Fermi level

An electronic circuit in thermodynamic equilibrium will have a constant Fermi level throughout its connected parts.

This also means that the voltage (measured with a voltmeter) between any two points will be zero, at equilibrium. Note that thermodynamic equilibrium here requires that the circuit be internally connected and not contain any batteries or other power sources, nor any variations in temperature.

The location of µ within a material's band structure is important in determining the electrical behaviour of the material.

It follows that the Fermi–Dirac distribution function can be written as

the maximum kinetic energy of a fermion in an idealized non-interacting, disorder free, zero temperature Fermi gas

Much like the choice of origin in a coordinate system, the zero point of energy can be defined arbitrarily. Observable phenomena only depend on energy differences. When comparing distinct bodies, however, it is important that they all be consistent in their choice of the location of zero energy, or else nonsensical results will be obtained. It can therefore be helpful to explicitly name a common point to ensure that different components are in agreement. On the other hand, if a reference point is inherently ambiguous (such as "the vacuum", see below) it will instead cause more problems.

The parameter that gives the best approximation to universality is the Earth-referenced Fermi level suggested above. This also has the advantage that it can be measured with a voltmeter.

In this case one must be precise about the thermodynamic definition of the chemical potential as well as the state of the device: is it electrically isolated, or is it connected to an electrode?