Download powerpoint diagram templates for making business, economic and development models. Qualitative and quantitative discussion kronigpenney model energywave number diagram 2. Kronig penney free download as powerpoint presentation. Kronig penney model the essential behaviour of electron may be studied by periodic rectangular well in one dimensional which was first discussed by kronig penney in 1931. Qualitative and quantitative discussion kronig penney model energywave number diagram 2. By beginning with a weak barrier potential where the energy is clearly seen to be a parabola mapped i.
The kronigpenney model is a simple, idealized quantummechanical system that consists of an infinite periodic array of square potential barriers. Kronigpenney model for surface states 209 the remainder of part il is devoted to discussing the relativistic kronigpenney model and its variants as applied to the surface problem. Introduction to the quantum theory of solids extension to three dimensions 110 1 dimensional model kronig penney model 1 potential pattern 100 direction 110 direction different direction different potential patterns ek diagram is given by a function of the direction in the crystal. Chapter3 introduction to the quantum theory of solids 1. Blochs theorem and kronigpenney model electronic band. The purpose of the solution is to illustrate much of bandstructure physics and also to develop a bag of. This applet is useful in visualizing key features of band structure. Kronigpenney model and free electron or empty lattice band. Suzuki department of physics state university of new york at binghamton.
Mar 07, 2011 the kronigpenney model is a simple, idealized quantummechanical system that consists of an infinite periodic array of square potential barriers. Kronig penney model masatsugu sei suzuki and itsuko s. Explicit wannier functions for the kronigpenney model are determined. For the solution of kronig penney model mentioned above, if the value of p is large i. Kronigpenney model overview and the ek diagram youtube. Ppt the bandstructure problem a onedimensional model. This means that the allowed bands are narrower and forbidden bands arc wider. Mar 28, 2018 here i go over the results of the kronig penney model. The motion of electrons in a periodic electric field the onedimensional kronigpenney model. Chapter3 introduction to the quantum theory of solids slideshare. Plotting this it is observed there exist restricted shaded forbidden zones for solutions.
Derivation of the kronigpenney model the solution to schrodingers equation for the kronig penney potential previously shown in figure 2. For this model the probability density of electron states has been calculated. The solution to schrodingers equation for the kronigpenney potential previously shown in. The first assumption is to consider a row of evenly spaced atoms with average distance a. It is a generalization of the free electron model, which assumes zero potential inside.
Lecture the kronigpenney modela unified model solving for tunneling through the potentials between the atoms introducing periodicity into the wave solutions. Chapter3 introduction to the quantum theory of solids. Kronig penney model nptel image mag kronig penney model nptel. Still, the kronigpenny model does a remarkable job of isolating the essential e. Thanks to the simplicity of the model, it is possible to solve for the band structure exactly, and th. Lecture 10 kronig penny model 101200 1 lecture 10 kronig penney model 1. Electrical conduction in solids drift current, electron effective mass, concept of hole energy band model. A free powerpoint ppt presentation displayed as a flash slide show on id. In quantum mechanics, the particle in a onedimensional lattice is a problem that occurs in the model of a periodic crystal lattice. These templates provide specific types of standard models with sample slides that can be edited to create professional looking models and diagrams in powerpoint.
The kronigpenney model 1 is a simplified model for an electron in a one dimensional periodic potential. General numerical method for the kronig penney model of. Consider the potential energy vx of an electron shown in the illustration with an infinite sequence of potential wells of depth v 0 and width a, arranged with a spacing b. The kronigpenney model solid state physics electronic band band theory of solids. For the energy bands of the kronig penney model, where is the density of states largest. The energies of electrons can be known by solving schrodingers wave equation in such a lattice. Energy bands powerpoint presentation, free download id. A lecture note on blochs theorem and kronig penney model.
He is noted for the discovery of particle spin and for his theory of xray absorption spectroscopy. Dec 01, 2017 the kronig penney model is a solvable problem in quantum mechanics that can either be viewed as an approximation of an electron in a 1d crystal potential or a generalization of a potentialbarrier problem to a 1d chain of potential barriers. Kronigpenney model from eric weissteins world of physics. This diagram determines which states the electrons are allowed to occupy, and is the fundamental result we. Bloch functions nearly free electron model kronigpenney model wave equation of electron in a periodic potential number of orbitals in a band. Recitation kronig penney the kronig penney model helps understand the nature of bands and band gaps starting form and very easy and simplified atomistic model. The specific relation between real and imaginary part of the frequency response described by kramerskronig guarantees that equation 1. Kronig penney model and ek diagrams electrical engineering. According to quantum free electron theory of metals, a conduction electron in a metal experiences constant or zero potential and free to move inside the crystal but will not come out of the metal because an infinite potential exists at the surface. Im writing a computer program in c, to explicitly compute the band structures for a 1d crystal modelled as an infinite array of rectangular potential barriers of width 2a and distance between nearest walls of two successive barriers 2b, i. We assume e penney model free download as powerpoint presentation. The kronig penney model is a simple, idealized quantummechanical system that consists of an infinite periodic array of square potential barriers. Dashed line is dimensioless energy for a free electron.
