《Lecture1-CASGS-纳米科学概论,低维体系量子力学.ppt》由会员分享，可在线阅读，更多相关《Lecture1-CASGS-纳米科学概论,低维体系量子力学.ppt（28页珍藏版）》请在三一办公上搜索。
1、,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,1 nm=10-9 m=10-3 m=10,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:quantum wires,nanowires,nanotubes,nanorods0
2、-D:quantum dots,macro-molecules,clusters,nano-crystallites,Between individual atoms/molecules and macroscopic bulk materials:Mesoscopic structures(介观结构),with distinct properties not available from atoms or bulk crystals,类型,材料性质随体系尺度的变化：量变到质变,Quantum confinement:quantization and reduced dimensionalit
3、y of electronic statesQuantum coherence and de-coherenceSurface/interface statesMetastability,adjustable size and shape Properties tunableHigh speed,compact density and efficiency,Unique properties of nanostructures:,Two approaches in our understanding and exploitation of material world:from the bot
4、tom 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 ULSI(0.1-0.05 m)?Shrinking and shrinking in
5、to deep sub-0.1-m,两种途径在纳米尺度相会,半导体工业路线图,Bottom-up approach can deal with systems consisting of 104 atoms quite accurately,纳米研究的目标,Search for new physical phenomena existing at nanoscalesFabricate nano-devices with novel functionsSearch for processes to fabricate nanostructures with high accuracy and
6、low cost Explore new experimental and theoretical tools to study nanostructures,Nanoscience&nanotechnology:,Multi-disciplinary and rapid-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,Quantum mechanics of low-dimensional systems,Time-independent Schrdinger equation:,Free particle with V(r)=0,plane wave:
7、,(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(r,t)=|(r,t)|2,For a free particle,the probability is the same everywhere,Potential well,quantization and bound states,1D potential wel
8、l of infinite depth:,V(x),0 a x,n,n,Confined,discrete energy levels,with n=1,2,3,Ground-state(n=1)energy=h2/(8ma2),zero-point or confinement energy,Potential wells of finite depth:,For negative E,only a certain number of E values are allowed.The particle remains confined,but not completely within th
9、e well.,For E above zero,any values are allowed,the probability of finding particle does not approach zero away from the well:The particle is free,Quantum well:particle confined by a 1-D potential well,but free in other 2-D,quantum states labeled by n,kx and ky:,Each n represents a branch or subband
10、,Quantum wire:particle confined by 2-D potential wells,free only in 1-D(1-D free particle),quantum states labeled by n1,n2 and kz:,Quantum dot:particle confined by potential wells in 3-D,quantum states labeled n1,n2 and n3:,All discrete levels,like in atom,Density of states(DOS):N(E),N(E)E=number of
11、 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:plane wave(x)=A exp(ikx),with periodic boundary conditions:,(L
12、)=(0)and,(L later),k and only take values:,n=0,1,2,k,0,1-D k-space&allowed states,Dispersion relation(k)for 1-D system,Count states in k-space:Allowed states are separated by a spacing 2/L,DOS in k-space N(k):,(2-fold spin degeneracy),n1D(k)=N1D(k)/L=1/Independent of L!,DOS in energy n1D(E):,n1D(E)E
13、=n1D(E)k=2n1D(k)k,n1D(E)=2n1D(k)/(d/dk)=,(k branches),n1D(E)diverges as E-when E 0,van Hove singularity,For a unit length:,DOS for a 2-D system:,n2D(E)=,It is a constant!,DOS for a 3-D system:,n3D(E)=,3-D k-space,DOS of a quantum well:sum up all branches,each has a 2-D DOS,Dispersion relation:,n2D(E
14、)=,Multi-step function of step size g0=m/2,DOS of a quantum wire:superposition of a series of individual 1D DOS functions,n(E)=,Energy gap due to confinement,DOS of a quantum dot:Summation of a set of-functions(as in atoms and molecules),Quantum tunneling:A particle can be reflected by or tunnel thr
15、ough a barrier of V0 E,V0,A exp(ikx),B exp(-ikx),C exp(ikx),Region I Barrier Region II,a,E,Define:,Tunneling probability:,For a thick or tall barrier,a 1,For an irregular shaped barrier,(a&b are classical turning points),Coherent quantum transport in 1-D channel,When phase coherence is maintained,el
16、ectrons should be treated as pure waves 1D electron transportation between two regions separated by an arbitrary potential barrier:,A exp(ik1z),B exp(-ik1z),C exp(ik2z),Region I Barrier Region II UII,UI,Transmission and reflection coefficients,T and R:,T+R=1,For same E,T21(E)=T12(E),Transport betwee
