Tham khảo tài liệu 'diffusion solids fundamentals diffusion controlled solid state episode 2 part 8', kỹ thuật - công nghệ, cơ khí - chế tạo máy phục vụ nhu cầu học tập, nghiên cứu và làm việc hiệu quả | Combined Dissociative and Kick-out Diffusion 427 k C k-1 Cfq CVq k 2 Cfq C c k-2 Cfq These ratios are constants which depend on temperature. Simplifications of Eqs. to which are usually justified under conditions of diffusion experiments 4 5 concern local equilibrium between the various species. For local equilibrium between the partners of Eqs. or the laws of mass action can be written as and C Cfq Ci Cv CC V Ci Cfq Cs Ci Clq Ceq In addition as indicated in Eq. the pure substitutional diffusivity Ds can often be neglected for hybrid diffusers. Even with these simplifications the coupled nonlinear system of partial diffusion-reaction Eqs. to cannot be solved analytically in full generality. Particular solutions CX x t are determined by the pertinent initial and boundary conditions. Often numerical methods of computational physics must be used to derive solutions. In the following we consider first the two limiting cases of practical importance already given in Chap. 24. Then we report an example for an intermediate case which requires numerical treatment. Diffusion Limited by the Flow of Intrinsic Defects Hybrid diffusion controlled by the slow flow products or transport products of self-interstitials and or vacancies emerges if the relationship CeqDi CpvqDv CfqDi is fulfilled. This condition can be realised in material that is completely or virtually free of inner sinks and sources of point defects. Dislocation-free Si wafers are commercially available3. Such wafers are the base materials for the fabrication of microelectronic devices. Ge and GaAs materials are available at least with very low values of the dislocation density. If dislocations and other extended defects are absent the sink and source terms in Eqs. and can be omitted . Kv KI 0. Then the interstitial-substitutional 3 This situation is very different from metals. Carefully grown metal single crystals still have .
