Impurity band ($W\sim E_b\exp [-n^{-1/3}/a_b]$)

An energy band formed when localized impurity levels hybridize. For hydrogenic donor states, a typical donor separation $n^{-1/3}$ gives an exponentially small hopping integral and hence an exponentially narrow bandwidth when $n^{-1/3}\gg a_b$. An idealized half-filled band with two spin states per donor has spin-summed density of states of order $2n/W$ per volume; its Pauli paramagnetism is $\chi \sim {\mu }_0(g{\mu }_B/2{)}^2(2n/W)$. That expression requires $k_{B}T\ll W$ and does not by itself describe localization or strong Coulomb interactions.