# PHYSICS OF NANOSTRUCTURES

**Academic Year 2021/2022**- 2° Year - Curriculum CONDENSED MATTER PHYSICS

**Teaching Staff:**

**Francesco RUFFINO**

**Credit Value:**6

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

**Taught classes:**42 hours

**Term / Semester:**1°

## Learning Objectives

The basic training aim is to acquire extended and in-depth knowledge concerning properties, preparation and stability of nanostructured materials, thermodynamics of nanostructures and transport mechanisms in nanostructures.

By the end of the course the student will be able to understand, within a general scientific and technological framework, the most recent developments concerning nanotechnologies, thermodynamic properties of nanostructures, transport processes in nanostructured materials, and applications of nanostructures interdisciplinary fields. The student will be able to apply the scientific method to complex physical situations and will be able to estimate orders of magnitude and the approximations necessary for the description of advanced phenomena related to the physics of nanostructures. The student will acquire independent deepening skills and will be able to find specialized literature for the specific insights. The student will acquire the ability to present a current research topic to an audience of specialists.

Furthermore, with reference to the so-called Dublin Descriptors, this course helps to acquire the following transversal skills:

**Knowledge and understanding abilities**

- Critical understanding of the most advanced developments of Modern Physics, both theoretical and experimental, and their interrelations, also across different subjects
- Remarkable acquaintance with the scientific method, understanding of nature, and of the research in Physics

**Applying knowledge and understanding ability**

- Ability to identify the essential elements in a phenomenon, in terms of orders of magnitude and approximation level, and being able to perform the required approximations
- Ability to use analogy as a tool to apply known solutions to new problems (problem solving)
- Ability to plan and apply experimental and theoretical procedures to solve problems in academic or applied research, or to improve existing results

**Ability of making judgements**

- Ability to convey own interpretations of physical phenomena, when discussing within a research team

**Communication skills**

- Ability to discuss about advanced physical concepts, both in Italian and in English
- Ability to present one's own research activity or a review topic both to an expert and to an non-expert audience

**Learning skills**

- Ability to access to specialized literature both in the specific field of one's expertise, and in closely related fields
- Ability to exploit databases and bibliographical and scientific resources to extract information and suggestions to better frame and develop one's study and research activity

## Course Structure

**Teaching**

Lectures (remote teaching may be adopted, if restriction apply following University’s guidances).

During each lesson, students will always be given time for questions and comments. The lecturer-student interaction will be one of the fundamental element during lectures.

**Prerequisites**

Extensive and in-depth knowledge of: Thermodynamics, Electromagnetism, Quantum Mechanics, Structure of matter, Physics of the solid state, Physics of semiconductors are fundamental.

**Attendance to lectures**

Mandatory

Should the circumstances require full or partial online teaching, appropriate modifications to what is hereby stated may be introduced in order to achieve the main objectives of the course.

**Exams**

Exams may take place online, depending on circumstances.

## Detailed Course Content

PART A

1) Introduction: Mescoscopic physics and nanotechnology

Trends in nanoelectronics-Characteristic lengths in mesoscopic systems-Quantum coherence- Quantum wells, wires, dots-Density of states and dimensionality-Semiconductor heterostructures.

2) Overview of some concepts of solid state physics

Wave-particle dualism and Heisenberg principle-Schrödinger equation and elementary applications-Fermi-Dirac distribution-Free electron model for a solid-Density function of states-Bloch theorem-Electrons in a crystalline solid-Dynamics of electrons in bands energetic (motion equation, effective mass, gaps) -Lattice vibrations and phonons

3) Overview of some concepts of semiconductor physics.

Energy bands in semiconductors - Intrinsic and extrinsic semiconductors - Concentrations of electrons and semiconductor gaps - Elementary transport properties in semiconductors (Transport in an electric field, mobility; Conduction by diffusion; Continuity equation, life span of carriers and length of diffusion) -Degenerate semiconductors.

