Solid state physics free electron model lecture 14 a. But quantum free electron theory permits only a fraction of electrons to gain energy. In solidstate physics, the free electron model is a simple model for the behaviour of. Charles kittel taught solid state physics at berkeley from 1951 to 1978 earlier he.
Superconductivity the most random atomic arrangement, that of a gas, was well understood in the. What links here related changes upload file special pages permanent link page. The course aims to introduce electronic properties of solids starting from a very simple example. The fifth chapter discusses band theory of solids with reference to energy spectrum, effective mass and semiconductors. According to quantum free electron theory, the free electrons always collides with the positive ions or electrons present in the metal. The electronic structure of solids we need a picture of the electronic structure of solid that we can use to explain experimental observations and make predictions why is diamond an insulator. Topics covered range from the breakdown of classical theory to atomic spectra and the old quantum theory, as well as the uncertainty principle of heisenberg and.
Electrons can be visualised as rattling around insde the metal, randomly changing direction when they collide with positive ions, much like a ball in a pinball machine. A modern presentation of theoretical solid state physics that. If a battery is connected in series with an ammeter and a piece of some material copper, silicon, glass, or such, a deflection in the ammeter will indicate a flow of charged particles a current i through the circuit see fig. Now we come to a very important concept of solid state physics which allows. This treats the electrons quantum mechanically but ignores the presence of ions, it is applied to the calculation of the specific heat and the thermopower. Paul drude constructed in 1900 a theory to explain the electrical and ther. Band theory and electronic properties of solids, by john singleton, oup more advanced material on electrons in solids. Each atom, when isolated, has a discrete set of electron. Mar 29, 2015 free electron theory of solids march 29, 2015 december 30, 2010 by mini physics electrons can be visualised as rattling around insde the metal, randomly changing direction when they collide with positive ions, much like a ball in a pinball machine.
Lecture notes theory of solids i physics mit opencourseware. In these solids, the transport of hot electrons has. Free electron model a free electron model is the simplest way to represent the electronic structure of metals. Pdf the phenomenon of electronic conduction in solids is studied in this chapter. Rather than sharing and exchanging electrons, a metal is essentially held together by a system of free electrons that wander throughout the solid. A solid contains an enormous number of atoms packed closely tog ether. Band theory of solids the energy band structure of a solid determines whether it is a conductor, an insulator or a semiconductor. Drude theory of conduction basics of free electron theory. This page contains materials for the session on the band theory of solids. Calculate the absorption edge, carrier density, and electrical conductivity of a material. Nearly free electron approximation and tight binding. Magnetism of electrons in solids comments and corrections please. Not all solids conduct electricity insulators, semiconductors, so the free electron model is not a valid description for all solids.
Researchers soon recognized that a broader system was needed to explain the behaviour of complex metals and semiconductors. Prominent examples are the alkali metals and aluminum. Srit unit iii free electron theory engineering physics. Solid state physics free electron theory of metals band theory of solids electrical. Solid state electronic devices, 7th global edition by streetman and banerjee book free to read online. B m s institute of technology classical free electron theory. Band theory models the behavior of electrons in solids by postulating the. Free electron theory of metals request pdf researchgate. L35 superconductivity properties and applications t36 tutorial. Some of the graphs in this chapter are revealing of the physical processes in the working of band structure. Topics covered range from the breakdown of classical theory to atomic spectra and the old quantum theory, as well as the uncertainty principle of heisenberg and the foundations of quantum mechanics. This in turn will affect the way the electron gas can absorb energy from an external source.
Much of electronics, including vacuum tubes, cathoderay tubes in their various manifestations, and electron microscopes, depend on the emission of electrons from metals and the manipulation of these electrons to perform various tasks. Treating the nearly free electron model using degenerate perturbation theory has been shown on the blackboard during lectures 3. Heres more on the history and theory of electron emission from solids. Quantum theory of solids kittel pdf quantum theory of solids charles kittel on. It features a 1hour lecture video, and also presents the prerequisites, learning objectives, reading assignment, lecture slides, homework with solutions, and resources for further study. Physicists more often develop the band model via the free electron theory, which is included here for completeness. In the lectures we have derived two simple rules, which are away from brillouinzone boundaries the electronic bands i. Especially classical free electron theory and quantum free electron theory of metals. A read is counted each time someone views a publication summary such as the title, abstract, and list of authors, clicks on a figure, or views or downloads the fulltext. The phenomena such a photoelectric effect, compton effect and the black body radiation couldnt be explained by classical free electron theory. In order to determine the actual number of electrons in a given energy rangede, it is necessary to know the.
Quantum theory of solids is a modern presentation of theoretical solid state physics it builds directly on the same author. Electrical conduction in metals, insulators, and semiconductors. Freeelectron theory of metals article about freeelectron. Metals, such as copper and aluminum, are held together by bonds that are very different from those of molecules. Chapter 3 magnetism of the electron trinity college, dublin. These free electrons move freely throughout the lattice and hence are termed as electron gas. Electron inelastic mean free path data for elastic and inelastic scattering of electron in solids are needed for determining the surface sensitivity of electron spectroscopies such as auger. Building on this, it develops the theory of electrons in an n atom solid the band concept and its application to electrical and thermal properties in solids. Band theory of electrical conductivity boundless chemistry. View notes engineering physics solid state physics. According to this theory, the free electrons obey quantum laws. By the mid1930s the freeelectron model was largely superseded by the band theory of solids. According to the classical free electron theory the value of specific heat of metals is given by 4. Topics covered include crystal structure and band theory, density functional theory, a survey of properties of metals and semiconductors, quantum hall effect, phonons, electron phonon interaction and superconductivity.
