Transcription of Free Electron Fermi Gas - University of Michigan
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33. 6. free Electron Fermi Gas Electrons in a metal Electrons in one atom One Electron in an atom (a hydrogen-like atom): the nucleon has charge +Z e, where Z is the atomic number, and there is one Electron moving around this nucleon Four quantum number: n, l and lz , sz . energy levels En with n = 1, 2, 3 .. Z2 e4 1. En = - ( ). 32 0 n2. 2 2 2. where = me m N Hme + m N L me where me is the mass of an Electron and m N is the mass of the nucleon. eV L Z2. En = - ( ). n2. For each n, the angular momentum quantum number [L2 = lHl + 1L ] can take the values of l = 0, 1, 2, 3, 4 , n - 1. These states are known as the s, p, d, f , g, states For each l, the quantum number for Lz can be any integer between -l and +l Hlz = -l, -l + 1, , l - 1, lL. For fixed n, l and lz , the spin quantum number sz can be +1/2 or -1/2 (up or down).
If we have N electrons, at T = 0, the electron occupies the lowest N’2 states. The energy of the highest filled state is known as the Fermi energy eF. The momentum of this state is known as the Fermi momentum PF. The wavevector of this state is known as the Fermi wavevector kF. Obviously, PF = ÑkF and eF = (6.13) PF 2 2 m = Ñ2 k F 2 2 m
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Density of States, Fermi Energy and Energy, Fermi energy, Fermi, Density of States, Energy, States, Density, Density of states fermi, Statistical Physics, Energy states, MOSFET Device Physics and Operation, UNIT 1 STANDARD OF MEASUREMENT, Quantum Mechanics: Fundamental Principles and, Quantum Mechanics: Fundamental Principles and Applications