INGLESE

1. The Drude and Sommerfeld Theory of Metals
2. Crystal Lattices
3. The Reciprocal Lattice
4. Determination of Crystal Structures by X-Ray Diffraction
5. Electron Levels in a Periodic Potential
6. Electrons in a Weak Periodic Potential
7. The Tight-Binding Method
8. The Semiclassical Model of Electron Dynamics
9. Basic Transport Phenomena
10. Beyond the Independent Electron
11. Classical Theory of Harmonic Crystal
12. Quantum Theory of Harmonic Crystal

Neil W. Ashcroft, N. Mermin, "Solid State Physics",Brooks/Cole
Dresselhaus M, Dresselhaus G., Cronin S. B., "Solid State Properties- From Bluk to Nano" Springer

- Knowledge and understanding:
The course intends to provide an introduction to solid state physics, with a particular focus on the thermal and electric properties in crystalline structures
- Applying knowledge and understanding:
At the end of the learning process, the students will acquire the basic knowledge that is needed to manage a large variety of theoretical tools for the calculation of transport properties in solid state materials.

Adequate Knowledge of Quantum Mechanic

The course is organized in 68 hours of frontal lectures.
Attendance is not compulsory but strongly recommended.

The examination consists in an oral interview based on the discussion of the topics treated during the course, with a typical duration of 40 minutes. Together with the evaluation of the degree of knowledge and understanding reached by the student, the interview is aimed to evaluate the students' ability in managing solid state problems.

1. The Drude and Sommerfeld Theory of Metals
1.1. Basic assumptions of the Drude Model
1.2. DC electrical conductivity of a metal
1.3. Thermal conductivity of a metal
1.4. Sommerfeld model; ground-state properties of the electron gas.
1.5. Outline on Fermi-Dirac distribution
1.6. Thermal properties of the free electron gas
1.7. The Sommerfeld Theory of conduction in metals
1.8. Failures of the free electron model

2. Crystal Lattices
2.1. Bravais Lattice
2.2. Infinite lattices and finite crystals; examples
2.3. Coordination number, Primitive cells, Unit cell; conventional unit cell; Wigner-Seitz cell
2.4. Lattice with a basis; definition and examples

3. The Reciprocal Lattice
3.1. Definition and examples of Reciprocal lattice
3.2. Volume of reciprocal lattice primitive cell; Brillouin zone; Lattice Planes

4. Determination of Crystal Structures by X-Ray Diffraction
4.1. Formulation of Bragg and Von Laue X-ray diffraction
4.2. Equivalence of the two formulations
4.3. Classification of Bravais Lattice and Crystal Structures

5. Electron Levels in a Periodic Potential
5.1. The Periodic Potential
5.2. Bloch’s Theorem. First proof.
5.3. The Born-Van Karman boundary condition and second proof of Bloch’s Theorem
5.4. General remarks about Bloch’s Theorem; The Fermi Surface
5.5. Density of Levels

6. Electrons in a Weak Periodic Potential
6.1. General Approach to the Schroedinger Equation when the potential is weak
6.2. Energy Levels near a single Bragg plane
6.3. Energy bands in one dimension
6.4. Energy-wave-vector curves in three dimensions
6.5. Brillouin zones

7. The Tight-Binding Method
7.1. General formulation
7.2. Application to an s-band arising from a single atomic s-level
7.3. General remarks on the Tight-Binding Method
7.4. Wannier Functions

8. The Semiclassical Model of Electron Dynamics
8.1. Wavepacket of Bloch electron
8.2. Description of the semiclassical model; comments and restrictions
8.3. Consequences of the semiclassical equations of motion: filled bands, holes;
8.4. Effective Mass Theorem and its application to donor impurity level in a semiconductor

9. Basic Transport Phenomena
9.1. The Boltzmann equation and relaxation time approximation
9.2. Electrical conductivity

10. Beyond the Independent Electron
10.1. Hartree Equation
10.2. Hartree-Fock Approximation
10.3. Hartree-Fock theory of free electrons
10.4. Screening and Thomas-Fermi Theory of screening

11. Classical Theory of Harmonic Crystal
11.1. Failures of the static lattice model
11.2. The harmonic approximation
11.3. The adiabatic approximation
11.4. Specific heat of a classical crystal: Dulong-Petit law
11.5. Normal modes of a one-dimensional monoatomic Bravais lattice
11.6. Normal modes of a one-dimensional lattice with a basis
11.7. Normal modes of a three-dimensional monoatomic Bravais lattice
11.8. Normal modes of a three-dimensional lattice with basis

12. Quantum Theory of Harmonic Crystal
12.1. Normal modes vs. Phonons
12.2. General form of lattice specific heat
12.3. High temperature specific heat
12.4. Low temperature specific heat
12.5. Intermediate temperature specific heat: Debye and Einstein models
12.6. Comparison of lattice and electronic specific heats

