Is the Fermi-Dirac distribution equal to zero at the state of highest energy?

[chikchok]

TL;DR

Fermi-Dirac distribution

I`m sorry if this seems too obvious, just trying to clarify something. When Fermi-Dirac distribution is equal to zero , can we assume it is the state of

the highest energy? (Because the propability of occupation is zero)

 

[DrClaude]

$f(\epsilon)$ goes to zero as $\epsilon \rightarrow \infty$ for a finite temperature ($T>0$).

At absolute zero, $T=0$, then $f(\epsilon > \epsilon_\mathrm{F}) = 0$, where $\epsilon_\mathrm{F}$ is the Fermi energy.