= Full ionization versus isolated donor occupation
The comparison $E_B\ll k_BT$ 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.
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