Pdf xxiii efnne resumos 021105 1 free download pdf. Kronigpenney model, bloch functions, energy gaps, electronic structures in a crystal. I explain in this video using the kronig penney model. 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. Kronigpenney model overview and the ek diagram youtube. On crossing the zone boundary, the phase velocity changes direction.
What is the origin of band structure and band diagram. May 25, 2009 ive got an exam tomorrow, and this is one of the topics i cant get my head around. Electron in a periodic field of a crystal the solid state. The solution to schrodingers equation for the kronigpenney potential previously shown in. To simplify the analysis, we only consider a onedimensional system where atoms are aligned and equally spaced. Download wolfram player to view and interact with wolfram notebooks. Lecture 7 normal in the last lecture we encountered the kronigpenney model, a simple one dimensional system in which the schrdinger equation. Calculating the energy band structure using sampling and. Will discrete bands of energy show up in the solution as expected. Kronigpenney potential, afind the general trascendental equation that comes as a result of applying the. In quantum mechanics, the particle in a onedimensional lattice is a problem that occurs in the.
The possible states that the electron can occupy are. The model is closely related to the more conceptual empty lattice approximation. In the lectures we have derived two simple rules, which are away from brillouinzone boundaries the electronic bands i. First make a function for the potential you want something that takes x as input and gives you the potential you want at that x. This diagram determines which states the electrons are allowed to occupy, and is the fundamental result we. Show that the average kinetic energy per electron in a free electron fermi gas at 0 k is 2. Kronig penney model unlike the nearly free electron model in this problem we consider the case where the. We check to see whether this energy dispersion relation coincides with that of the free particle. The possible states that the electron can occupy are determined by the schrodinger equation, in the case of the kroning penney model, the potential vx is a periodic square wave. The kronigpenney model the kronigpenney modelwe now solve the timeindependent schrdinger equation. For details of the calculation, see for example kittel introduction to. This model, like the freeelectron model, does not take into account electronelectron interactions. Here i go over the results of the kronigpenney model.
The kronigpenney model 1 is a simplified model for an electron in a one dimensional periodic potential. It is a generalization of the free electron model, which assumes zero potential inside the lattice. Still, the kronig penny model does a remarkable job of isolating the essential e. 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 freely through the crystal lattice of a solid. 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. January 25, 2012 the kronig penney model describes electron motion in a period array of rectangular barriers fig.
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. You might have to try to implement periodic boundary conditions on this so that you can model an infinitely extendin. Kronigpenny model, band theory of solids, bloch, zone theory, potential well, potential barrier, engineering physics, applied physics. The main result is an expression for the localisation length. We know from secondyear quantum mechanics that square well potentials are quite easy to deal with. The kronigpenney model 1 is a simplified model for an electron in a onedimensional periodic potential. Engage with live, interactive examples, reports and files. 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.
This theory successfully explains electrical conductivity, specific heat. The model enables understanding and calculating the electronic band structure of especially metals. In typical undergraduate and graduate introductory texts in solidstate physics, the standard treatment is to introduce the nearly free electron model followed by the tightbinding model some canonical texts are ref. Mar 28, 2018 here i go over the results of the kronig penney model. Featured software all software latest this just in old school emulation msdos games historical software classic pc games software. Sala 6 electron paramagnetic resonance of the organic free radical in petroleum, eduardo di mauro, fernando. Scribd is the worlds largest social reading and publishing site. Treating the nearly free electron model using degenerate perturbation theory has been shown on the blackboard during lectures 3. The nearlyfree electron model university of oxford. The opposite extreme to the nearlyfree electron model assumes the electrons in the crystal behave much like an assembly of constituent atoms. Featured software all software latest this just in old school emulation msdos games historical software classic pc games software library. Ive got an exam tomorrow, and this is one of the topics i cant get my head around.
A speci c example relevant to current interest is the hexagonal lattice of graphene. January 25, 2012 the kronigpenney model describes electron motion in a period array of rectangular barriers fig. We study the localisation properties of the eigenstates in the kronigpenney model with weak compositional and structural disorder. Top kodi archive and support file community software vintage software apk msdos cdrom software cdrom software library. How to write code for the kronigpenney model with changeable. Derivation of the kronigpenney model the solution to schrodingers equation for the kronig penney potential previously shown in figure 2. In typical undergraduate and graduate introductory texts in solidstate physics, the standard treatment is to introduce the nearlyfree electron model followed by the tightbinding model some canonical texts are ref. Henry edwards is emeritus professor of mathematics at the university of georgia. Homework statement homework equations the attempt at a solution ive calculated that alpha4. Energy bands from the kronigpenney model physics forums. Other readers will always be interested in your opinion of the books youve read. Overestimation of the linear contribution to the low temperature speci c heat of metalloids e. In this paper, a new method based on greens function theory and.
The kronig penney model the kronig penney modelwe now solve the timeindependent schrdinger equation. Kronig penny model 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. Explore thousands of free applications and opensource resources. The picture below shows the kronigpenney model and the solutions of the schrdinger equation in the two regions of the system. Calculating the energy band structure using sampling and greens function techniques milad khoshnegar, amir hossein hosseinia, nima arjmandi, and sina khorasani school of electrical engineering, sharif university of technology, p. Anomalous properties of the kronigpenney model with. Effects of finite size and supernetwork interfaces in inp. Well examine the assumption of a constant potential. Solid state theory physics 545 kronnig penney modelpenney model. Lecture 7 normal in the last lecture we encountered the kronig penney model, a simple one dimensional system in which the schrdinger equation. As we saw previously, by applying both the continuity condition and blochs theorem we arrive at a somewhat intimidating expression at the top of the righthand slide. Descargue como doc, pdf, txt o lea en linea desde scribd.
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