表面重構(gòu)課-薛其坤

1、表面重構(gòu),清華大學(xué)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, 瓊角XRD等,Bonding at a surface,Why 原子間的鍵合 （1）Surface: heterogeneous at microscopic scale （2）Surface processes: adsorption/d

3、esorption, diffusion, reaction 外來原子與表面原子的相互作用/鍵合,金屬鍵 共價鍵（Si，Ge，GaAs/InAs/AlAs, GaN, ZnO） 離子鍵（MgO, Al2O3, NaCl),孤立分子中原子間的成鍵 固體中原子間的成鍵,p,s,a,h,b,化學(xué)鍵,局域化學(xué)鍵的角度去理解晶體中原子的鍵合,Orbitals and Bonding One-Electron Picture,1023-body problem,Tight-Binding Approach,電子的原子能級 固體中能帶,Lwdin Theorem：Sab(Ri Rj )=abij,兩個軌道間

4、的成鍵 雙原子分子（H2或者LiH）,H11 H12 S12 H*11 S*12 H22 ,(,),(,),1,2,=0,Atomic Orbitals and Their Interaction,AN B8-N,三個假定： （1） s, Px , Py and Pz （2） Sab(Ri Rj )=abij （3） 最近鄰和次近鄰相互作用 ， 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雜化,sp2雜化,sp雜化,(1)同原子內(nèi)軌道相互作用,1A,(1B),2A,(2B),(2)原子之間軌道相互作用,3,4,4,6,5,a,h,b,sp

6、3,Hirabayashi, J. Phys. Soc. Jpn. 27. 1475(1969),Dangling Bonds,A,B,問題：切斷一個公價鍵時，兩個電子如何分配？,cost= 3,K,J,2D wave vector,J,對電子態(tài)的影響,對電子態(tài)的影響,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),費米能級以下的表面態(tài)必須全部占據(jù) Bonding and non-

11、bonding surface states 費米能級以上的表面態(tài)必須全部空著 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

19、s typical for zinc blende structure III-V semiconductors with buckling angle,GaAs(110),R. M. Feenstra et al., PRL 1987,110,As,Ga,empty,filled,GaAs(110),R. M. Feenstra et al., PRL 1987,The GaAs(110) is the cleavage surface, the reconstructed surface still preserves an ideal 1x1 periodicity. Such a re

20、construction is typical for zinc blende structure III-V semiconductors with buckling angle,As,Ga,Ga,As,As-rich,Ga-rich,Ga 覆蓋度增加方向,GaAs (001)：one of the most important surfaces,001,110,110,GaAs (001)-1x1 surface,(001),(110),(110),(110),Top-view,費米能級以下的表面態(tài)必須全部占據(jù) Bonding and non-bonding surface states

21、費米能級以上的表面態(tài)必須全部空著 non-bonding and antibonding states,Electron Counting Model,Xue et al., Progress in Surface Science, 56, (1997) p1-p131,s,(110),(110),Top-view,Side-view,Models of 2x4 Surface,GaAs(001) As-rich 2x4,GaAs(001)-2x4 surface,(110),Bilayer two-As-dimer model,Three-As-dimer model,Hashizume a

22、nd Xue et al., PRL 73, 2208（1994）,Another two models,Two-As-dimer model with second layer Ga dimerized,Extra-As-dimer model,(110),GaAs(001) Ga-rich 4x2 surface,Three-Ga-dimer model,Ga-bilayer model,As model,(110),(110),STM image of Ga-rich 4x6 structure,Xue et al. Phys. Rev. Lett. 74, 3177 (1995),Mi

23、rror symmetry of As-rich 2x4 and Ga-rich 4x2,As-rich 2x4,Ga-rich 4x2,Monolayer of Ga adsorption on As-rich surface results in Ga-rich 4x2 phase, Monolayer of As adsorption on Ga-rich surface results in As-rich 2x4 phase.,Phase evolution diagram,Q.K. Xue, T. Hashizume, and T. Sakurai, Scanning Tunnel

