表面重构课薛其坤

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1、表面重构表面重构清华大学物理系清华大学物理系薛其坤薛其坤Outline1.Brief introductionBrief introduction Bonding at a surface2.Principle of Surface Reconstruction2.Principle of Surface Reconstruction 3.Reconstruction Elements3.Reconstruction Elements 3.1 Chains 3.2 Dimers(trimers)3.3 Adatoms4.Typical reconstruction surfaces4.Typi

2、cal reconstruction surfaces 4.1 Metal Surface4.1 Metal Surface 4.2 Insulator Surface 4.2 Insulator Surface 4.3 Semiconductor Surface 4.3 Semiconductor Surface5.Summary5.Summary1.Brief introductionTwo types of atomic rearrangements Relaxation Reconstruction Wood：A(hkl)-n m-BExamples1.Si(111)-p2x22.Si

3、(111)-3x 3-30-Ga3.Si(100)-c(2x2)-O常用的研究手段：常用的研究手段：LEED,RHEED,STM,琼角琼角XRD等等Bonding at a surfaceWhy 原子间的键合原子间的键合 （1）Surface:heterogeneous at microscopic scale （2）Surface processes:adsorption/desorption,diffusion,reaction 外来原子与表面原子的相互作用外来原子与表面原子的相互作用/键合键合金属键金属键共价键（共价键（Si，Ge，GaAs/InAs/AlAs,GaN,ZnO）离子键（离

4、子键（MgO,Al2O3,NaCl)孤立分子中原子间的成键孤立分子中原子间的成键 固体中原子间的成键固体中原子间的成键psahb化学键化学键局域化学键的角度去理解晶体中原子的键合局域化学键的角度去理解晶体中原子的键合Orbitals and BondingOne-Electron Picture1023-body problemTight-Binding Approacha,i (x)=a i a(xRi)(LCAO)电子的原子能级电子的原子能级 固体中能带固体中能带b,jHab(Ri,Rj)Sab(Ri Rj)bj=0Lwdin Theorem：Sab(Ri Rj)=abij H (x)=(

5、x)晶体中单电子的薛定谔方程晶体中单电子的薛定谔方程两个轨道间的成键两个轨道间的成键 双原子分子（双原子分子（H2或者或者LiH）H11 H12 S12 H*11 S*12 H22 ()()1 2=0a,i (x)=a i a(xRi)LiHs(H)s(Li)Atomic Orbitals and Their InteractionAN B8-N三个假定：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最近邻和次近邻相互作用，且且 Hab(Ri,Rj)=Hab(RiRj)d=RiRjpdn n n Lwdin Theorem：Sab(

6、Ri Rj)=abij Interatomic Matrix ElementsVss Vsp Vpp Vpp Vabk=abkh2md2 ss =1.32 sp =1.42 pp =2.22 pp=0.63Slater and Koster,Phys.Rev.94.1498(1954)Bonding HybridsElectrons are localized between atoms along the bonding direction Atomic orbitals along the bonding directionsp3杂化杂化sp2杂化杂化sp杂化杂化AB(1)(1)同原子内轨

7、道相互作用同原子内轨道相互作用 1A(1B)2A (2B)(2)(2)原子之间轨道相互作用原子之间轨道相互作用 3 4 4 6 5 a h b sp3Hirabayashi,J.Phys.Soc.Jpn.27.1475(1969)Dangling Bonds ABSi(111)DB B问题：切断一个公价键时，问题：切断一个公价键时，两个电子如何分配？两个电子如何分配？cost=3K J2D wave vector J对对电子态的影响电子态的影响对对电子态的影响电子态的影响 br=sp3 2 DB=sp3+2(110)K J2D wave vector J2.Principle of Recon

8、struction The surface structure observed will be the The surface structure observed will be the lowest free-energy structure kinetically lowest free-energy structure kinetically accessible under the preparation conditions.accessible under the preparation conditions.Si(111)-2x1 Si(111)-2x1 7x7 7x7 by

9、 annealing by annealing Ge(111)-2x1 Ge(111)-2x1 c(2x8)c(2x8)by annealingby annealingBoth of the above are stable upon subsequent cooling indicate that the first 2x1 structure Both of the above are stable upon subsequent cooling indicate that the first 2x1 structure obtained by low-temperature cleava

10、ge is only a local stable structure,but not the lowest free-obtained by low-temperature cleavage is only a local stable structure,but not the lowest free-energy structure which is obtained for both surfaces by annealing and subsequent cooling.In the energy structure which is obtained for both surfac

11、es by annealing and subsequent cooling.In the two processes,high temperature is necessary to overcome the energy barrier between different two processes,high temperature is necessary to overcome the energy barrier between different structure and to generate the structure and to generate the adatomsa

