  When a nucleus in an atom undergoes a collision, there is a small probability
to inelastically excite an electron as a result of the Migdal effect. In this
Letter, we present a first complete derivation of the Migdal effect from dark
matter-nucleus scattering in semiconductors, which also accounts for
multiphonon production. The rate can be expressed in terms of the energy loss
function of the material, which we calculate with density functional theory
(DFT) methods. Because of the smaller gap for electron excitations, we find
that the rate for the Migdal effect is much higher in semiconductors than in
atomic targets. Accounting for the Migdal effect in semiconductors can
therefore significantly improve the sensitivity of experiments such as DAMIC,
SENSEI and SuperCDMS to sub-GeV dark matter.
