CFU

6

Length

14 Weeks

Semester DD

First

1. Crystalline structures

6.1. Direct Lattice (DR)

6.1.1. Crystalline Systems

6.1.2. Bravais lattices

6.1.2.1. Primitive cell

6.1.2.2. Unitary cell

6.1.3. Basis

6.1.3.1. Examples

6.2. Reciprocal Lattice (RL)

6.2.1. Primitive vectors

6.2.1.1. Cubic System

6.2.2. Miller indexes

7. Diffraction

7.1.1. Fourier transform of the carrier density

7.1.2. Experimental set up for diffraction measurements

7.1.2.1. Sphere of Ewald and its construction

7.1.2.1.1. Laue methods

7.1.2.1.2. Rotating crystal methods

7.1.2.1.3. Powder methods

7.1.3. Atomic Form Factor and Structure Factor

7.1.3.1. Atomic Approximation

7.1.3.2. Connection with the reciprocal lattice forbidden reflections

7.1.3.2.1. Example:: fcc, bcc diffraction, diamond diffraction

8. The electronic structure

8.1. Independent electron approximation

8.1.1. Hartree-Fock Approach

8.1.1.1. Cononical Form.

8.1.1.2. Koopmans’ theorem

8.1.1.3. Homogeneous electron gas

8.2. Sum rule due to translation invariance

8.3. The Bloch theorem

8.4. Born Von Karman Boundary condition

8.5. The densitu of states

8.5.1. Van Hoove singularities in 1D, 2D,and 3D.

8.6. Energy band concept

8.6.1. Nearly free electron

8.6.1.1. Nearly free electron in a cubic crystal

8.6.2. Semi-empirical tight binding

8.6.2.1. Two centre approximation

8.6.2.1.1. Koster and Slater integrals for s and p stated.

8.6.2.1.2. Example: linear chain, fcc s states and p states, graphene only pz, nanotubes.

8.7. Electron velocity and effective mass

8.8. Holes

9. Phonons

9.1. 1D chain

9.2. 1D chain two atoms per cell

9.3. 3D generalization

10. Semiconductors

10.1. Si, Ge, GaAs: band structures

10.2. Equilibrium carrier concentration

10.2.1. Effective mass and density of states in Si and Ge

10.2.2. Mass action law

10.3. Intrinsic semiconductor

10.3.1. Chemical potential behaviour

10.4. Extrinsic semiconductors

10.4.1. Hamiltonian; effective mass approximation

10.4.2. Population of impurity levels

10.5. Chemical potential behaviour as a function of temperature

10.6. Currents in semiconductors and p-n junctions

11. Optical properties

6.4 Maxwell equation in a dielectric

6.5 Interaction between radiation and dielectric

6.6 Absorption and dispersion

6.6.1 Lorentz model

6.6.2 Drude model

6.6.3 Dielectric function

6.6.4 Plasma Frequency

LEARNING OUTCOMES:

The course of study is aimed at providing an advanced preparation of Condensed Matter Physics, with knowledge of specialized topics of recent research in this field. It aims to complete training in the field of quantum physics applied to the study of microscopic and macroscopic properties of crystalline materials. The aim of the course is to provide the main knowledge on theoretical and experimental methods that allow the student to understand and interpret the physical properties of crystalline materials.

KNOWLEDGE AND UNDERSTANDING:

The course aims to provide the student with the tools necessary to understand the structural, vibrational, electronic and optical properties of materials in terms of a microscopic quantum-mechanical description.

The lessons focus on the mathematical derivation and physical interpretation of the main tools of theoretical and experimental investigation for the study of the structural, vibrational, electronic and spectroscopic properties of crystalline materials. Applications relating to materials of current interest in the field of Condensed Matter Physics are illustrated during lectures in order to broaden the student's knowledge of the state of the art in this field of research.

APPLYING KNOWLEDGE AND UNDERSTANDING:

Students must be able to identify the essential elements of a physical problem related to the study of crystalline materials and know how to model them, making the necessary approximations. In fact, the course aims to provide mathematical-physical tools that allow students to understand scientific articles dedicated to the study of materials and to interpret, through their knowledge, various experimental physical observables of interest in condensed matter physics. The student must also be able to identify and understand the theoretical and / or experimental method suitable for the characterization of the physical properties of crystalline materials and be able to interpret analysis and data discussions related to these methods. The student must also be able to tackle new scientific problems and to read texts and scientific articles in English on topics related to the study of structural, vibrational, electronic and optical properties of crystalline materials.

MAKING JUDGEMENTS:

Particular attention is paid to the ability to use the knowledge acquired during the lessons appropriately and in a conceptually coherent and rigorous context

COMMUNICATION SKILLS:

The final exam aims to practice and improve the student's communication skills.