Space charge layer band bending

Understanding of the electrostatics across nanocrystalline semiconductor film-electrolyte junctions presents interesting challenges, particularly from a theoretical perspective. Concepts related to space-charge layers, band-bending, flat-band potential and the like (Section 1.3) are not really applicable here because the crystallite dimensions comprising these layers are comparable to (or even smaller than) nominal depletion layer widths. 

Although the observations for PPV photodiodes of different groups are quite similar, there are still discussions on the nature of the polymer-metal contacts and especially on the formation of space charge layers on the Al interface. According to Nguyen et al. [70, 711 band bending in melal/PPV interfaces is either caused by surface states or by chemical reactions between the polymer and the metal and... 

Figure 8.7 Tunneling through the space-charge layer at equilibrium and for an anodic overpotential. Note that the band bending is stronger after the application of the overpotential. The arrows indicate electrons tunneling through the space-charge barrier.

The surface Fermi level, Cp, which depends on the surface state, is not the same as the interior Fermi level, ep, which is determined by the bulk impurity and its concentration. As electron transfer equilibrium is established, the two Fermi levels are equilibrated each other (ep = ep) and the band level bends downward or upward near the surface forming a space charge layer as shown in Fig. 2-31. 

The space charge layer caused by the band bending generates an electrostatic potential between the interior and the siuface,Vsc = ( c )/e, called thepoteraft cZ... 

Fig ures 5-43 and 5—44 illustrate the band bending and the concentration profile of charge carriers in these four types of space charge layers. 

As anodic or cathodic polarization increases, the band level bending in a space charge layer (a depletion layer) becomes steeper, and the electron tunneling through the space charge layer is then ready to occur particularly in semiconductor electrodes of high concentrations of donors or acceptors where the space charge layer is thin. 

Upon immersion of the CdSe semiconductor into the electrolyte, electron exchange at the interface occurs until equilibrium is attained. At equilibrium, the Fermi level of the semiconductor is adjusted by the presence of a space charge layer at the semiconductor surface. This layer is due to the difference between the Fermi level of the semiconductor and the Fermi level of the electrolyte which is measured at the redox couple (X) The potential drop at the space charge layer and the amount of band bending also depend on the degree of Fermi level mismatch at the semiconductor-... 

Fig. 4.12 Diagram illustrating space charge layer formation in microcrystalline and nanocrystalline particles in equilibrium in a semiconductor-electrolyte interface. The nanoparticles are almost completely depleted of charge carriers with negligibly small band bending.

Fig. 5.1 Schematic energy band bending for (A) large particle, (B) small particle, and (C) metal-deposited particle. R, radius of the particle Lsc, space charge layer E(red/ox), redox level in solution E , Fermi level in semiconductor

Due to the simplicity to determine the onset potential (Uon) experimentally, it has been widely accepted to substitute Up, with Uon. Ideally, Um should coincide with Up, [61]. In most n-type semiconductors, however, Uon is shifted a few tenths of a Volt, to more anodic potentials than Up, [104]. This represents the situation when sufficient band bending has been established in the semiconductor space charge layer, which enables an efficient hole transfer to the reduced species in the solution. 

Fig. 9.3. Band bending and space charge layer formation at an n-type semiconductor-electrolyte interface (a) accumulation layer,...

The potential distribution, and hence the extent of the band bending, within the space charge layer of a planar macroscopic electrode may be obtained by solution of the one-dimensional Poisson-Boltzmann equation [95]. However, since the particles may be assumed to have spherical geometry, the Poisson-Boltzmann for a sphere must be solved. This has been done by Albery and Bartlett [131] in a treatment that was recently extended by Liver and Nitzan [125]. For an n-type semiconductor particle of radius r0, the Poisson-Boltzmann equation for the case of spherical symmetry takes the form ... 

Fig. 9.4. Comparison of the band bending, space charge layer formation and Fermi levels (E,r) for a large particle when r = r throughout the depletion layer and equation (9.18) applies, and for a small particle when r = tv and equation (9.19) applies. The semiconductor particles are considered to be in thermodynamic equilibrium with a redox pair of Nernst...

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