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1、纳米结构物理学纳米结构物理学 课程内容课程内容1.纳米科学概论, 低维体系量子力学 2.固体物理, 表面/界面科学及材料生长简介3.纳米结构常用分析与制备方法 4.纳米线(管,带,杆)5.团簇与晶粒6.磁性纳米结构及自旋电子学 1 nm = 10-9 m = 10-3 m = 10 纳米结构纳米结构 (Nanostructures): material systems with length scale of 1-100 nm in at least one dimension 2-D: quantum wells, thin films, 2-D electron gas 1-D: quan
2、tum wires, nanowires, nanotubes, nanorods0-D: quantum dots, macro-molecules, clusters, nano-crystallitesBetween individual atoms/molecules and macroscopic bulk materials: Mesoscopicstructures (介观结构介观结构), with distinct properties not available from atoms or bulk crystals类类型型材料性质随体系尺度的变化：量变到质变量变到质变Qua
3、ntumconfinement:quantizationandreduceddimensionalityofelectronicstatesQuantumcoherenceandde-coherenceSurface/interfacestatesMetastability,adjustablesizeandshapePropertiestunableHighspeed,compactdensityandefficiencyUnique properties of nanostructures:Two approaches in our understanding and exploitati
4、on of material world: from the bottom up and from the top down The bottom-up approach: Atoms, simple molecules (well-understood sub-nm world) Macro-molecules, polymers clusters, crystallites, nanowires, bio-molecules The top-down approach: Bulk crystals Discrete devices Integrated circuits LSI VLSI
5、ULSI ( 0.1-0.05 m) ? Shrinking and shrinking into deep sub-0.1-m 两种途径在纳米尺度相会For up-to-date Edition visit http:/半半导导体体工工业业路路线线图图Bottom-up approach can deal with systems consisting of 104 atoms quite accurately纳米研究的目标纳米研究的目标Search for new physical phenomena existing at nanoscalesFabricate nano-devices
6、 with novel functionsSearch for processes to fabricate nanostructures with high accuracy and low cost Explore new experimental and theoretical tools to study nanostructures Nanoscience & nanotechnology: Multi-disciplinaryandrapid-developing现状与未来现状与未来: 一个学术界，政府和产业部门高度一个学术界，政府和产业部门高度重视的战略性研究领域重视的战略性研究
7、领域 Quantum mechanics of low-dimensional systems Time-independent Schrdinger equation:Free particle with V(r) = 0, plane wave: (r , t) = A exp(ikr - iEt/)Energy and momentum of the particle:E=2k2/(2m)=2(kx2+ky2+kz2)/(2m)=(k)p = k de Broglie wavelength: =h/pProbability of finding the particle at r : P
8、(r , t) = |(r , t)|2For a free particle, the probability is the same everywhere Potential well, quantization and bound states 1D potential well of infinite depth: V(x)0axnnConfined,discreteenergylevels,withn=1,2,3Ground-state(n=1)energy=h2/(8ma2),zero-pointorconfinementenergyPotential wells of finit
9、e depth: FornegativeE,onlyacertainnumberofEvaluesareallowed.The particle remains confined, but not completely within the well.ForEabovezero,anyvaluesareallowed,theprobabilityoffindingparticledoesnotapproachzeroawayfromthewell:The particle is freeQuantum well:particleconfinedbya1-Dpotentialwell,butfr
10、eeinother2-D,quantumstateslabeledbyn,kxandky:Each n represents a branch or subbandQuantum wire:particleconfinedby2-Dpotentialwells,freeonlyin1-D(1-Dfreeparticle),quantumstateslabeledbyn1,n2andkz:Quantum dot:particleconfinedbypotentialwellsin3-D,quantumstateslabeledn1,n2andn3:All discrete levels, lik
11、e in atomDensity of states (DOS): N(E)N(E)E = number of states with energies of E to E + E Plays a important role in many physical processes: conductivity, light emission, magnetism, chemical reactivity A measurable quantity to characterize a physical system, e.g. to determine the dimensionality 1-D
12、:planewave(x)=A exp(ikx),withperiodicboundaryconditions:(L)=(0)and(Llater)k and only take values:,n=0,1,2,k01-Dk-space&allowedstatesDispersion relation (k) for 1-D systemCountstatesink-space:Allowedstatesareseparatedbyaspacing2/LDOS in k-space N(k): (2-foldspindegeneracy)n1D(k)=N1D(k)/L=1/Independen
13、t of L!DOSinenergyn1D(E):n1D(E)E=n1D(E)k=2n1D(k)kn1D(E)=2n1D(k)/(d/dk)=(kbranches)n1D(E) diverges as E- when E 0, van Hove singularityForaunitlength:DOS for a 2-D system:n2D(E)=It is a constant!DOSfora3-Dsystem:n3D(E)=3-Dk-spaceDOS of a quantum well: sumupallbranches,eachhasa2-DDOS Dispersionrelatio
14、n:n2D(E)=Multi-stepfunctionofstepsizeg0=m/2DOS of a quantum wire:superpositionofaseriesofindividual1DDOSfunctionsn(E)=Energy gap due to confinementDOS of a quantum dot:Summationofasetof-functions(asinatomsandmolecules)Quantum tunneling: AparticlecanbereflectedbyortunnelthroughabarrierofV0EV0Aexp(ikx
