Effective excess charge plane

This plane of the center of mass of the excess ionic charge o,(x) is the effective excess charge plane on the solution side, which may be compared with the effective image plane on the metal side. In simple cases, the effective excess charge plane coincides with the outer Helmholtz plane (the plane of closest approach of hydrated ions) as shown in Fig. 5-21. 

Fig. 6-21. Charge distribution profile across a metal/aqueous solution interface (M/S) (a) the hard sphere model of aqueous solution and the jellium model of metal (the jellium-sphere model), (b) the effective image plane (IMP) and the effective excess charge plane x, (c) reduction in distance /lxd,p to the closest approach of water molecules due to electrostatic pressure, o, = differential excess charge on the solution side og = total excess charge on the solution side Oy = total excess charge on the metal side.

Fig. 6-20. Charge distribution profile across an interface between metal and vacuum (MAO (a) ionic pseudo-potential in metal, (b) diffuse electron tailing away from the jellium metal edge, (c) excess charge profile. n(x) s electron density at distance x = electron density in metal x, = effective image plane On = differential excess charge On = 0 corresponds to the zero charge interface.

Fig. 6-22. Effect of interfadal excess charge, om, on the effective image plane, Xi , the shift of the plane of closest approach of water molecules, the inverse interfacial capadty on the metal side, 1 /Cm and the interfadal capacity on the solution side, Cs. M/vac = metaWacuum interface M/sol = metal/solution interface.

This theory was followed by one in which it was assumed that the excess charge on the solution side is not localized at the interfacial plane on the solution side but is diffuse due to the net effect of the electrical and thermal influences (5,7). According to this model (diffuse layer theory) there is a parabolic dependence of the capacity on charge which is found to be in agreement with experiment at low concentrations. However, at higher concentration, the predicted values of the capacity are too high. 

Consider a plane-parallel condenser of capacitance C whose plates are a p-type semiconductor (e.g., a CP) and a metal, and polarize the latter negatively. Excess positive charges (i.e., holes) appear at the surface of the semiconductor, and since its conductivity is low, they are in fact distributed over a certain thickness within the material. These excess holes, or at least part of them, should take part in the conduction. Applying a voltage to an external electrode not in contact with the semiconductor modulates its conductivity. This is the principle of the field effect, and clearly this control of the current through a gate electrode opens the possibility of transistor action without requiring the existence of p-n junctions. 

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