August 29, 2011 dirackronig penney model describes dynamics of electrons in a periodic potential. To obtain the relativistic kronigpenney relation and the energy expression for surface states we will use the direct matching procedure i. Charles myles powerpoint ppt presentation free to download other cost tools for cost control and performance evaluations j. In the discussion we emphasize phase choices connected with maximally localized wannier functions, here denoted wannierkohn. 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. Jul 01, 2000 kronig penney applet the kronig penney applet provides solution for the electron wave functions and energies in the classic band structure model of an infinite sequence of periodic rectacular potential barriers in one dimension. The periodic potential is shown in the figure below. January 25, 2012 the kronigpenney model describes electron motion in a period array of rectangular barriers fig. The kronigpenney model 1 is a simplified model for an electron in a onedimensional periodic potential.
Aug 23, 2017 for the love of physics walter lewin may 16, 2011 duration. Explicit wannier functions for the kronig penney model are determined. Another simplifications in the quasi free mode is neglect of electron electron interaction. Is this the right place to ask for assistance with plotting ek diagrams for valence and conduction bands and the kronig penney model. Chapter 11 semiconductor theory and devices ppt download 16 kronigpenney model. Blochs theorem for particles in a periodic potential. The development requires no quantum mechanics beyond that taught in most physical chemistry courses and can be taught in a single onehour lecture. Another simplifications in the quasi free mode is neglect of electron. Derivation of the kronigpenney model the solution to schrodingers equation for the kronigpenney potential previously shown in figure 2. Find powerpoint presentations and slides using the power of, find free presentations research about band theory of solids ppt. Problem plotting kronig penney model dispersion curves. A single lecture illustrating the band structure of solids donald a. Kronig penney electron hole electronic band structure. Lecture 10 kronig penney model carleton university.
Recitation kroning penney massachusetts institute of. Here i go over the results of the kronigpenney model. A simple derivation of the kramerskronig relations from the. Based on this plot, answer the following questions. May 20, 2018 14 kronig penney model since the electrons are not free their energies are less than the height v0 of each of the potentials, but the electron is essentially free in the gap 0 kronig penney model. Ralph kronig 10 march 1904 16 november 1995 was a german physicist. The specific relation between real and imaginary part of the frequency response described by kramers kronig guarantees that equation 1.
It is assumed that when an electron is near the positive ion site, potential energy is taken as zero. Penny model and effective mass 2 these powerpoint color diagrams can only be used by instructors if the 3rd edition. Quantitative methods for bandstructure calculations. Hi there, i want to plot a graph of the right hand side of the equation vs the energy, e, in ev for a periodic array of square wells each of depth 300ev, width 0. The kronigpenney model is a solvable problem in quantum mechanics that can either be viewed as an approximation of an electron in a 1d crystal potential or a generalization of a potentialbarrier problem to a 1d chain of potential barriers. The essential behaviour of electron may be studied by periodic rectangular well in one dimensional which was first discussed by kronig penney in 1931. It is often used as a pedagogical model to illustrate how periodic potentials can lead to the formation of electronic energy bands and band gaps.
Kronigpenney model for surface states sciencedirect. A simple model of a crystalline solid that leads to an electronic band structure is presented. The possible states that the electron can occupy are. A simple derivation of the kramerskronig relations from. Blochs theorem and kronigpenney model free download as powerpoint presentation. The possible states that the electron can occupy are determined by the schrodinger equation, in the case of the kroningpenney model, the potential vx is a periodic square wave. The kronigpenney model wolfram demonstrations project. Kronigpenney model original lecture notes prepared by. Scribd is the worlds largest social reading and publishing site.
Quantitative methods for bandstructure calculations 15. Kronig penney applet the kronig penney applet provides solution for the electron wave functions and energies in the classic band structure model of an infinite sequence of periodic rectacular potential barriers in one dimension this applet is useful in visualizing key features of band structure. An idealized, onedimensional model of a crystal which exhibits many of the basic features of the electronic structure of real crystals. So, kronig and penney approximated these potentials inside the crystal to the shape of rectangular steps as shown in fig. Maslov department of physics, university of florida dated. Explain the meaning and origin of forbidden band gaps begin to understand the brillouin zone. The kronig penney model, in its simplest form, is a one dimensional infinite chain of square well potentials, periodically spaced, that represents the total interaction between the ions and the conduction electrons 2,5. Download ppt kronigpenney model and free electron or empty lattice band structure outline. These model templates are highly customizable and you can edit content right down to objects and curves depicted in the sample slides.