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Question: Pure germanium has a band gap of 0.67 eV . The Fer...

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Pure germanium has a band gap of 0.67 eV . The Fermi energy is in the middle of the gap.

Part A: For temperature of 265 K calculate the probability f(E) that a state at the bottom of the conduction band is occupied.

Part B: For the temperature in part A, calculate the probability that a state at the top of the valence band is empty.

Part C: For temperature of 315 K calculate the probability f(E) that a state at the bottom of the conduction band is occupied.

Part D: For the temperature in part C, calculate the probability that a state at the top of the valence band is empty.

Part E: For temperature of 350 K calculate the probability f(E) that a state at the bottom of the conduction band is occupied.

Part F: For the temperature in part E, calculate the probability that a state at the top of the valence band is empty.

Explanation / Answer

using equation

f ( E ) = 1 / 1 + exp ( E - EF / k T )

E = Eg / 2 = 0.67 / 2 = 0.335 eV = E - EF

Part A:

For temperature of 265 K

f ( E ) = 1 / 1 + exp ( E - EF / k T )

f ( E ) = 1 / ( 1 + exp ( 0.335 X 1.6 X 10-19 / 1.38 X 10-23 X 265 ) )

f ( E ) = 4.31 X 10-7

Part B:

For the temperature in part A is

f ( E ) = 1 / 1 + exp ( E - EF / k T )

f ( E ) = 1 / ( 1 + exp ( 0.335 X 1.6 X 10-19 / 1.38 X 10-23 X 265 ) )

f ( E ) = 4.31 X 10-7

Part C:

For temperature of 315 K

f ( E ) = 1 / 1 + exp ( E - EF / k T )

f ( E ) = 1 / ( 1 + exp ( 0.335 X 1.6 X 10-19 / 1.38 X 10-23 X 315 ) )

f ( E ) = 4.41 X 10-6

Part D :

For the temperature in part C is

f ( E ) = 1 / 1 + exp ( E - EF / k T )

f ( E ) = 1 / ( 1 + exp ( 0.335 X 1.6 X 10-19 / 1.38 X 10-23 X 315 ) )

f ( E ) = 4.41 X 10-6

Part E:

For temperature of 315 K

f ( E ) = 1 / 1 + exp ( E - EF / k T )

f ( E ) = 1 / ( 1 + exp ( 0.335 X 1.6 X 10-19 / 1.38 X 10-23 X 350 ) )

f ( E ) = 1.59 X 10-5

Part F :

For the temperature in part E is

f ( E ) = 1 / 1 + exp ( E - EF / k T )

f ( E ) = 1 / ( 1 + exp ( 0.335 X 1.6 X 10-19 / 1.38 X 10-23 X 350 ) )

f ( E ) = 1.59 X 10-5

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