course ID

Lecturer

Massimo Fanfoni

CFU

6

Length

14 Weeks

Semester DD

Second

Course details

1) Electronic states in crystals

1.1) Case 1D

1.1.1) Bloch-Floquet theorem

1.1.2) Kronig-Penney model

1.1.3) Narrow attachment approximation

1.1.3.1) Huckel model for a closed chain

1.2) 3D case

1. 2.1) Recalls on the direct lattice and on the reciprocal lattice

1.2.2) Bloch's theorem in 3D

1.2.3) Cyclic boundary conditions or Born-von Karman conditions

1.2.4) Density of states (DOS) and critical points in 1, 2 and 3 dimensions

1.3) Band theory

1.3.1) Tight binding method (TB-LCAO)

1.3.2) Drude model

1.3.3) Homogeneous electron gas (Jellium model)

2) The phononic structure

2.1) Chain of atoms: 1 atom per cell

2.2) Chain with 2 atoms per cell

2.3) Generalization to the 3D case

3) Semiconductors

3.1) Currents in semiconductors: Drift and diffusion

3.1) Concept of gap

3.2) Carrier density

3.2.1) Effective mass and density of the states in Si and Ge

3.2.2) Law of mass action

3.3) Intrinsic semiconductors

3.4) Neutrality of charge, position of the Fermi level (Chemical potential)

3.5) Extrinsic semiconductors

3.5.1) Hamiltonian; approximation of the effective mass

3.5.2) Position of the Fermi level (Chemical potential)

3.6) PN junction and hints on MOSFETs

4) Magnetism in solids

4.1) Concept of Magnetization

4.1.1) Bohr-van Leeuwen theorem

4.2) Energy levels for a 2D electron gas in a magnetic field (Landau gauge); Landau levels and their degeneration

4.3) Energy levels for a 3D electron gas in a magnetic field

4.3.1) Orbital magnetic susceptibility; De Hass effect - van Alphen

4.4) MagnetoResistivity - Hall effect (classical)

4.4.1) Isotropic medium with one band (magnetoconductivity tensor): parallel magnetoresistivity, Hall magnetoresistivity, Hall coefficient

4.4.2) Isotropic medium with two bands

4. 5) Diamagnetism and paramagnetism

4.5.1) Susceptibility of insulators with closed shells: Larmor's diamagnetism

4.5.2) Susceptibility of insulators with open shells: paramagnetism: Curie's law

4.5.3) Susceptibility of metals: Pauli paramagnetism

4.5.4) Diamagnetism of electrons of conduction and doped semiconductors.

4.6) Interaction of electrons and magnetic structures

4.6.1) Dipolar interaction

4.6.2) Magnetic properties of a system with 2 electrons (singlet and triplet states)

4.6.3) Magnetic interactions in free electron gas

4.7 ) Magnetic Order

4.7.1) High temperature susceptibility

4.7.2) Critical points: medium field theory

Co-Teaching: Dr. Salvatore Matteo

Objectives

tbd