For Ge semiconductor, assume the Fermi energy level is 0.1 eV below the conduction band energy Ec. Let the absolute temperature T for items i and ii be 200 K. i. Find the number of quantum states between Ec and Ec +0.1x4.6xkbT. ii.Determine the probability of a state being empty of an electron at Ec+0.1x4.6x kbT. iii. Find the temperature at which there is an electron at the state Ec+0.01x4.6× kbT with probability 30%. iv. Repeat item iii by using the Boltzmann approximation rather than the Fermi-Dirac distribution. v. Find the difference in temperature between items iii and iv above and express this difference as percentage.

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For Ge semiconductor, assume the Fermi energy level is 0.1 eV
below the conduction band energy
Ec. Let the absolute temperature T for items i and ii be 200 K.
i. Find the number of quantum states between Ec and Ec
+0.1x4.6xkbT.
ii.Determine the probability of a state being empty of an electron
at Ec+0.1x4.6x kbT.
ii. Find the temperature at which there is an electron at the state
Ec+0.01x4.6x
kbT with probability 30%.
iv. Repeat item iii by using the Boltzmann approximation rather
than the
Fermi-Dirac distribution.
v. Find the difference in temperature between items iii and iv
above and express this difference as
percentage.
Transcribed Image Text:For Ge semiconductor, assume the Fermi energy level is 0.1 eV below the conduction band energy Ec. Let the absolute temperature T for items i and ii be 200 K. i. Find the number of quantum states between Ec and Ec +0.1x4.6xkbT. ii.Determine the probability of a state being empty of an electron at Ec+0.1x4.6x kbT. ii. Find the temperature at which there is an electron at the state Ec+0.01x4.6x kbT with probability 30%. iv. Repeat item iii by using the Boltzmann approximation rather than the Fermi-Dirac distribution. v. Find the difference in temperature between items iii and iv above and express this difference as percentage.
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