Copper is a promising interconnect for silicon. However, it is undesirable to have copper impurities in silicon. It is proposed that two types of copper impurities exist: Cu i + and CuSi 3-. It has been reported that the Cu defect concentrations in intrinsic Si at 25°C are as follows:

Your supervisor suggests that the total copper concentration will be reduced if Si is doped with phosphorus.
Write defect equilibria equations for the incorporation of each of these species to examine the effect of phosphorus doping on each type of Cu impurity. At what concentration of P will you get the minimum total Cu concentration. By how much will the amount of Cu be reduced over intrinsic Si? Assume that the silicon vacancy concentration does not change with impurity concentration.

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Cut = 106 cm-3 3- and Cusi = 10 cm-3