Electronic States at the Interface

The distribution of electronic states in the acceptor ion in solution can be expressed as  

Most of the theory of electrochemistry, in its electrodic aspect, has been worked out in respect to metal-solution interfaces. Only in the last 20 years, and to a quite restricted extent, have semiconductor-interfaces been considered in detail, and here the work of Gerischer is to be cited as of particular value (cf. the founding papers which were by Clark and Garrett and, in the electrode kinetic form, by Green.  

Garrett and Brattain were the first to attack this problem, and they relied upon the similarity to the distribution of ions in solution when they considered the distribution of electrons and holes inside semiconductors. Thus, deep inside an intrinsic semiconductor the excess charge density must be zero because of the equality of electrons and holes. 

In the surface of a charged semiconductor the numbers of electrons and holes are not equal (this, of course, is just another statement of the fact that the surface is charged). 

One can treat the charge density at a distance x inside the semiconductor by using the Poisson-Boltzmann equation and obtain 

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Fig. 1.1. Electronic states at the interface between a metal electrode and a redox couple A/B in solution at equal concentrations of the electroactive species. The applied potential corresponds to (a) equilibrium, (b) cathodic (electroreduction) and (c) anodic (electrooxidation) conditions.

We now present a theoretical model suited to non-reactive adhesion, which describes the electronic states at the interface between a thick metallic overlayer and an oxide, as a function of the metal and oxide characteristics (Bordier and Noguera, 1991 1992). 

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