Doping changes the Fermi energy of a semiconductor. Consider silicon, with a gap of 1.11 ev between the top of the valence band and the bottom of the conduction band. At 300 K the Fermi level of the pure material is nearly at the midpoint of the gap. Suppose that silicon is doped with donor atoms, each of which has a state 0.10 eV below the bottom of the silicon conduction band, and suppose further that doping raises the Fermi level to 0.075 eV below the bottom of that band (see the figure below). For (a) pure and (b) doped silicon, calculate the probability that a state at the bottom of the silicon conduction band is occupied. (c) Calculate the probability that a donor state in the doped material is occupied. Conduction band Fermi level Donor 1.11 eV level Valence band
Doping changes the Fermi energy of a semiconductor. Consider silicon, with a gap of 1.11 ev between the top of the valence band and the bottom of the conduction band. At 300 K the Fermi level of the pure material is nearly at the midpoint of the gap. Suppose that silicon is doped with donor atoms, each of which has a state 0.10 eV below the bottom of the silicon conduction band, and suppose further that doping raises the Fermi level to 0.075 eV below the bottom of that band (see the figure below). For (a) pure and (b) doped silicon, calculate the probability that a state at the bottom of the silicon conduction band is occupied. (c) Calculate the probability that a donor state in the doped material is occupied. Conduction band Fermi level Donor 1.11 eV level Valence band
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Transcribed Image Text:Doping changes the Fermi energy of a semiconductor. Consider silicon, with a gap of 1.11 eV between the top of the valence band and the bottom of the conduction
band. At 300 K the Fermi level of the pure material is nearly at the midpoint of the gap. Suppose that silicon is doped with donor atoms, each of which has a state 0.10
eV below the bottom of the silicon conduction band, and suppose further that doping raises the Fermi level to 0.075 eV below the bottom of that band (see the figure
below). For (a) pure and (b) doped silicon, calculate the probability that a state at the bottom of the silicon conduction band is occupied. (c) Calculate the probability
that a donor state in the doped material is occupied.
Conduction band
Fermi
Donor
1.11 eV
level
level
Valence band
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