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Surface physics 1

A.Y. 2020/2021

Learning objectives

The learning objectives are:. to develop knowledge on the theory and phenomenology of surfaces in general, covering both classical and quantum descriptions, and developing specific knowledge and individual in-depth skills.

The teaching is also aimed at providing the student with the tools necessary to understand the

scientific literature at the state-of-the-art.

The teaching is also aimed at providing the student with the tools necessary to understand the

scientific literature at the state-of-the-art.

Expected learning outcomes

At the end of the course the student must know:

1. The relevance and the role played by Surface Physics in the main developments of Condensed Matter Physics over the past 50 years;

2. The physical reasons that make it necessary, for the realization of many experiments in Surface Physics, to work in the so-called Ultra High Vacuum (UHV) conditions.

3. How to correctly set the problem of the stability of a solid surface from the thermodynamical point of view, and will be able to relate it to the concept of surface tension.

4. What are the main experimental techniques giving access to the direct lattice and / or to the reciprocal surface lattice.

5. The concepts associated with the applications of the two-dimensional Fourier transform in relation to the possible 2D periodic structures (the five Bravais lattices, their elementary cells, the two-dimensional Brillouin zone).

6. The physical mechanisms underlying the phenomena of Surface relaxation and Surface reconstruction. He will know the currently used notations for the identification of surface reconstructions, also in presence of adsorbates.

7. The principles of surface diffraction, and will be able to relate them to the analogous principles valid for diffraction by a three-dimensional lattice (Ewald sphere).

8. The main surface preparation techniques, with their relative fields of application, advantages and disadvantages: e.g . cleavage, ion sputtering, molecular beam epitaxy (MBE, CBE, MOCVD).

9. The phenomenology of the growth of thin films, and will know the main experimental techniques that allow their characterization.

10. The principles of operation of the low-energy electron diffraction technique (LEED); will be able to recognize some examples of LEED spectra; will know the advantages and limitations of LEED compared to other techniques.

11. The principles and potentialities of the Auger spectroscopy. He will be able to recognize some examples of Auger spectra.

12. Some principles of ion scattering-based techniques, such as Secondary Ion Mass Spectroscopy (SIMS) and Rutherford Backscattering (RBS).

13. The main stages of the discovery of scanning tunneling microscopy (STM). He will know the working principles, and the theoretical and phenomenological description (Tersoff and Hamann model). He will know the most classic application examples, such as the one on the (111) surface of Silicon with its famous (7x7) reconstruction.

He will also be aware of the technique known as atomic force microscopy (AFM) and its most common applications.

14. The reasons why the creation of a surface can induce the existence (otherwise unacceptable) solutions of the Schroedinger equation (surface states), and will know some examples of such solutions (e.g., Schockley, Tamm). He will be able to deduce the consequences and make the connection with the phenomena of Band narrowing and Surface Core-Level Shift.

15. The conditions under which the so-called Image States can be produced.

16. The phenomenon of surface optical reflectivity in the Fresnel scheme, and will know the origin of the deviations of the real reflectivity from the Fresnel-expected one.

17. The principles of optical spectroscopy based on reflection anisotropy (RAS) and differential reflectivity (SDR).

18. The concept of surface phonon, and surface vibrational resonances. He will know how to classify the surface phonons in terms of their polarization (SP, SH). He will be able to describe the vibrational behavior of a surface in the limit of the elastic continuum (Rayleigh wave and its applications).

1. The relevance and the role played by Surface Physics in the main developments of Condensed Matter Physics over the past 50 years;

2. The physical reasons that make it necessary, for the realization of many experiments in Surface Physics, to work in the so-called Ultra High Vacuum (UHV) conditions.

3. How to correctly set the problem of the stability of a solid surface from the thermodynamical point of view, and will be able to relate it to the concept of surface tension.

4. What are the main experimental techniques giving access to the direct lattice and / or to the reciprocal surface lattice.

5. The concepts associated with the applications of the two-dimensional Fourier transform in relation to the possible 2D periodic structures (the five Bravais lattices, their elementary cells, the two-dimensional Brillouin zone).

6. The physical mechanisms underlying the phenomena of Surface relaxation and Surface reconstruction. He will know the currently used notations for the identification of surface reconstructions, also in presence of adsorbates.

7. The principles of surface diffraction, and will be able to relate them to the analogous principles valid for diffraction by a three-dimensional lattice (Ewald sphere).

8. The main surface preparation techniques, with their relative fields of application, advantages and disadvantages: e.g . cleavage, ion sputtering, molecular beam epitaxy (MBE, CBE, MOCVD).

9. The phenomenology of the growth of thin films, and will know the main experimental techniques that allow their characterization.

10. The principles of operation of the low-energy electron diffraction technique (LEED); will be able to recognize some examples of LEED spectra; will know the advantages and limitations of LEED compared to other techniques.