English

1. The Drude and Sommerfeld Theory of Metals
2. Crystal Lattices
3. The Reciprocal Lattice
4. Determination of Crystal Structures by X-Ray Diffraction
5. Electron Levels in a Periodic Potential
6. Electrons in a Weak Periodic Potential
7. The Tight-Binding Method
8. The Semiclassical Model of Electron Dynamics
9. Basic Transport Phenomena
10. Beyond the Independent Electron
11. Classical Theory of Harmonic Crystal
12. Quantum Theory of Harmonic Crystal

Neil W. Ashcroft, N. Mermin, "Solid State Physics",Brooks/Cole
Dresselhaus M, Dresselhaus G., Cronin S. B., "Solid State Properties- From Bluk to Nano" Springer

- Knowledge and understanding:
The course intends to provide an introduction to solid state physics, with a particular focus on the thermal and electric properties in crystalline structures
- Applying knowledge and understanding:
At the end of the learning process, the students will acquire the basic knowledge that is needed to manage a large variety of theoretical tools for the calculation of transport properties in solid state materials.

Adequate Knowledge of Quantum Mechanic

The course is organized in 68 hours of frontal lectures.
Attendance is not compulsory but strongly recommended.

The examination consists in an oral interview based on the discussion of the topics treated during the course, with a typical duration of 40 minutes. Together with the evaluation of the degree of knowledge and understanding reached by the student, the interview is aimed to evaluate the students' ability in managing solid state problems.

1. The Drude and Sommerfeld Theory of Metals
1.1. Basic assumptions of the Drude Model
1.2. DC electrical conductivity of a metal
1.3. Thermal conductivity of a metal
1.4. Sommerfeld model; ground-state properties of the electron gas.
1.5. Outline on Fermi-Dirac distribution
1.6. Thermal properties of the free electron gas
1.7. The Sommerfeld Theory of conduction in metals
1.8. Failures of the free electron model

2. Crystal Lattices
2.1. Bravais Lattice
2.2. Infinite lattices and finite crystals; examples
2.3. Coordination number, Primitive cells, Unit cell; conventional unit cell; Wigner-Seitz cell
2.4. Lattice with a basis; definition and examples

3. The Reciprocal Lattice
3.1. Definition and examples of Reciprocal lattice
3.2. Volume of reciprocal lattice primitive cell; Brillouin zone; Lattice Planes

4. Determination of Crystal Structures by X-Ray Diffraction
4.1. Formulation of Bragg and Von Laue X-ray diffraction
4.2. Equivalence of the two formulations
4.3. Classification of Bravais Lattice and Crystal Structures

5. Electron Levels in a Periodic Potential
5.1. The Periodic Potential
5.2. Bloch’s Theorem. First proof.
5.3. The Born-Van Karman boundary condition and second proof of Bloch’s Theorem
5.4. General remarks about Bloch’s Theorem; The Fermi Surface
5.5. Density of Levels

6. Electrons in a Weak Periodic Potential
6.1. General Approach to the Schroedinger Equation when the potential is weak
6.2. Energy Levels near a single Bragg plane
6.3. Energy bands in one dimension
6.4. Energy-wave-vector curves in three dimensions
6.5. Brillouin zones

7. The Tight-Binding Method
7.1. General formulation
7.2. Application to an s-band arising from a single atomic s-level
7.3. General remarks on the Tight-Binding Method
7.4. Wannier Functions

8. The Semiclassical Model of Electron Dynamics
8.1. Wavepacket of Bloch electron
8.2. Description of the semiclassical model; comments and restrictions
8.3. Consequences of the semiclassical equations of motion: filled bands, holes;
8.4. Effective Mass Theorem and its application to donor impurity level in a semiconductor

9. Basic Transport Phenomena
9.1. The Boltzmann equation and relaxation time approximation
9.2. Electrical conductivity

10. Beyond the Independent Electron
10.1. Hartree Equation
10.2. Hartree-Fock Approximation
10.3. Hartree-Fock theory of free electrons
10.4. Screening and Thomas-Fermi Theory of screening

11. Classical Theory of Harmonic Crystal
11.1. Failures of the static lattice model
11.2. The harmonic approximation
11.3. The adiabatic approximation
11.4. Specific heat of a classical crystal: Dulong-Petit law
11.5. Normal modes of a one-dimensional monoatomic Bravais lattice
11.6. Normal modes of a one-dimensional lattice with a basis
11.7. Normal modes of a three-dimensional monoatomic Bravais lattice
11.8. Normal modes of a three-dimensional lattice with basis

12. Quantum Theory of Harmonic Crystal
12.1. Normal modes vs. Phonons
12.2. General form of lattice specific heat
12.3. High temperature specific heat
12.4. Low temperature specific heat
12.5. Intermediate temperature specific heat: Debye and Einstein models
12.6. Comparison of lattice and electronic specific heats