# SEMICONDUCTOR PHYSICS AND APPLICATIONS

## Learning outcomes of the course unit

Knowledge.

At the end of the course, it is expected that the student has acquired a good skill in the following actions: good sensitivity in the application of the fundamental physical principles of solid matter in a modeling-experimental approach, suitable to study the most important properties of a semiconductor; quite good knowledge of the basic investigation methods of the semiconductor physics and of the main technologies of device processing; c) an introduction to basic device structures and physical and technological problems to be solved.

Knowledge and ability to understand.

At the end of the course the student should have acquired a comprehensive knowledge of the subjects, showing ability to connect together the various aspects of the physics of semiconductor materials.

Communication skills.

The student should have the ability to expose the acquired concepts in a clear and organic way.

Making judgments.

The student should have focused the aspects peculiar of the semiconductor physcs and be able to learn independently and to discuss critically a theme chosen from those covered in the course.

## Prerequisites

Knowledge of Mathematics, Physics, Classical Statistical Mechanics, Physics of Matter and Quantum Mechanics that have been acquired during the three-year degree course, are enough to follow the course with profit in the first year of the Master Course.

## Course contents summary

The course aims to provide a good basic knowledge of physical principles and laws, interpretative models of phenomena and the main experimental investigation techniques that concerne inorganic semiconductors, in particular, semiconductors with tetrahedral coordination and wide band-gap semcionductors. The physical properties of semiconductors will be discussed in the light of the electronic states, by highlighting phenomenological aspects to favour the understanding of the operation of the main microelectronic devices. Particular emphasis will be given to the relationship between structure-property-applications for their influence on the ability to designand model technologically innovative solutions. The areas to which research on semiconductors is now oriented will be outlined.

## Course contents

Program

1. INTRODUCTION: The electronic materials. 2. BASIC PHYSICAL PROPERTIES: • PERIODIC STRUCTURES. The crystalline structures, the space lattice. Primitive cells and conventional cells, symmetry operations of the Bravais lattice. The base unit; simple and composite structures. Operations of symmetry of the crystal, some examples of structures. The reciprocal lattice: definition, vectors of the reciprocal lattice and lattice planes, some examples. Analysis of crystal structures with diffraction techniques. • ELECTRONIC STATES IN CRYSTALS. Valence and core electrons. Single electron approximation. Consequences of translational invariance. Model for free electrons in solids. Bloch theorem and Brillouin zones. Dispersion relations. Boundary conditions and density of states. The Fermi energy. Basic aspects of theband structure. Bragg diffraction and ranges of forbidden energies. Classification of solids. • BAND STRUCTURE OF SEMICONDUCTORS WITH TETRAHEDRAL COORDINATION. Outline on the determination of the band structure: principal models. Outline on band structures in 3D semiconductors in tetrahedral coordination. • ELECTRON DYNAMICS. The semiclassical scheme. The electron as almost classical particle. The effective mass tensor. The concept of gap. • HYDROGENIC IMPURITIES (doping). Qualitative description: donors and acceptors. Hydrogenic levels in the effective mass approximation. Experimental methods to study the electrically active impurities. Doped semiconductor. Semiinsulating materials and compensation. Deep levels and occupancy level. • STATISTICS OF CHARGE CARRIERS IN EQUILIBRIUM THERMODYNAMIC CONDITIONS. Charge state of hydrogen-like impurities, statistics of the carriers in termodinamiocal equilibrium. Density of carriers and Fermi energy. Classical anddegenerate carrier gas. Intrinsic semiconductor. 3. TRANSPORT PROPERTIES AND MAGNETOTRANSPORT. Bloch oscillationsand collisions. Relaxation time approximation. Boltzmann equation formalism. Electrical conductivity and Ohm's law. Localization and transport among localized states. Introduction to magnetotransport. Charge in a magnetic field. Cyclotron resonance. The validity of the semiclassical limits. The magneto-resistive and magneto-conductive tensor. Hall Effect. Experimental methods. Hall coefficient for non-monokinetic carriers. Introduction to physical magnetoresistance, mixed conduction effects, geometrical magnetoresistance. 4. OPTICAL PROPERTIES. Optical constants and macroscopic model. Transmission, absorption and reflection. Interference from thin layers. Fundamental processes of absorption and absorption coefficient for direct and indirect transitions. Notes on the optical spectroscopy. Experimental methods. 5. CARRIERS IN NON-EQUILIBRIUM CONDITIONS. Levels of injection of excess carriers. The processes of carrier generation and recombination. Carrier lifetime. Diffusivity and diffusion length. Einstein relations. Continuity equation and ambi-polar diffusion equations. 6. INHOMOGENEOUS SEMICONDUCTORS AND DEVICES:• JUNCTION METAL-SEMICONDUCTOR. Ohmic and rectifying contacts. Schottkydiode. MOS structures. • THE P/N JUNCTION. The ideal p/n junction. Equilibrium configuration. Steady currents. Junction capacitance. Notes on the deviation from ideality. Breakdown of the junction. Generation and recombination in the depletion region. Zener diode. Tunnel diode. • HETEROJUNCTIONS. p/n Heterojunction. Isotype heterostructures and intrinsic heterostructures. Epitaxial heterostructures and adaptation of the lattice: control andconsequences of the lattice mismatch. Band engineering. Elements of massive and epitaxial growth technologies. Low dimensional systems. Introduction to the main properties and applications. • JUNCTION DEVICES. Transistor BJT, MOSFET, detectors, LEDs, solar cells. • THE FRONTIERS OF PHYSICS OF SEMICONDUCTORS

## Recommended readings

Carlo Ghezzi: "Introduzione alla Fisica dei Semiconduttori". For the study of particular topics: 1) M. Wolf, N. Holonyak, G.E. Stillman “Physical properties of semiconductors” Prentice Hall International Editions; 2) J.I. Pankove “Optical processes in semiconductors” Dover Publ. Inc. 3) M.S. Tyagi “Semiconductor materials and devices” John Wiley & Sons; 4) S. Sze “Introduction to Semiconductor devices: Physcs and technology” John Wiley & Sons; 5) R.S. Muller, T.I. Kamins “Device electronics for integrated circuits“ John Wiley & Sons; 6) P. Bhattacharya “Semiconductor optoelectronic devices” Prentice Hall International Editions.

## Teaching methods

The course will be developed through lectures of the teacher, with the use of slides/videos that will be made available to students. The lessons will be delivered in the form of pre-recorded videos, or face-to-face lessons, or in streaming in relation to the evolution of the Sars-Cov2 pandemic, also taking into account the preferences expressed by students enrolled in the course. Discussions during lessons on the topics proposed will be stimulated.

## Assessment methods and criteria

The exam consists of a talk, in which the student will discuss in depth a topic chosen among those proposed in the course. This presentation will be integrated by a discussion on the most general aspects of the program developed. The final evaluation will depend for 50% on the global comprehension of the topics and the ability to make connections, 30% on the quality of the in-depth analysis chosen and 20% on the clarity of the exposition. In relation to the evolution of the pandemic from Sars-Cov2, the exams will be carried out either in person or remotely via the Microsoft Teams platform.

## Other informations

If it is required by students, a couple of additional seminars can be arranged, by experts in the field of electron microscopy experimental techniques and/or X-ray diffraction, or in the field of device process technologies. Interested students can integrate the theoretical lectures with a brief experimental activity and tutorials on electrical and optical techniques of semiconductor characterization.