Normalized complete Fermi-Dirac integral
= Normalized complete Fermi-Dirac integral
{c}
{title2=$F_j(\eta)$}
The convention $F_j(\eta)=\Gamma(j+1)^{-1}\int_0^\infty x^j/[1+e^{x-\eta}]\,dx$ is useful for parabolic-band carrier densities. In three dimensions, a spin-degenerate single valley has $n=2[mk_BT/(2\pi\hbar^2)]^{3/2}F_{1/2}[(\mu-E_c)/(k_BT)]$. Other conventions omit the gamma normalization, so prefactors must be stated.