Pauli reduction of the pinned-edge mass-action product

For chemical potential at the conduction edge, divide the exact product by the classical prediction. The ratio is $F_{1/2}(0)e^x{F}_{1/2}(-x)$, where $x=E_g/(k_{B}T)$. It is less than one, approaches $F_{1/2}(0)$ as $T\to 0$, and approaches its square in the formal high-temperature parabolic model.