Quasi-Fermi energy levels

At pH 7 versus NHE. 3Fe(OH)2 Fe(OH)2Cl /i H2O where 3 > n > 2 (63), [Fe(II)4 Fe(III)2 (0H)i2]2+ [S04 2H20]2- (64), Single crystal. Quasi-Fermi energy level for electrons. This is the Fermi energy level under illumination (nonequilibrium conditions). For n-type semiconductors where electrons are the majority carriers, the quasi-Fermi energy level is approximately equal to the Fermi energy level (65),... 

Fig. 1. The energy levels in a semiconductor. Shown are the valence and conduction bands and the forbidden gap in between where represents an occupied level, ie, electrons are present O, an unoccupied level and -3- an energy level arising from a chemical defect D and occurring within the forbidden gap. The electrons in each band are somewhat independent, (a) A cold semiconductor in pitch darkness where the valence band levels are filled and conduction band levels are empty, (b) The same semiconductor exposed to intense light or some other form of excitation showing the quasi-Fermi level for each band. The energy levels are occupied up to the available voltage for that band. There is a population inversion between conduction and valence bands which can lead to optical gain and possible lasing. Conversely, the chemical potential difference between the quasi-Fermi levels can be connected as the output voltage of a solar cell. Fquilihrium is reestabUshed by stepwise recombination at the defect levels D within the forbidden gap.

The electrons produced in the conduction band as a result of illumination can participate in cathodic reactions. However, since in n-type semiconductors the quasi-Fermi level is just slightly above the Fermi level, the excited electrons participating in a cathodic reaction will almost not increase the energy effect of the reaction. Their concentration close to the actual surface is low hence, it will be advantageous to link the n-type semiconductor electrode to another electrode which is metallic, and not illuminated, and to allow the cathodic reaction to occur at this electrode. It is necessary, then, that the auxiliary metal electrode have good catalytic activity toward the cathodic reaction. 

Such an interfacial degeneracy of electron energy levels (quasi-metallization) at semiconductor electrodes also takes place when the Fermi level at the interface is polarized into either the conduction band or the valence band as shown in Fig. 5-42 (Refer to Sec. 2.7.3.) namely, quasi-metallization of the electrode interface results when semiconductor electrodes are polarized to a great extent in either the anodic or the cathodic direction. This quasi-metallization of electrode interfaces is important in dealing with semiconductor electrode kinetics, as is discussed in Chap. 8. It is worth noting that the interfacial quasi-metallization requires the electron transfer to be in the state of equilibrimn between the interface and the interior of semiconductors this may not be realized with wide band gap semiconductors. 

Fig, 10-1. Splitting of Fermi level, cnsci, into both quasi-Fermi level of electrons, bCp, and quasi-Fermi level of holes, pSp, in photoezcited semiconductors (a) in the dark, (b) in photon irradiation. SC = semiconductor hv = photon energy. 

The quasi-Fermi level of interfacial holes nearly equals the Fermi level pe , ( pEp,.) in photoexcited p-type electrodes, but the quasi-Fermi level pej. of interfacial holes is lower than the Fermi level aSp,. (> p p,) in photoexcited n-type electrodes as shown in Fig. 10-21. It then follows that the range of electrode potential, where the anodic reaction occurs on the photoexcited n-type electrode, shifts itself, from the range of potential where the same anodic reaction occurs on the dark p-type electrode, toward the caliiodic (more negative) direction by an energy equivalent to (nEp - p p,). 

Fig. 10-23. Energy levels and polarization curves for a redox reaction of anodic redox holes at a photoexdted n-type electrode and at a dark p-type electrode of the same semiconductor curve (1) = polarization curve of anodic transfer of photoexdted holes at an n-type electrode curve (2)= polarization curve of anodic transfer of holes at a p-type electrode in the dark (equivalent to a curve representing anodic current as a function of quasi-Fermi level of interfadal holes in a photoexdted n-type electrode) i = anodic transfer current of holes Eredox = equilibriiun potential of redox hole transfer N = anodic polarization at potential n (t) of a photoexdted n-type electrode P = anodic polarization at potential pE(i) of a dark p-type electrode.

Fermi level of standard redox electrons in complexed redox particles Fermi level of standard redox electrons in adsorbed redox particles Fermi level of n-type or p-type semiconductor electrodes quasi-Fermi level of electrons in semiconductor electrodes quasi-Fermi level of holes in semiconductor electrodes energy of a particle i... 

Figure 3. Schematic of a semiconductor-aqueous electrolyte solution interface, ignoring band bending, Ec and are the band edges of the conduction and valence bands, respectively, Ef(H20/h2> and Ef(02/h20) are the Fermi levels in the solution for the redox reactions indicated. The quasi-Fermi levels with illumination by light of energy hv are designated Ef and pEi respectively, for electrons and holes (13).

Fig. 3. Schematic energy level diagram of a p+-n junction showing the edges of the space-charge region, x = 0 to x, and x = x2 to W, within which a deep trap does not trap and emit carriers. EFp and EF are the quasi-Fermi levels for holes and electrons.

Figure 6 A schematic band diagram (electrical potential energy versus distance) of a conventional p-n homojunction solar cell at equilibrium (left) and at short circuit under spatially uniform illumination (right). The energies of the conduction- and valence-band edges are Ecb and Evb. respectively. EF is the Fermi level at equilibrium and EFn and EFp are the quasi-Fermi levels of electrons and holes, respectively, under illumination.

The energy level of the quasi-Fermi level of positive holes, pEp, which gives a measure of the average energy of positive holes, is given by Eq 5. 

METALLIC BONDING in this bonding, electrons are not paired and are quasi-free to roam throughout the system. Because of unpaired electron spin, they follow the Fermi-Dirac statistics and consequently obeying the Pauli Exclusion Principle. Therefore they are known as fermions where no two electrons can occupy the same energy level and results in an energy band. The three distinct type of bonding as described above is too abstract and... 

Unlike atomic or solid-state lasers, the lasing transitions in a semiconductor laser are transitions between continua of extended states rather than between localised states. The inversion criterion [4] then is that the electron and hole quasi-Fermi levels must be separated by more than the bandgap energies. The spectrum of the optical gain g is given by [5,6]... 

Fig. 5.29. Energy bands and quasi-fermi levels of a p-n junction under illumination...

Quasi-Fermi level — The quasi-Fermi level is a hypothetical energy level introduced by W. Shockley to de-... 

---