  Different dark matter (DM) candidates could have different types of DM-lepton
and/or DM-quark interactions. For direct detection experiments, this leads to
diversity in the recoil spectra, where both DM-electron and DM-nucleus
scatterings may contribute. Furthermore, kinematic effects such as those of the
inelastic scattering can also play an important role in shaping the recoil
spectra. In this work, we systematically study signatures of the light
exothermic inelastic DM from the recoil spectra including both the DM-electron
scattering and Migdal effect. Such inelastic DM has mass around (sub-)GeV scale
and the DM mass-splitting ranges from 1keV to 30keV. We analyze the direct
detection sensitivities to such light inelastic DM. For different inelastic DM
masses and mass-splittings, we find that the DM-electron recoil and Migdal
effect can contribute significantly and differently to the direct detection
signatures. Hence, it is important to perform combined analysis to include both
the DM-electron recoil and Migdal effect. We further demonstrate that this
analysis has strong impacts on the cosmological and laboratory bounds for the
inelastic DM.
