Extended Definitions of Fermi Level and Fermi Energy and How Lattice Expansion Affects Fermi Energy

Literature and internet discussions about the basic statistical mechanics of electron emitters often display inconsistency in terminology. To counteract confusion, this Poster gives careful “extended” / “adjusted” definitions for the terms “Fermi level” and “Fermi energy”. The definitions given are unambiguous, are valid for all materials (metals and non-metals), are valid for both small and large bodies, are valid at all temperatures of practical interest, and are suitable for use in the context of electronic circuits. It is also confirmed that, in the theory of temperature effects in the Sommerfeld model, the total-energy difference K
F
(T) between the Fermi level and the Sommerfeld-well base is much more significantly affected by thermally induced lattice-expansion effects than by the constant-volume statistical-mechanical effects discussed in textbooks. To show this, simple formulas for the lattice-expansion effect on K
F
(T) are reported. The resulting numerical predictions have not been found in existing literature. In absolute terms the temperature-dependent change in Fermi energy due to lattice expansion is relatively small compared to the Fermi energy itself (typically around 1% or less), so significant practical implications would not be expected.