Electron-Matter Interactions

Transcription

1 Electron-Matter Interactions examples of typical EM studies properties of electrons elastic electron-matter interactions scattering processes; coherent and incoherent image formation; chemical contrast; electron diffraction inelastic electron-matter interactions analytical electron microscopy: generation of X-rays; electron energy loss spectroscopy; plasmons, phonons, cathodoluminescence scanning electron microscopy: secondary electrons beam damage Why do Stinging Nettles Sting? Scanning electron microscopy image of a leaf surface Examples Hollow needles contain formic acid 1

2 How do crystals look like? Shape? SEM images of zeolithes (left) and metal organic frameworks (MOF, right) Examples: electron microscopy for catalyst characterization Was Ötzi a Smoker? TEM Image Elemental Distribution Image Examples FELMI-ZFE Graz 2

3 Catalyst: Pd and Pt supported on alumina: Size of the particles? Alloy or separated? STEM + EDXS: Point Analyses Al C O Pt Pd Cu Pt Pt C Al HAADF-STEM image O Pt Pd Cu Pt Pt Examples What is the Structure of Aperiodic Compounds like? Examples Dodecagonal quasicrystal in the system Ta-Te 3

4 Electron Microscopy Methods (Selection) STEM Electron diffraction HRTEM X-ray spectroscopy SEM Examples Properties of Electrons Dualism wave-particle De Broglie (1924): = h/p = h/mv : wavelength; h: Planck constant; p: momentum U acc kv Rel. pm Mass x m 0 v rel x 10 8 m/s Electron Rest mass of an electron: m 0 = x kg Speed of light in vacuum: c = x 10 8 m/s 4

5 Interactions of Electrons with Matter SEM EDXS (EDX, EDS), WDS, EPMA AES SEM elastic scattering: TEM, HRTEM, STEM, SAED, CBED Electron-matter interactions inelastic scattering: EELS, ESI Interactions of Electrons with Matter Incident electrons with energy E 0 pass through a sample or are scattered without energy transfer. E el = E 0 Inelastic interaction Transfer of energy from the electron to the matter, causing various effects, e.g., ionization. E el < E 0 Electron-matter interactions 5

6 Elastic Electrons-Matter Interactions Elastic scattering of a incoming coherent electron wave: Scattering of electrons by individual atoms scattered waves are incoherent Scattering of electrons by a collective of atoms (crystal) scattered waves are coherent Coherent waves have the same wavelength and are in phase with each other period: time for one complete cycle for an oscillation frequency: periods per unit time (measured in Hertz) Incoherent waves Elastic Scattering of Electrons by an Atom F = Q 1 Q 2 / 4πε 0 r 2 ε 0 : dielectric constant Weak Coulomb interaction within the electron cloud low-angle scattering Strong Coulomb interaction close to the nucleus high-angle scattering or even backscattering Rutherford regime atomic-number (Z) contrast dσ e /dω ~ Z 2 6

7 Interaction Cross Section : effective interaction area /r atom : likelyhood that an interaction will occur R. Peierls: «If I throw a ball at a glass window one square foot in area, there may be one chance in ten that the window will break and nine chances that the ball will just bounce. In the physicist s language this particular window, for a ball thrown in this particular way, has a disintegration (inelastic!) crosssection of 0.1 square feet and an elastic cross-section of 0.9 square feet.» From: Williams & Carter: Transmission Electron Microscopy Interaction Cross Section : effective interaction area /r atom : likelyhood that an interaction will occur = r 2 r elast = Ze/U (r: effective radius) (U: acceleration voltage, e: charge, Z: atomic number, scattering angle) 7

8 Electron Scattering Monte-Carlo Simulations MC-Demo.ex VB40032.DLL Scanning Electron Microscopy and X-Ray Microanalysis J. Goldstein, D. Newbury, D. Joy, C. Lyman, P. Echlin, E. Lifshin, L. Sawyer, J. Michael, Kluwer Academics/Plenum Publishers, 3 rd Ed., New York

9 Exercises: Monte-Carlo simulations Simulate the electron trajectories for (a) 100 kv and (b) 300 kev (typical voltages for TEM) through 100 nm thick foils of Al, Fe, and Au. Note the beam broadening and the number of back-scattered electrons. Make the same calculations for (a) 10 and (b) 30 kev (typical voltages for SEM). If you want to analyze small areas (i.e. with high local resolution), which voltage would you prefer to use in the (a) TEM and (b) the SEM? Interaction Cross Section σ total = σ elastic + σ inelastic Total cross-section Q T : Q T = N T = N 0 T / A Q T t = N 0 T t / A (N: number of atoms, N 0 : Avogadro s number, A: atomic weight, : density) (t: specimen thickness) mass-thickness Alternative description: mean free path = 1 / Q Electron-matter interactions 9

10 Contrast Formation A strong decrease of incoming electron beam intensity occurs if many atoms scatter, i.e. in thick areas if heavy atoms scatter Mass-Thickness Contrast Dark contrast in BF-TEM images appears if many atoms scatter (thick areas darker than thin areas) if heavy atoms scatter (areas with heavy atoms darker than such with light atoms) 10

