Fermi level

Niveau de Fermi (Fr). Fermi-Energie, Fermi-Niveau (Ge). Livello di Fermi (It). Энергия Ферми (Ru). フェルミ準位 (Ja). Nivel de Fermi, Energía de Fermi (Sp).

Definition

The Fermi level is also known as the Fermi energy. Two definitions are proposed; the first concentrates on a general formal definition while the second focusses on theoretical convergence for use by XAS users and programs.

(1) In an independent particle approach to the description of a fermion system (i.e. particles obeying Pauli’s exclusion principle), the Fermi level is the energy value lying between the highest occupied level and the lowest unoccupied level, usually defined as their average. If the energy level spectrum is a continuum (or almost a continuum) the three levels coincide. In a many-body approach, the Fermi level is the energy necessary for adding or subtracting a particle from the system. This definition encompasses the non-interacting case.

Like all energy states, the Fermi level is measured from the vacuum level. In XAS spectra the Fermi level is below or at the first allowed transition, depending on the system and the absorption edge.

(2) In X-ray absorption spectroscopy (XAS), the Fermi energy dictates possible pre-edge features and explains the possibility or impossibility of open scattering channels adding to the near-edge structure. When theoretical formalisms compute the reference Fermi energy, crucial for the XANES region, the convergence of the complete quantum mechanical system is an absolute requirement, whether atomic, cluster, or periodic boundary conditions are used. The lack of convergence for theoretical formalisms can at this time lead to systematic errors in the determination of the Fermi energy and corresponding pre-edge structure of order 1-10 eV in the X-ray regime and should be considered carefully as this affects the interpretation of XAFS and XANES.