Low Energy Electron Diffraction and Microscopy

Physics 9826bLecture 3Surface Structure, continued:Low Energy Electron Diffraction and MicroscopyHow to determine surface structure:- Theoretical background- Low Energy Electron Diffraction (LEED)- Reflection High-Energy Electron Diffraction (RHEED)- Low Energy Electron Microscopy (LEEM)Additional: Scanning Electron MicroscopyReferences:1) Zangwill, Chapter 32) Woodruff & Delchar, Chapter 2 and pp. 449-4603) Attard and Barnes, pp,25-28, 47-624) Kolasinski, pp.84-915) LEEM: http://www.research.ibm.com/leem/#item2Lecture 3 1Electron Backscattering: concepts of diffractionElectron diffraction and microscopy:Elastic backscattered e - , ~ few % at 100eVe“Universal curve” for electronsShort inelastic mean free path forelectrons means that elastic scatteringof electrons is very surface sensitiveLecture 3 2Lecture 3, January 21, 2013 1

Physics 9826b3.1 Real Space and Reciprocal Space Lattices- Given a unit cell with basis vectors ( a 1,a2) - There is a complementary reciprocal lattice ( a *, *) 1a2 aiaj* ij( i,j 1,2) a1* a2and a2* a1a Rectangular Lattice1 a Area of unit cell A* aa 1a*2a A |a1|| a2| sin a 2* A*|a1*||a2*|sin a *1A*Areal spaceNon-rectangular latticea 1**a 2reciprocal spacea 1**a 2reciprocal spacereal spaceLecture 3 3Substrate and Overlayer StructuresSuppose overlayer (or reconstructed surface layer) lattice different from substrateTTAB2 na1 ma nb mb121 122222a 12aOverlayer real space lattice: b1 G11a1 G12a2 b G a G aGjj*det G *a Overlayer reciprocal lattice: b1* G11*a1* G12*a2* b2* G21*a1* G22*a2*~ 1where G* G (inverse transposed matrix)GiiGij Gji*b 1det G *bb 2Lecture 3 4Lecture 3, January 21, 2013 2

Physics 9826b3.2 Reciprocal Lattice and DiffractionRecall the de Broglie relation: l Incident electronplane waved hkPeriodic arraywith direction [h k] o2kConstructive interference when path length difference = n ld (sin sin ) nl,n integerhkFor electrons :l(Å)For Heatom : l(Å)For normal incidence :od150,E(eV)0.02E(eV)hksin n~ 1- 2Å12.2E(eV )hpo150o 0, 90 , n 1:E 2dhk- as E , beam moves towards normalLecture 3 5- solution for a direction, not intensity3.3 LEED InstrumentationLEED patterns for O /Cu(001):(a) clean Cu(001); (b) p(2 1) O; (c) c(2 3)O /Cu(001)Screen-type apparatus; also measurebeam widths and intensity with Faraday cupfrom www.omicron.deGeometrical Theory of Diffraction:• Analysis of LEED beam direction (position ofspots) to give symmetry and geometry of unit cell• Strong interaction between low energy electronsand matter dynamic theory for intensities• Simplification: elastic interactions as scattering ofwaves at a 2D latticeLecture 3 6Lecture 3, January 21, 2013 3

Physics 9826bInterference ConditionsIn 1D case, interference condition is: ai(sin sino) nlk o2k ' ai (sin sin o)2(for 1D case)l na i2Periodic array with kdirection [1 0]l 2 2aik aisin o,aik' aisin ll In 2D case: a1(k ' k) 2h;h,k are integers a ( k ' k) 2k2What does this have to do with the reciprocal lattice?The equations are satisfied if:kII ( k'k)II 2( ha1 * ka2*) a k'k)II a (2h)a * a(2k) a * 21( 1 1 1 2hProve by substitution:Direction of interference maxima determined by vectors of reciprocal lattice:ghk ( ha * ka*) T *21 2 aLecture 3 7Energy and momentum conservationRecall: energy is conserved in an elastic collision:2 2 kE 2m2 2k k'or k2II k2 k'k'2IIParallel momentum is conserved in diffraction:122 ' kII kII ghk; where ghk 2( ha1* ka2*) g 2( hb * kb*)hk substrate overlayerk k IIk the LEED pattern is an image of the surface reciprocal netAside: Ewald sphere – a graphical solution to interference eq.Lecture 3 8Lecture 3, January 21, 2013 4

Physics 9826b3.4 Analysis of a simple diffraction patternSketch of diffraction pattern (reciprocal lattice):OverlayerpeaksReal space structure:Substratepeaks• Relations between overlayer and substratereciprocal lattices• Construct real-space substrate lattice• Next: construct overlayer lattice based onc(4 2)Lecture 3 9knowledge of a 1 and a 2Lecture 3 103.5 Applications and Complications of LEEDApplications of LEED:1. Surface order and cleanliness – most common2. Surface atomic structure – need theory3. Step density – get step height/density from angular beam profile (SPALLED)4. Phase transition in overlayers - structure may undergo transition withchange in coverage or T5. Dynamics of ordering, disordering, growth, phase transitions - time evolutionComplications and other aspects of LEED:1. Electron beam damage – sensitive molecular adsorbates2. Domain structure– if two domains with different structure coexist easy to distinguish– sometimes difficulties exist (e.g., 3 domains of p(2x1) on fcc(111) = (2x2)3. Transfer width (for real experimental system ~0.01, E~0.5eV)- the dimensions of ordered regions on the surface are limited to the “transferwidth” (Woodruff, p.36-37)Lecture 3, January 21, 2013 5