11 Bright Field TEM Images thin C thick Amorphous SiO 2 on C foil Mainly thickness contrast Au particles on TiO 2 Mainly mass contrast Elastic Scattering of Electrons by an Atom 50 nm Applications HAADF-STEM of Au particles on titania (Z contrast imaging) dσ e /dω ~ Z 2 SEM of Pt particles on alumina: imaging with secondary electrons (left) and back-scattered electron (right) 11

12 Image of rocksalt crystals Crystals A crystal is characterized by an array of atoms that is periodic in three dimensions. Its smallest repeat unit is the unit cell with specific lattice parameters, atomic positions and symmetry. Crystal structure of NaCl Na blue; Cl red Crystallographic data of NaCl - symmetry: cubic; space group: Fm3m lattice parameters: a = b = c = Å = = = 90 atom positions: Na ½, ½, ½ Cl 0, 0, 0 Interference of Waves linear superposition waves in phase constructive interference waves not in phase destructive interference 12

13 Coherent Scattering Scattering of electrons at atoms generation of secondary spherical wavelets Interference of secondary wavelets strong direct beam (0 th order) and diffracted beams at specific angles Coherent Scattering Plane electron wave generates secondary wavelets from periodically ordered scattering centers (atoms in a crystal lattice). Constructive interference of these wavelets leads to scattered beams. Electron Diffraction 0 th order 13

14 Coherent Scattering 1 th order Plane electron wave generates secondary wavelets from periodically ordered scattering centers (atoms in a crystal lattice). Constructive interference of these wavelets leads to scattered beams. Electron Diffraction 0 th order Coherent Scattering 2 th order 1 th order Plane electron wave generates secondary wavelets from periodically ordered scattering centers (atoms in a crystal lattice). Constructive interference of these wavelets leads to scattered beams. Electron Diffraction 0 th order 14

15 Bragg Description of Diffraction Constructive interference between the waves reflected with an angle at atom planes of spacing d occurs if the path difference between the two waves is 2d sin. Bragg law: 2dsin = n Electron Diffraction Electron Diffraction Bragg law: 2dsin = n el = nm (1.97 pm) for 300 kv If d = 0.2 nm = > > 1 Reflecting lattice planes are almost parallel to the direct beam Electron Diffraction 15

16 Electron Diffraction formation of direct beam formation of diffracted beams influence of lattice distance influence of wave length Electron Diffraction on a Lattice Crystal Because of small diffraction angles, the electron beam is parallel to the zone axis of the diffracting lattice planes Diffraction pattern Electron diffraction pattern of a single crystal of Al along [111] 16

17 Coherent scattering Bragg Contrast Diffracted beams lead to a decreased intensity of crystalline areas (crystalline areas appear darker than amorphous areas) BF-TEM Image Increasing thickness ZrO 2 micro crystals; crystals orientated close to zone axis appear dark Mainly Bragg contrast 17

18 Electron Diffraction + High Resolution Transmission Electron Microscopy Nb 7 W 10 O 47 threefold superstructure of the tetragonal tungsten bronze type Inelastic Electron-Matter Interactions Energy is transferred from the electron to the specimen causing: 1. Bremsstrahlung uncharacteristic X-rays 2. Inner-shell ionisation generation of characteristic X-rays and Auger Electrons 3. Secondary electrons low energy (< 50 ev) loosely bound electrons (e.g., in the conduction band) can easily be ejected (application: SEM) 4. Phonons lattice vibrations (heat) ( beam damage) 5. Plasmons oscillations of loosely bound electrons in metals 6. Cathodoluminescence photon generated by recombination of electron-hole pairs in semiconductors 18

19 Bremsstrahlung (Braking Radiation) Deceleration of electrons in the Coulomb field of the nucleus Emission of X-ray carrying the surplus energy E (Bremsstrahlung, continuum X-rays) X-ray intensity theoretical Characteristic X-ray peaks Bremsstrahlung E/keV X rays of low energy are completely absorbed in the sample and the detector Generation of Characteristic X-rays L K 1s 2s 2p 19

20 Generation of Characteristic X-rays 1. Ionization 2. X-ray emission Generation of Characteristic X-rays 1 1. Ionization 2. X-ray emission

21 Electron Configuration of Ti: 1s 2 2s 2 2p 6 3s 2 3p 6 4s 2 3d 2 energy N 4s 4p 3d M 3s 3p L 2s 2p K 1s Electron Configuration of Ti: 1s 2 2s 2 2p 6 3s 2 3p 6 4s 2 3d 2 energy N 4s 4p 3d M 3s 3p L 2s 2p K K K 1s 21

22 Electron Configuration of Ti: 1s 2 2s 2 2p 6 3s 2 3p 6 4s 2 3d 2 energy N 4s 4p 3d M 3s L 3p L 2s 2p K 1s Energy-Dispersive X-ray Spectroscopy (EDXS) Au-Particles on TiO 2 Intensity / counts Ti L Energy / kev 22

