Lecture1-CASGS-纳米科学概论,低维体系量子力学

,纳米结构物理学课程内容,纳米科学概论,低维体系量子力学固体物理,表面/界面科学及材料生长简介纳米结构常用分析与制备方法纳米线(管,带,杆)团簇与晶粒磁性纳米结构及自旋电子学,1nm=10-9m=10-3m=10,纳米结构(Nanostructures):materialsystemswithlengthscaleof1-100nminatleastonedimension,2-D:quantumwells,thinfilms,2-Delectrongas1-D:quantumwires,nanowires,nanotubes,nanorods0-D:quantumdots,macro-molecules,clusters,nano-crystallites,Betweenindividualatoms/moleculesandmacroscopicbulkmaterials:Mesoscopicstructures(介观结构),withdistinctpropertiesnotavailablefromatomsorbulkcrystals,类型,材料性质随体系尺度的变化：量变到质变,Quantumconfinement:quantizationandreduceddimensionalityofelectronicstatesQuantumcoherenceandde-coherenceSurface/interfacestatesMetastability,adjustablesizeandshapePropertiestunableHighspeed,compactdensityandefficiency,Uniquepropertiesofnanostructures:,Twoapproachesinourunderstandingandexploitationofmaterialworld:fromthebottomupandfromthetopdown,Thebottom-upapproach:Atoms,simplemolecules(well-understoodsub-nmworld)Macro-molecules,polymersclusters,crystallites,nanowires,bio-molecules,Thetop-downapproach:BulkcrystalsDiscretedevicesIntegratedcircuitsLSIVLSIULSI(0.1-0.05m)?Shrinkingandshrinkingintodeepsub-0.1-m,两种途径在纳米尺度相会,Forup-to-dateEditionvisit,半导体工业路线图,Bottom-upapproachcandealwithsystemsconsistingof104atomsquiteaccurately,纳米研究的目标,SearchfornewphysicalphenomenaexistingatnanoscalesFabricatenano-deviceswithnovelfunctionsSearchforprocessestofabricatenanostructureswithhighaccuracyandlowcostExplorenewexperimentalandtheoreticaltoolstostudynanostructures,Nanoscience&nanotechnology:,Multi-disciplinaryandrapid-developing,现状与未来:一个学术界，政府和产业部门高度重视的战略性研究领域,Quantummechanicsoflow-dimensionalsystems,Time-independentSchrdingerequation:,FreeparticlewithV(r)=0,planewave:,(r,t)=Aexp(ikr-iEt/),Energyandmomentumoftheparticle:E=2k2/(2m)=2(kx2+ky2+kz2)/(2m)=(k)p=kdeBrogliewavelength:=h/pProbabilityoffindingtheparticleatr:P(r,t)=|(r,t)|2,Forafreeparticle,theprobabilityisthesameeverywhere,Potentialwell,quantizationandboundstates,1Dpotentialwellofinfinitedepth:,V(x),0ax,n,n,Confined,discreteenergylevels,withn=1,2,3,Ground-state(n=1)energy=h2/(8ma2),zero-pointorconfinementenergy,Potentialwellsoffinitedepth:,FornegativeE,onlyacertainnumberofEvaluesareallowed.Theparticleremainsconfined,butnotcompletelywithinthewell.,ForEabovezero,anyvaluesareallowed,theprobabilityoffindingparticledoesnotapproachzeroawayfromthewell:Theparticleisfree,Quantumwell:particleconfinedbya1-Dpotentialwell,butfreeinother2-D,quantumstateslabeledbyn,kxandky:,Eachnrepresentsabranchorsubband,Quantumwire:particleconfinedby2-Dpotentialwells,freeonlyin1-D(1-Dfreeparticle),quantumstateslabeledbyn1,n2andkz:,Quantumdot:particleconfinedbypotentialwellsin3-D,quantumstateslabeledn1,n2andn3:,Alldiscretelevels,likeinatom,Densityofstates(DOS):N(E),N(E)E=numberofstateswithenergiesofEtoE+EPlaysaimportantroleinmanyphysicalprocesses:conductivity,lightemission,magnetism,chemicalreactivityAmeasurablequantitytocharacterizeaphysicalsystem,e.g.todeterminethedimensionality,1-D:planewave(x)=Aexp(ikx),withperiodicboundaryconditions:,(L)=(0)and,(Llater),kandonlytakevalues:,n=0,1,2,k,0,1-Dk-space&allowedstates,Dispersionrelation(k)for1-Dsystem,Countstatesink-space:Allowedstatesareseparatedbyaspacing2/L,DOSink-spaceN(k):,(2-foldspindegeneracy),n1D(k)=N1D(k)/L=1/IndependentofL!,DOSinenergyn1D(E):,n1D(E)E=n1D(E)k=2n1D(k)k,n1D(E)=2n1D(k)/(d/dk)=,(kbranches),n1D(E)divergesasE-whenE0,vanHovesingularity,Foraunitlength:,DOSfora2-Dsystem:,n2D(E)=,Itisaconstant!,DOSfora3-Dsystem:,n3D(E)=,3-Dk-space,DOSofaquantumwell:sumupallbranches,eachhasa2-DDOS,Dispersionrelation:,n2D(E)=,Multi-stepfunctionofstepsizeg0=m/2,DOSofaquantumwire