Born june 24, 1909 william penney studied at the imperial college of science and completed his postdoctoral research at london university. Thanks to the simplicity of the model, it is possible to solve for the band structure exactly, and th. Kronig penney free download as powerpoint presentation. 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. Kronigpenney model overview and the ek diagram youtube. Introduction the canonical example of a solvable onedimensional periodic array is the kronig penney model,1 which yields analyticallyconstrained solutions. To simplify the analysis, we only consider a onedimensional system where atoms are aligned and equally spaced. The kronigpenney model wolfram demonstrations project. What is the origin of band structure and band diagram.
The 1d potential function can be simplified as a series of potential barriers with an identical barrier width and period. Kronig penney electron hole electronic band structure. Suplemento especial 4 potenciales cuanticos periodicos y. The kronigpenney model 1 is a simplified model for an electron in a onedimensional periodic potential. To develop the concept of allowed and forbidden energy levels using schrodingers wave equation we consider kronig. Solid state theory physics 545 kronnig penney modelpenney model. The kronig penney model is a simple, idealized quantummechanical system that consists of an infinite periodic array of square potential barriers. The kronigpenney model 1 is a simplified model for an electron in a one dimensional periodic potential. The possible states that the electron can occupy are. The periodic potential has the form ux 2 2m 0 x1 n1 x na 6 with aas lattice constant and. Still, the kronig penny model does a remarkable job of isolating the essential e. Derivation of the kronigpenney model the solution to schrodingers equation for the kronig penney potential previously shown in figure 2. The kronig penney model inspired by the work of felix bloch, ralph kronig and william penney came up with a simple way to model a crystal lattice.
Scribd is the worlds largest social reading and publishing site. The first assumption is to consider a row of evenly spaced atoms with average distance a. Overestimation of the linear contribution to the low temperature speci c heat of metalloids e. In quantum mechanics, the particle in a onedimensional lattice is a problem that occurs in the. 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. January 25, 2012 the kronig penney model describes electron motion in a period array of rectangular barriers fig. This diagram determines which states the electrons are allowed to occupy, and is the fundamental result we.
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. Blochs theorem, kronig penney model exercise 2 kronig penney model one of the simplest models of a periodic potential where the band structure can be computed analytically is the kronig penney model in one dimension. Kronig penney model the essential features of the behavior of electrons in a periodic potential may be explained by a relatively simple 1d model which was first discussed by kronig and penney. So, kronig and penney approximated these potentials inside the crystal. Here i go over the results of the kronig penney model. I explain in this video using the kronig penney model. The kronig penney model demonstrates that a simple onedimensional periodic potential yields energy bands as well as energy band gaps. Thus, the kronigpenney model is one of the simplest periodic potentials to exhibit a band. We assume that the potential energy of an electron has the form of a periodic array of square wells. Descargue como doc, pdf, txt o lea en linea desde scribd.986 1320 999 591 1402 1167 243 1307 1387 1447 150 175 1103 800 79 1180 957 106 478 264 1047 149 901 642 1233 1542 231 344 1307 1017 209 1025 1088 416 1301 1253 93 240 359