For the Boltzmann approximation to be valid for a semiconductor, the Fermi level must be at least 3kT below the donor level in an n-type material and at least 3kT above the acceptor level in a p-type material. If T = 300 K, determine the maximum electron concentration in an n-type semiconductor and the maximum hole concentration in a p-type semiconductor for the Boltzmann approximation to be valid in (a) silicon and (b) gallium arsenide.
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