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•• In an intrinsic semiconductor, the concentration (n) of conduction electrons equals the concentration (p) of valence holes: n = p = ni where ni is a temperature-dependent parameter called the intrinsic concentration. In a doped semiconductor, the product np = ni2 turns out to be independent of the donor concentration Nd or acceptor concentration Na. For instance, as donors are added, n increases, but p decreases (due to increased rate of electron-hole recombination) and np remains fixed. The fact that the product np is independent of impurity concentration is called the law of mass action. (a) Write a formula for the hole concentration p for a donor-doped semiconductor, in terms of ni and Nd, assuming that Nd ≫ ni and the temperature is high enough that all donors are ionized, (b) In silicon at room temperature, ni = 4.6 × 1010 cm−3. What donor concentration will result in a hole concentration of 10−4 ni?
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