Impurity concentration phase diagram

Fig. 4.5. Schematic of top left corner of the "silicon-impurity" phase diagram. To make things simple, we assume that the liquidus and solidus lines ore straight. The impurity concentration in the solid is then always less than that in the liquid by the factor k (called the distribution coefficient).

The fact that n-type crystals thus grown are semi-insulating cannot be explained from the viewpoint of the phase diagram. The semi-insulating phase is regarded as a pseudo-intrinsic semiconductor, i.e. the concentration of free carriers is very low, due to the carrier compensation in some sense. Holmers et al. have concluded from their data that the concentration of free carrier called EL2 , Nq, is compensated for by that of acceptors derived from impurity carbon, Ta et carried out a similar investigation independently and reached the same conclusion. 

The solubility is defined with respect to a second precipitated phase. The solubility of an impurity is the maximum concentration, which can be incorporated in the liquid or solid phase without precipitating a second phase. For most impurities in solid silicon at high-temperatures, equilibrium is achieved with the liquid phase governed by the liquidus in the phase diagram. Solid solubility is temperature-dependent as represented by the solidus or solvent curves in the phase diagram. At lower temperatures, the reference phase is usually a compound or an impurity-rich alloy. When the impurity is volatile, the saturated crystal is in equilibrium with the vapor, and the impurity solubility also depends on its vapor pressure. 

Fig. 3.12. Phase diagram of the alloy model, as obtained from the CPA self-energy. 6 denotes the critical value of 6 for the appearance of a mobility gap at a given concentration, 8 q the opening of a gap in the density of states, and 6 a the Anderson transition for the impurity states. The concentration above which the Anderson transition no longer takes place is denoted...

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