12、datoms in the lowest free-energy structure.in the lowest free-energy structure.Basic PrincipleBasic Principle：Three main principlesThree main principlesPrinciple 1.Principle 1.A surface tends to minimize the number of A surface tends to minimize the number of dangling bonds by the formation of new b

13、onds.The dangling bonds by the formation of new bonds.The remaining dangling bonds tend to be saturated.remaining dangling bonds tend to be saturated.Reconstruction tend either to saturate surface dangling bonds via Reconstruction tend either to saturate surface dangling bonds via rehybridizationreh

14、ybridization or convert them or convert them into non-bonding electronic states which may be filled by a lone pair of electrons or be completely into non-bonding electronic states which may be filled by a lone pair of electrons or be completely empty.Ge(111)c(2x8),C(100)2x1empty.Ge(111)c(2x8),C(100)

15、2x1Principle 2.Principle 2.A surface tends to compensate charges.A surface tends to compensate charges.Vacancy reconstruction on GaAs(111)2x2Vacancy reconstruction on GaAs(111)2x2Principle 3.Principle 3.A semiconductor surface tends to be A semiconductor surface tends to be insulating(or insulating(

16、or semiconductingsemiconducting).).Tilting of the Tilting of the dimersdimers on Si(100)and Ge(100)on Si(100)and Ge(100)费米能级以下的表面态必须全部占据费米能级以下的表面态必须全部占据Bonding and non-bonding surface states费米能级以上的表面态必须全部空着费米能级以上的表面态必须全部空着non-bonding and antibonding statesElectron Counting Model3.Reconstruction Elem

17、ents3.1 Chains3.2 Dimers(trimers)3.3 Adatoms2.1 ChainsZig-zag chainsBinary IV-IV(SiC),III-V and II-VI compound semiconductors have planar zig-zag chains of alternating cations and anions along a direction in their 110 surfaces chains(111)surfaces of diamond,Si,Ge have this kind of chains.11011211111

18、2(111)-2x1Using NN approximation of TBA,considering the DB interactionBand structure of -bonded chain model two surface bandsV=H12(d1)+H12(d2)S(k)=i eikdi H11 H12 H*12 H22 LwdinTheorem：Sab(Ri Rj)=abij()()1 2=02.2 DimersTight-binding Hamiltonian:Tight-binding Hamiltonian:Trimer 2.3 Adatomsoften on(11

19、1)surfaces1101121111124.Typical reconstruction surfaces4.1 Metal Surfaces4.1 Metal Surfaces4.2 Insulator Surfaces4.2 Insulator Surfaces4.3 Semiconductor Surfaces4.3 Semiconductor Surfaces 4.1 Metal Surface4.1 Metal Surface Although most metal surfaces are relaxed instead of Although most metal surfa

20、ces are relaxed instead of recosntructionrecosntruction,some noble and near-noble some noble and near-noble fccfcc metals,Au,metals,Au,Ir Ir,Pt and bcc transition,Pt and bcc transition metals,W and Mo,display metals,W and Mo,display recosntructionsrecosntructions.Wll et al.Phys.Rev.B 39,7988-7991(19

21、89)1x2 missing-row 1x2 missing-row reduces the surface reduces the surface energy.energy.Pt(110),Au(110)T.R.Linderoth,S.Horch,E.Lgsgaard,I.Stensgaard,and F.Besenbacher,PRL,78,49784.2 Insulator Surfaces4.2 Insulator SurfacesNaCl(111)-1x1Hebenstreit et al.,Phys.Rev.Lett.85,5376(2000)(a)50nm x 50 nm,21

22、.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)-2x1Bobrov et al.,Natrue 413,616(2001)4.3 Semiconductor Surfaces4.3 Semiconductor SurfacesChem.Rev.96,1237-1259(1996)Charles B.DukeSTM on III-V(100)Surface ReconstructionsX

23、ue et al.,Progress in Surface Science 56,p001-p131(1997)Element semiconductor surfaceSi(100)industryindustrySi(111)cleavedcleavedGe(111)Ge(100)K.Oura,V.G.Lifshits et al.Si(001)surface(001)Dimerization:reduce dangling bonds(110)Si(100)-2x1Tromp et al.,PRL 1985 Si(100)-2x1 c(4x2)filled states(-1.0 V)e

24、mpty states(1.0 V)at 63K.Unit cellTakashi Yokoyama*et al.PRB,61,8Si(111)Si(111)-Si(111)-2x12x1 7x7 7x7 disorder”1x1”disorder”1x1”(metastablemetastable)Heating to about 400Heating to about 850irreversiblyreversiblySi(111)-2x1K.C.Pandey,PRL,47,26The -bonded chain modelby Pandeyfor the cleavedSi(111)-2