Physics 9826b3.6 Theory of LEED IntensitiesPositions of LEED spots give information only about surface geometry (unit cell)Need intensity analysis for determining positions of overlayer atomsKinetic Theory – “single scattering” theoryBasic assumption: electron undergoes only a single scattering event wheninteracting with ion coresOther assumptions:e Incident wave can be described by plane wave:ik ri o ik re i(After scattering, the wave from a single atom is S o f k,k ' eR R jRk’For a 2D array: I k k') Rj I FStructure factor: F SphericalwaveS22j1 Gf e i(k ' k) Rj(sum over unit cell)Lecture 3 11j2AtomicscatteringfactorInterferencefunctionPhase shiftcaused by pathdifferencebetween atomand originResults of Kinematic TheoryHow does intensity vary?- need to fulfill “Bragg condition”- no explicit E dependence, except for atomic scattering factor slow as E- theory predicts Bragg peak positions, but poorly estimates relative intensitydExample: get interference because of(i) in-plane (2D) scattering(ii) between-plane scattering = d (1 + cos ) = n lNeed multiplescattering approach!!!Lecture 3 12Lecture 3, January 21, 2013 6

Physics 9826bMultiple Scattering TheoryHighly computational; includes- ion core scattering- multiple scattering- inelastic scattering- temperature effectsEach atom experiences a flux that includes the incident fluxand contributions from the other atoms• Direct (transform of diffr. int.) – highly debatable?!• Assume a trial structure, do multiple scattering calculations,use R-factor analysis(or Pendry factor; the smaller the better!!!)Lecture 3 133.7 Reflection High-Energy Electron Diffraction (RHEED)Elements of RHEED: high energy electrons (5-50keV); grazing incidence oncrystalline sample; often in Molecular Beam Epitaxy (MBE) setupscf. Luth, pp.201-209RHEED pattern consists of streaks and spots (some controversy about causes of streaks)- streaking: diffraction from perfect planes, and nearly “flat” Ewalds sphere;- spots: surface roughnessLecture 3 14Lecture 3, January 21, 2013 7

Physics 9826bExample RHEED patternsImportant use:RHEED oscillations for MBE tomonitor growth conditionsLecture 3 15Comparison of Experimental Specs for LEED and RHEEDRange of elements: all, but not element specific bothDestructive:no, except in special cases of electron-beam damage bothDepth probed: 4-20Å (LEED) 2-100Å (RHEED)Detection limits:0.1ML; atomic positions to 0.1Å bothResolving power:typically 200Å; best systems 5mm bothLateral resolution:typically 0.1mm; best systems ~10mm (LEED)200mm x 4mm; best systems 0.3nm x 6 nm (RHEED)Imaging capability:no; need special instruments – LEEMMain uses:analysis of surface crystallography (LEED)monitoring surface structure, in-situ growth (RHEED)Cost:

Physics 9826b3.8 Low Energy Electron Microscope (LEEM)LEEM history• 1962 Invention by Ernst Bauer• 1985 Operational LEEM instrument (Telieps and Bauer)• 1991 IBM LEEM-I (Tromp and Reuter)• 1998 IBM LEEM-II• 2006 SPECS FE-LEEM P90Lecture 3 17Phase contrastLecture 3 18Lecture 3, January 21, 2013 9

Physics 9826bIBM LEEM IIAfter diffraction, electrons areaccelerated from ~ 1 eV to ~10,000 eVSurf. Reviews and Lett. 5 (1998) 1189Lecture 3 19LEEM operating parameters• 0 - 100 eV electron energy• field of view 1 - 100 µm• 5 nm resolution in plane• vertical resolution: atomic steps, 0.1 nm• in situ growth, etching• RT – 1200 o C extremely useful tool to study crystal growth in situ* From R.M TrompLecture 3 20Lecture 3, January 21, 2013 10

Physics 9826b3.9 Scanning Electron Microscopy (SEM)Scanning electron microscopy (SEM)- topology, morphology, chemicalinformation (BSE and EDX)• 0.5-1000keV electron energy• field of view 0.1 - 100 µm• 5 nm resolution in plane• Magnification 10x – 300,000x• Typical operating pressure

Physics 9826bSEM/e-beam lithography in the NanofabThe e-beam lithography system (right) isa LEO 1530 field emission scanningelectron microscope (FE-SEM) fitted witha laser interferometer controlled stage(middle right).The micrograph (bottom right) shows a square array of300nm holes on 700nm pitch written in PMMA on Si.Also shown is an array of Cr dots on Si patterned by e-beam lithography and liftoff (below).http://www.uwo.ca/fab/Lecture 7 23Schematic diagram of SEMFilament (cathode): free e’s bythermionic emission of W, LaB 6Wehnelt Cylinder: focuses the e-beam and stabilizes beam currentAnode Plate: maintains the HVdifference between the anode and thecathode, and accelerates the freeelectrons down the columnCondenser Lens: reduces thediameter of the electron beam toproduce a smaller spot sizeScan Coils: electromagnetically rasterthe e-beam on the surfaceFinal Objective Lens: focuses the e-beam on the surface; the smallest spotis about 5 nm (~ 1nm with a FI source)Detectors: within the scope chamber,but not part of the column are theLecture 7 detectors24Lecture 3, January 21, 2013 12

Physics 9826bSEM DetectorsEverhart-Thornley (E-T) detectorEDX spectrometerLecture 7 25Contrast of secondary electron micrographContributions from (a) sample topography and (b) compositional contrastQ: Why do the backscattered electron micrographs, rather than secondaryelectron micrographs reveal the compositional contrast?Lecture 7 26Lecture 3, January 21, 2013 13