= Donor charge-state degeneracy
{title2=$n_{\rm full}/n_{\rm empty}=r e^{\beta(\mu-\epsilon_D)}$}
Let an isolated <donor impurity> admit an empty ionized state with statistical weight $g_0$ and a singly occupied neutral state with statistical weight $g_1$, with double occupation excluded. Its <grand canonical ensemble> weights are $g_0$ and $g_1e^{-\beta(\epsilon_D-\mu)}$, so $r=g_1/g_0$ multiplies the occupied-to-empty ratio. A nondegenerate empty state and two allowed <electron spin> orientations give $r=2$; a simplified single-state occupation model uses $r=1$. With negligible <electron holes> and uncompensated <donor impurities>, <charge neutrality> and nondegenerate conduction occupation imply $n^2/(N_D-n)=(N_c/r)e^{-E_i/(k_BT)}$, where $E_i$ is the donor binding <energy> and $N_c$ the <effective density of states>.
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