15、)Bexp(-ikx)Cexp(ikx)RegionIBarrierRegionIIaEDefine:Tunneling probability: For a thick or tall barrier,a 1For an irregular shaped barrier,(a& b areclassicalturningpoints)Coherent quantum transport in 1-D channel When phase coherence is maintained, electrons should be treated as pure waves 1Delectront
16、ransportationbetweentworegionsseparatedbyanarbitrarypotentialbarrier:Aexp(ik1z)Bexp(-ik1z)Cexp(ik2z)Region I Barrier Region II UIIUITransmissionandreflectioncoefficients,TandR:T+R=1ForsameE,T21(E)=T12(E)Transport between two 1DEG with Fermi level difference: I-II=eVIIIeVUIUII Current due to electron
17、s from region I to II:(FormofcurrentdensityJ = nqv,dk/2countsstatesin1D) Fermi distribution function: step function at low TCurrent due to electrons from region II to I: Forcoherenttransport,T21=T12=T,thenetcurrent:(f step function at low T)ForsmallbiasV,T(E)aconstant, Landauer formula of conductanc
18、e:Quantumconductanceunit:G0=2e2/h=7.75SQuantumresistanceunit:R0=h/2e2=12.9kForaperfectquantumwireT =1,itsconductanceisG= 2e2/h,independent of its length!For a system with Ntrans transmitted states (modes) : Classicalcase:aperfectwirehasnoresistance(superconductor),oritincreaseswithlength2Delectronga
19、s(2DEG)低维电子系统制备与输运实验Double hetero-junction quantum welle.g.,AlGaAs-GaAs-AlGaAsSingle hetero-junction & MOSEF反相层反相层低维电子系统制备与输运实验Further confinement to 2DEG 1DEG (Q-wire) 0D (QD)Quantumpoint-contact量子触点Conductance through a short wire or constriction (quantum point contact) between two leads of 2DEG Q
20、uantizedconductanceasafunctionofgatevoltageVgNtrans can be changed by varying split-gate bias Vg Classical effect in transport through nanoparticles:CoulombblockadeCouplingofQDtoexternalworldWeakcoupling:thenumberofelectronslocatedattheQDiswelldefinedCoulombrepulsionenergybetweenelectronsinaQDofsize
21、a:ThediscretenatureofelectronchargebecomesstronglyevidentwhenECkBT. Forr5,T=300K,thisoccursata10nmCoulomb blockade:oneelectronlocatedonaQDcreatesanenergybarriertostopthefurthertransferofelectronsontotheQDClassical effect in transport through nanoparticles:CoulombblockadeFurthermore,the charging ener
22、gycanstopanyelectronjumpingonaQDElectrostatic energy stored in this capacitor is: CapacitanceforobservingCoulombblockadeatRT: C310-18FSphericalQDofradiusaatadistancel(a)aboveagroundplane,thecapacitanceofthissystem:Fortypicalsemiconductors,r10,a2.7nmatRTEnergy diagramofadouble-junctionQDstructurewith
23、CoulombblockadeInequilibriumUnderanappliedbiasExperimental(A)andtheoretical(BandC)I-VcurvesofaSTMtip/10-nmInisland/AlOxfilm/AlsubstrateWhene/2CVa3e/2C,maximumoccupationnumberofQDisn=1oneelectronatatimejumpthroughQDcurrentisnearlyaconstantSingle electron transistor (SET)Thirdelectrode-gate-toadjustQD
24、potentialindependentlyAnotherversionofSETVG=V0+V1cos(2ft)I=ef,SETcanbeusedasacurrentstandardApplication example of SET:参考文献参考文献1.P.Moriarty,Nanostructuredmaterials,Rep. Prog. Phys.64,297(2001).2.G.Timp(ed),Nanotechnology(Springer,NewYork,1999).3.HariSinghNalwa(ed),Nanostructured materials and nanote
25、chnology (AcademicPress,London,2002).4.For2003InternationalTechnologyRoadmapforSemiconductors(ITRS),seewebsitehttp:/ to quantum mechanics(PrenticeHall,NewJersey,1995).7.J.H.Davis,The physics of low-dimensional semiconductors: an introduction(CambridgeUniversityPress,NewYork,1998).8.A.Shik,Quantum we
26、lls: physics and electronics of two-dimensional systems(WorldScientific,Singapore,1997).9.K.Barnham,D.Vvedensky(eds.),Low-dimensional semiconductor structures: Fundamentals and device applications(CambridgeUniversityPress,NewYork,2001).10.D.K.Ferry,S.M.Goodnick,Transport in nanostructures(CambridgeU
27、niversityPress,NewYork,1997).11.T.Andoet al.,Mesoscopic physics and electronics(Springer,Berlin,1998).12.S.Datta,M.J.McLennan,Quantumtransportinultrasmalldevices,Rep. Prog. Phys.53,1003(1990).13.T.J.Thornton,Mesoscopicdevices,Rep. Prog. Phys.57,311(1994).14.C.G.Smith,Low-dimensionalquantumdevices,Re
28、p. Prog. Phys.59,235(1996).15.D.Ferry,J.R.Barker,C.Jacaboni(eds.),Granular Nanoelectronics(Plenum,NewYork,1990).16.H.Grabert,M.H.Devoret(eds.),Single charge tunneling: Coulomb blockade phenomena in nanostructures(Plenum,NewYork,1992).17.H.Koch,H.Lbbig(eds.),Single-electron tunneling and mesoscopic d
29、evices(Springer,Berlin,1992).18.S.M.Reimann,M.Manninen,Electronicstructureofquantumdots,Rev. Mod. Phys.74,1283(2002).19.E.H.Visscher,Technology and applications of single-electron tunneling devices(DelftUniversityPress,Delft,1996).20.K.K.Likharev,Single-electrondevicesandtheirapplications,Proc. IEEE87,606(1999).
