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1、ElectronBandModelReporter：LiuZhu2021/7/181济南大学材料科学与工程学院Weknowthattheelectronsofisolatedatoms(forexampleinagas)canbeconsideredtoorbitatvariousdistancesabouttheirnuclei.Theseorbitsconstitutedifferentenergies.Specifically,thelargertheradiusofanorbit,thelargertheexcitationenergy

2、oftheelectron.Thisfactisoftenrepresentedinasomewhatdifferentfashionbystatingthattheelectronsaredistributedondifferentenergylevels,asschematicallyshownontherightsideofFigure2.Now,thesedistinctenergylevels,whicharecharacteristicforisolatedatoms,(Figure1)widenintoenergybandswhe

3、natomsapproacheachotherandeventuallyformasolidasdepictedontheleftsideofFigure2.2021/7/182济南大学材料科学与工程学院Filledband、conductionbandandForbiddenBandFilledband（Filledelectronic）Emptyband（Unscheduledelectronic）Valenceband（Notfilledelectronic）ForbiddenBand（Cannotberankedelectronic）c

4、onductionband2021/7/183济南大学材料科学与工程学院FilledbandNocontributiontothecurrentValencebandContributiontothecurrentcurrentcurrentofvalenceband2021/7/184济南大学材料科学与工程学院AllowedBand{EnergybandAtomicEnergyLevels{{ForbiddenBandAtomicOrbitaldpsenergy(E)ForbiddenBandFig1Atomicenergylevelspli

5、tting（分裂）fortheenergybandForbiddenBand:禁带AllowedBand:允带AtomicOrbital:原子轨道AtomicEnergyLevels:原子能级2021/7/185济南大学材料科学与工程学院Fig2.Schematicrepresentationofenergylevels(asforisolatedatoms)wideningoftheselevelsintoenergybandswithdecreasingdistancebetweenatoms.Energybandsforaspecific

6、caseareshownattheleftofthediagram.2021/7/186济南大学材料科学与工程学院Quantummechanics(量子力学)postulatesthattheelectronscanonlyresidewithinthesebands,butnotintheareasoutsideofthem.Theallowedenergybandsmaybenoticeablyseparatedfromeachother.Inothercases,dependingonthematerialandtheenergy,the

7、ymaypartiallyorcompletelyoverlap.Inshort,eachmaterialhasitsdistinctelectronenergybandstructure.CharacteristicbandstructuresforthemainclassesofmaterialsareschematicallydepictedinFigure4.6.2021/7/187济南大学材料科学与工程学院量子力学的假设量子力学的理论框架是由下列五个假设构成的：（波函数ψ）微观体系的运动状态由相应的归一化波函数描述（本征态、本征值和S

8、chrodinger方程）微观体系的运动状态波函数随时间变化的规律遵从薛定谔方程（算符）力学量由相应的线性算符表示2021/7/188济南大学材料科学