Mott and Cabrera

Passing on to the discussion of very thin layers of 10 to 100 X, such as those forming during oxidation of metals and alloys and also passive layers such as those formed on iron in nitric acid at low temperatures (0 to 200°C). one must consider additional phenomena which are characteristic of the reaction mechanisms involved. Our discussion of these phenomena are based, with certain limitations, on the theory of Mott and Cabrera. 

The theory of Mott and Cabrera for the growth of very thin oxide films did not satisfactorily explain the results. The governing kinetic factor was found to be the increase in oxide thickness rather than the total oxide-film thickness. A mechanism based on the formation of metal lattice vacancies and their elimination by heating is proposed. 

In a recent theoretical development, Mott and Cabrera (f) have attempted a mathematical explanation of the oxidation in the very thin film range from a few angstroms to about 100 A. They have successfully applied their concepts to the experimental results of aluminum oxidation. Rhodin... 

If it is assumed that regeneration does not disturb the oxide already present on the surface, then further oxidation should be governed by the transference of cobalt cations from the metal-oxide interface to the oxide-gas interface where reaction takes place. The rate would be dependent on the total film thickness if the theory of Mott and Cabrera were valid. The limiting thickness then would be the sum of the defined limiting thickness Xl for a particular oxidation plus the thickness of the oxide layers previously formed. These total limiting thicknesses for successive oxidations, desig-... 

The first assumption is due to Mott and Cabrera [MOT 48], which assumes that the potential difference at the boundaries of the layer MG is constant for any given thickness, the layer is thus comparable with a plane condenser with constant potential difference and thus a charge on the electrodes inversely proportional to its thickness X. This assumption is translated in the form ... 

The second assumption is due to Grimley and Trappnell [GRI 56], which considers that the layer has a constant charge, that is, an electric field that does not depend on the thickness of the layer. Now, we will use the Mott and Cabrera approximation. 

We now study layer thickness mnch lower than Xq (defined by [15.5]). The electric field is thus prevalent and the concentration gradient has a negligible effect. The diffusion flux is thus given by eqnation [15.6], keeping the Mott and Cabrera assumption. Consider then ... 

In contrast, Mott [75,76] and Cabrera [15, 48] considered the ITR of metal ions at the interface M/ox, that is. Reaction (15) as rate determining step. Since both models yield the same Eq. (31), a decision is still open. 

Growth of surface oxide films takes place only if cations, anions, and electrons can diffuse through the oxide layer. The growth kinetics of very thin films ( 10-50 A) often follow the Mott or Cabrera-Mott mechanisms in which electrons tunnel through the film and associate with oxygen atoms to produce oxide ions at the surface. A large local electric field (10 -10 V/cm) results at the surface which facilitates cation diffusion from the metal-oxide interface to an interstitial site of the oxide. The film thickness Z at time t is given by... 

This constancy of the field implies that either electroneutrality prevails in the bulk of the film or the concentration of ions is not controlled by electroneutrality, but that the films are so thin, and the density of carriers so low, that the space charge due to the carriers causes negligible change in field across the film. The first case was that considered implicitly by Verwey, who was the first to apply Frenkel s theory to these systems. The second was proposed by Mott, and was discussed by Mott and Gurney, and by Cabrera and Mott. ... 

Thin oxide films formed by oxidation of metal surfaces have been center stage in semiconductor research since Walter Schottky formulated his ideas on electronic barriers in solids during the 1920s and 30s. In 1948, Nevill Mott and Nicolas Cabrera embraced these same ideas, in attempts to describe and explain the elementary processes involved in oxide layer formation. Scientists at the Department of Chemical Physics have made use of Schottky s ideas to approach a variety of seemingly disjunct problems, two of which will be outlined below. 

A detailed theory of the spiral growth of crystals has been developed by Burton, Cabrera, Frank, Mott and Levine [4.33-4.41] who have considered the case of spiral growth from a supersaturated vapor phase. Later the theory was adapted to electrocrystahization by Vermilyea [4.44] and Fleischmann and Thirsk [4.48] and developed further and verified experimentally by Budevski, Bostanov, Staikov, Nanev et al. [4.28, 4.69-4.75] (see also the pioneering work of Kaischew, Budevski and MaUnovski [4.76]). 

A strong electric field is formed in very thin films (with a thickness of about 10 5 cm) during current flow. If the average electrochemical potential difference between two neighbouring ions in the lattice is comparable with their energy of thermal motion, kTy then Ohm s law is no longer valid for charge transport in the film. Verwey, Cabrera, and Mott developed a theory of ion transport for this case. 

Numerous other models have been proposed to explain the deviation of dry oxidation from linear-parabolic kinetics. For example, field-assisted oxidant diffiision during the oxidation of metals was proposed by Cabrera and Mott (75) and used by Deal and Grove (69) to explain the results for thin oxides. Ghez and van der Meulen (76) proposed the dissociation of molecular oxygen into atomic oxygen at the Si-Si02 interface and the re-... 

Employing now the assumption made by Cabrera and Mott [30] of a constant voltage VB, the growth rate can be written as... 

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