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Docente
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POLIMENI ANTONIO
(programma)
Strutture cristalline, reticoli di Bravais. Reticolo reciproco. Diffrazione e solidi cristallini, fattore di struttura. Approssimazione di Born-Oppenheimer. Vibrazioni reticolari, fononi, calore specifico nei solidi (modelli di Einstein, Debye, densità degli stati). Elettroni nei solidi, teorema di Bloch. Bande elettroniche. Elettrone quasi-libero. Metodo dell’eletrone fortmenente legato. Concetto di lacuna e massa efficace. Elettroni in metalli e interazione col campo elettromagnetico (funzione dielettrica, proprietà di trasporto nei metalli): modello di Drude e di Sommerfeld. Semiconduttori intrinseci ed estrinseci. Dipendenza dalla temperatura del numero dei portatori. Fisica della giunzione p-n.
Bravais lattice in 2D and 3D.
Primitive vectors and primitive unit cell. Wigner-Seitz unit cell. Conventional unit cell.
Basis. Examples: graphene, graphite, cubic lattices (face-centered and body-centered cubic cell).
AM: Ch. 4, GPP: Ch. 2.1-2.3, K: Ch. 1
Examples: simple hexagonal and hexagonal close-packed structure. Lattice planes and Miller indexes. Reciprocal lattice as Fourier transform of direct lattice.
Examples and Brillouin zone. Family of lattice planes and reciprocal lattice vectors.
AM Ch. 4 and 5, K Ch. 1 and 2, GPP Ch. 2.4 and 2.5
Diffraction: x-ray, neutrons and electrons. Laue diffraction and reciprocal lattice.
AM: Ch. 6, BG: Ch. 2.1-2.2 K: Ch. 2.
Laue and Bragg diffraction.
AM: Ch. 6, BG: Ch. 2.1-2.3, K: Ch. 2
Structure factor: geometrical structure factor + atomic form factor (examples).
AM: Ch. 6, BG: Ch. 2.4-2.5, K: Ch. 2.
Ewald sphere and different experimental configurations.
AM: Ch. 6, BG: Ch. 2.7, K: Ch. 2
Structure factor: examples.
AM: Ch. 6, BG: Ch. 2.7, K: Ch. 2
Structure factor: examples.
AM: Ch. 6, BG: Ch. 2.7, K: Ch. 2
Exercises.
AM: Ch. 6, K: Ch. 2.
Born-Oppenheimer approximation.
GPP: Ch. 8.1 and 8.2, BG: Ch. 3.1, 3.2, 3.3
Motion equations of a linear chain and dynamical matrix.
GPP: Ch. 9.1, AM: Ch. 22
Oscillation normal modes: elemental unidimensional lattice. Dispersion relation and density of states.
GPP: Ch. 9.1, 9.2, AM: Ch. 22
Oscillation normal modes: unidimensional lattice with basis. Dispersion relation. Acoustic and optical modes.
GPP: Ch. 9.1, 9.2, AM: Ch. 22
Summary of acoustic and optical modes in a linear chain with basis.
GPP: Ch. 9.1, 9.2, AM: Ch. 22
Exercise on linear chain featuring nth-nearest neighbor interaction.
Quantization of the elastic field and phonons
(GPP: Ch. 9.4, AM: Ch. 23)
Dynamical matrix in three-dimensions
(GPP9.3, AM Ch. 22)
Dynamical matrix in three-dimensions
(GPP9.3, AM Ch. 22).
Dynamical matrix in three-dimensions and its Hermitian character
(GPP9.3, AM Ch. 22)
Specific heat: classical and quantum-mechanical treatment. Debye and Einstein models.
AM: Ch. 23, K: Ch. 5, GPP: Ch. 9.5, BG: Ch. 8.1
Debye temperature and chemical trends (examples: diamond, germanium, silicon, graphene).
Phonon modes in bidimensional CuO2
Phonon modes in bidimensional square lattice with 1st and 2nd nn interaction.
Lecture notes and O. Madelung, Introduction to Solid-State Theory (Ch. 3.3.5).
Phonon modes in bidimensional square lattice with 1st and 2nd nn interaction.
Lecture notes and O. Madelung, Introduction to Solid-State Theory (Ch. 3.3.5).
Specific heat of a two-dimensional square lattice (lecture notes).
Bloch’s theorem: I proof (AM Ch 8) Bloch’s theorem: II proof (K Ch. 7)
Kronig-Penney model (K Ch. 7) Energy banfìds (K Ch. 7)
Central equation (K Ch 7) Central equation and empty lattice approximation(K Ch 7)
Weak potential approximation: perturbative approach (AM Ch. 9, K Ch. 7).
Weak potential approximation and band gap opening (AM Ch. 9, K Ch. 7)
Electron Bragg reflection (AM Ch. 9, K Ch. 7). Metals and insulators (K Ch. 7) Electronic specific heat (AM Ch. 2, K Ch. 6)
Sommerfeld integral (AM Ch. 2) Electronic specific heat (AM Ch. 2, K Ch. 6)
Tight binding (AM Ch 10)
Exercise: weak-electron method in an FCC crystal (AM Ch. 9 ex. 3) Tight binding (AM Ch 10). Exercise: tight binding method applied to a SC crystal
Tight binding: polyacetylene bands (lecture notes) Tight binding: graphene bands (lecture notes)
Tight binding: graphene bands, Dirac cone, massless relativistic fermions, hexagonal boron nitride (lecture notes) Semiclassical model: motion equations (AM Ch. 12)
Semiclassical model: motion equations (AM Ch. 12): filled bands, holes, effective mass Boltzmann equation part I (GPP 11.3)
Boltzmann equation part II (GPP 11.3) Static conductivity in metals (GPP 11.4)
Semiconductors: main properties (GPP 13.1, AM Ch. 28)
Number of carriers in thermal equilibrium: the intrinsic case (AM Ch. 28; GPP 13.1)
Effective mass theorem and envelope wavefunction (GPP 13.2)
Effective mass theorem and envelope wavefunction (GPP 13.2, BG 11.3.1) and impurities (BG 11.3.1) Conduction band electrons and Landau levels in three dimensions (BG 9.6, GPP 15.2)
Doping: donors and acceptors. Level statistics (AM 28, GPP 13.2) Chemical potential and number of carriers vs temperature (AM 28,GPP 13.3)
Chemical potential and number of carriers vs temperature (AM 28,GPP 13.3)
 AM: N. W. Ashcroft, N. D. Mermin, Solid State Physics, Saunders College Publishing international series.
K: C. Kittel, Introduction to Solid State Physics, J. Wiley & Sons, New York
GPP: G. Grosso, G. Pastori Parravicini, Solid state physics, Giuseppe Grosso, Giuseppe Pastori Parravicini. - 2. ed. - Oxford : Academic Press, 2014
BG: F. Bassani, U. M. Grassano, Fisica dello Stato Solido, Bollati Boringhieri, Torino
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