Derive expressions for concentrations of free carriers in a semiconductor doped with both, donor and acceptor impurities.

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Derive expressions for concentrations of free carriers in a semiconductor doped with both, donor and acceptor impurities. Determine the conductivity type and calculate the concentrations of carriers in silicon at T = 300 K, if it is doped with:

(a) NA =1016 cm-3> > ND.

(b) ND = 1016 cm-3> > NA.

(c) ND = NA ¼ 1016 cm-3.

Assume that all impurities are ionized and ni = 1.38 × 1010 cm-3 at 300 K. 

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