1) Consider the FermiDirac Distribution, what is the probability of finding an electron with:
(a)
an energy that is 4% higher than the Fermi energy at 0K?
(b)
an energy that is 4% lower than the Fermi energy at 0K?
(c)
an energy that is 4% higher than the Fermi energy at 298K?
(d)
an energy that is 4% lower than the Fermi energy at 298K?
(e)
an energy that is 4% higher than the Fermi energy at 1000K?
(f)
an energy that is 4% lower than the Fermi energy at 1000K?
For each case consider than the Fermi energy is 5 eV.
Draw a graph of energy vs. the FermiDirac Distribution for the three temperatures indicated above and
demark the energies that are 4% lower/higher than the Fermi energy, as well as the corresponding
probabilities.
Solution:
Using the FermiDirac Distribution
(
29
1
exp
1
+

=
T
k
E
E
E
F
B
F
Probability at
Temperature
(K)
E 4%
higher
E 4%
lower
0
0
1
298
0.0004142
7
0.999585
7
1000
0.0893991
6
0.910600
8
Ef (eV)
5
E 4% higher
(eV)
5.2
E 5% lower
(eV)
4.8
F(E)
E
0
E
F
=5eV
1
T=0K
T=1000K
T=298K
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2) Consider a monovalent metal such as gold and a divalent metal such as zinc.
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 Fall '10
 Takamura
 Electron, Fundamental physics concepts, Fermi energy, Fermi, FermiDirac distribution

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