Two-level donor occupancy (source code)

= Two-level donor occupancy
{title2=$P_b=[1+g e^{-\Delta/(k_BT)}]^{-1}$}

A nondegenerate donor-bound state of <energy> zero and an excited representative conduction level of <energy> $\Delta>0$ and degeneracy $g$ have the displayed bound <probability> by canonical state counting. The inferred degeneracy from one measurement is $g=(P_b^{-1}-1)e^{\Delta/(k_BT)}$. At finite fixed $g$, the <probability> decreases from1 toward $1/(1+g)$ as <temperature> grows. A temperature-independent effective degeneracy is an assumed two-level approximation; a full conduction-band <density of states> can behave differently.