35426 - Chemical Physics of Solid Materials M

Learning outcomes

At the end of the course, the student knows basic concepts, mathematical  structure and computational methods of quantum mechanics and solid state physics. He acquires also knowledges of quantum theory of electronic transport, and information on recent results and open problems in the applications of theoretical methodologies to the study of new materials interesting for technological applications.  The student is able to use these knowledges to formulate and solve problems concerning structural, electronic and optical properties of atoms, molecules and crystals. He is also able to tackle simple problems of quantum transport in nanoelectronic devices.

Course contents

Prerequisites: basic knowledge of classical physics, differential and integral calculus, linear algebra and chemistry are requested.          

Program:

• BASIC QUANTUM MECHANICS:  Concepts and postulates - Measurements of observables - Mathematical formalism - Symmetry and angular momenta - Matrix quantum mechanics - Wave mechanics in position and momentum representations: time-independent Schroedinger equation - Time evolution of quantum states: time-dependent Schroedinger equation - Light-matter interaction.

• QUANTUM MECHANICS OF ATOMIC AND MOLECULAR SYSTEMS:  Methods for approximate solutions of time-independent Schroedinger equation: Hartree-Fock and  Density Functional Theory - Calculation of electronic energies and states of atoms and molecules - Calculation of roto-vibrational energies and states of molecules.
  

• ELEMENTS OF SOLID STATE PHYSICS:  Geometrical Description of Crystals: simple lattices and composite lattices; simple and composite crystal structures; Wigner-Seitz primitive cells. Reciprocal lattices:  definitions and basic properties; planes and directions in Bravais lattices.Brillouin zones. Translational symmetry and quantum-mechanical aspects: Bloch Wavefunctions; the parametric k.p Hamiltonian; cyclyc boundary conditions; density-of-states and critical points. Quantum theory of the free-electron gas: Fermi-Dirac distribution function and chemical potential; electronic specific heat in metal and thermodynamic functions. 

• ELECTRONIC TRANSPORT IN NANODEVICES:  Model of a nanoscale transistor - An atomistic view of the electrical resistence - Energy levels diagram - Flow of electrons and rate equations - Current in one-level channel - The quantum of conductance - Potential profiles and iterative procedures for calculating the I/V characteristic - Coulomb blockade - Calculation of the current in multi-level channel.
  

Readings/Bibliography

The use of notes taken during the lections will be crucial, together with lecture notes and other material provided by the teacher. For further investigations, the following books are recommended:

• J.J. Sakurai, Modern Quantum Mechanics, ed. Wiley.
• C.Cohen-Tannoudji, B.Diu, F.Laloe, Quantum Mechanics, ed. Wiley.
• G.Grosso and G.Pastori Parravicini, Solid State Physics, ed. Academic Press.
• S.Datta, Quantum Transport. Atom to Transistors, ed. Cambridge.
  

Teaching methods

The course is organized in frontal lectures, where basic concepts, fundamental principles and mathematical techniques of quantum mechanics, solid state physics, are presented and explained together with elements of quantum theory of the charge transport. After the theoretical explanation of each subject,  lections will be devoted to the solution of exercises and specific problems involving prototype atomic, molecular and solid state systems and models of nanoelectronic devices.  This procedure aims to aid the student in acquiring the ability to convert a physical problem into a theoretical-computational procedure able to give quantitative results.

Assessment methods

The final  test is an oral examination, that verifies the achievement of the following teaching targets:
-  knowledge of basic concepts, mathematical structure and main computational methods of quantum mechanics and solid state physics;
-  ability of using the theoretical tools to formulate and solve problems relative to the calculation of  structural, electronic and optical properties of atoms, molecules and crystals;
- modeling the electronic transport in a nanotransistor.
The oral exam  ends with the request of solving a problem on topics of the course. The solution of the problem does not require explicit numerical calculations.

Teaching tools

Lecture notes and other didactic material are made available in electronic format.
Attending to the Solid State Physical Chemistry course is suggested, where the Molecular Quantum Mechanics is studied in more detail both in its computational techniques and in the applications to specific molecular properties.

Office hours

See the website of Renato Colle