The energy values of the free electrons are discontinuous because of which the energy levels are discrete. The simplest model of a metal is the free electron model. Classical free electron theory, derivation of ohms law, mean free path, relaxation time and drift velocity, failures of classical free electron theory, quantum free electron theory, fermidirac distribution, fermi energy, failures of quantum free electron theory. Nptel video lectures, iit video lectures online, nptel youtube lectures, free video lectures, nptel online courses, youtube iit videos nptel courses. Treating the nearly free electron model using degenerate perturbation theory has been shown on the blackboard during lectures 3. Periodic crystal potential and blochs theorem for the wavefunction lecture 56 applying perturbation theory to free electron wavefunctions and nearly free electron model lecture 57 applying perturbation theory to free electron wavefunctions and creation of energy gap at zone boundaries. Imagine that vr is a perturbation on free electrons what e ect does vr have on the \free electron. Free electron approximation, tight binding approximation. In solidstate physics, the nearly free electron model or nfe model is a quantum mechanical model of physical properties of electrons that can move almost.
Free electron model periodic boundary conditions add a second piece of crystal the same size. Freeelectron theory of metals article about freeelectron. Unit 2 introduction to drudes free electron theory of metals. It is possible that many electron may possess same energy. It is seen that the richness of quantum physics will greatly a ect the future generation technologies in many aspects. The treatment of a metal as containing a gas of electrons completely free to move within it.
The nearlyfree electron model university of oxford. Unit 9 blochs theorem for wavefunction of a particle in a. This is true for any k,but a periodic perturbation has nonzero matrix elements only between particular states. Crown ethers are named using both the total number of atoms in the ring and the number of oxygen atoms. Distributed generation technologies, distributed storage technologies, distribution system protection, circuit breaker coordination, symmetrical component analysis and sequence excitation, modeling of distribution system components, protection components, impact of distributed generation of distribution. There are four major assumptions within the drude model. Introduction to drudes free electron theory of metals, electrical conductivity ohms law and hall effect. Mod01 lec9 the free electron theory of metals youtube. Alan doolittle lecture 24 mosfet basics understanding with no math reading.
Parts of the model can be filled in or extended by other kinds of calculations and models like the nearlyfree electron model. Translational symmetry is not essential for producing a band gap amorphous solids also have band gaps. The free electron model the quantum state of an electron is described by the timeindependent schrodinger equation. Handout 2 sommerfeld model for metals free fermion gas. The theory was originally proposed in 1900 to describe and correlate the electrical and thermal properties of metals. Parts of the model can be filled in or extended by other kinds of calculations and models like the nearly free electron model. If 0, we assume the electron to be traveling in a weak potential, and can thus expand the wave function into two parts. In the free state electron to be found also in the conductors, when it can freely be. Maxwell boltzmann statistics, limitations of the drude model, elementary quantum mechanics. The tightbinding model has a long history and has been applied in many ways and with many different purposes and different outcomes.
Electronic transport drude model the simplest treatment of the electrical conductivity was given by drude. The starting point of the hartreefock method is to write a variational wavefunction, which is built from these singleparticle orbitals. This model considers electrons as plane waves as in the free electron model that are weakly perturbed by the periodic potential associated with the atoms in a. According to this model, the valence electrons of the constituent atoms of the crystal become conduction electrons and travel freely throughout the crystal. To apply the drude model, the density of the gas formed by the free electrons must be known. 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. Each electron feels the presence of the other electrons indirectly through an e. Free electron model put free electrons into a very wide potential well the same size as the crystal i. Free electron theory, band structure of solids, metals, insulators and semiconductors, intrinsic and doped semiconductors, effective mass, electrons and holes, hall effect and cyclotron resonance, galvanomagnetic phenomena, carrier lifetime, semiconductor devices. Sommerfelds free electron theory of metals physics assignment. Free electron model of metals 37 where nf is the radius of our fermi sphere in nspace separating. The free electrons, which constitute the electron gas can have continuous energy values.
Energy spectrum of a nearlyfree electron model in 1d the eigenstates of free problem in 1d. Lecture 24 mosfet basics understanding with no math. The free electron approximation remains a good approximation well away from the edges of the brillouin zone only wavevectors close to a multiple of. According to the classical free electron theory the value of specific heat of metals is. In the lectures we have derived two simple rules, which are away from brillouinzone boundaries the electronic bands i. Free electron model definition of free electron model by. The phenomena such a photoelectric effect, compton effect and the black body radiation couldnt be explained by classical free electron theory. Solid state physics nearly free electron model nanopdf.
Calculation of the density of states in 1, 2 and 3. Calculation of the density of states in 1, 2 and 3 dimensions we will here postulate that the density of electrons in kspace is constant and equals the physical length of the sample divided by 2. Particle in a spherically symmetric potential problem. Find materials for this course in the pages linked along the left. Unit 2 introduction to drudes free electron theory of metals, electrical conductivity. One corresponding to a plane wave, or a free electron, and another corresponding to a periodic correction factor. L z the electrons inside the box are confined in a threedimensional infinite. Understanding the focusing of charged particle beams in a.
Tr 3 pm4 pm please help your instructor by doing your work neatly. Mod01 lec11 large systems and statistical mechanics. We can use the extended zone scheme left or displace all the segments of the dispersion curve back into the. This parameter is called the conduction electron density n the number of free electrons per volume.
If the wavelength of the electron is related to the lattice parameter a, then the electron cannot \travel through the crystal. Electronics nptel online videos, courses iit video lectures. 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. Metals conduction electrons form highly degenerate fermi gas. Density of allowed states in reciprocal k space is. Lecturenotesforsolidstatephysics 3rdyearcourse6 hilaryterm2012. Particle in a box with applications to the free electron model. The nearly free electron model is a modification of the freeelectron gas model which includes a weak periodic perturbation meant to model the interaction between the conduction electrons and the ions in a crystalline solid. Free electron model a free electron model is the simplest way to represent the electronic structure of metals. Ohmsohms lawlaw andand electronelectron driftdrift electric fieldelectric field e drift velocity v d current densitycurrent densityjij ia volume element. The conduction electron density is computed by assuming that each atom contributes z v conducting electrons.
Solutions due wednesday, 11 at the time of the class instructor. History and significant concepts, the drude sommerfeld model, fermi dirac statistics, density of. Atomic physics lecture notes pdf 141p this lecture note covers the following topics. Every algebraic nal result must be supplemented by a check of units. We first consider the simple onedimensional case in which electrons move freely along a line, such as through a very thin metal rod.
The liquiddrop model of electron and atom electron can be found in the bound state in the constitution of atom, and also in the free state in the form of electron beams or near the incandescent cathode in the electronic devices. Thus 18crown6 is an 18membered ring with six oxygen atoms part a in figure 18. Free electron model synonyms, free electron model pronunciation, free electron model translation, english dictionary definition of free electron model. Potential well of infinite and finite depths, the linear harmonic oscillator. Solid state physics nearly free electron model contd. A numerical method to obtain solutions of the schrodinger equation will also be discussed and a software to understand basic concepts in quantum mechanics will also be demonstrated. Energy bands nearlyfree electron model electron diffraction and energy gap bloch theorem the central equation emptylattice approximation tightbinding model see chap 9 nfe model is good for na, k, al etc, in which the lattice potential is only a small perturbation to the electron sea.
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