Pure germanium has a band gap of 0.67 EV. The Fermi energy is in the middle of the gap. For temperatures of 250K, 300K and 350K, calculate the probability f(E) that a state at the bottom of the conduction band is occupied. b) For each temperature in part a), calculate the probability that a state at the top of the valence band is empty.
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To calculate the probability that a state at the top of the valence band is empty, we can use the Fermi-Dirac distribution function and the fact that the probability that a state is empty is just 1 minus the probability that it is occupied.
This means that:
At 250K:
f(E) = 1 / (e^((E - 0.335 eV)/(8.6*10^-5 eV/K * 250K)) + 1)
probability that a state at the top of the valence band is empty = 1 - f(E)
At 300K:
f(E) = 1 / (e^((E - 0.335 eV)/(8.6*10^-5 eV/K * 300K)) + 1)
probability that a state at the top of the valence band is empty = 1 - f(E)
At 350K:
f(E) = 1 / (e^((E - 0.335 eV)/(8.6*10^-5 eV/K * 350K)) + 1)
probability that a state at the top of the valence band is empty = 1 - f(E)