Fermi levels valence electron energy state

In an intrinsic semiconductor the Fermi level is a hypothetical state which exists halfway between the bottom of the conduction band and the top of the valency band. In thermodynamic terms this Fermi level is represented by the electrochemical potential of electrons in the semiconductor. The fact that the Fermi level exists halfway inside the energy gap, and where ideally no electrons or holes can exist, is of small consequence. The Fermi level represents the energy state at which the probability of existing electron and hole are equal and half each. The Fermi level within the semiconductor represents an ideal situation which is calculable and is in fact equivalent to the electrochemical potential inside the semiconductor. 

Consider Figure la, which shows the electronic energy states of a solid having broadened valence and conduction bands as well as sharp core-level states X, Y, and Z. An incoming electron with energy Eq may excite an electron ftom any occupied state to any unoccupied state, where the Fermi energy Ap separates the two... 

Figure 8-11 shows as a function of electron energy e the electron state density Dgdit) in semiconductor electrodes, and the electron state density Z e) in metal electrodes. Both Dsd.t) and AKe) are in the state of electron transfer equilibrium with the state density Z>bei)ox(c) of hydrated redox particles the Fermi level is equilibrated between the redox particles and the electrode. For metal electrodes the electron state density Ai(e) is high at the Fermi level, and most of the electron transfer current occurs at the Fermi level enio. For semiconductor electrodes the Fermi level enao is located in the band gap where no electron level is available for the electron transfer (I>sc(ef(so) = 0) and, hence, no electron transfer current can occur at the Fermi level erso. Electron transfer is allowed to occur only within the conduction and valence bands where the state density of electrons is high (Dsc(e) > 0). 

The highest energy occupied allowed band of a metal, or conduction band, is only partially filled with electrons, up to the so-called Fermi level. Hence, electrons located close to this Fermi energy are easily excited to the unoccupied level of the band, where they behave as free electrons. In a semiconductor (like in an insulator), the highest occupied allowed band is totally filled, and called valence band (VB), whereas the conduction band (CB) corresponds to the lowest unoccupied allowed band, which is completely empty. The injection of electrons in the CB occurs either thermally (in an intrinsic semiconductor) or through doping (extrinsic semiconductor). Electrons in the conduction band of metals or semiconductors move in delocalized states, and their wave function can be approximated to that of a free electron, that is, a progressive plane wave... 

We now describe the behavior of charge carriers in an intrinsic semiconductor (i.e., pure) at equilibrium. The electrical properties of any extended solid depend on the position of the Fermi level, defined as the highest occupied state at T = 0 K. An alternative definition, stemming from the Fermi-Dirac statistics that govern the distribution of electrons, the Fermi level is the energy at which the probability of finding an electron is If the Fermi level falls within a band, the band is partially filled and the material behaves as a conductor. As shown in Fig. 3, the valence and conduction band edges of an intrinsic semiconductor straddle the Fermi level. At T = 0 K, no conduction is possible since all of the states in the valence band are completely filled with electrons while aU of the states in the conduction band are empty. 

Each energy level in the band is called a state. The important quantity to look at is the density of states (DOS), i.e. the number of states at a given energy. The DOS of transition metals are often depicted as smooth curves (Fig. 6.10), but in reality DOS curves show complicated structure, due to crystal structure and symmetry. The bands are filled with valence electrons of the atoms up to the Fermi level. In a molecule one would call this level the highest occupied molecular orbital or HOMO. 

A theoretical interpretation relating the valence electron concentration and the structure was put forward by H. Jones. If we start from copper and add more and more zinc, the valence electron concentration increases. The added electrons have to occupy higher energy levels, i.e. the energy of the Fermi limit is raised and comes closer to the limits of the first Brillouin zone. This is approached at about VEC = 1.36. Higher values of the VEC require the occupation of antibonding states now the body-centered cubic lattice becomes more favorable as it allows a higher VEC within the first Brillouin zone, up to approximately VEC = 1.48. 

The distribution of electronic states of the valence band for the colored film at 1.25 Vsce resembles very much the valence band of pure Ir02 as reported by Mattheiss [93], The maximum of the l2g band occurs at 1.6 eV below EF, the 02p region extends from roughly 4 eV to 10 eV and a finite density of electronic states at the Fermi level. Upon proton (and electron) insertion the l2g band, which can host 6 electrons, is completely filled and moves to a binding energy of 2.5 eV. Simultaneously, the density of states at EF is reduced to zero and an additional structure, indicating OH bond formation, occurs in the 02p band. The changing density of states... 

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