Electronic Structure in Solids – Definitions
- Complementary Techniques
When discussing various principles of photoemission, a number of terms will be used which may not be commonplace among the vernacular of every chemist or materials scientist. It is important to hold a grasp upon to what these terms refer, so in this article we hope to cover the relevant terms of which knowledge is helpful for the understanding of XPS and related techniques. We will cover these terms using a simplified model of a semiconductor system (since such systems contain all the terms we wish to describe) in figure 1. 
This is formally known as the single particle energy gap, or transport gap EG. This is defined as the energy between the conduction band minimum (CBM) and valence band maximum (VBM) energy levels (inorganic semiconductors) or the highest occupied molecular orbital and lowest unoccupied molecular orbital (organic semicondutors).(1) This is interchangeable with the optical band gap EOPT (excitiation via photon absorption) for inorganic semiconductors, but distinct from EOPT for organic semiconductors.(2)
Moving out of the solid now, we have the vacuum level, EVAC, which is the energy level of an electron removed from the solid and at rest. The term is slightly vague in that it refers to an electronic state at rest (zero kinetic energy, Ek) at a distance where it may still experience the surface dipole, usually defined as a ‘few nanometers’. A second term, EVAC(∞) described the electron at a distance far removed from the effects of the surface.
Next, we describe the Fermi level, EF, which is defined as the highest energy level of the electronic states in a solid when at absolute zero.
The work function, WF, may be simple characterized as the energy to take an electron from EF to EVAC. A more technical description is that the work function is the difference betweeen the electrochemical potential (μ¯ ) of electrons in the bulk and the electrostatic potential energy (−eΦvac) of an electron in the vacuum just outside the surface WF=−eΦvac−μ¯.(3)
Finally we have our ionization energy (IE) and electron affinity (EA). While ionization energy should be familiar to most readers (the minimum energy to remove an electron to EVAC) electron affinity has a slightly different definition than some will be familiar with. When dealing with solid state chemistry (or physics), the electron affinity is defined as the energy released when an electron moves from EVAC to the lowest energy state in the conduction band (CBM/LUMO), aka EA = IE – EG.
References
- Kahn, A. (2016). “Fermi level, work function and vacuum level.” Materials Horizons 3(1): 7-10. Read it online here.
- Bredas, J.-L. (2014). “Mind the gap!” Materials Horizons 1(1): 17-19. Read it online here.
- Helander, M. G., et al. (2010). “Pitfalls in measuring work function using photoelectron spectroscopy.” Applied Surface Science 256(8): 2602-2605. Read it online here.