# PHYSICS OF NANOSTRUCTURES

**Academic Year 2022/2023**- Teacher:

**FRANCESCO RUFFINO**

## Expected Learning Outcomes

**FRANCESCO RUFFINO**

**Email: francesco.ruffino@ct.infn.it**

**Building/Address: Dipartimento di Fisica ed Astronomia- Via S. Sofia 64- Building 6- Office 244 (second floor) Phone: 0953785461**

**Office hours for students: Monday 15:00-17:00, Wednesday 15:00-17:00. The teacher is, also, available for recePtion meeting electronically, by appointment. Any unavailability notices will be sent through Microsoft Teams and/or Studium.**

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 nonexpert 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

6 ECTS of lectures corresponding to 42 hours (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.

## Required Prerequisites

Fundamental is extensive and in-depth knowledge of: Thermodynamics, Electromagnetism, Quantum Mechanics, Structure of matter, Physics of the solid state, Physics of semiconductors.

## Attendance of Lessons

Normally mandatory (as stated in the Didactic Regulation of the course)

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.

## Detailed Course Content

PART A: NANOTECHONOLOGY, NANOSTRUCTURES AND ELECTRONIC TRANSPORT IN NANOSTRUCTURES

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: THERMODYNAMICS OF NANOSTRUCTURES AND RELATED STRUCTURAL CHARACTERISTICS

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

## Course Planning

Subjects | Text References | |

1 | Introduction: Mescoscopic physics and nanotechnologyTrends in nanoelectronics-Characteristic lengths in mesoscopic systems-Quantum coherence- Quantumwells, wires, dots-Density of states and dimensionality-Semiconductor heterostructures (2 hour) | 1,3 |

2 | Overview of some concepts of solid state physicsWave-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, effectivemass, gaps) -Lattice vibrations and phonons (1 hour) | 1,4 |

3 | Overview of some concepts of semiconductor physics. Energy bands in semiconductors - Intrinsic and extrinsic semiconductors - Concentrations of electronsand 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 (1 hour) | 1,4 |

4 | Physics of low-dimensional semiconductors. Fundamental properties of two-dimensional semiconductor nanostructures-Quantum well-Quantum wires-Quantum dots- Band diagram for quantum wells (3 hours) | 1,2,3,4 |

5 | Semiconductor nanostructures and heterostructures. MOSFET-Heterojunctions-Quantum well multiple-Heterostructures structures (the concept ofheterostructure and the Kronig-Penney model) (2 hour) | 1,2,3,4 |

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) (5 hours) | 1,2,3,4 |

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 (5 hours) | 1,2,3,4 |

8 | Electronic devices based on nanostructures. MODFET-Bipolar heterojunction transistor-Resonant tunneling transistor- Esaki diode-Single electron transistor-Transistor based on graphene (2 hour) | 1,2,3,4 |

9 | 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) (4 hours) | 5,6,7,8 |

10 | Solid-liquid transition in nanostructures (size-dependent cohesive energy and melting temperature, theoretical models and comparisons to experimental data) (2 hours) | 5,6,7,8 |

11 | 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 (2 hours) | 5,6,7,8,10 |

12 | 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 (3 hours) | 6, didactic material by the teacher |

13 | Processes inducing thin film dewetting (furnace annealing, laser irradiations, electronic irradiations, ionic irradiations)-Dewetting on pre-patterned substrates (2 hours) | 6, didactic material by the teacher |

14 | 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 (2 hours) | 5,6,8 |

15 | 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 (2 hours) | 9 |

16 | 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 (4 hours) | Didactic material by the teacher, 10 |

## Learning Assessment Procedures

The exam consists of a presentation/essay developed by the student on a topic relating to the course program and agreed with the teachers. Taking a cue from the presentation/essay developed by the student, questions will follow on the remaining part of the program. The evaluation will take into account the level of depth of the topic, the knowledge of the basic topics, the property of language, the clarity of presentation, the ability to identify applications, including interdisciplinary ones.

The typical duration of the oral exam ranges from 30 to 45 minutes.

Verification of learning can also be carried out electronically, should the conditions require it.

EXAMINATION APPEALS

For the oral exam, there are 2 exam sessions in the first exam session period, 2 exam sessions in the second exam session period and 2 exam sessions in the third exam session period.

There are also 2 sessions reserved for students who are out of course and laggards (paragraphs 5 and 5 bis of the university teaching regulations) during the suspension of teaching activities, generally in the period April/May or November/December.

There are no further exams in addition to those officially indicated by the didactic secretariat. Consult the Exam Calendar at the website: https://www.dfa.unict.it/corsi/LM-17/esami.

## Examples of frequently asked questions and / or exercises

The topics listed below are not an exhaustive list but are just a few examples:

1) Density of electronic states in zero-, one-dimensional, two-dimensional nanostructures

2) Characteristics of charge transport in zero-, one-dimensional, two-dimensional nanostructures

3) Tunneling transport

4) Heterostructures and superlattices

5) Landauer formula

6) Quantization of conductance

7) Quantization of the magnetic flux

8) Single electron effects: Coulomb blockade, Coulomb staircase, Coulomb oscillations

9) Single electron effects: charge energy and constant interaction model

10) Integer quantum Hall effect

11) Resonant tunnel diode

12) Negative differential resistance

13) Single electron transistor

14) Aharonov-Bohm effect

15) Landau levels

16) Equilibrium shape of nanocrystals and Wulff construction

17) Evolution of the melting temperature of nanostructures with size

18) Rayleigh instability

19) Differences between solid and liquid thin film dewetting

20) VLS mechanism for the growth of one-dimensional nanostructures

21) Surface energy of nanostructures

22) Dealloying process for the formation of nanoporous metals