= Chemical potential of a two-dimensional ideal Fermi gas
{title2=$\mu=\epsilon_F+k_BT\ln(1-e^{-\epsilon_F/(k_BT)})$}
For a constant total <density of states> $D$ above a zero-energy band bottom, integrating the Fermi-Dirac occupation gives $N=Dk_BT\ln(1+e^{\mu/(k_BT)})$. With $\epsilon_F=N/D$, inversion gives the displayed <chemical potential>. It approaches $\epsilon_F$ from below with an exponentially small correction at low <temperature>, rather than the usual three-dimensional quadratic correction. This formula assumes an ideal parabolic band extending to arbitrarily high <energy>.
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