17、n two 1DEG with Fermi level difference:I-II=eV,Current due to electrons from region I to II:,(Form of current density J=nqv,dk/2 counts states in 1D),Fermi distribution function:,step function at low T,Current due to electrons from region II to I:,For coherent transport,T21=T12=T,the net current:,(f
18、 step function at low T),For small bias V,T(E)a constant,Landauer formula of conductance:,Quantum conductance unit:G0=2e2/h=7.75 S,Quantum resistance unit:R0=h/2e2=12.9 k,For a perfect quantum wire T=1,its conductance is G=2e2/h,independent of its length!,For a system with Ntrans transmitted states(
19、modes):,Classical case:a perfect wire has no resistance(superconductor),or it increases with length,2D electron gas(2DEG),低维电子系统制备与输运实验,Double hetero-junction quantum well e.g.,AlGaAs-GaAs-AlGaAs,Single hetero-junction&MOS,EF,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),Quantum p
20、oint-contact,量子触点,Conductance through a short wire or constriction(quantum point contact)between two leads of 2DEG,Quantized conductance as a function of gate voltage Vg,Ntrans can be changed by varying split-gate bias Vg,Classical effect in transport through nanoparticles:Coulomb blockade,Coupling
21、of QD to external world,Weak coupling:the number of electrons located at the QD is well defined,Coulomb repulsion energy between electrons in a QD of size a:,The discrete nature of electron charge becomes strongly evident when EC kBT.For r 5,T=300 K,this occurs at a 10 nm,Coulomb blockade:one electr
22、on located on a QD creates an energy barrier to stop the further transfer of electrons onto the QD,Classical effect in transport through nanoparticles:Coulomb blockade,Furthermore,the charging energy can stop any electron jumping on a QD,Electrostatic energy stored in this capacitor is:,Capacitance
23、for observing Coulomb blockade at RT:,C 3 10-18 F,Spherical QD of radius a at a distance l(a)above a ground plane,the capacitance of this system:,For typical semiconductors,r 10,a 2.7 nm at RT,Energy diagram of a double-junction QD structure with Coulomb blockade,In equilibrium Under an applied bias
24、,Experimental(A)and theoretical(B and C)I-V curves of a STM tip/10-nm In island/AlOx film/Al substrate,When e/2C Va 3e/2C,maximum occupation number of QD is n=1 one electron at a time jump through QD current is nearly a constant,Single electron transistor(SET),Third electrode-gate-to adjust QD poten
25、tial independently,Another version of SET,VG=V0+V1 cos(2ft),I=ef,SET can be used as a current standard,Application example of SET:,参考文献,1.P.Moriarty,Nanostructured materials,Rep.Prog.Phys.64,297(2001).2.G.Timp(ed),Nanotechnology(Springer,New York,1999).3.Hari Singh Nalwa(ed),Nanostructured materials
26、 and nanotechnology(Academic Press,London,2002).4.For 2003 International Technology Roadmap for Semiconductors(ITRS),see website.5.The Royal Society,Nanoscience and nanotechnologies:opportunities and uncertainties,(July 2004).6.D.J.Griffiths,Introduction to quantum mechanics(Prentice Hall,New Jersey
27、,1995).7.J.H.Davis,The physics of low-dimensional semiconductors:an introduction(Cambridge University Press,New York,1998).8.A.Shik,Quantum wells:physics and electronics of two-dimensional systems(World Scientific,Singapore,1997).9.K.Barnham,D.Vvedensky(eds.),Low-dimensional semiconductor structures
28、:Fundamentals and device applications(Cambridge University Press,New York,2001).,10.D.K.Ferry,S.M.Goodnick,Transport in nanostructures(Cambridge University Press,New York,1997).11.T.Ando et al.,Mesoscopic physics and electronics(Springer,Berlin,1998).12.S.Datta,M.J.McLennan,Quantum transport in ultr
29、asmall devices,Rep.Prog.Phys.53,1003(1990).13.T.J.Thornton,Mesoscopic devices,Rep.Prog.Phys.57,311(1994).14.C.G.Smith,Low-dimensional quantum devices,Rep.Prog.Phys.59,235(1996).15.D.Ferry,J.R.Barker,C.Jacaboni(eds.),Granular Nanoelectronics(Plenum,New York,1990).16.H.Grabert,M.H.Devoret(eds.),Single
30、 charge tunneling:Coulomb blockade phenomena in nanostructures(Plenum,New York,1992).17.H.Koch,H.Lbbig(eds.),Single-electron tunneling and mesoscopic devices(Springer,Berlin,1992).18.S.M.Reimann,M.Manninen,Electronic structure of quantum dots,Rev.Mod.Phys.74,1283(2002).19.E.H.Visscher,Technology and applications of single-electron tunneling devices(DelftUniversity Press,Delft,1996).20.K.K.Likharev,Single-electron devices and their applications,Proc.IEEE 87,606(1999).,
