4.6 电子的准经典运动以及课程小结.pdf

Chapter 4 Energy Bands 4.1 One electron approximation 4.2 Bloch theorem and Energy bands 4.3 Kronig-Penney Model 4.4 Nearly Free Electron Approximation 4.5 Tight-binding Approximation 4.6 Motion of Electron 4.6 Motion of Electron · Group velocity · Effective mass · Holes Electrons in crystals Bloch theorem Formation of energy Free electron Electron in an atom Constructing the Nearly Free Tight-binding Physical energy bands Electron Model Approximation image Conductor, Semiconductor, Insulator Effective mass Motion of electron Holes 4.6 Motion of Electron · Group velocity · Effective mass · Holes Effective Mass When an electric field ε acts on a free electron, it exerts a force eε that, from Newtons law, will produce an acceleration inversely proportional to its mass, a = eε/m. What happens when the electron to be accelerated is not free but happens to be in a crystal under the influence of the potential of the lattice ions? The answer is that it will still accelerate according to Newtons law; however, the electron responds as if it had some effective mass m*, which is different from its true mass. As we will show, this is because ε is not the only electric field acting on the electron inside the crystal. We will introduce this concept by using a semi-classical picture: an argument that is half classical and half quantum mechanical. The quantum mechanical part lies in the fact that the motion of an electron