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By Jenö Sólyom, Attila Piróth
The reader is preserving the second one quantity of a three-volume textbook on solidstate physics. This publication is the outgrowth of the classes i've got taught for a few years at Eötvös college, Budapest, for undergraduate and graduate scholars less than the titles Solid-State Physics and glossy Solid-State Physics. the most motivation for the booklet of my lecture notes as a booklet used to be that not one of the really quite a few textbooks coated all these components that I felt will be integrated in a multi-semester direction. specifically, if the direction strives to provide solid-state physics in a unified constitution, and goals at discussing not just vintage chapters of the subject material but in addition (in kind of aspect) difficulties which are of significant curiosity for today’s researcher in addition.
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Extra resources for Fundamentals of the Physics of Solids - Electronic Properties
Sample text
The states are neither fully occupied nor completely empty here. At energies that are farther than a few times kB T from the chemical potential, states within the Fermi sphere continue to be completely filled, as if they were frozen in, while states outside the Fermi sphere remain empty. f0(e) df (e) - 0 de 1 e eF Fig. 6. The equilibrium distribution function of particles obeying the Fermi– Dirac statistics and its derivative with respect to energy As mentioned above, μ = εF at T = 0. 59) k,σ as the number of electrons is not changed by thermal excitation.
The result is indeed independent of the choice of the boundary condition. Even though the quantum mechanical description is based on an extended wavefunction, the Wigner–Seitz sphere can be defined for conduction electrons as well: it is a sphere of radius r0 whose volume is equal to the volume per conduction electron. Thus, 1 4πr03 V . 919 = . 32) is often used to specify the electron density. 6 contains the calculated density of electrons, the radius of the spherical volume per electron, as well as the values of the Fermi wave number, Fermi velocity, and Fermi energy determined in the free-electron model for some simple metals.
15) where nx , ny , and nz are arbitrary integers. 16) make up a regular lattice of lattice constants 2π/Lx , 2π/Ly , 2π/Lz . This lattice is shown in Fig. 4. Fig. 4. Allowed values of the wave vector Since each value of k is associated with a volume (2π/Lx )(2π/Ly )(2π/Lz ) in k-space, the number of allowed states in volume dk is20 V Lx Ly Lz dk = dk . 21 It should be noted that this relation between the momentum and wave vector of the particle is rigorously valid only for free particles. The quantum mechanical particle-current density is jn = 20 21 1 k 1 (ψ ∗ ∇ψ − ψ∇ψ ∗ ) = .