Pauli reduction of the pinned-edge mass-action product
= Pauli reduction of the pinned-edge mass-action product
{c}
For <chemical potential> at the conduction edge, divide the exact product by the classical prediction. The ratio is $F_{1/2}(0)e^xF_{1/2}(-x)$, where $x=E_g/(k_BT)$. It is less than one, approaches $F_{1/2}(0)$ as $T\to0$, and approaches its square in the formal high-<temperature> parabolic model.