# ELECTRONIC MATERIALS

## Learning outcomes of the course unit

Knowledge

At the end of the course, the student should have acquired a good skill in the following actions:

a) good sensitivity in the application of the fundamental physical principles of the solids in a modeling-experimental approach, suitable to study the most important properties of a semiconductor

b) sufficient knowledge of the main features of some basic methods of investigation and the main technologies of processing

c) an introduction to basic device structures and physical and technological problems to be solved

d) an introduction to design and fabrication of low-dimensional systems having ad hoc properties for particular applications (nanostructures and related nanotechnology).

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 will have the ability to expose the concepts acquired in a clear and organic way.

Making judgments

The student will be able to learn independently 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, even in the first year of the Master Course.

## Course contents summary

The course aims to provide a good basic knowledge of physical principles, laws and models of the phenomena that characterize the materials for electronics, with particular regard to semiconductors. Phenomenological aspects of the physical properties of the semiconductor will be highlighted, by giving appropriate examples of basic structures to allow 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 design and model technologically innovative solutions.

## Course contents

Program

1. INTRODUCTION: The electronic materials.

2. BASIC PHYSICAL PROPERTIES:

• PERIODIC STRUCTURES. The crystalline structure, 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: spectrum of e.m. waves, interaction with matter, X-rays - electrons, neutrons. The physics of X-rays. Diffraction by periodic structures waves. The elastic scattering of X-rays.

• 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 the band 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. 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. Semi-insulating materials and compensation.

• 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 and degenerate carrier gas. Intrinsic semiconductor.

3. TRANSPORT PROPERTIES AND MAGNETOTRANSPORT. Bloch oscillations and collisions. Relaxation time approximation. Boltzmann equation formalism. Electrical conductivity and Ohm's law. 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 generation and recombination. Carrier lifetime. Diffusivity and diffusion length. Einstein relations. Continuity equation and ambi-polar diffusion equations. Examples.

6. INHOMOGENEOUS SEMICONDUCTORS AND DEVICES:

• JUNCTION METAL-SEMICONDUCTOR. Ohmic and rectifying contacts. Schottky diode. 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 and consequences of the lattice mismatch.

• JUNCTION DEVICES. Detectors, LEDs, solar cells.

7. NANOTECHNOLOGIES AND NANO STRUCTURES. Band engineering. Elements of massive and epitaxial growth technologies. Low dimensional systems. Introduction to the main properties and applications.

## 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 “Optica 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 which will be made available to students. Discussions during lessons on the topics proposed will be stimulated.

## Assessment methods and criteria

The exam consists of a talk in which it will be discussed in deep 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 done.

## 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.

Interested students can integrate the theory part with a brief experimental activity, with tutorials, on the electrical and optical characterization of semiconductor techniques.