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Extra info for Defects and Impurities in Silicon Materials: An Introduction to Atomic-Level Silicon Engineering
5 numerical solutions are presented to demonstrate the significance of the model parameters for the time evolution of the concentration profiles. 29) determine the process that mediates the formation of As (see Eqs. 46)). 28). 46) simplifies to equations for C six model parameters. e. kV D 0, and highly dislocated Si is considered. These cases are treated in the following two paragraphs. Diffusion in Dislocation-Free Crystals The third term on the right hand side of Eq. 43), which expresses the contribution of internal sources and sinks to the formation of V, can be neglected for diffusion in a defect-free crystal (kV D 0).
115) Eqs. 115) yield . m e eV k D CAV0 nQ C eAms C k/ nQ . 116) eAV0 eAms because C 1. , CAms exceeds nin , nQ C holds and Eq. 113) transforms with Eq. C Am s m k 2 : For high concentrations of acceptors Ams (m 2 f 1; 2; : : :g) with pQ Eq. 117) with eAms /mCk Deff D . 119) 1 Diffusion and Point Defects in Silicon Materials 43 is obtained. 119) reveal that in case of dopant diffusion via the vacancy mechanism the effective dopant diffusion coefficient Deff is interrelated Am s eq eq to the reduced diffusion coefficient DV k D CV k DV k =CAms and thus to the transport capacity of V k .
At this stage the eq eq As profiles are insensitive to the model parameter CAi =CAs and fully described by the solution of Eq. 61). Since this case was already discussed in Sect. 3, it is not illustrated in Fig. 9. eq eq The impact of CI =CAs on the diffusion of As for different times is illustrated by Fig. 10. The corresponding distributions of I for 64 s and 720 s are shown for comparison (see Fig. 10b). 5 s) the parameter does not affect the distribution of As . At this stage, the velocity of the formation of the reaction products is high and As and I are formed very shortly.