Deep-layer regime

Up to a scalar multiplier of normalization, the deep layer regime is described by the leading eigemnode i(r, u, 7,) of the transfer equation (1), i.e.. 

Semiconductor fabrication techniques permit the feature size of Si-based devices to reach into the deep submicron regime [i]. Additionally, Si can be anodized electrochemically or chemically (e.g., in an HF-containing electrolyte) to produce a sponge-like porous layer of silicon, with pore dimensions that range from several microns in width to only a few nanometers [ii]. These properties of Si make it a useful substrate for fabricating sensor platforms, photonic devices and fuel cell electrodes [iii]. 

Fig. 7.32 Intensity map of the reflection R (measured through the substrate) during hydrogen uptake of a sample 250 nm Mg2Ni/7nm Pd. At low resistivity (i.e. in the metallic state) R is high. At around r= 130mJ2cm x 0.8) R exhibits a deep minimum over the entire visible wavelength regime. A double layer system Mg2NiHo.3-Mg2NiH4 is formed and sub-...

The factor 2 on the right-hand side manifests the effect of Tafel slope doubling. As discussed above, at high currents, owing to poor ionic conductivity of the CL, ions do not penetrate deep into the catalyst layer and the electrochemical conversion runs at the electrolyte (membrane) interface. This regime of conversion requires a much higher polarization voltage. Note that the transport terms in Eqs. (23.35) and (23.37) coincide. 

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