Lecture

Free Electron Dispersion and Kronig-Penney Model

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In course

MSE-484: Properties of semiconductors and related nanostructures

This course explains the origin of optical and electrical properties of semiconductors. The course elaborates how they change when the semiconductors are reduced to sizes of few nanometers. The course provides also the basis to use software to calculate th ...

Description

This lecture covers the free electron dispersion relation, Bloch theorem, and the Kronig-Penney model, explaining the periodicity in crystal structures and the band gap in materials.

Instructors (2)

Anna Fontcuberta i Morral

2014 Associate Professor at the Institut des Matériaux, EPFL 2008 Assistant Professor Tenure Track at the Institut des Matériaux, EPFL 2009 Habilitation in Physics, Technische Universität München 2005-2010 Marie Curie Excellence Grant Team Leader at Walter Schottky Institut, Technische Universität München, on leave from Centre National de la Recherche Scientifique (CNRS, France) 2004-2005 Visiting Scientist at the California Institute of Technology, on leave from CNRS; Senior Scientist and co-founder of Aonex Technologies (a startup company for large area layer transfer of InP and Ge on foreign substrates for the main application of multi-junction solar cells) 2003 Permanent Research Fellow at CNRS, Ecole Polytechnique, France 2001-2002 Postdoctoral Scholar at the California Institute of Technology Study of wafer bonding and hydrogen-induced exfoliation processes for integration of mismatched materials in views of photovoltaic applications Sponsor: Professor Harry A. Atwater 1998-2001 PhD in Materials Science, Ecole Polytechnique Study of polymorphous silicon: growth mechanisms, optical and structural properties. Application to Solar Cells and Thin Film Transistors Advisor: Pere Roca i Cabarrocas 1997-1998 Diplôme dEtudes Approfondis (D.E.A.) in Materials Science at Université Paris XI, France . 1993-1997 BA in Physics at Universitat de Barcelona

Valerio Piazza

Teaching & PhD PhD Students Claire Valentine Blaga, Matilde Cantele, Julia Sarah Marhic Past EPFL PhD Students as codirector Michele Zendrini Courses Functional properties of materials MSE-210 The main objective of this course is to present the concepts allowing the understanding of the fundamental principles that enable to predict the properties of the materials. The goal is that with these concepts, one will be able to realize material design and/or to understand novel materials.

Official source

Related concepts (22)

Bloch's theorem

In condensed matter physics, Bloch's theorem states that solutions to the Schrödinger equation in a periodic potential can be expressed as plane waves modulated by periodic functions. The theorem is named after the physicist Felix Bloch, who discovered the theorem in 1929. Mathematically, they are written where is position, is the wave function, is a periodic function with the same periodicity as the crystal, the wave vector is the crystal momentum vector, is Euler's number, and is the imaginary unit.

Nearly free electron model

In solid-state physics, the nearly free electron model (or NFE model and quasi-free electron model) is a quantum mechanical model of physical properties of electrons that can move almost freely through the crystal lattice of a solid. The model is closely related to the more conceptual empty lattice approximation. The model enables understanding and calculation of the electronic band structures, especially of metals. This model is an immediate improvement of the free electron model, in which the metal was considered as a non-interacting electron gas and the ions were neglected completely.

Particle in a one-dimensional lattice

In quantum mechanics, the particle in a one-dimensional lattice is a problem that occurs in the model of a periodic crystal lattice. The potential is caused by ions in the periodic structure of the crystal creating an electromagnetic field so electrons are subject to a regular potential inside the lattice. It is a generalization of the free electron model, which assumes zero potential inside the lattice. When talking about solid materials, the discussion is mainly around crystals – periodic lattices.

Crystal structure

In crystallography, crystal structure is a description of the ordered arrangement of atoms, ions, or molecules in a crystalline material. Ordered structures occur from the intrinsic nature of the constituent particles to form symmetric patterns that repeat along the principal directions of three-dimensional space in matter. The smallest group of particles in the material that constitutes this repeating pattern is the unit cell of the structure.

Effective mass (solid-state physics)

In solid state physics, a particle's effective mass (often denoted ) is the mass that it seems to have when responding to forces, or the mass that it seems to have when interacting with other identical particles in a thermal distribution. One of the results from the band theory of solids is that the movement of particles in a periodic potential, over long distances larger than the lattice spacing, can be very different from their motion in a vacuum.

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