Anodic growth rate

Because the film growth rate depends so strongly on the electric field across it (equation 1.115), separation of the anodic and cathodic sites for metals in open circuit is of little consequence, provided film growth is the exclusive reaction. Thus if one site is anodic, and an adjacent site cathodic, film thickening on the anodic site itself causes the two sites to swap roles so that the film on the former cathodic site also thickens correspondingly. Thus the anodic and cathodic sites of the stably passive metal dance over the surface. If however, permanent separation of sites can occur, as for example, where the anodic site has restricted access to the cathodic component in the electrolyte (as in crevice), then breakdown of passivity and associated corrosion can follow. 

It would seem easy in principle to separate cracking that proceeds by anodic dissolution from hydrogen-assisted cracking by investigating the effects of polarisation on the crack growth rate, time to failure or some... 

If measurements are made in thin oxide films (of thickness less than 5 nm), at highly polished Al, within a small acceptance angle (a < 5°), well-defined additional maxima and minima in excitation (PL) and emission (PL and EL) spectra appear.322 This structure has been explained as a result of interference between monochromatic electromagnetic waves passing directly through the oxide film and EM waves reflected from the Al surface. In a series of papers,318-320 this effect has been explored as a means for precise determination of anodic oxide film thickness (or growth rate), refractive index, porosity, mean range of electron avalanches, transport numbers, etc. 

The growth rates of anodic oxides depend on electrolyte composition and anodization conditions. The oxide thickness is reported to increase linearly with the applied bias at a rate of 0.5-0.6 nm V-1 for current densities in excess of 1 mA cnT2 and ethylene glycol-based electrolytes of a low water content [Da2, Ja2, Crl, Mel2] (for D in nm and V in V) ... 

Fig. 6.3 Optical micrographs of edges of cleaved Si wafers showing different crystal planes anodized at 100 mA cm"2 in ethanoic HF (1 1). (a) The growth rate of meso PS formed on a highly doped n-type substrate (2xl018 crrT3, 2 min) shows a clear dependence on crystal orientation, (b) An orientation dependence is not observed for micro PS formed on moderately doped p-type samples (1.5 xlO16 cm-3, 4 min) but the PS thickness becomes inhomogeneous because of local variations in the current density caused by the edge geometry.

If one studies the growth rate as a function of anodization current density for different PS structures prepared in the same electrolyte, as shown in Fig. 6.5, some inherent laws can be observed. In the regime of stable macropore formation on n-type silicon the growth rate is found to be virtually independent of the applied current density. This is simply a consequence of JPS being present at any pore tip, as described by Eq. (9.5). For the growth rate rPS (in nm s 1) of micro PS in ethanoic... 

A lateral variation of the anodization current will produce different growth rates and consequently an interface roughness for porous layers. Note that this is not the case for stable macro PS formation on n-type, because here the growth rate is independent of current density. An inhomogeneous current distribution at the O-ring seal of an anodization cell or at masked substrates produces PS layer thickness variations, as shown in Fig. 6.6. Inhomogeneities of the current distribution become more pronounced for low doped substrates, as shown in Figs. 6.3 b and 6.5 d [Kr3]. 

Having discussed the causes of pore wall passivity, we will now focus on the active state of the pore tip, which is caused by its efficiency in minority carrier collection. Usually the current density at the pore tip is determined by the applied bias. This is true for all highly doped as well as low doped p-type Si electrodes and so the pore growth rate increases with bias in these cases. For low doped, illuminated n-type electrodes, however, bias and current density become decoupled. The anodic bias applied during stable macropore formation in n-type substrates is... 

The relative growth rate per cycle v is calculated from the anodic peak current of the respective polymer oxidation using Eq. (8)... 

In this expression, i is current density, p is density, n is the number of electron equivalents per mole of dissolved metal, M is the atomic weight of the metal, F is Faraday s constant, r is pit radius, and t is time. The advantage of this technique is that a direct determination of the dissolution kinetics is obtained. A direct determination of this type is not possible by electrochemical methods, in which the current recorded is a net current representing the difference between the anodic and the cathodic reaction rates. In fact, a comparison of this nonelectrochemical growth rate determination with a comparable electrochemical growth rate determination shows that the partial cathodic current due to proton reduction in a growing pit in A1 is about 15% of the total anodic current (26). 

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