Semiconductors Fermi level splitting

Fig. 2.20 Band diagram for a PEC cell based on an n-type semiconducting photoanode that is electrically connected to a metal counter electrode in equilibrium in the dark (left) and under illumination (right). Illumination raises the Fermi level and decreases the band bending. Near the semiconductor/eiectroiyte interface, the Fermi level splits into quasi-Fermi levels for the electrons and holes...

The concept of the quasi-Fermi level split is extremely important to how much useable photopotential a semiconductor device can generate, specifically in relation... 

Fermi Level Splitting in the Semiconductor-Electrolyte Junction... 

The maximum quasi-Fermi-level splitting in a semiconductor under illumination is also affected by nanostructuring. This potential difference (V c) will be smaller for the nanowire photoelectrode for several reasons. For example, in a traditional planar photoelectrode geometry under low-level injection, the highest achievable np product in Si is ultimately limited by SRH recombination in the bulk. For a macroscale, planar n-type semiconductor photoelectrode operating under this limitation, the maximum possible is given by ... 

Suspended semiconductor nanoparticles also differ from high-aspect-ratio semiconductor photoelectrodes in another aspect. High-aspect-ratio nanowire/macroporous photoelectrodes in low-level injection are connected to current collectors and are thus intended to operate at a specific power point (i.e., at a particular combination of current-potential values that maximizes the product of the quasi-Fermi-level splitting and the net photocurrent). In contrast, a suspended semiconductor nanoparticle functions without any external contacts at precisely open-circuit conditions. That is, at the operational conditions, photoexcited semiconductor nanoparticles suspended in a solution pass no net current, that is, 0=0, and their quasi-Fermi levels are offset by the maximum value possible under the operative illumination and recombination conditions. 

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. 

In the dark, thermal equilibrium is established between electrons in the conduction band and holes in the valence band so that both the quasi-Fermi level of electrons and the quasi-Fermi level of holes equal the oiiginal Fermi level of the semiconductor (nCr = pC, = ep). Under the condition of photoexdtation, however, the quasi-Fermi level of electrons is higher and the quasi-Fermi level of holes is lower than the original Fermi level of the semiconductor (nSp > cp > pCp). Photoexdtation consequently splits the Fermi level of semiconductors into two quasi-Fermi levels the quasi-Fermi level of electrons for the conduction band and the quasi-Fermi level of holes for the valence band as shown in Fig. 10-1. 

Fig. 10-2. Splitting of Fenni level of electrode, cnsci. into quasi-Fermi levels of electrons, ep, and of holes, pCp, respectively, in a surface layer of photoexcited n-type and p-type semiconductors a shift of quasi-Fermi levels from original Fermi level is greater for minmity charge carriers than for majority charge carriers.

Since photoexcited electron-hole pairs are formed only within a limited depth from the semiconductor surface to which the irradiating photons can penetrate, the photon-induced split of the Fermi level into the quasi-Fermi levels of electrons and holes occurs only in a surface layer of limited depth as shown in Fig. 10-2. 

Even though the active (excited) state of the catalyst is restored in both catalysed photolysis and photogenerated catalysis, the kinetic parameters are different (Serpone et al, 2000), since we deal with a different excited state of the catalyst, i.e. effectively we deal with different catalysts. Indeed, under irradiation the state of the catalyst e.g. a semiconductor) may be characterised by the splitting of the Fermi level into two quasi-Fermi levels (in catalysed photolysis), whereas in photogenerated catalysis the state of the catalyst is characterised by a unique Fermi level (in the dark). This level may however be shifted compared with the original state of the catalyst because of the possibility of having different excited states after pre-excitation of the catalyst. 

Let us consider a light excitation of electrons and holes (An = Ap) within a doped n-type semiconductor so that Am < no and A/ >p(). Then the Fermi level of electrons, fipn, remains unchanged with respect to the equilibrium case, whereas that of holes, Epp, is shifted considerably downwards, as illustrated in Fig. 1.17b. In many cases, however, the excitation of electron-hole pairs occurs locally near the sample surface because the penetration of light is small. Then the splitting of the quasi-Fermi levels is... 

Figure 8. Diagram illustrating the splitting of the Fermi level into quasilevels of electrons and holes (a) in the dark (b) under illumination of the semiconductor.

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