11. The principles and potentialities of the Auger spectroscopy. He will be able to recognize some examples of Auger spectra.

12. Some principles of ion scattering-based techniques, such as Secondary Ion Mass Spectroscopy (SIMS) and Rutherford Backscattering (RBS).

13. The main stages of the discovery of scanning tunneling microscopy (STM). He will know the working principles, and the theoretical and phenomenological description (Tersoff and Hamann model). He will know the most classic application examples, such as the one on the (111) surface of Silicon with its famous (7x7) reconstruction.

He will also be aware of the technique known as atomic force microscopy (AFM) and its most common applications.

14. The reasons why the creation of a surface can induce the existence (otherwise unacceptable) solutions of the Schroedinger equation (surface states), and will know some examples of such solutions (e.g., Schockley, Tamm). He will be able to deduce the consequences and make the connection with the phenomena of Band narrowing and Surface Core-Level Shift.

15. The conditions under which the so-called Image States can be produced.

16. The phenomenon of surface optical reflectivity in the Fresnel scheme, and will know the origin of the deviations of the real reflectivity from the Fresnel-expected one.

17. The principles of optical spectroscopy based on reflection anisotropy (RAS) and differential reflectivity (SDR).

18. The concept of surface phonon, and surface vibrational resonances. He will know how to classify the surface phonons in terms of their polarization (SP, SH). He will be able to describe the vibrational behavior of a surface in the limit of the elastic continuum (Rayleigh wave and its applications).

**Lesson period:** First semester
(In case of multiple editions, please check the period, as it may vary)

**Assessment methods:** Esame

**Assessment result:** voto verbalizzato in trentesimi

Course syllabus and organization

### Single session

Responsible

Lesson period

First semester

**Course syllabus**

This course introduces ideas and concepts which are at the basis of physical phenomena occurring at surfaces and interfaces.

While focusing on the main conceptual points, this course also provides a wide overview on phenomenology and on the main experimental techniques.

This course is meant to bring students starting from elementary concepts of quantum mechanics and solid-state physics to the knowledge of the main tools allowing them to understand the most recent literature in surface physics.

The detailed programme of the course is the following:

1) Development of Surface Physics in the second half of the 20th century. Impinging rate. Langmuir isotherm.

2) Surface thermodinamics: equimolar Gibbs surface. Surface free energy. Surface tension. Perfectly elastic and plastic deformations. Faceting.

3) Crystal structure: The five Bravais lattices in 2D, 2D unit cells. Miller indices and ideal surfaces. 2D reciprocal lattice. Relaxation and reconstruction. Adsorbates. Examples. Vicinal surfaces.

4) Overview of experimental techniques giving access to structural and /or compositional properties. Techniques to access directly the 2D reciprocal lattice. LEED. Examples of LEED spectra. Advantages and limitations of the LEED techniques. High-Energy Electron Diffraction (RHEED). Introduction to Auger spectroscopy (AES) and related theoretical tools and theoretical interpretation.

7) Theory of Scanning Tunneling Microscopy (STM) within the Tersoff-Hamann approximation. Examples; basics of Atomic Force Microscopy (AFM); examples.

8) Metal surfaces in the Jellium model. Work function, macroscopic field, contact potential. Surface states: Tamm and Shockley models. Surface projection of three-dimensional bulk bands. Resonances. Band narrowing. Surface Core Level Shifts.

9) Fresnel reflectivity and deviations. RAS and SDR spectra. Example: Si(100). Excitonic effects: optical gap and quasiparticle gap, examples.

10) Surface phonons. Resonances. Examples: graphite, LiF (001). Surface mode polarization. Elastic continuum limit. Rayleigh wave and applications.

11) Density Functional Theory. Local Density Approximation. Similarities and differences compared to Hartree-Fock. Slabs and supercells for the calculation of electronic and phonon surface bands.

While focusing on the main conceptual points, this course also provides a wide overview on phenomenology and on the main experimental techniques.

This course is meant to bring students starting from elementary concepts of quantum mechanics and solid-state physics to the knowledge of the main tools allowing them to understand the most recent literature in surface physics.

The detailed programme of the course is the following:

1) Development of Surface Physics in the second half of the 20th century. Impinging rate. Langmuir isotherm.

2) Surface thermodinamics: equimolar Gibbs surface. Surface free energy. Surface tension. Perfectly elastic and plastic deformations. Faceting.

3) Crystal structure: The five Bravais lattices in 2D, 2D unit cells. Miller indices and ideal surfaces. 2D reciprocal lattice. Relaxation and reconstruction. Adsorbates. Examples. Vicinal surfaces.

4) Overview of experimental techniques giving access to structural and /or compositional properties. Techniques to access directly the 2D reciprocal lattice. LEED. Examples of LEED spectra. Advantages and limitations of the LEED techniques. High-Energy Electron Diffraction (RHEED). Introduction to Auger spectroscopy (AES) and related theoretical tools and theoretical interpretation.

