Depletion layer anodization

We consider, now, an electron-depleted space charge layer that is gradually polarized in the anodic direction. As long as the Fermi level is located away from the surface state, the interfacial capacity is determined by the capacity of the depletion layer that obeys a Mott-Schottlsy relation as shown in Fig. 5-61. 

As the Fermi level reaches the surface state level, the interfacial capacity is determined by the capacity of the compact layer (the maximum capacity of the surface state) and remains constant in a range of potential where the Fermi level is pinned. A further increase in anodic polarization leads again to the capacity of the depletion layer in accordance with another Mott-Schottky plot parallel to the former plot as shown in Fig. 5-61. The flat band potential, which is obtained from the Mott-Schottlo plot, shifts in the anodic direction as a result of anodic charging of the siuface state. This shift of the flat band potential equals a change of potential of the compact layer, (Q /C = Q./Ch), due to the anodic charging of the surface state. 

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. 

When the cell circuit is closed in the dark, as shown in Fig. 10-25(b), the Fermi level is equilibrated between the metallic cathode and the n-lype semiconductor anode. As a result, a depletion layer of space charge (potential barrier, is formed in the semiconductor anode, thereby shifting the potential of the anode from the flat band potential to a more anodic (more positive) potential (= + ). In the dark, however, the anodic hole transfer... 

A similar procedure can be used to determine the space charge distribution in n-type Si in the dark with a positive bias polarization so as to generate a depletion layer within the semiconductor substrate. In this case, the situation is somewhat different because the positive polarization in HF results in an anodic etching of the sample with a nonnegligible current density near 7 pA cm . Nevertheless, similar results were obtained, the components of the equivalent circuit were a capacitance of a few 10 F cm , and a resistance term ranging from 1 to 10Mf2cm for a bias potential varying from —0.1 to -1-0.9 V vs. SCE. 

Under anodic bias potential, the behavior of n-type Si in the HF solution must be discussed because of the onset of a depletion layer with a resistance of several megaohms per square centimeter, which should limit the DC density to less than... 

Also, from Fig. 5 it appears that the anodic current density with n-type Si is extremely low due to the buildup of the depletion layer with a more than 1 Mf2 resistance. In fact, obtaining a few mA cm with n-type Si in the dark needs a very high polarization potential, up to 6-10 V so as to induce breakdown within the highly resistant depletion layer. Nevertheless, PS structure can be obtained on n-type Si, either using heavily doped samples, alternatively under light activated silicon surfaces. 

Most of the available inorganic semiconductors with wide enough band gap to prevent energy transfer have -type character. The conditions for studying electron injection from excited dye molecules are therefore most favourable with these materials since a depletion layer (compare Fig. 11) can easily be formed by anodic polarisation. This barrier layer prevents electronic currents in the absence of illumination (or keeps the dark current at least very small) and makes the system most sensitive for photocurrents. 

The energy levels in the solution are kept constant, and the applied voltage shifts the bands in the oxide and the silicon. The Gaussian curves in Figure 4b represent the ferrocyanide/ferricyanide redox couple with an excess of ferrocyanide. E° is the standard redox potential of iron cyanide. With this, one can construct (a) to represent conditions with an accumulation layers, (b) with flatbands, where for illustration, we assume no charge in interface states, and (c) with an inversion or deep depletion layer (high anodic... 

The expected Tafel slope of 60mV/decade is not always found. There are a number of reasons for this, aside from kinetic effects in the bulk of the semiconductor. The kinetic effects associated with faradaically active surface states is of considerable significance, as shown below, but another common problem is that part of the potential change may appear across the Helmholtz layer rather than across the depletion layer. A well-known case in point is germanium, for which the surface is slowly converted from "hydride to "hydroxylic forms as the potential is ramped anodically. This conversion gives rise to a change in the surface dipole and hence Aij/ AT. In fact, the anodic dissolution of p-germanium is found to follow a law [106]... 

In semiconductors of high-dopant density and correspondingly thin depletion layers, tunneling may occur directly between the electrons in the conduction band and the surface of the electrode provided acceptor states or redox species in solution are available. The tunneling contribution to the total current has been considered by a number of workers [118-121] and the total anodic current can be written, with some generality, as... 

Quantum Confinement Model. To account for the formation of micropores of less than a few nanometers formed on p-Si, Lehmann and Gosele in the early 1990s postulated that instead of the depletion layer, which is involved in macropores, quantum carrier confinement is responsible for the formation of the micropores on p-Si. The confinement occurs due to an increase in band-gap energy and energy barrier caused by the quantum size porous structure, which prevents the carriers from entering the wall regions of the PS as illustrated in Fig. 8.61. Due to the quantum confinement the pore walls are depleted of carriers and thus do not dissolve during the anodization. 

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