The nearlyfree electron model university of oxford. Local is to be distinguished from absolute vacuum level work function is a characteristic of surfaces. It did not, for example, take into account the interaction of free electrons with the metal ions. Quantum free electron theory was proposed by arnold sommerfeld. These assumptions should be contrasted with those of the kinetic theory of conventional gases. Drude in 1900 and developed by lorentz in 1909 to explain electrical conduction in selection from engineering physics book. The simplest model of a metal is the free electron model.
According to classical free electron theory of metals electrical conductivity is given by, from the above equation, relation between temperature and electrical conductivity is given by hence, classical free electron fails to explain the temperature dependence of electrical conductivity. Classical free electron theory permits all electrons to gain energy. If is related to the fermi level which is a property of solids, but contains an additional term that is a property of. Atomic selectrons are delocalised due to overlap of outer orbits. If is related to the fermi level which is a property of solids, but contains an. The electron distribution in insulators and semiconductors. In order to determine the actual number of electrons in a given energy rangede, it is necessary to know the number of statesdns which have energy in that range. Database of electron inelastic mean free path for elemental. L34 electrical conduction in metals, insulators and semiconductors. The treatment of a metal as containing a gas of electrons completely free to move within it. In the free electron model, we assume that the valence electrons can be treated as free, or at least moving in a region constant potential, and noninteracting. The main assumptions of classical free electron theory are.
Also used in the condensed matter option 4th year course. If the voltage of the battery is varied, i will vary. This is the first term of a theoretical treatment of the physics of solids. Although the free electron model is a great oversimplification of the reality, surprisingly in many cases it works pretty well, so that it is able to describe many important properties of metals. There are large numbers of allowed energy levels for electrons in solid materials. Quantum free electron theory of metals pdf the turn of the twentieth century, of a free electron theory of metals and the writing by arnold sommerfeld and. Find the relation between the amplitudes of electric files and deformation for the. Free electron theory of solids mini physics learn physics. According to this theory, the metals containing free electrons obey the laws of classical mechanics.
Download solid state electronic devices, 7th global edition by streetman and banerjee in pdf. The development of the quantummechanical electron theory of metals. Inelastic mean free patha electron energy ev 21 inorganic compounds minima at 70 ev to 80 ev imfp range. An introduction to the electron theory of solids introduces the reader to the electron theory of solids. In solid state physics, the electronic band structure or simply band structure of a solid describes the range of energy levels that electrons may have within it, as well as the ranges of energy that they may not have called band gaps or forbidden bands band theory derives these bands and band gaps by examining the allowed quantum mechanical wave functions for an electron in a large. Simultaneously there will be a voltage drop v across the sample as measured by a voltmeter.
It was developed in 1927, principally by arnold sommerfeld, who combined the classical drude model with quantum mechanical fermidirac statistics and hence it is also known as the drudesommerfeld model. There are electrons that are not bound to atoms but are able to move through the whole crystal. By the mid1930s the free electron model was largely superseded by the band theory of solids. Some appreciation of the term of relaxation time dt. This chapter also discusses electronic conductivity in solids and in. In this script we follow closely the excellent textbook solid state physics by. From atomic theory, we are used to the idea that different. The focus then changes to the quantum theory of crystalline solids. Free electron theory of metals metals are good conductors both electrical and thermal electronic heat capacity has an additional temperature dependent contribution from the electrons.
An introduction to the electron theory of solids 1st edition. Free electron theory many solids conduct electricity. Quantum free electron theory of metals science key. In solidstate physics, the free electron model is a simple model for the behaviour of charge carriers in a metallic solid. Free electron model in solid state physics, the free electron model is a simple model for the behaviour of valence electrons in a crystal structure of a metall slideshare uses cookies to improve functionality and performance, and to provide you with relevant advertising. Describe the free electron gas model and its shortcomings in explaining the physical properties of metals. Fundamental relations for optical phenomena, drude theory free carrier contribution to the optical properties, interband transitions, the joint density of states and critical points, absorption of light in solids, optical properties of solids over a wide frequency range, impurities and excitons. It is the energy difference between the local vacuum level and the fermi level. Even more complicated energy band structures exist. Why does the conductivity of silicon increase when you heat it.
Electrons in a periodic potential nearly free electron. Ohmsohms lawlaw andand electronelectron driftdrift electric fieldelectric field e drift velocity v d current densitycurrent densityjij ia volume element. The theory was originally proposed in 1900 to describe and correlate the electrical and thermal properties of metals. Nergy of an electron at a point x distance from the origin is equal to the potential.
The scattering of conduction electrons are due to 1. A model of a metal in which the free electrons, that is, those giving rise to the conductivity, are regarded as moving in a potential due to the metal ions in the lattice and to all the remaining free electrons which is approximated as constant everywhere inside the metal. A discussion is given of electronic correlations in molecules and solids. Then sommerfelds elementary quantum mechanical theory of metals. Strong dependence of electron scattering on the details of the band structure was also observed in semiconductors and insulators.
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