# PHYSICS OF NANOSTRUCTURES

**Academic Year 2019/2020**- 2° Year - Curriculum CONDENSED MATTER PHYSICS

**Teaching Staff:**

**Maria Grazia GRIMALDI**and

**Francesco RUFFINO**

**Credit Value:**6

**Scientific field:**FIS/01 - Experimental physics

**Taught classes:**42 hours

**Term / Semester:**1°

## Learning Objectives

Gain in-depth knowledge of the properties, preparation and stability of nanostructured materials and of the transport mechanisms in nanostructures.

At the end of the course the student will be able to understand and frame in a general context the most recent developments concerning nanotechnologies, the optical properties of nanostructures, transport in nanostructured materials, and their application also in the interdisciplinary field. The student will have mastered the scientific method and will be able to apply it even to complex situations by mastering the estimation of orders of magnitude and the approximations necessary for the description of the phenomenon. The student will acquire autonomous in-depth knowledge and will be able to find the specialized literature for the selected studies. The student must demonstrate to have acquired the ability to present a topic of current research to an audience of specialists.

## Course Structure

Lectures and tutorials.

## Detailed Course Content

1) Introduction: mesoscopic Physics and Nanotechnology

Trends in nanoelectronics- characteristic length in mesoscopic systems- Quantum Coherence - quantum-wells, wires, dots-density of states and dimensionality-Heterostructures

2) Recall of some solid state physics concepts

Wave-particle duality and the principle of Heisenberg-Schrödinger equation and its application- Fermi-Dirac distribution -free electron model in a solid- density of states- Bloch theorem- electrons in a crystalline solid- dynamics of electrons in bands energy (equation of motion, effective mass, holes) - phonons

3) Recall of some concepts of physics of semiconductors

energy bands in semiconductor-intrinsic and extrinsic semiconductors-concentrations of electrons and holes in semiconductors - transport in semiconductors (transport in an electric field, mobility, diffusion; continuity equation, the carrier lifetime and diffusion length) – degenerate semiconductors

4) Physics of low-dimensional semiconductors

fundamental properties of two-dimensional semiconductor nanostructures – quantum well- quantum wires- quantum dots- band diagram

5) semiconductor nanostructures and heterostructures

MOSFET - heterojunctions- Quantum well multiple heterostructures (the concept of the heterostructure and the Kronig-Penney model)

6) Transport in nanostructures due to electric field

parallel transport (electronic scattering mechanisms, some experimental observations) - perpendicular transport (Resonant Tunneling, electric field effects in heterostructures) - quantum transport in nanostructures (quantized conductance; Landauer formula; Formula Landauer-Büttiker; Coulomb blockade)

7) transport in nanostructures in presence of external the magnetic field and quantum Hall effect

Effect of a magnetic field on a crystal - low-dimensional systems in a magnetic field - density of states of a two-dimensional system in a magnetic field -the effect Aharonov-Bohm - the effect Shubnikov de Haas -The quantum Hall effect (experimental facts and elementary theory, the border states, extended and localized states) - fractional quantum Hall effect

8) Electronic devices based on nanostructures

MODFET - heterojunction bipolar transistor – resonant tunneling transistor - Esaki diode – single electron transistor - graphene based transistor.

9) Nanotechnologies and stability

Review of thermodynamics

Binary phase diagrams

Surface energy

Forms of equilibrium of solids, gamma plot

Atomic clusters

First and second order phase transitions

Phase stability, overheating and supercooling

Physical methodologies for the realization of nanostructures

Far from equilibrium treatments for the realization of nanostructures

## Textbook Information

1) “Nanotechnology for Microelectronics and Optoelectronics”, J. M. Martinez-Duart, R. J. Martin-Palma, F. Agullo-Rueda, Elsevier 2006

2) “Quantum Transport-Atom to transistor”, S. Datta, Cambridge University Press 2005

3) “Transport in Nanostructures”, D. K. Ferry, S. M. Goodnick, J. Bird, Cambridge University Press 2009

4) “The Physics of low-dimensional semiconductors-an introduction”, J. H. Davies, Cambridge University Press 1998.