Roughly, the energy up to which a material’s electron states are filled – like the water line in a partly filled glass. Where it sits relative to the decides how many charges can move and whether they are , the empty places electrons leave behind. A raises and lowers it, like pouring water in or out.
Going deeper
The Fermi level is the energy at which a state would be half occupied. It need not correspond to any state that exists – in a semiconductor it usually sits inside the gap – and where it lies decides how many carriers there are and whether they are electrons or holes.
Not a level, but a reference
In thermal equilibrium the probability that a state of energy E is occupied is given by the Fermi–Dirac function, which equals one half at the Fermi level. At absolute zero this is a sharp step: every state below is full, every state above is empty. At finite temperature the step softens over an energy of roughly kT, about 26 meV at room temperature.
Strictly, the Fermi level is the electrochemical potential of the electrons, which is why it must be flat across any system in equilibrium – that is what “levels line up” means when two materials touch. In a it usually lies inside the band gap, where there are no states at all, and no contradiction arises: it is a reference for occupation, not a state.
Why its position matters
The distance from the Fermi level to a band edge sets the exponentially: a shift of 60 meV changes it by about a factor of ten at room temperature. Near the conduction band the material is n-type, near the valence band p-type, near mid-gap it is nearly intrinsic and resistive. The same reasoning applies at an interface, where the offset between the Fermi level and the band edges of the neighbour fixes barrier heights.
In the position is unusually movable. A gate voltage shifts it directly, adsorbates and shift it by , and in graphene, with no gap, a modest gate sweeps it through the and turns electrons into holes. can track this: the frequencies of graphene shift measurably as the Fermi level moves, which is how gated doping is calibrated optically.
When it refuses to move: pinning
At a metal–semiconductor contact one would expect the barrier to follow the metal’s . Often it does not. States induced in the semiconductor gap by the metal, and defects created by deposition, can hold the Fermi level near a fixed position regardless of which metal is used – Fermi-level pinning – which is why contact engineering in 2D semiconductors is so difficult and why gentle, damage-free contacting schemes matter.
Two more cautions. Out of equilibrium there is no single Fermi level: under illumination or bias, electrons and holes are described by separate quasi-Fermi levels. And a measured work function is a surface property, easily changed by an adsorbed layer, so it should be quoted with the preparation that produced it.
For specialists
The electrochemical potential of electrons: the energy at which a state has 50 % occupation in thermal equilibrium. Its position relative to the band edges sets carrier density and type; at metal–semiconductor contacts, interface states can pin it and fix the Schottky barrier.