One early and surprisingly successful model of metals is the free electron model which assumes that the valence electrons are free to. This is in direct contrast to the behaviour of an electron in free space where it may have. Classical free electron theory permits all electrons to gain energy. He derives the valence and conduction band structures for electrons in metals e.
Drudes classical theory of electrical conduction drude assumed that a metal is composed of ions, which are stationary, and valence electrons, which are free to move. In band theory, the mos form an electron highway through a solid. If the wavelength of the electron is related to the lattice parameter a, then the electron cannot. Metals conduct electricity with the help of valence electrons present in them. According to the classical free electron theory the value of specific heat of metals is. The amount of electrostatic potential between two points in space. The classical free electron theory ofmetals drude lorentz theory of metals lecture2postulates. To be highly conducting like a metal, two things must be true. Band theory of solids a useful way to visualize the difference between conductors, insulators and semiconductors is to plot the available energies for electrons in the materials. Most of such limitations of free electron theory were overcome by considering a more realistic model of solid. Aluminum al has the electron configuration 1s22s22p63s23p1. The band theory of solids understanding the properties of matter.
In the free electron theory, all materi als with mobile valence electrons are metals. View notes engineering physics solid state physics. Instead of having discrete energies as in the case of free atoms, the available energy states form bands. In 1928, felix bloch had the idea to take the quantum theory and apply it to solids. 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.
Free classical electrons l consider a gas of free classical electrons moving under the influence of electric and area a magnetic fields. The conduction band is an empty band or partially filled band, but when the external field is applied to the electrons in the valence band, the electrons jump from the valence band to the conduction band and becomes free electron. The momentum and energy of an electron are connected. Each atom, when isolated, has a discrete set of electron. In 1928, sommerfeld developed a new theory applying quantum mechanical concepts and fermidirac statistics to the free electrons in the metal. Quantum free electron theory was proposed by arnold sommerfeld.
Free electron theory consider free electrons in a metal an electron gas. It did not, for example, take into account the interaction of free electrons with the metal ions. B m s institute of technology classical free electron theory. Band theory quantum mechanics of conduction in one formulation of quantum mechanics, we describe how the electrons are distributed inmomentum space.
The amount of energy needed to excite an electron from the filled band to the empty band is smalllarge circle one. Band theory models the behavior of electrons in solids by postulating the. We know that in an atom, the protons and the neutrons constitute the central part called the nucleus. This theory is called quantum free electron theory. Band theory was developed with some help from the knowledge gained during the quantum revolution in science. A solid contains an enormous number of atoms packed closely tog ether. In the nearly free electron approximation, interactions between electrons are completely. The statement of this relationship constitutes the description of an energy band. Ohmsohms lawlaw andand electronelectron driftdrift electric fieldelectric field e drift velocity v d current densitycurrent densityjij ia volume element. The valence electrons of the constituent atoms become conduction electrons and move about freely through the volume of the metal. Quantum free electron theory of metals science key.
Expected to form a 1s band, a 2s band, a 2p band, a 3s band, and. The valence electrons of atoms are free to move about the whole volume of the metals like the molecules of a perfect gas in a container. Band theory of solids article about band theory of. The behaviour of an electron in a solid and hence its energy is related to the behaviour of all other particles around it. In a crystal, however, the electrons are not free because of the effect of the crystal binding and the forces exerted on them by the atoms. The nearlyfree electron model university of oxford.
The simplest metals are the alkali metals lithium, sodium, potassium, na, cesium, and rubidium. The energy band formed by the energy levels of the free electrons is called conduction band. Treating the nearly free electron model using degenerate perturbation theory has been shown on the blackboard during lectures 3. In an atom electrons revolue around the nucleus and a metal is composed of such atoms. Solid state physics freeelectron theory of metals band theory of solids electrical. By means of the nearly free electron model explained in this lecture. Even in the context of a freeelectron gas, there are strong coulomb interactions between electrons which are frequently neglected in the freeelectron theory of metals. In a substance, as many atoms are close to each other, the energy levels of the atom form a continuous band, where in the electrons move. The valence electrons of atoms are free to move about the whole volume of the metal, like the molecules of a perfect gas in a container. Band theory, in solidstate physics, theoretical model describing the states of electrons, in solid materials, that can have values of energy only within certain specific ranges. The phenomena such a photoelectric effect, compton effect and the black body radiation couldnt be explained by classical free electron theory. Electron band separation in semiconducting substances, a multitudes of semiconducting close atoms still results in a significant band gap, b multitudes of close metal atoms for reference.
The atomic orbitals of the metals having the same energy combine to form molecular orbitals which are close in energy to each other so as to form a band. See band theory of solids, bloch theorem, fermidirac statistics, statistical mechanics. Free electron model a free electron model is the simplest way to represent the electronic structure of metals. In solidstate 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. As examples of applications the fieldemission microscope and quartzhalogen lamps are discussed. We first find the band structure using the nearly free electron model. At low temperatures, little thermal energy is available to push valence electrons across this gap, and the semiconducting material acts more as an insulator. The main assumptions of classical free electron theory are. These free electrons move freely throughout the lattice and hence are termed as electron gas. By the mid1930s the freeelectron model was largely superseded by. To this end, we consider the effect of the potential on the free electron wavefunctions given by and on the interval. But quantum free electron theory permits only a fraction of electrons to gain energy. The density of states and the fermidirac distribution function are discussed, leading to the specific heat of the electrons, the work function, thermionic emission, and the schottky effects. Free electron theory of metals request pdf researchgate.
A group of energy levels close to each other is called as energy band. A partially filled or low lying empty band of energy levels. The calculation of band structures and fermi surfaces 1. The model of the free electron theory is presented. The classical theory had several conspicuous successes, notably the derivation of the form of ohms law and the relation between the. In the lectures we have derived two simple rules, which are away from brillouinzone boundaries the electronic bands i. As per his investigation, the behavior of free electron in different possible energy states is explained, how the large number of electrons are disturbed in the energy states. Band theory, where the molecular orbitals of a solid become a series of continuous energy levels, can be used to explain the behavior of conductors, semiconductors and insulators. Given its simplicity, it is surprisingly successful in.
Srit unit iii free electron theory applied physics. Crucial to the conduction process is whether or not there are electrons in the conduction band. It was proposed that in a solid, electrons move under. Ron ballinger gives todays lecture, explaining how the behavior of electrons in aggregate solids determines their electrical and thermal conductivities, optical absorption, and other physical properties.
Assumptions or salient features in classical free electron theory the classical free electron theory is based on the following postulates. Cbse ncert notes class 12 physics semiconductor electronics. Quinn and others published free electron theory of metals find, read and cite all the research you need on researchgate. 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. Band theory of electrical conductivity boundless chemistry. Ueep2024 solid state physics topic 3 free electron in metals 2. Cu, be using lcaomo, and then extends this approach. Chapter 6 free electron fermi gas national tsing hua.
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