Edge exclusion region

Baker [17] derived an elegant description of the edge effect based on the mechanics of the pad and of the wafer. He argued that the peak in the edge exclusion region is proportional to where C is the slope of... 

If we replace the previously determined relation (3.83) for dn/dy into (3.88) and utilize the fact that the majority concentration and doping level are approximately equal, we obtain for the threshold value of the current at the edge of the exclusion region... 

At the crystal corners C9,10 atoms are located their number is six, irrespective of the crystal size. The number of C79 atoms, occurring along the edges, varies linearly with the crystallite size. The faces are built up of C93 atoms, whose number is a quadratic function of the crystallite size. Hence, the surface of a very large octahedron consists almost exclusively of C93 atoms, whereas in a very small crystallite it is made up to a substantial degree of C9,10 atoms. One may reasonably assume that somewhere in between these extremes there will be a region of crystallite diameters where a considerable fraction of the surface atoms are C79 atoms. For quantitative confirmation we refer to Fig. 2, in which the quantities N(Cpj q r " ) /Ns for the various atom types are plotted versus die. (In this and other similar plots the lines drawn through the points merely serve as an illustration, and do not refer to any actual crystals.) The main conclusions that can be drawn from Fig. 2 are ... 

Figure 2. (a) Interaction of small spherical molecules. The molecule at 2, on the inner edge of a square potential well of width x, is in contact with the central molecule 1. At 2 it is on the outer edge of the well. The radius 2r defines the exclusion volume around the central molecule the shell between radius 2r and (2r+x) defines its interaction volume. (6) Interaction of spherical shell-molecules. Atoms 1 and 2 on their respective shells are in contact on the inner edge of a square well of width x. Atoms 1 and 2 are beyond the outer edge of the well. If the shell-atoms are taken as uniformly smeared around the shells, the energy of interaction between the molecules should be approximately proportional to the overlap volume Va, the region in which the shells are closer than x. 

Anion exclusion volumes calculated on the disk model [34] for a particle with a large radius (ro > 250 nm) are similar to those obtained from the infinite-plane model because, for a large particle, the anion exclusion volume contributed from the region outside the edge surface is relatively smaller than that from above the basal plane. Very large values of the anion exclusion volume are found on the disk model for small particles (r0 = lOnm) in dilute electrolyte solutions because anion depletion outside the edge surface becomes very important for small particles [34]. 

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