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Boltzmann approximation of Fermi function f(E)e-(E-E)/KT EN Maxwell- T E, +3kT Boltzmann Ef. + 2kT E₁ + kT Ef E₁ - kT E₁ - 2kT E - 3kT Fermi- Dirac f(E) 1-e-(Ef-E)/kT ·ƒ(E) 0.5 1 1 f(E)= 1+e' (E-Eƒ)/kT E-E,>> KT f ƒ (E) ≈ e² (E-E₁ ) / kT E-E, <<-kT ƒ (E) = 1 − e−(E₁-E)/kT Non-degenerate semiconductors Non-degenerate semiconductors are defined as semiconductors for which the Fermi energy is at least 3KT away from either band edge. 3kT E EF here... Degenerate semiconductor EF here... Nondegenerate semiconductor Ev EF here... Degenerate semiconductor 3kT The approximation of non-degenerate semiconductors allows the Fermi function to be replaced with the simple exponential Boltzmann function. In many cases, solid state electronic devices operate on the principles of non- degenerate semiconductors. Fermi function 1. Calculate probability for an electron to have an energy of 3kT above the Fermi level. 2. Calculate probability for a hole to have an energy of 3kT below the Fermi level. 3. Compare this data with that calculated using Boltzmann approximation.

Boltzmann approximation of Fermi function f(E)e-(E-E)/KT EN Maxwell- T E, +3kT Boltzmann Ef. + 2kT E₁ + kT Ef E₁ - kT E₁ - 2kT E - 3kT Fermi- Dirac f(E) 1-e-(Ef-E)/kT ·ƒ(E) 0.5 1 1 f(E)= 1+e' (E-Eƒ)/kT E-E,>> KT f ƒ (E) ≈ e² (E-E₁ ) / kT E-E, <<-kT ƒ (E) = 1 − e−(E₁-E)/kT Non-degenerate semiconductors Non-degenerate semiconductors are defined as semiconductors for which the Fermi energy is at least 3KT away from either band edge. 3kT E EF here... Degenerate semiconductor EF here... Nondegenerate semiconductor Ev EF here... Degenerate semiconductor 3kT The approximation of non-degenerate semiconductors allows the Fermi function to be replaced with the simple exponential Boltzmann function. In many cases, solid state electronic devices operate on the principles of non- degenerate semiconductors. Fermi function 1. Calculate probability for an electron to have an energy of 3kT above the Fermi level. 2. Calculate probability for a hole to have an energy of 3kT below the Fermi level. 3. Compare this data with that calculated using Boltzmann approximation.

Introductory Circuit Analysis (13th Edition)
Introductory Circuit Analysis (13th Edition)
13th Edition
ISBN:9780133923605
Author:Robert L. Boylestad
Publisher:Robert L. Boylestad
Chapter1: Introduction
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Problem 1P: Visit your local library (at school or home) and describe the extent to which it provides literature...
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Boltzmann approximation of Fermi function f(E)e-(E-E)/KT EN Maxwell- T E, +3kT Boltzmann Ef. + 2kT E₁ + kT Ef E₁ - kT E₁ - 2kT E - 3kT Fermi- Dirac f(E) 1-e-(Ef-E)/kT ·ƒ(E) 0.5 1 1 f(E)= 1+e' (E-Eƒ)/kT E-E,>> KT f ƒ (E) ≈ e² (E-E₁ ) / kT E-E, <<-kT ƒ (E) = 1 − e−(E₁-E)/kT Non-degenerate semiconductors Non-degenerate semiconductors are defined as semiconductors for which the Fermi energy is at least 3KT away from either band edge. 3kT E EF here... Degenerate semiconductor EF here... Nondegenerate semiconductor Ev EF here... Degenerate semiconductor 3kT The approximation of non-degenerate semiconductors allows the Fermi function to be replaced with the simple exponential Boltzmann function. In many cases, solid state electronic devices operate on the principles of non- degenerate semiconductors. Fermi function 1. Calculate probability for an electron to have an energy of 3kT above the Fermi level. 2. Calculate probability for a hole to have an energy of 3kT below the Fermi level. 3. Compare this data with that calculated using Boltzmann approximation.
Transcribed Image Text:Boltzmann approximation of Fermi function f(E)e-(E-E)/KT EN Maxwell- T E, +3kT Boltzmann Ef. + 2kT E₁ + kT Ef E₁ - kT E₁ - 2kT E - 3kT Fermi- Dirac f(E) 1-e-(Ef-E)/kT ·ƒ(E) 0.5 1 1 f(E)= 1+e' (E-Eƒ)/kT E-E,>> KT f ƒ (E) ≈ e² (E-E₁ ) / kT E-E, <<-kT ƒ (E) = 1 − e−(E₁-E)/kT Non-degenerate semiconductors Non-degenerate semiconductors are defined as semiconductors for which the Fermi energy is at least 3KT away from either band edge. 3kT E EF here... Degenerate semiconductor EF here... Nondegenerate semiconductor Ev EF here... Degenerate semiconductor 3kT The approximation of non-degenerate semiconductors allows the Fermi function to be replaced with the simple exponential Boltzmann function. In many cases, solid state electronic devices operate on the principles of non- degenerate semiconductors. Fermi function 1. Calculate probability for an electron to have an energy of 3kT above the Fermi level. 2. Calculate probability for a hole to have an energy of 3kT below the Fermi level. 3. Compare this data with that calculated using Boltzmann approximation.
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