
Published online:
17 December 2013
Published in print:
01 March 2012
Online ISBN:
9780191775123
Print ISBN:
9780199646944
Contents
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29.1 Tight-Binding Approximation 29.1 Tight-Binding Approximation
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29.2 Bloch’s Theorem 29.2 Bloch’s Theorem
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29.3 Nearly-Free Electrons 29.3 Nearly-Free Electrons
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29.3.1 Free Electrons 29.3.1 Free Electrons
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29.3.2 The ‘Empty’ Lattice 29.3.2 The ‘Empty’ Lattice
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29.3.3 Non-Zero Periodic Potential 29.3.3 Non-Zero Periodic Potential
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29.4 Energy Bands and Energy Gaps 29.4 Energy Bands and Energy Gaps
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29.5 Where is the Fermi Energy? 29.5 Where is the Fermi Energy?
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29.6 Fermi Energy in a Band (Metals) 29.6 Fermi Energy in a Band (Metals)
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29.7 Fermi Energy in a Gap 29.7 Fermi Energy in a Gap
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29.8 Intrinsic Semiconductors 29.8 Intrinsic Semiconductors
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29.9 Extrinsic Semiconductors 29.9 Extrinsic Semiconductors
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29.9.1 Donor Impurities 29.9.1 Donor Impurities
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29.9.2 Acceptor Impurities 29.9.2 Acceptor Impurities
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29.10 Semiconductor Statistics 29.10 Semiconductor Statistics
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29.10.1 Derivation of Semiconductor Statistics 29.10.1 Derivation of Semiconductor Statistics
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29.10.2 Simplified Illustration of Semiconductor Statistics 29.10.2 Simplified Illustration of Semiconductor Statistics
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29.10.3 A More Realistic Model of a Semiconductor 29.10.3 A More Realistic Model of a Semiconductor
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29.11 Semiconductor Physics 29.11 Semiconductor Physics
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Chapter
29 29 Insulators and Semiconductors
Get access
Pages
351–367
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Published:March 2012
Cite
Swendsen, Robert H., '29 Insulators and Semiconductors', An Introduction to Statistical Mechanics and Thermodynamics, 1st edn, Oxford Graduate Texts (Oxford , 2012; online edn, Oxford Academic, 17 Dec. 2013), https://doi.org/10.1093/acprof:oso/9780199646944.003.0029, accessed 6 May 2025.
Abstract
Electrons in a crystal provide the most important example of a Fermi-Dirac system in a periodic potential. Due to Bloch's theorem, gaps occur in the density of states in such systems. When the Fermi energy lies in one of the gaps in the density of states, the properties of the Fermi gas change dramatically, giving rise to the behaviour of insulators and semiconductors.
Keywords:
insulators, semiconductors, density of states, Bloch's theorem, Fermi energy, Fermi-Dirac system
Subject
Condensed Matter Physics
Collection:
Oxford Scholarship Online
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