Electrical conduction in solids

Overview

ABSTRACT

The electrical transport properties in solids arise quite logically from the properties of the electrons present in the material. In an approach primarily phenomenological, Drude Lorentz’s conventional model and Sommerfeld's quantum model are used. The latter takes the first hypothesis and includes the quantum properties of electrons; it introduces key concepts such as the charge density, the mean free path or the density of states. These models make it possible to connect the charge transport properties to other properties in solids and in particular those of heat transport. However, this approach is limited; the theory of electrons in a periodic array takes over, with the basic concepts of band structure, surface energy, effective mass, resulting in the semi-classical conclusion of transport charge.

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AUTHORS

Olivier BOURGEOIS: Doctorate in Condensed Matter Physics - Researcher at the French National Center for Scientific Research (CNRS)
Hervé Guillou: Doctorate in Condensed Matter Physics - Senior lecturer at Joseph Fourier University, Grenoble - Researcher at LIMMS/CNRS-IIS

INTRODUCTION

After an introduction to the properties of electrons in matter, we turn to the properties of electrical transport in solids. Our approach here is essentially phenomenological. The classical Drude-Lorentz model and Sommerfeld's quantum model of electrons as fermions are used to introduce essential concepts such as charge density, mean free path and density of state. In addition to Ohm's law, these models enable charge transport properties to be linked to other properties of solids, notably heat transport properties. The limitations of these phenomenological models are highlighted, and the theory of electrons in a periodic lattice is presented. This allows us to introduce the fundamental concepts of band structure, energy surface and effective mass, and to pose an equation describing charge transport in a semi-classical way. These concepts are used in the following [D 2 602] dossier, which deals with the most modern aspects of electron transport properties in a statistical way.

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