4.4 近自由电子近似.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 Energy Bands · Profile One electron Electrons in crystals approximation Bloch theorem Kronig-Penney Model Formation of energy bands Free electron Electron in an atom Nearly Free Tight-binding Model Electron Model Constructing the Physical image energy bands 4.4 Nearly Free Electron Approximation · Energy gap · Constructing energy bands · Fermi Surface Energy gap ← Bragg Reflection 1) Far from Brillouin zone interface Far from BZ boundary, Bragg Reflection does not happen 2 2 energies  x eikx E  k approach free   dash line 2m electron values. 2) Near Brillouin Zone interface Bragg Reflection leads the two possible combinations of the right and the left going waves: ix ix      e a e a  2 cos x / a       ix ix  a  a    e e  2i sin x / a      2     =4cos2 x / a         2   =   4sin2 x