7) Theory of Scanning Tunneling Microscopy (STM) within the Tersoff-Hamann approximation. Examples; basics of Atomic Force Microscopy (AFM); examples.

8) Metal surfaces in the Jellium model. Work function, macroscopic field, contact potential. Surface states: Tamm and Shockley models. Surface projection of three-dimensional bulk bands. Resonances. Band narrowing. Surface Core Level Shifts.

9) Fresnel reflectivity and deviations. RAS and SDR spectra. Example: Si(100). Excitonic effects: optical gap and quasiparticle gap, examples.

10) Surface phonons. Resonances. Examples: graphite, LiF (001). Surface mode polarization. Elastic continuum limit. Rayleigh wave and applications.

11) Density Functional Theory. Local Density Approximation. Similarities and differences compared to Hartree-Fock. Slabs and supercells for the calculation of electronic and phonon surface bands.

**Prerequisites for admission**

1. Elementary diffraction theory;

2. Basic knowledge of thermodynamics. Thermodynamic potential concept;

3. Boltzmann and Fermi-Dirac statistics;

4. Fourier Transform;

5. Plane and spherical waves;

6. Elementary quantum mechanics: wavefunction, Schroedinger equation, potential barrier, hydrogen atom, many-electrons atoms;

7. Elements of band theory in solids (at least the one-dimensional case);

8. Elements of phonon theory in solids (at least the one-dimensional case);

9. Classical and quantum harmonic oscillator;

10. Maxwell's equations in vacuum and in materials;

11. Perturbation theory for the calculation of corrections to the eigenvalues and eigenvectors to first order.

2. Basic knowledge of thermodynamics. Thermodynamic potential concept;

3. Boltzmann and Fermi-Dirac statistics;

4. Fourier Transform;

5. Plane and spherical waves;

6. Elementary quantum mechanics: wavefunction, Schroedinger equation, potential barrier, hydrogen atom, many-electrons atoms;

7. Elements of band theory in solids (at least the one-dimensional case);

8. Elements of phonon theory in solids (at least the one-dimensional case);

9. Classical and quantum harmonic oscillator;

10. Maxwell's equations in vacuum and in materials;

11. Perturbation theory for the calculation of corrections to the eigenvalues and eigenvectors to first order.

**Teaching methods**

Teaching is provided in a traditional way, with lectures and frontal exercises. Each lesson typically lasts 2 hours, with an interval of 10-15 minutes after the first part. Intensive use of the blackboard is made, with projection of some slides to support if deemed useful. The teacher provides paper (photocopies) and online material for various insights and examples, and for the details of some particularly long calculations. Attendance is strongly recommended.

The course includes one or more visits to laboratories and / or numerical exercises on the computer.

COURSE WEB PAGE: http://sites.google.com/site/fisicadellesuperfici/ .

The course includes one or more visits to laboratories and / or numerical exercises on the computer.

COURSE WEB PAGE: http://sites.google.com/site/fisicadellesuperfici/ .

**Teaching Resources**

Bibliography:

1. Hans Luth, "Solid Surfaces, Interfaces and Thin Films", 4th edition, Springer, Berlin, 2001. (The 3rd edition was

published with the title: "Surfaces and Interfaces of Solid Materials")

2. Friedhelm Bechstedt, "principles of surface physics" (Advanced texts in physics), Springer, Berlin, 2002

3. M.C.Desjonqueres, D. Spanjaard, "concepts in surface physics" , Springer, Berlin, 1993

4. A.Zangwill, "physics at surfaces", Cambridge univ. press Cambridge, 1988.

Web page of the course:

http://sites.google.com/site/fisicadellesuperfici/

1. Hans Luth, "Solid Surfaces, Interfaces and Thin Films", 4th edition, Springer, Berlin, 2001. (The 3rd edition was

published with the title: "Surfaces and Interfaces of Solid Materials")

2. Friedhelm Bechstedt, "principles of surface physics" (Advanced texts in physics), Springer, Berlin, 2002

3. M.C.Desjonqueres, D. Spanjaard, "concepts in surface physics" , Springer, Berlin, 1993

4. A.Zangwill, "physics at surfaces", Cambridge univ. press Cambridge, 1988.

Web page of the course:

http://sites.google.com/site/fisicadellesuperfici/

**Assessment methods and Criteria**

The exam consists in an oral discussion focused on the topics covered in the course, and lasts between 45 and 60 minutes. The student can choose to focus the exam more on experimental-applicative topics, or more on theoretical aspects, according to his specific interests. The course may include one or more visits to laboratories and / or one or more numerical (computer) exercises, contributing to the student's evaluation.

Professor(s)

Reception:

Wednesday afternoon, better by e-mail appointment

Via Celoria 16, LITA Building, ground floor (Latitude 45.47606 N Longitude 9.23026 E)