25、x1 structure.Compound semiconductor surfaceGaAs(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 is typical for zinc blende structure III-V semiconductors with buckling angle

26、GaAs(110)R.M.Feenstra et al.,PRL 1987110AsGaemptyfilledGaAs(110)R.M.Feenstra et al.,PRL 1987110The GaAs(110)is the cleavage surface,the reconstructed surface still preservesan ideal 1x1 periodicity.Such a reconstruction is typical for zinc blende structure III-V semiconductors with buckling angle As

27、GaGaAsc(4x4),2x4/c(2x8),2x6,3x1,1x3,4x2/c(8x2),4x6As-richGa-richGa 覆盖度增加方向覆盖度增加方向GaAs(001)：one of the most important surfaces001110110GaAs(001)-1x1 surface(001)Dimerization:reduce dangling bonds(110)AsGa(110)(110)Top-view费米能级以下的表面态必须全部占据费米能级以下的表面态必须全部占据Bonding and non-bonding surface states费米能级以上的表面

28、态必须全部空着费米能级以上的表面态必须全部空着non-bonding and antibonding statesElectron Counting ModelXue et al.,Progress in Surface Science,56,(1997)p1-p131s(110)(110)Top-viewSide-viewModels of 2x4 SurfaceGaAs(001)As-rich 2x4As-Rich 2x4Hashizume and Xue et al.,PRL 73,2208（1994）110110110110GaAs(001)-2x4 surface(110)(110)

29、Bilayer two-As-dimer model Three-As-dimer model Hashizume and Xue et al.,PRL 73,2208（1994）Another two modelsTwo-As-dimer model with secondlayer Ga dimerizedExtra-As-dimer model(110)(110)GaAs(001)Ga-rich 4x2 surface Three-Ga-dimer model Ga-bilayer model As model(110)(110)GaAsSTM image of Ga-rich 4x6

30、structureXue et al.Phys.Rev.Lett.74,3177(1995)Mirror symmetry of As-rich 2x4 and Mirror symmetry of As-rich 2x4 and GaGa-rich 4x2-rich 4x2As-rich 2x4Ga-rich 4x2Monolayer 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

31、2x4 phase.Phase evolution diagramQ.K.Xue,T.Hashizume,and T.Sakurai,Scanning Tunneling Microscopy of III-V Compound Semiconductor(001)Surface,Progress in Surface Science 56,P1-P132(1997)Si(111)-7x7 reconstructionSchlierSchlier and Farnsworth,and Farnsworth,J.Chem.Phys30,917(1959)J.Chem.Phys30,917(195

32、9)Theoretic model of Si(111)-7x7Adatoms(addAdatoms(add-atoms)in the outermost layer was proposed-atoms)in the outermost layer was proposed by Harrison.by Harrison.While the energy to form a vacancy on a silicon(111)While the energy to form a vacancy on a silicon(111)surface is very large,silicon ato

33、ms outside the nominal surface is very large,silicon atoms outside the nominal surface should be quite stable.This suggests that the 7 surface should be quite stable.This suggests that the 7 7 reconstruction is a pattern of add-atoms rather than 7 reconstruction is a pattern of add-atoms rather than

34、 a pattern of vacancies.a pattern of vacancies.Harrison,Surf.Harrison,Surf.SciSci.55,1.55,1 The LEED:stacking fault in the The LEED:stacking fault in the surface layersurface layer Bennett et Bennett et al,PRBal,PRB 1983 1983STM:STM:BinnigBinnig et al.PRL 50,120 et al.PRL 50,120Based on the above ob

35、servations,Based on the above observations,HimpselHimpsel(left below)and McRae(right below)(left below)and McRae(right below)predicted that the boundary between the faulted and predicted that the boundary between the faulted and unfaultedunfaulted triangular subunits triangular subunits incorporates

36、 an array of incorporates an array of dimersdimers and deep holes.and deep holes.PRB.27,12PRB.28,4TED by TED by TakayanagiTakayanagi et al.et al.Model with Model with dimersdimers,adatomsadatoms and stacking faults,and stacking faults,which known as DAS model.which known as DAS model.TakayanagiTakay

37、anagi,Surf.Sci.164,367,Surf.Sci.164,36710 Faulted HalfUnfaulted HalfAdatomRest atomCorner hole112110Electronic structure of DAS modelElectronic structure of DAS model+2v+1.45v-1.45v-0.35v-0.8v-1.7v小结小结:半导体表面半导体表面1.(100)-like表面表面：2 DBs/atom。dimer形成其主导作用。形成其主导作用。2.对化合物对化合物,dimer-missing3.再构：偶数再构：偶数x偶数

