Lattice defects diffusion, semiconductors

The studies on Cu2 aO mentioned above concluded that CujO is a metal-deficient p-type semiconductor with cation vacancies. It was not established, however, which kinds of defects (Vcu, Vcu) were dominant and what the effect of Q (interstitial oxygen) was on non-stoichiometry. To clarify these points, Peterson and Wiley measured the diffusion coefficient, D, of Cu in Cu2 O, by use of "Cu as a tracer over the temperature range 700-1153 °C and for oxygen partial pressures, greater than 10 atm. It has been widely accepted that lattice defects play an important role in the diffusion of atoms or ions. Accordingly it can be expected that the measurement of D gives important information on the lattice defects. 

However, real solids are more complex. In the common case where the concentration of the diffusant is much higher than that of vacant sites, one must consider vacancies as the diffusing entities, in a similar fashion to the hole formalism used in semiconductors. More generally, the concentration to be used is that of the diffusing lattice defects, e.g. vacancies, interstitial ions, etc. The result is still of the Arrhenius form, however, and plots of In(crr) vs. l/T are linear with a slope of — EJkT. Consequently, the requirement for high mobility is simply a low activation energy, as expected for an open structure. 

It is clear that the diffusion of H through semiconductors is a very complicated issue not only does the motion itself involve complex interactions between the impurity and the lattice, but the calculation of a diffusion coefficient requires the inclusion of different charge states plus the interaction of H with itself (molecule formation) and with other defects and impurities in the crystal. Chapter 10 of this volume discusses this problem in more detail. 

The idea of point defects in crystals goes back to Frenkel, who in 1926 proposed the existence of point defects to explain the observed values of ionic conductivity in crystalline solids. In a crystal of composition MX such as a monovalent metal halide or a divalent metal oxide or sulfide, volume ionic conductivity occurs by motion of positive or negative ions in the lattice under the influence of an electric field. If the crystal were perfect, imperfections, such as vacant lattice sites or interstitial atoms, would need to be created for ionic conductivity to occur. A great deal of energy is required to dislodge an ion from its normal lattice position and thus the current in perfect crystals would be very, very small under normal voltages. To get around this difficulty, Frenkel proposed that point defects existed in the lattice prior to the application of the electric field. This, of course, has been substantiated by subsequent work and the concept of point defects in all classes of solids, metals, ionic crystals, covalent crystals, semiconductors, etc., is an important part of the physics and chemistry of crystalline solids, not only with respect to ionic conductivity but also with respect to diffusion, radiation damage, creep, and many other properties. 

Defects in these crystal structures are essential to determining the properties of the materials. The crystalline defects relevant to semiconductors will be discussed in detail in Chapter 7. Amorphous materials have no regular order so there are no well-defined defects in the material. Nonetheless, we will see in Chapter 8 that the continuum of distortions in the structures of amorphous semiconductors play a key role in determining their properties. Here we will list only the types of atomic-scale (point) defects in crystalline materials and leave more complex structures and detailed discussion to Chapters 7 and 8. Point defects in crystals include vacancies, interstitials, and antisites. Vacancies are missing atoms in the crystal structure. They are essential to the diffusion of atoms among lattice sites in many materials. Interstitials are atoms lying in spaces between atoms in the crystal structure. More open lattices such as the diamond structure accommodate interstitial atoms relatively... 

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