23 Possible Transitions Between Electron Shells Causing Characteristic K, L, and M X-rays Generation of Auger Electrons 1. Ionization 2. Electron hole is filled by L 1 electron that transfers surplus energy to another electron (here: L 3 ) 3. Auger electron emission Energy of Auger electron is low (ca. 100 to some 1000 ev). Strong absorption in sample Surface technique 23

24 Cathodoluminescence 1. Incoming electron interacts with electrons in the valence band (VB) 2. Electron is promoted from the VB to the conduction band (CB), generating electron-hole pairs 3. Recombination: hole in the VB is filled by an electron from the CB with emission of surplus energy as photon (CL) incoming electron CB band gap VB e - h energy loss electron Important in semiconductor research: determination of band gaps Inelastic Scattering of Electrons Energy is transferred from the electron to the specimen causing: 1. Inner-shell ionization 2. Bremsstrahlung 3. Secondary electrons 4. Phonons 5. Plasmons 6. Cathodoluminescence Because of energy transfer to the specimen, the electron has a diminished kinetic energy E < E 0 after any inelastic scattering event. 24

25 Electron Energy Loss Spectroscopy Threshold Energy in EELS Threshold (or binding) energy: Minimum energy necessary to transfer an electron from its initial to the lowest unoccupied state This excited electron can carry any amount of excess energy (kinetic energy of ejected electrons) signal is extended above the threshold energy building up an edge 25

26 EELS: Observable Ionization Edges Edge intensity drops with increasing energy loss EELS is limited to the appr. energy range ev Almost all elements have observable edges in this energy range: K edges: Li-Si L edges: Mg-Sr M edges: Se-Os N edges: Os-U Electron Energy Loss Spectroscopy Relationship between the EEL Spectrum and a Core-Loss Exication within the Band Structure N(E) Filled states E F Near edge fine structure Empty states E Extended fine structure ELNES: Electron Energy Loss Near Edge Structure - reflects local density of unoccupied states (DOS) - corresponds to XANES in X-ray diffraction EXELFS: Extended Energy Loss Fine Structure - information on local atomic arrangements - corresponds to EXAFS in X-ray diffraction 26

27 Fine Structures in EELS * sp 2 sp 3 Characteristics of the C_K edge depend on hybridization Characteristics of the Cu_L 2,3 edges depend on oxidation state of Cu Cu 0 : 1s 2 2s 2 2p 6 3s 2 3p 6 3d 10 4s 1 Interactions of Electrons with Matter SEM EXDS (EDX, EDS), WDS, EPMA AES SEM elastic scattering: TEM, HRTEM, STEM, SAED, CBED Electron-matter interactions inelastic scattering: EELS, ESI 27

28 Interaction Volume in Compact Samples Secondary electrons (SE) Low energy < 50 ev (inelastic interactions) Information about topology and morphology Back-scattered electrons (BSE) High energy E 0 (mostly elastic interactions) Morphology and chemical information Electron-matter interactions Cu Z=29 Au (Z=79) Elastic Scattering of Electrons Amount of high-angle scattering or even backscattering of incident electrons increases with increasing atomic number (e. g., scattering cross section Au >> Cu ) decreases with increasing electron energy Monte-Carlo simulations of paths of scattered electrons As a general effect of scattering events, the incoming electron beam is weakened and broadened brightness of the direct beam depends on the material contrast between different materials 28

29 Dependence of Interaction Volume on Electron Energy 10 kev Penetration depth increases with increasing electron energy 20 kev 30 kev Monte-Carlo simulations of electron trajectories in Fe SEM: Dependence on Electron Energy Electron-matter interactions Penetration depth of electrons in matter increases with increasing V acc decreases with increasing atomic number 29

30 Radiolysis Beam Damage Ionization breaking of chemical bonds (e.g., in polymers) Knock-on damage Displacement of atoms in crystal lattice point defects (metals) Phonon generation Charging Specimen heating sample drift, structure destruction, melting Electron-matter interactions Summary no energy transfer coherent scattering on crystals (diffraction) incoherent scattering on atoms energy is transferred from the incident electron to the sample X-rays secondary electrons (low energy SE, Auger electrons) phonons, plasmons, cathodoluminescence Electron-matter interactions 30

31 Explain the following abbreviations. Is the corresponding method based on elastic or on inelastic electron-matter interactions? HRTEM SEM STEM EDXS EELS EFTEM After passing a thin sample, two types of electron beams (namely one scattered into low and one into high angles, respectively) are present besides the direct beam (s. scheme). Which one is more likely caused by elastic and which by inelastic scattering? 31

32 Additional material: Interaction.pdf on Next week: Image Processing Please bring your laptop and download software Digital Micrograph (Gatan) (commercial product; demo version available) ImageJ (National Institute of Health) (public domain software; Java) Links on: Images and DM on: 32