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Show that the probability of an energy state being occupied AE above the Fermi energy is the same as the probability of a state being empty AE below the Fermi level. (a) Determine for what

Show that the probability of an energy state being occupied AE above the Fermi energy is the same as the probability of a state being empty AE below the Fermi level. (a) Determine for what

Introductory Circuit Analysis (13th Edition)
Introductory Circuit Analysis (13th Edition)
13th Edition
ISBN:9780133923605
Author:Robert L. Boylestad
Publisher:Robert L. Boylestad
Chapter1: Introduction
Section: Chapter Questions
Problem 1P: Visit your local library (at school or home) and describe the extent to which it provides literature...
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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
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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