Why $\E_f$ instead of $\mu$ in the energy integral?

Physics Q&A
1

Hi,
In calculating the energy of electrons using the integral: E = E_g(E) \frac{1}{e^{(E - \mu)/kT} + 1} \ dE why do we use E_f (Fermi energy) instead of (\mu) in the Fermi distribution? I thought that E_f was defined as the chemical potential only at T = 0 K. So, why do we use E_f in this integral when the integral is not just for T = 0 K but for all temperatures?

2

You are completely right that, strictly speaking, we should use \mu instead of E_F. However, \mu\approx E_F whenever k_BT\ll E_F, which is true at any reasonable temperature, since T_F\approx 10000 K. Therefore, we can safely replace \mu by E_F