 Full ionization versus isolated donor occupation

The comparison $E_B\ll k_{B}T$ alone does not establish full ionization for arbitrary donor concentration. Localized-level occupation depends on the chemical potential through charge neutrality. If donor orbit radii greatly exceed their separation, an independent isolated-hydrogenic-level model itself fails and overlapping impurity states or band reconstruction are needed. A stipulated extended-carrier density can still define a conductivity calculation, but it must not simultaneously be interpreted as an independently verified dilute-donor equilibrium result.