38、偶数4.1D特点特点:Buckling/tilting/distortion2.(111)-like表面：表面：1 DBs/atom。adatom形成其主导作用。形成其主导作用。3.再构：奇数再构：奇数x奇数（有理数奇数（有理数x有理数）有理数）4.3.Strong interaction direction:strong dispersion2 inch Si wafer100nmx100nm27nmx27nmSi(111)-7x7Si(111)-7x7上的上的AlAl纳米团簇的有序阵列纳米团簇的有序阵列Li et al.,Phys.Rev.Lett.88,066101(2002)Jia e

39、t al.,Phys.Rev.B66,165408(2002)Jia et al.,Appl.Phys.Lett.80,3186(2002)5.Summary Surface is beautiful Small is beautifulThank you!How ECR works in practiceFor GaAs,Vn=5,Vp=3,thus:M.D.Pashley,Phys.Rev.B40,10481(1990)Satisfy the principles of semiconductor surface reconstrucionPrinciple 1.Reconstructio

40、n tend either to saturate surface“dangling”Principle 1.Reconstruction tend either to saturate surface“dangling”bongdbongd via via rehybridizationrehybridization or to convert them into nonbonding electronic states.or to convert them into nonbonding electronic states.Principle 2.Surface can lower the

41、ir energies by atomic relaxations leading to Principle 2.Surface can lower their energies by atomic relaxations leading to semiconductingsemiconducting(as opposed to metallic)surface state (as opposed to metallic)surface state eigenvalueeigenvalue spectra.spectra.Principle 3.The surface structure ob

42、served will be the lowest free-energy Principle 3.The surface structure observed will be the lowest free-energy structure kinetically accessible under the preparation conditions.structure kinetically accessible under the preparation conditions.Principles 1-3 are only for space-charge free elemental

43、semiconductors,but for Principles 1-3 are only for space-charge free elemental semiconductors,but for compound semiconductors principles1-2 will be replaced by other principles compound semiconductors principles1-2 will be replaced by other principles.C.B.DukeC.B.Duke Chem.Rev,96,1237 Chem.Rev,96,12

44、37Xue et al.,Progress in Surface Science,56,(1997)pp.1-131s Band structure of GaAs(001)which is sp3 hybridized in the bulkGaAs(001)As-rich 2x4RHEED 110595C550C505C2.Reconstruction Elements 2.1 2.1 Reconstruction and Bondingsp3杂化杂化sp2杂化杂化sp杂化杂化s-like dangling hybridPz-like dangling hybrid(111)(100)关于

45、关于GaAs(001)和和GaN(0001)表面重构的文章表面重构的文章 GaAs(111)is a polar surface which contains two terminated surfaces.GaGa-terminated(111)surface,also called GaAs(111)or GaAs(111)A-terminated(111)surface,also called GaAs(111)or GaAs(111)A surface.surface.As-terminated(111)surface,also called GaAs(-1-1-1)or GaAs(1

46、11)As-terminated(111)surface,also called GaAs(-1-1-1)or GaAs(111)B surfaceB 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

47、 is missing and the spacing between the surface Ga layer and subsurface As layer is strongly contracted to make an almost flat atomic configuration.The charge transfer completely from Ga dangling bonds to As dangling bonds to reduce energy.(similar reconstructions also in(111)of GaP,GaSb,InSb.GaAs(1

48、11)B surface.GaAs(111)B 2x2GaAs(111)B 2x2 structure in this surface is accepted to consistof As trimers directly over Ga atoms in the lowerlayer.The As deficiency can results in a surface with structure.Biegelsen et al.PRL,65,4Ge(111)-2x1R.M.Feenstra et al.,PRB 64,081306 R(2001)Ge(111)c(2x8)R.S.Beck

49、er et al.PRB,39,3Unit cell Tilted Tilted dimersdimers on both Si(100)and(10-10)surface on both Si(100)and(10-10)surface of of wurtzitewurtzite compound semiconductors compound semiconductorsUntilted dimer on GaAs(100)Pt(100)In the case of Pt(100),the surface reconstructed into a close-packed quasi-I

50、n the case of Pt(100),the surface reconstructed into a close-packed quasi-hexagonal layer and the structure has either very large periodicity or is hexagonal layer and the structure has either very large periodicity or is incommensurate because of the different symmetries of incommensurate because of the different symmetries of overlayeroverlayer and and substrate.Au(100)and Ir(100)also have the similar reconstructions.substrate.Au(100)and Ir(100)also have the similar reconstructions.100 x100 G.Ritz,M.Schmid,and P.Varga et al,PRB,56,10518