表面重构课_薛其坤.ppt
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1、表面重构,清华大学物理系 薛其坤,Outline,Brief introduction Bonding at a surface 2. Principle of Surface Reconstruction 3. Reconstruction Elements 3.1 Chains 3.2 Dimers (trimers) 3.3 Adatoms 4. Typical reconstruction surfaces 4.1 Metal Surface 4.2 Insulator Surface 4.3 Semiconductor Surface 5. Summary,1. Brief intr
2、oduction,Two types of atomic rearrangements Relaxation Reconstruction Wood:A(hkl)-nm-B,Examples,1. Si(111)-p2x2 2. Si(111)-3x3-30-Ga 3. Si(100)-c(2x2)-O,常用的研究手段: LEED, RHEED, STM, 琼角XRD等,Bonding at a surface,Why 原子间的键合 (1)Surface: heterogeneous at microscopic scale (2)Surface processes: adsorption/d
3、esorption, diffusion, reaction 外来原子与表面原子的相互作用/键合,金属键 共价键(Si,Ge,GaAs/InAs/AlAs, GaN, ZnO) 离子键(MgO, Al2O3, NaCl),孤立分子中原子间的成键 固体中原子间的成键,p,s,a,h,b,化学键,局域化学键的角度去理解晶体中原子的键合,Orbitals and Bonding One-Electron Picture,1023-body problem,Tight-Binding Approach,电子的原子能级 固体中能带,Lwdin Theorem:Sab(Ri Rj )=abij,两个轨道间
4、的成键 双原子分子(H2或者LiH),H11 H12 S12 H*11 S*12 H22 ,(,),(,),1,2,=0,Atomic Orbitals and Their Interaction,AN B8-N,三个假定: (1) s, Px , Py and Pz (2) Sab(Ri Rj )=abij (3) 最近邻和次近邻相互作用 , 且 Hab(Ri, Rj )= Hab(RiRj ),d=RiRj,p,d,n,n,n ,Lwdin Theorem:Sab(Ri Rj )=abij,Interatomic Matrix Elements,Vss,Vsp,Vpp,Vpp,Vabk=
5、abk,h2,md2,ss = 1.32,sp = 1.42,pp = 2.22,pp= 0.63,Slater and Koster, Phys. Rev. 94. 1498(1954),Bonding Hybrids Electrons are localized between atoms along the bonding direction,Atomic orbitals along the bonding direction,sp3杂化,sp2杂化,sp杂化,(1)同原子内轨道相互作用,1A,(1B),2A,(2B),(2)原子之间轨道相互作用,3,4,4,6,5,a,h,b,sp
6、3,Hirabayashi, J. Phys. Soc. Jpn. 27. 1475(1969),Dangling Bonds,A,B,问题:切断一个公价键时,两个电子如何分配?,cost= 3,K,J,2D wave vector,J,对电子态的影响,对电子态的影响,K,J,2D wave vector,J,2. Principle of Reconstruction,The surface structure observed will be the lowest free-energy structure kinetically accessible under the preparat
7、ion conditions. Si(111)-2x1 7x7 by annealing Ge(111)-2x1 c(2x8) by annealing,Both of the above are stable upon subsequent cooling indicate that the first 2x1 structure obtained by low-temperature cleavage is only a local stable structure, but not the lowest free-energy structure which is obtained fo
8、r both surfaces by annealing and subsequent cooling. In the two processes, high temperature is necessary to overcome the energy barrier between different structure and to generate the adatoms in the lowest free-energy structure.,Basic Principle:,Three main principles,Principle 1. A surface tends to
9、minimize the number of dangling bonds by the formation of new bonds. The remaining dangling bonds tend to be saturated. Reconstruction tend either to saturate surface dangling bonds via rehybridization or convert them into non-bonding electronic states which may be filled by a lone pair of electrons
10、 or be completely empty. Ge(111)c(2x8), C(100)2x1 Principle 2. A surface tends to compensate charges. Vacancy reconstruction on GaAs(111)2x2 Principle 3. A semiconductor surface tends to be insulating (or semiconducting). Tilting of the dimers on Si(100) and Ge(100),费米能级以下的表面态必须全部占据 Bonding and non-
11、bonding surface states 费米能级以上的表面态必须全部空着 non-bonding and antibonding states,Electron Counting Model,3. Reconstruction Elements,3.1 Chains 3.2 Dimers (trimers) 3.3 Adatoms,2.1 Chains,Zig-zag chains Binary IV-IV(SiC),III-V and II-VI compound semiconductors have planar zig-zag chains of alternating cati
12、ons and anions along a direction in their 110 surfaces, chains,(111) surfaces of diamond, Si, Ge have this kind of chains.,110,112,111,112,(111)-2x1,Using NN approximation of TBA, considering the DB interaction,Band structure of -bonded chain model,two surface bands,H11 H12 H*12 H22 ,LwdinTheorem:Sa
13、b(Ri Rj )=abij,(,),(,),1,2,=0,2.2 Dimers,Tight-binding Hamiltonian:,Trimer,2.3 Adatoms,often on (111) surfaces,4. Typical reconstruction surfaces,4.1 Metal Surfaces 4.2 Insulator Surfaces 4.3 Semiconductor Surfaces,4.1 Metal Surface Although most metal surfaces are relaxed instead of recosntruction,
14、 some noble and near-noble fcc metals, Au, Ir, Pt and bcc transition metals, W and Mo, display recosntructions.,Wll et al. Phys. Rev. B 39, 7988-7991(1989),1x2 missing-row reduces the surface energy.,Pt(110), Au(110),T. R. Linderoth, S. Horch, E. Lgsgaard, I. Stensgaard, and F. Besenbacher, PRL,78,4
15、978,4.2 Insulator Surfaces,NaCl (111)-1x1,Hebenstreit et al.,Phys. Rev. Lett. 85, 5376(2000),(a) 50nm x 50 nm, 21.2 V, 0.06 nA.,(b) NaCl(111) island with atomic resolution (7nm x 7 nm, 21.2 V, 0.3 nA).,(c) Structure model of an NaCl(111) island.,C(100)-2x1,Bobrov et al., Natrue 413, 616(2001),4.3 Se
16、miconductor Surfaces,Chem. Rev. 96, 1237-1259 (1996),Charles B. Duke,STM on III-V (100) Surface Reconstructions,Xue et al., Progress in Surface Science 56, p001-p131(1997),Element semiconductor surface,Si(100) industry Si(111) cleaved Ge(111) Ge(100),K.Oura, V.G.Lifshits et al. ,Si(001) surface,(001
17、),(110),Si(100)-2x1,Tromp et al., PRL 1985,Si(100)-2x1 c(4x2),filled states (-1.0 V) empty states (1.0 V) at 63K.,Unit cell,Takashi Yokoyama* et al. PRB,61,8,Si(111),Si(111)-2x1 7x7 disorder”1x1” (metastable),Heating to about 400,Heating to about 850,irreversibly,reversibly,Si(111)-2x1,K.C.Pandey,PR
18、L,47,26,The -bonded chain model by Pandey for the cleaved Si(111)-2x1 structure.,Compound semiconductor surface,GaAs(110) GaAs(100) GaAs(111),Very complicated!,GaAs(110),The GaAs(110) is the cleavage surface, the reconstructed surface still preserves an ideal 1x1 periodicity. Such a reconstruction i
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