Lecture1CASGS-纳米科学概论

单击此处编辑母版标题样式,单击此处编辑母版文本样式,第二级,第三级,第四级,第五级,*,*,*,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,nanorods,0-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 dimensionality of electronic states,Quantum coherence,and de-coherence,Surface/interface,states,Metastability,adjustable size and shape Properties tunable,High speed,compact density and efficiency,Unique properties of nanostructures:,Two approaches in our understanding and exploitation 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 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:/public.,itrs,.net,半导体工业路线图,Bottom-up approach can deal with systems consisting of,10,4,atoms,quite accurately,纳米研究的目标,Search for new physical phenomena existing at,nanoscales,Fabricate,nano,-devices with novel functions,Search for processes to fabricate nanostructures with high accuracy and 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:,(,r,t,)=,A,exp(,i,k,r,-,iEt,/,),Energy and momentum of the particle:,E,=,=,2,k,2,/(2m)=,2,(,k,x,2,+,k,y,2,+,k,z,2,)/(2m)=,(,k,),p,=,k,de,Broglie,wavelength,:,=,h,/,p,Probability 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 well of infinite depth:,V,(,x,),0,a,x,n,n,Confined,discrete energy levels,with n=1,2,3,Ground-state,(n=1)energy=,h,2,/(8m,a,2,),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 the 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,k,x,and,k,y,:,Each,n,represents a,branch,or,subband,Quantum wire:,particle confined by 2-D potential wells,free only in 1-D(1-D free particle),quantum states labeled by,n,1,n,2,and,k,z,:,Quantum dot:,particle confined by potential wells in 3-D,quantum states labeled,n,1,n,2,and,n,3,:,All discrete levels,like in atom,Density 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:,plane wave,(,x,)=,A,exp(,ikx,),with p,eriodic,boundary conditions:,(,L,)=,(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),n,1D,(,k,),=,N,1D,(,k,)/,L,=1/,Independent of L!,DOS in energy,n,1D,(,E,):,n,1D,(,E,),E,=,n,1D,(,E,),k,=2,n,1D,(,k,),k,n,1D,(,E,),=2,n,1D,(,k,)/(,d,/dk,)=,=,(,k,branches),n,1D,(,E,)diverges as,E,-,when,E,0,van Hove singularity,For a unit length:,DOS for a 2-D system:,n,2D,(,E,)=,It is a constant!,DOS for a 3-D system:,n,3D,(,E,)=,3-D,k,-space,DOS of a quantum well:,sum up all branches,e,ach has a 2-D DOS,Dispersion relation:,n,2D,(,E,),=,Multi-step function of step size,g,0,=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 through a barrier of,V,0,E,V,0,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,electrons should be treated as pure waves,1D electron transportation between two regions separated by an,arbitrary potential barrier,:,A,exp(,ik,1,z