:superpositionofaseriesofindividual1DDOSfunctions,n(E)=,Energygapduetoconfinement,DOSofaquantumdot:Summationofasetof-functions(asinatomsandmolecules),Quantumtunneling:AparticlecanbereflectedbyortunnelthroughabarrierofV0E,V0,Aexp(ikx),Bexp(-ikx),Cexp(ikx),RegionIBarrierRegionII,a,E,Define:,Tunnelingprobability:,Forathickortallbarrier,a1,Foranirregularshapedbarrier,(a&bareclassicalturningpoints),Coherentquantumtransportin1-Dchannel,Whenphasecoherenceismaintained,electronsshouldbetreatedaspurewaves1Delectrontransportationbetweentworegionsseparatedbyanarbitrarypotentialbarrier:,Aexp(ik1z),Bexp(-ik1z),Cexp(ik2z),RegionIBarrierRegionIIUII,UI,Transmissionandreflectioncoefficients,TandR:,T+R=1,ForsameE,T21(E)=T12(E),Transportbetweentwo1DEGwithFermileveldifference:I-II=eV,CurrentduetoelectronsfromregionItoII:,(FormofcurrentdensityJ=nqv,dk/2countsstatesin1D),Fermidistributionfunction:,stepfunctionatlowT,CurrentduetoelectronsfromregionIItoI:,Forcoherenttransport,T21=T12=T,thenetcurrent:,(fstepfunctionatlowT),ForsmallbiasV,T(E)aconstant,Landauerformulaofconductance:,Quantumconductanceunit:G0=2e2/h=7.75S,Quantumresistanceunit:R0=h/2e2=12.9k,ForaperfectquantumwireT=1,itsconductanceisG=2e2/h,independentofitslength!,ForasystemwithNtranstransmittedstates(modes):,Classicalcase:aperfectwirehasnoresistance(superconductor),oritincreaseswithlength,2Delectrongas(2DEG),低维电子系统制备与输运实验,Doublehetero-junctionquantumwelle.g.,AlGaAs-GaAs-AlGaAs,Singlehetero-junction&MOS,EF,反相层,低维电子系统制备与输运实验,Furtherconfinementto2DEG1DEG(Q-wire)0D(QD),Quantumpoint-contact,量子触点,Conductancethroughashortwireorconstriction(quantumpointcontact)betweentwoleadsof2DEG,QuantizedconductanceasafunctionofgatevoltageVg,Ntranscanbechangedbyvaryingsplit-gatebiasVg,Classicaleffectintransportthroughnanoparticles:Coulombblockade,CouplingofQDtoexternalworld,Weakcoupling:thenumberofelectronslocatedattheQDiswelldefined,CoulombrepulsionenergybetweenelectronsinaQDofsizea:,ThediscretenatureofelectronchargebecomesstronglyevidentwhenECkBT.Forr5,T=300K,thisoccursata10nm,Coulombblockade:oneelectronlocatedonaQDcreatesanenergybarriertostopthefurthertransferofelectronsontotheQD,Classicaleffectintransportthroughnanoparticles:Coulombblockade,Furthermore,thechargingenergycanstopanyelectronjumpingonaQD,Electrostaticenergystoredinthiscapacitoris:,CapacitanceforobservingCoulombblockadeatRT:,C310-18F,SphericalQDofradiusaatadistancel(a)aboveagroundplane,thecapacitanceofthissystem:,Fortypicalsemiconductors,r10,a2.7nmatRT,Energydiagramofadouble-junctionQDstructurewithCoulombblockade,InequilibriumUnderanappliedbias,Experimental(A)andtheoretical(BandC)I-VcurvesofaSTMtip/10-nmInisland/AlOxfilm/Alsubstrate,Whene/2CVa3e/2C,maximumoccupationnumberofQDisn=1oneelectronatatimejumpthroughQDcurrentisnearlyaconstant,Singleelectrontransistor(SET),Thirdelectrode-gate-toadjustQDpotentialindependently,AnotherversionofSET,VG=V0+V1cos(2ft),I=ef,SETcanbeusedasacurrentstandard,ApplicationexampleofSET:,参考文献,1.P.Moriarty,Nanostructuredmaterials,Rep.Prog.Phys.64,297(2001).2.G.Timp(ed),Nanotechnology(Springer,NewYork,1999).3.HariSinghNalwa(ed),Nanostructuredmaterialsandnanotechnology(AcademicPress,London,2002).4.For2003InternationalTechnologyRoadmapforSemiconductors(ITRS),seewebsite8.A.Shik,Quantumwells:physicsandelectronicsoftwo-dimensionalsystems(WorldScientific,Singapore,1997).9.K.Barnham,D.Vvedensky(eds.),Low-dimensionalsemiconductorstructures:Fundamentalsanddeviceapplications(CambridgeUniversityPress,NewYork,2001).,10.D.K.Ferry,S.M.Goodnick,Transportinnanostructures(CambridgeUniversityPress,NewYork,1997).11.T.Andoetal.,Mesoscopicphysicsandelectronics(Springe