Question

In Boltzmann distribution, f(E)=A*exp(-E/kT).
If E=Fermi-Energy(Ef), then It can be written as f(E)=A*exp(-Ef/2kT).

Do you know anyway that I can have Boltzmann distribution either:

f(E)=A*exp(-E/2kT)


or



f(E)=A*exp(-Ef/2*2kT)