When the periodic structure of a crystal lattice is terminated at a surface, electronic states particular to the surface are created. These are states that have no equivalent in the band structure of the bulk crystal. Surface-specific states can be true surface states with wave functions which are peaked near the surface plane and which decay in amplitude away from the surface, both toward vacuum and toward the bulk crystal. Surface-specific states can also be surface resonant states that have enhanced amplitudes at the surface but are coupled to bulk states. Of course, the distribution of surface-specific states depends on the atomic structure of the surface, and conversely, the atomic structure of the surface is determined more or less as a result of the minimization of the surface energy, to which the surface-specific states are a major contribution. Surface-specific states are present at the surfaces of all matters. On metallic surfaces, they are known to lead to a surface dipole which contributes to the work function of the metal surface. On semiconductors, the presence of surface states in the band gap is known to "pin" the Fermi level position of the semiconductor. Pinning does not happen on every semiconductor surface, however, because surface states are not positioned inside the band gap of some semiconductor surfaces, such as the non-polar (110) surfaces of III-V semiconductors. So, on some cleaved non-polar surfaces, there is little band bending.

Central to the concept of Fermi level pinning by gap states is the charge neutrality level (CNL) concept, which can be roughly defined as follows. At zero temperature, the surface states are populated from the lowest energy states up to the Fermi level. If electrons are filled to a point short of the CNL, i.e. when the Fermi level is lower than the CNL, the very surface region, meaning the first few atomic planes of the surface, has a positive net charge. If the Fermi level is above the CNL, the surface has an excess of electrons and is negatively charged. Since the Fermi level is a constant throughout all regions of a semiconductor, the CNL allows a unique correspondence to be made between the band bending at the semiconductor surface and the population of surface states. To calculate the exact pinning position of the surface Fermi level, one can assume the density of surface states, DGS, to be roughly constant near the CNL. The net charge per unit area of the surface, QGS, is then simply

QGS = e DGS ( FoB,n + fCNL - EG ) ,

where fCNL is the CNL position with respect to the valence band maximum, and FoB,n is the difference between the FL and the CBM at the surface. Note that DGS has the unit of # of states per area per energy (cm-2 eV-1). Here the subscript "GS" (gap states) is used to represent surface states, to be consistent with later notations. As FoB,n is analogous to the n-type SBH at an MS interface, here it is allowed to retain its usual symbol even though there is no Schottky barrier at a semiconductor surface. One should also note that the definition of the CNL at a surface involves a tacit assumption: the energy levels of surface states are assumed to be referenceable to the bulk bands of the semiconductor. Since the bulk bands are considerably modified near a surface, strictly speaking there is no CBM right on the atomic plane of a semiconductor surface. The location closest to the surface where bulk semiconductor bands can be identified is a few lattice spacings away and it is the CBM position at that location which provides the reference point. Since the definition of a CNL involves states that are spatially separated, it may be subject to variation due to changes in the relative electric potential (chemical shift). While this definition does not lead to any ambiguities on the determination of the FL position on a semiconductor surface, it can render the concept of CNL fuzzy for MS interfaces.

For an intrinsic (meaning undoped) semiconductor with homogeneous surfaces, the Fermi level should coincide with the CNL of the surface states. For uniformly doped semiconductors, the surface Fermi level position deviates slightly from the CNL to yield the necessary surface net charge which balances the charge due to exposed dopants in the space charge region:

e DGS ( FoB,n + fCNL - EG ) + [ 2es ND ( FoB,n -e VN ) ]1/2 = 0

This equation can be used to solve for the Fermi level position at the surface of a semiconductor. Alternatively, one notes that FoB,n can be obtained graphically, as shown in this figure, by plotting both terms of the above equation on the same graph. The graphical method is of some value as its results can be more transparent than analytic expressions, especially when the system gets more complex. As shown by the above equation, even a relatively low density of surface states, say 1x1013 cm-2 eV-1, can quite effectively fixate the surface Fermi level to within 0.05eV of the CNL independent of the doping type or the doping level of a moderately doped (ND < 1x1017 cm-3) semiconductor. The surface states are said to pin the Fermi level near the CNL under these conditions. Often, the density of surface states is thought to have peaks at certain energetic positions, such as due to states associated with defects or dangling bonds. With a non-uniform density of surface states, the net charge due to surface states, the first term of the above equation is replaced by an integral. For a distribution of gap states with discrete peak(s), as schematically illustrated in this figure, the surface Fermi level can be pinned tightly at the position of the peak. A review of the figures makes it clear that only those gap states with energy above the CNL, i.e. acceptors, affect the surface Fermi level position on an uncharged, n-type semiconductor; and only gap states with energy below the CNL (donors) can affect the Fermi level position on a p-type semiconductor surface.

Perhaps because the net surface charge is the only relevant parameter for the determination of surface Fermi level, the surface pinning concept is clear and straightforward. An important aspect of the surface states is the formation of the surface dipole, which directly affect the electron affinity of the semiconductor. The magnitude of a surface dipole has to do with the entire spatial distribution of charge. It is not difficult to imagine that patches of the surface that have the same net charge desnity, or even the same density of surface states distribution, can turn out to have different surface dipoles.