24、ing Microscopy of III-V Compound Semiconductor (001) Surface, Progress in Surface Science 56, P1-P132 (1997),Si(111)-7x7 reconstruction,Schlier and Farnsworth, J.Chem.Phys30, 917(1959),Theoretic model of Si(111)-7x7,Adatoms(add-atoms) in the outermost layer was proposed by Harrison. While the energy

25、 to form a vacancy on a silicon (111) surface is very large, silicon atoms outside the nominal surface should be quite stable. This suggests that the 7 7 reconstruction is a pattern of add-atoms rather than a pattern of vacancies.,Harrison, Surf. Sci. 55,1,The LEED: stacking fault in the surface lay

26、er Bennett et al,PRB 1983,STM: Binnig et al. PRL 50,120,Based on the above observations, Himpsel( left below) and McRae( right below) predicted that the boundary between the faulted and unfaulted triangular subunits incorporates an array of dimers and deep holes.,PRB.27,12,PRB.28,4,TED by Takayanagi

27、 et al. Model with dimers, adatoms and stacking faults, which known as DAS model.,Takayanagi, Surf.Sci.164,367,Electronic structure of DAS model,+2v,+1.45v,-1.45v,-0.35v,-0.8v,-1.7v,小結(jié): 半導(dǎo)體表面,(100)-like表面：2 DBs/atom。 dimer形成其主導(dǎo)作用。 對化合物, dimer-missing 再構(gòu)：偶數(shù)x偶數(shù) 1D特點: Buckling/tilting/distortion (111)-

28、like表面：1 DBs/atom。adatom形成其主導(dǎo)作用。 再構(gòu)：奇數(shù)x奇數(shù)（有理數(shù)x有理數(shù)） 3. Strong interaction direction: strong dispersion,2 inch Si wafer,100nmx100nm,27nmx27nm,Si(111)-7x7上的Al納米團(tuán)簇的有序陣列,Li et al., Phys. Rev. Lett. 88, 066101 (2002) Jia et al., Phys. Rev. B66, 165408 (2002) Jia et al., Appl. Phys. Lett. 80, 3186 (2002),S

29、ummary Surface is beautiful Small is beautiful,Thank you !,How ECR works in practice,For GaAs, Vn=5, Vp=3,thus:,M. D. Pashley, Phys. Rev. B40, 10481 (1990),Satisfy the principles of semiconductor surface reconstrucion,Principle 1.Reconstruction tend either to saturate surface “dangling” bongd via re

30、hybridization or to convert them into nonbonding electronic states. Principle 2.Surface can lower their energies by atomic relaxations leading to semiconducting (as opposed to metallic) surface state eigenvalue spectra. Principle 3.The surface structure observed will be the lowest free-energy struct

31、ure kinetically accessible under the preparation conditions. Principles 1-3 are only for space-charge free elemental semiconductors, but for compound semiconductors principles1-2 will be replaced by other principles . C.B.Duke Chem.Rev,96,1237,Xue et al., Progress in Surface Science, 56, (1997) pp.

32、1-131,s,Band structure of GaAs(001) which is sp3 hybridized in the bulk,GaAs(001) As-rich 2x4,RHEED 110,595C,550C,505C,2. Reconstruction Elements 2.1 Reconstruction and Bonding,sp3雜化,sp2雜化,sp雜化,s-like dangling hybrid,Pz-like dangling hybrid,(111),(100),關(guān)于GaAs(001)和GaN(0001)表面重構(gòu)的文章,GaAs(111) is a pol

33、ar surface which contains two terminated surfaces. Ga-terminated (111) surface, also called GaAs(111) or GaAs(111) A surface. As-terminated (111) surface, also called GaAs(-1-1-1) or GaAs(111) B surface Both of them exhibit 2x2 reconstructions, but these reconstructions are essentially different.,GaAs(111),GaAs(111) A surface.,K. W. Heberern, M. D. Pashley, PRB, 41,5,In this recosntruction, one out of every four Ga surface atoms is missing