# Why is there a difference between Fermi levels in metals and metal-oxide semiconductors (MOS)?

Why are Fermi levels in metals lower than the Fermi level of $\text{p}$-substrates in metal-oxide semiconductors (MOS)? Specifically, why is there a difference of $qV$?

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The metal gate and the semiconductor, separated by an insulator in the MOS structure, can be each be considered to be a system in thermodynamic equilibrium und thus have a separate electrochemical potential, i.e. Fermi level. When you apply a voltage $V$ between the systems the Fermi levels will be separated energetically by $qV$. When the metal gate and the semiconductor of a MOS structure are short circuited, they constitute a single system with one Fermi level. This corresponds to the Fermi levels being aligned for an applied zero voltage $V=0$.
• @NailTosun - When there is a potential difference between two thermodynamic systems, of which each is in equilibrium (here the gate and the semiconductor bulk), the chemical potentials (Fermi levels) of these systems will differ by $qV$. – freecharly May 23 '18 at 22:35