  Recent theoretical studies have suggested that the suddenly recoiled atom
struck by dark matter (DM) particle is much more likely to excite or lose its
electrons than expected. Such Migdal effect provides a new avenue for exploring
the sub-GeV DM particles. There have been various attempts to describe the
Migdal effect in liquids and semiconductor targets. In this paper we
incorporate the treatment of the bremsstrahlung process and the electronic
many-body effects to give a full description of the Migdal effect in bulk
semiconductor targets diamond and silicon. Compared with the results obtained
with the atom-centered localized Wannier functions (WFs) under the framework of
the tight-binding (TB) approximation, the method proposed in this study yields
much larger event rates in the low energy regime, due to a $\omega^{-4}$
scaling. We also find that the effect of the bremsstrahlung photon mediating
the Coulomb interaction between recoiled ion and the electron-hole pair is
equivalent to that of the exchange of a single phonon.
