tron in the valence band over the range E,- 2kT eV< beng emply by an el E< E. 3.35 The probability that a state at E. + kT is occupied by an electron is equal to the prob- ability that a state at E, - kT is empty. Determine the position of the Fermi energy | level as a function of E, and Ey. 3.36 Six free electrons exist in a one-dimensional infinite potential well of width a = 12 Å. Determine the Fermi energy level at T = 0 K. 3.37 (a) Five free electrons exist in a three-dimensional infinite potential well with all three widths equal to a = part (a) for 13 electrons. 3.38 Show that the probability of an energy state being occupied AE above the Fermi energy is the sáme as the probability of a state being empty AE below the Fermi level. 3.39 (a) Determine for what energy above EF (in terms of kT) the Fermi-Dirac probability function is within 1 percent of the Boltzmann approximation. (b) Give the value of the probability function at this 3.40 The Fermi energy level for a particular material at T trons in this material follow the Fermi-Dirac distribution function. (a) Find the probability of an electron occupying an energy at 5.80 eV. (b) Repeat part (a) if the temperature is increased toT = 700 K. (Assume that EF is a constant.) (c) Determine the temperature at which there is a 2 percent probability that a state 0.25 eV below the Fermi level will be empty of an electron. 12 Å. Determine the Fermi energy level at T= 0 K. (b) Repeat energy. = 300 K is 5.50 eV. The elec- 5.41 The Fermi energy for copper at T = 300 K is 7.0 eV. The electrons in copper follow the Fermi-Dirac distribution function. (a) Find the nrohahility of an energy lexel at
tron in the valence band over the range E,- 2kT eV< beng emply by an el E< E. 3.35 The probability that a state at E. + kT is occupied by an electron is equal to the prob- ability that a state at E, - kT is empty. Determine the position of the Fermi energy | level as a function of E, and Ey. 3.36 Six free electrons exist in a one-dimensional infinite potential well of width a = 12 Å. Determine the Fermi energy level at T = 0 K. 3.37 (a) Five free electrons exist in a three-dimensional infinite potential well with all three widths equal to a = part (a) for 13 electrons. 3.38 Show that the probability of an energy state being occupied AE above the Fermi energy is the sáme as the probability of a state being empty AE below the Fermi level. 3.39 (a) Determine for what energy above EF (in terms of kT) the Fermi-Dirac probability function is within 1 percent of the Boltzmann approximation. (b) Give the value of the probability function at this 3.40 The Fermi energy level for a particular material at T trons in this material follow the Fermi-Dirac distribution function. (a) Find the probability of an electron occupying an energy at 5.80 eV. (b) Repeat part (a) if the temperature is increased toT = 700 K. (Assume that EF is a constant.) (c) Determine the temperature at which there is a 2 percent probability that a state 0.25 eV below the Fermi level will be empty of an electron. 12 Å. Determine the Fermi energy level at T= 0 K. (b) Repeat energy. = 300 K is 5.50 eV. The elec- 5.41 The Fermi energy for copper at T = 300 K is 7.0 eV. The electrons in copper follow the Fermi-Dirac distribution function. (a) Find the nrohahility of an energy lexel at
University Physics Volume 3
17th Edition
ISBN:9781938168185
Author:William Moebs, Jeff Sanny
Publisher:William Moebs, Jeff Sanny
Chapter9: Condensed Matter Physics
Section: Chapter Questions
Problem 68P: What is the longest wavelength for a photon that can excite a valence election into the conduction...
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Question
Q7.6 using fermi Dirac distribution with no approximations
Transcribed Image Text:probability of a state
being empty by an electron in the valence band over the range E, - 2kT eV <
E E,.
The probability that a state at E. + kT is occupied by an electron is equal to the prob-
ability that a state at E,
level as a function of E. and E.
3.35
kT is empty. Determine the position of the Fermi energy
3.36
Six free electrons exist in a one-dimensional infinite potential well of width a = 12 Å.
Determine the Fermi energy level at T = 0 K.
3.37 (a) Five free electrons exist in a three-dimensional infinite potential well with all three
12 Å. Determine the Fermi energy level at T = 0 K. (b) Repeat
widths equal to a =
part (a) for 13 electrons.
Show that the probability of an energy state being occupied AE above the Fermi
energy is the sáme as the probability of a state being empty AE below the Fermi level.
3.39 (a) Determine for what energy above EF (in terms of kT) the Fermi-Dirac probability
function is within 1 percent of the Boltzmann approximation. (b) Give the value of the
probability function at this energy.
3.38
3.40
The Fermi energy level for a particular material at T = 300 K is 5.50 eV. The elec-
trons in this material follow the Fermi-Dirac distribution function. (a) Find the
probability of an electron occupying an energy at 5.80 e V. (b) Repeat part (a) if the
temperature is increased toT = 700 K. (Assume that Er is a constant.) (c) Determine
the temperature at which there is a 2 percent probability that a state 0.25 eV below the
Fermi level will be empty of an electron.
3.41
The Fermi energy for copper at T = 300 K is 7.0 eV. The electrons in
the Fermi-Dirac distribution function. (a) Find the probability of an energy level at
7.15 eV being occupied by an electron. (b) Repeat part (a) for T = 1000 K. (Assume
copper
follow
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