4.5 紧束缚近似(1).pdf

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1、Chapter 4 Energy Bands4.1 One electron approximation 4.2 Bloch theorem and Energy bands4.3 Kronig-Penney Model4.4 Nearly Free Electron Approximation4.5 Tight-binding Approximation4.6 Motion of ElectronBloch theoremFormation of energy bandsNearly Free Electron ModelTight-binding ModelElectrons in cry

2、stalsFree electronElectron in an atomConstructing the energy bands Physical image One electron approximation ProfileEnergy BandsKronig-Penney ModelLCAO:Linear Combination of Atomic OrbitalsWave function of electron surrounding atom l:222jjjVm rRrRrRV(rRl)：Potential energy of the atom at the Rllattic

3、e sitej：Energy level of the electron(non-degenerate)j(r-Rl)：Wave function of the electronlr-Rl0 Linear Combination of Atomic Orbitals Physical Image Conductor,semiconductor,insulator4.5 Tight-binding Approximation-i()()kjuelk r RrrR()()kkuunrRr()()()kkHErkrLCAO:Linear Combination of Atomic Orbitalsr

4、-Rl0Wave function of electron surrounding atom l:222jVm rRrRjj rR jCrrR i()kkCeuk rrrilCCelk R ikjCelk RrrR-i()ikjCeelk r Rk rrrRIn crystal:Linear Combination of Atomic Orbitals Physical Image Conductor,semiconductor,insulator4.5 Tight-binding Approximation 222U rrErm UVUVVVrrRrrRrRrRPotential of th

5、e atom lPerturbation of other atoms 222VVrErm rRrR2ii2()2jjVVeEem llk Rk RkrRrRrRrR(,)()e(mimnsnEEk RRkLCAO:Linear Combination of Atomic OrbitalsEs:zeroth approximation of E(k):constant integration of crystal field(Rm):integration of interacting Linear Combination of Atomic Orbitals Physical Image C

6、onductor,semiconductor,insulator4.5 Tight-binding Approximation(,)(e(misnmnEEk RRk Linear Combination of Atomic Orbitals Physical Image Conductor,semiconductor,insulator4.5 Tight-binding Approximation Linear Combination of Atomic Orbitals Physical Image Conductor,semiconductor,insulator4.5 Tight-bin

7、ding Approximation(,)(e(misnmnEEk RRkInteratomic distanceEnergy Linear Combination of Atomic Orbitals Physical Image Conductor,semiconductor,insulator4.5 Tight-binding Approximation4.5 Tight-binding Approximation Linear Combination of Atomic Orbitals Physical Image Conductor,semiconductor,insulator

8、Linear Combination of Atomic Orbitals Physical Image Conductor,semiconductor,insulator4.5 Tight-binding ApproximationComparison with nearly free e-modelBloch theoremFormation of energyNearly Free Electron ModelTight-binding ApproximationElectrons in crystalsFree electronElectron in an atomConstructing the energy bands Physical image Conductor,Semiconductor,InsulatorMotion of electronEffective massHoles Linear Combination of Atomic Orbitals Physical Image Conductor,semiconductor,insulator4.5 Tight-binding Approximation