Point defect concentrations in surface layers of binary oxides

Abstract

The dependence of point defect concentrations in the surface layer (the outer most layer of the bulk) of binary oxides, on oxygen partial pressure, P(O2), and acceptor concentration, Ab, is evaluated. With one calibration point the defect concentration, at constant temperature, under any P(O2) and Ab can be determined. The method of calculation is demonstrated on binary oxides which exhibit oxygen vacancies, electrons and holes. A relation between the dependence on P(O2) and Ab of concentrations of point defects in the surface layer, and the dependence of the concentrations of the corresponding defects deep in the neutral bulk, is presented. Two types of surface layers are distinguished according to their electron states. One that forms a band which is partially populated by electrons, leading to a two dimensional metallic surface and Fermi level pinning (FLP) and a second, insulating one and no FLP. Four characteristic cases are identified: FLP or the absence of FLP in the surface layer combined with the presence or absence of significant chemisorption. It is shown that the dependence on P(O2) and Ab of the defect concentrations in the surface layer may be the same as that of the corresponding defects deep in the neutral bulk. The difference is only in the magnitude. The conditions for that to take place are an insulating surface and low concentration of chemisorbed particles. The latter conditions are quite common, as the surface of oxides is mostly not metallic, oxygen chemisorption is low at elevated temperature and for acceptor doped, p-type oxides, chemisorption is also low at low temperature. Different relations are derived under other conditions. In particular, for metallic surface, the oxygen vacancy concentration in the surface layer follows only one dependence, P(O2)−1/2, irrespective of the dependence on P(O2) and Ab of the bulk vacancy concentration and irrespective of chemisorption. The electrical potential distribution is derived for the four cases.