Fermi energy represents the chemical potential of the electrons is true or false
Answers
The Fermi level or chemical potential μμ for a system of electrons is defined as the number needed to make the distribution function,
f(ϵ)=1exp[(ϵ−μ)/kBT]+1f(ϵ)=1exp[(ϵ−μ)/kBT]+1
where ϵϵ is the energy, kBkB is the Boltzmann constant and TT is the temperature, match the actually energy distribution of electrons in the systemno electrons at energies outside of the bands, but given an allowed energy ϵϵ the probability of finding an electron in that energy state is proportional to f(ϵ)f(ϵ). If there are NN electrons in the system, the chemical potential is defined by the relation,
N≡∑ϵg(ϵ)exp[(ϵ−μ)/kBT]+1N≡∑ϵg(ϵ)exp[(ϵ−μ)/kBT]+1
where g(ϵ)g(ϵ) is the degeneracy of the energy ϵϵ. If you work out the free energy of the electrons, you find that it is equal to F(T,V,N)=−pV+NμF(T,V,N)=−pV+Nμ, where pp is the pressure and VV is the volume. So, the energy required to add an electron to the system, keeping the volume and temperature constant, is
F(T,V,N+1)−F(T,V,N)=μ