Potential Drops in Different Phases of the Current Path

Potential Drops in Different Phases of the Current Path. There are five possible physical phases in the current path in which significant potential drops may occur as illustrated in Fig. 8.71. They are the substrate, the space charge layer, the Helmholtz layer, the surface oxide film, and the electrolyte. The overall change in the applied 

FIGURE 8.71. Schematic illustration of the potential drop along the cunent path in a pore. AVsi, potential drop in silicon substrate AV potential drop in the space charge layer AVo, potential drop in oxide AVh, potential drop in the Helmholtz layer AVd, potential drop in electrolyte. 

The last term, AVei. in Eq. (8.17) is the resistance of the electrolyte. It causes a potential drop that is linearly distributed in the electrolyte inside the pores and thus does not have an effect on the current distribution on the pore bottom although it takes a significant amount of in the applied potential. However, as will be discussed later, the potential drop in the electrolyte has an important effect in maintaining the flat growth front of the PS layer. 

In the case when the substrate is moderately doped and the surface is free of oxide, the rates of reactions are determined by the resistance in the space charge layer and in the Helmholtz double layer. The reactions under these conditions have a great tendency to localize because the rates of charge transfer in both layers are sensitive to geometric factors. The reaction that is kinetically limited by the space charge layer is sensitive to the radius of curvature and that by the Helmholtz layer to the orientation of the surface. Depending on the relative effect of each layer, the curvature effect versus anisotropic effect can vary. 

When the pore bottom is covered with an oxide, partially or fully, the change of applied potential occurs almost entirely in the oxide due to the very high resistance of the oxide. The rate of reactions is now limited by the chemical dissolution of the oxide on the oxide-covered area and when the entire pore bottom is covered with an oxide the rate of reaction is the same on the entire surface of the pore bottom. As a result, the bottom flattens and no PS forms. The change of oxide coverage on the pore bottom can also occur when diffusion of the electrolyte inside deep pores becomes the rate-limiting process. A decreased HF concentration at the pore bottom due to the diffusion effect can result in the formation of an oxide on the bottom of deep pores under conditions in which it does not occur in shallow pores. 

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