4) Physics of low-dimensional semiconductors

Fundamental properties of two-dimensional semiconductor nanostructures-Quantum well-Quantum wires-Quantum dots- Band diagram for quantum wells.

5) Semiconductor nanostructures and heterostructures

MOSFET-Heterojunctions-Quantum well multiple-Heterostructures structures (the concept of heterostructure and the Kronig-Penney model).

6) Transport by electric field in nanostructures

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; Landauer-Büttiker formula; Coulomb blockade).

7) Transport by magnetic field in nanostructures and quantum Hall effect

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

8) Electronic devices based on nanostructures

MODFET-Bipolar heterojunction transistor-Resonant tunneling transistor- Esaki diode-Single electron transistor-Transistor based on graphene.

PART B

1) Thermodynamics of Nanostructures

Size and confinement effects-Surface atoms and surface/volume ratio-Surface energy and surface stress-Effect on lattice parameter-Surface energy and Wulff theorem: Wulff construction and equilibrium shape of nanocrystals-Inverse Wulff construction-Equilibrium Shape of supported nanoscystals (the Wulff-Kaichew theorem)-Solid-liquid transition in nanostructures (size-dependent cohesive energy and melting temperature, theoretical models and comparisons to experimental data).

2) Nanostructures on substrates an in matrices

Control of size and number of nanoparticles on substrates and in matrices- Nucleation and growth thermodynamics and kinetics (basic concepts and experimental data)-Ripening and Coalescence (basic rate equations and experimental data)-Typical activation energies and diffusion coefficients.

3) Thin films dewetting on substrates

Thermodynamic stability and instability of thin films on substrates-Wetting, dewetting, contact angle, Young equation-Dewetting process of a thin film on a substrate towards formation of nanoparticles-Liquid-state and solid-state dewetting-Rayleigh instability-Nanoparticles size- and spacing-dependence on film thickness and further process parameters- Processes inducing thin film dewetting (furnace annealing, laser irradiations, electronic irradiations, ionic irradiations)-Dewetting on pre-patterned substrates.

4) Vapor-Liquid-Solid (VLS) Growth of Nanowires

The VLS mechanism-Role of the surface energies-Role of the size-dependent effects-Role of the phase diagrams and eutectic point-Growth equations-Lenght-radius dependence-Temperature conditions in the VLS mechanism-Experimental data and focus on semiconductor nanowires (Si, Ge)-Solid-Liquid-Solid (SLS) synthesis of one-dimensional nanostructures.

5) Nanoporous Systems

Nanoporous Systems: introduction and general concepts-Importance of nanoporous metals-Nanoporous gold: properties and applications-Fabrication of nanoporous gold by the dealloying processes of bimetallic alloys: basic principles, thermodynamics and kinetics parameters; Composition control, porosity control-Porous gold nannostructures.

6) Special nanostructural changes

Shape control of metal nanostructures embedded in insulating matrices by high energy ion irradiations: elongation and inverse ripening-Thermodynamic instability of nanorods and spontaneous reshaping-Shadowed depositions of films on substrates to produce complex-morphology nanostructures-Nanoparticles embedding in polymeric films.

## Textbook Information

PART A

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

PART B

5) "Nanomaterials and Nanochemistry", C. Bréchignac, P. Houdy, M. Lahmani, Springer 2006

6) "Nanoscience-Nanotechnologies and Nanophysics", C. Dupas, P. Houdy, M. Lahmani, Springer 2004

7) "Introduction to surface and thin film processes", J. A. Venables, Cambridge University Press 2003

8) "Nucleation theory and growth of nanostructures", V. G. Dubrovskii, Springer 2014

9) "Nanoporous gold-from an ancient technology to a high-tech material", A. Wittstock, J. Biener, J. Erlebacher, M. Baumer, RSC Publishing 2012

10) "Polymer films with embedded metal nanoparticles", A. Heilmann, Springer 2003