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.
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