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Chapter25_Carrier-Statistics

Chapter25_Carrier-Statistics - 2.5 Carrier Statistics 2.5.1...

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2.5 Carrier Statistics 2.5.1 Density of States 2.5.2 Fermi Function & Fermi Energy Physical Interpretation Characteristics 2.5.3 Carrier Densities Intrinsic/Extrinsic Semiconductor Intrinsic Fermi Energy Mass Action Law Temperature Dependence 2.5.4 Charge Neutrality Relationship 2.5.5 Non-Complete Ionization Pierret, Chapter 2.4-2.6, page 40-68 Slides courtesy of Prof. Oliver Brand
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2 2.5.1 Density of States From quantum mechanics, we not only obtain the band structure, i.e., the E(k) relations, but also the density of states g(E)dE, i.e., how many allowed states are in the range E…E+dE: g C (E)dE = m n * 2m n * E E C ( ) π 2 3 dE E E C ( ) 1/2 g V (E)dE = m p * 2m p * E V E ( ) π 2 3 dE E V E ( ) 1/2
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3 Density of States Band Gap E C E V E g C (E) g V (E) g(E) Units of g(E)dE are [cm -3 ]
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4 2.5.2 Fermi Function & Fermi Energy What determines whether an allowed state is occupied by an electron or not? Fermi Function f(E): f(E) is a probability function which gives the probability whether a state is occupied or not E F is the Fermi Energy f(E) = 1 1 + e (E E F )/kT
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5 Characteristics of Fermi Function Because of Pauli principle: 0 f(E) 1 f(E = E F ) = 0.5 The probability that a state is occupied at the Fermi energy is 50% f(E) is symmetric around E F : f(E F + E) = 1 – f(E F – E) For T = 0 the Fermi function becomes a step function, i.e. all states below E F are occupied, all states above E F empty Energy E [eV] Fermi Function f(E) E F = 1 eV kT = 0.0259 eV
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