This preview has intentionally blurred sections. Sign up to view the full version.View Full Document
Unformatted text preview: 1 18. DYNAMIC EQUILIBRIA OF POINT DEFECTS All high temperature experimental processes affect the crystal point defect concentrations. In inert ambient or in vacuum, annealing of elemental crystals such as metals, Ge, and Si, causes the point defects vacancies and self-interstitials to attain their appropriate thermal equilibrium concentrations in the crystal interior. The same holds for GaAs or other compound semiconductors when annealed in an ambient consisting of vapor phases of self-elements with appropriate pressures. To reach thermal equilibrium concentration, point defects are generated at the crystal surfaces that subsequently diffuse into the crystal to populate its interior, or vise versa. A surface vacancy is the lack of an atom at a surface atom site on an otherwise smooth crystal surface, and a surface self-interstitial is an additional self-atom existing on an otherwise smooth crystal surface. Very close to the surface, a point defect species in the crystal interior always reaches its thermal equilibrium concentrations after a short time at the high temperature. This time is usually taken as zero and the free crystal surface is regarded as a prefect point defect source or sink. Upon reaching thermal equilibrium in also the crystal interior, the point defect concentration anywhere in the crystal ceases to change. This free surface process, i.e., the surface-generation/diffusion process, of point defect concentration change is the lowest in Gibbs free energy among all possible processes. As a result, the different point defect species (not meant for that of the same species in different charge states), e.g., I Si and V Si in Si, attain thermal equilibrium concentration values independently, provided the crystal is not an ionic compound. That is, the effect of mutual interactions is either totally absent or negligibly small when compared to that of the free surface processes. The alternative process of generating point defects from within a non-ionic single crystal containing no dislocations is energetically not favorable, because only the simultaneous generation of a V and an I is possible. The formation Gibbs free energy of the pair is g V f +g I f which is much larger than g V f or g I f alone. In polycrystalline materials or in crystals containing dislocations to a large concentration, grain boundaries and dislocations play a role similar to the crystal free surfaces. Therefore, for most purposes, grain boundaries and dislocations are also regarded as perfect sources/sinks of point defects. The role of dislocations will be discussed later. Grain boundaries are composed of arrays of dislocations. In high temperature experiments other than annealing in vacuum, particularly for semiconductors, the involved experimental processes often cause the point defect concentrations 2 to deviate away from their thermal equilibrium values to a sizable extent. Such processes may be chemical or physical in nature and can be occurring either at the crystal surface or in the crystal...
View Full Document
- Fall '11
- Thermodynamics, Gibbs