 10^6$ and modal volumes
as low as $V = 3.56~ \mu m^3$ in the telecommunication regime. We further prove
the robustness of our method through the statistical study of multiple
fabricated devices. Our work provides a new method of light trapping, which can
find potential applications in photonic integration, nonlinear optics and
quantum computing.
