Modelo de kronig penney pdf

Suplemento especial 4 potenciales cuanticos periodicos y. Derivation of the kronigpenney model the solution to schrodingers equation for the kronig penney potential previously shown in figure 2. Born june 24, 1909 william penney studied at the imperial college of science and completed his postdoctoral research at london university. 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. Descargue como doc, pdf, txt o lea en linea desde scribd. 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. This diagram determines which states the electrons are allowed to occupy, and is the fundamental result we.

To simplify the analysis, we only consider a onedimensional system where atoms are aligned and equally spaced. Still, the kronig penny model does a remarkable job of isolating the essential e. Kronig penney electron hole electronic band structure. Scribd is the worlds largest social reading and publishing site. We assume that the potential energy of an electron has the form of a periodic array of square wells. Kronig penney free download as powerpoint presentation. Overestimation of the linear contribution to the low temperature speci c heat of metalloids e. 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. 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.

The kronigpenney model 1 is a simplified model for an electron in a one dimensional periodic potential. Thanks to the simplicity of the model, it is possible to solve for the band structure exactly, and th. So, kronig and penney approximated these potentials inside the crystal. 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. A single lecture illustrating the band structure of solids donald a. January 25, 2012 the kronig penney model describes electron motion in a period array of rectangular barriers fig. Thus, the kronigpenney model is one of the simplest periodic potentials to exhibit a band. The first assumption is to consider a row of evenly spaced atoms with average distance a. Kronigpenney model overview and the ek diagram youtube. The kronigpenney model 1 is a simplified model for an electron in a onedimensional periodic potential. The 1d potential function can be simplified as a series of potential barriers with an identical barrier width and period. The kronig penney model demonstrates that a simple onedimensional periodic potential yields energy bands as well as energy band gaps.

Introduction the canonical example of a solvable onedimensional periodic array is the kronig penney model,1 which yields analyticallyconstrained solutions. In quantum mechanics, the particle in a onedimensional lattice is a problem that occurs in the. 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. Here i go over the results of the kronig penney model. To develop the concept of allowed and forbidden energy levels using schrodingers wave equation we consider kronig. I explain in this video using the kronig penney model. 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.