Carrier densities with chemical potential pinned to a band edge
= Carrier densities with chemical potential pinned to a band edge
For equal-mass conduction and valence edges at $0,-E_g$ and fixed $\mu=0$, $n=N(T)F_{1/2}(0)$ and $p=N(T)F_{1/2}[-E_g/(k_BT)]$, where $N(T)=2[mk_BT/(2\pi\hbar^2)]^{3/2}$. Other states pinning the <chemical potential> can compensate the unequal carrier charges; imposing intrinsic <charge neutrality> in addition would change the problem.