Learning objectives
To introduce students who have learned the basic principles of physics to the study of complex physical systems such as solids.
Prerequisites
Recommened propaedeutics: General physics. Introduction to the physics of atoms and molecules. Introduction to quantum mechanics.
Course unit content
<br />Periodic structures<br />The periodic structure of crystals: basic unit and Bravais lattice. Primitive and conventional unit cells. The Wigner-Seitz cell. Symmetry operations of the Bravais lattice and symmetry operations of the crystal. Examples of crystal structures.<br />The reciprocal lattice: definitions and properties. Reciprocal lattice vectors and and direct lattice planes. The Miller indices. Examples.<br />Determination of the crystal structure. The kinematical theory of X-rays diffraction. Geometry of the diffracted beams: Bragg law and the determination of the Bravais lattice.The Ewald construction. Intensity of the diffracted beams and the determination of the basic unit. The structure factor of the unit cell and the atomic scattering factors. Examples. Neutron and electron diffraction (brief outline).<br />Lattice dynamics<br />Thermal vibrations of the lattice in the harmonic approximation. Vibrations of linear chains with monoatomic and biatomic base. Acoustical and optical modes. Generalization to a 3D lattice with any base. Normal vibrations and properties of Bloch waves. Symmetry of the dispersion laws. The Brillouin zone. Boundary conditions and the density of states.<br />The phonon concept. The inelastic scattering of thermal neutrons and the determination of the phonon dispersion laws. Examples. The inelastic scattering of light (Raman and Brillouin scattering).<br />Thermal properties of solids. The lattice specific heat: explanation of the temperature dependence. The Debye model.<br />Electron states in crystals<br />Motion of the valence electrons in the one-electron approximation. Properties of Bloch states and symmetry of the electron dispersion laws. Density of states and the Fermi energy.<br />The free electron approximation. Effects of the periodic potential: Bragg diffraction and forbidden energy gaps. Classification of solids:metals, insulators and semiconductors. The energy band structure of solids. The weak binding approximation and plane waves expansions. The tight binding approximation and expansions in atomic orbitals. Example of energy band structures. <br />Dynamics of electrons and holes<br />Electron motion in crystal under weak external forces. The wave function as a packet of Bloch states. The semiclassical approximation: group velocity and time dependence of the spectral baricenter of th wave group. The concept of effective mass. Dynamics of positive holes. The effective mass approximation in the quantum description. An example: hydrogenlike impurities in semiconductors.
Full programme
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Bibliography
<br />---NOTES BY THE LECTURER<br />--For a reference textbook see "Solid State Physics" H.Ibach and H.Luth, Springer 2002 (third edition).
Teaching methods
<br />Teaching method: oral lecture<br />Evaluation method: oral examination
Assessment methods and criteria
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Other information
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