Electron Energy Loss Spectroscopy EELS: Large signal for Z< 33 90% collection efficiency Spatial resolution is 0.1-1 nm composition and bonding information needs very thin samples (< 50 nm) EDX: Low x-ray yield for Z<10, good for detecting heavy elements Poor (1-3%) collection efficiency Spatial resolution is 1-10 nm composition only samples can be up to 100 nm (if you don t mind absorption corrections) Reading and References: Fingerprints of most materials Muller, Singh and Silcox, Phys Rev B57, 8181 (1998) Theory of EELS as a LDOS V. Keast et al, (review of EELS) 1
Discrete Energy Spectra for Atoms Unique spectrum for every atom used to identify unknown materials KE=ΔE-E K 3000 M 5 M 4 M 3 M 2 M 1 L 3 L 2 L 1 K 3d 5/2 3d 3/2 3p 3/2 3p 1/2 3s 1/2 2p 3/2 2p 1/2 2s 1/2 1s 1/2 Binding Energy (ev) 2500 2000 1500 1000 n=1 n=2 n=3 n=4 E 0 E 0 -ΔE Measured by EELS (Electron Energy Loss Spectroscopy In a TEM) 500 n=5 0 0 20 40 60 80 100 Atomic Number Z 2
Electron Shells and Transitions 1) Ionization 2a) X-ray Emission 2b) Auger electron KE=ΔE-E K KE = * ( E E ) K L M 2 1 M 5 M 4 M 3 M 2 M 1 3d 5/2 3d 3/2 3p 3/2 3p 1/2 3s 1/2 M 5 M 4 M 3 M 2 M 1 3d 5/2 3d 3/2 3p 3/2 3p 1/2 3s 1/2 hω = E K E L2 M 5 M 4 M 3 M 2 M 1 3d 5/2 3d 3/2 3p 3/2 3p 1/2 3s 1/2 L 3 2p 3/2 L 3 2p 3/2 L 3 2p 3/2 L 2 2p 1/2 L 2 2p 1/2 L 2 2p 1/2 L 1 2s 1/2 L 1 2s 1/2 L 1 2s 1/2 K 1s 1/2 K 1s 1/2 K 1s 1/2 E 0 E 0 -ΔE Measured by EELS (Electron Energy Loss Spectroscopy In a TEM) Measured by EDS/XRF (X-ray fluorescence in an SEM or TEM) Measured by AES (Auger Spectroscopy in a SAM, Leaves atom doubly charged) 3
O 6 O 5 O O 4 N M L Electron Shells and Transitions O 8 O 7 5f 7/2 5f 5/2 O 3 O 2 O 1 N 7 4f 7/2 N 6 4f 5/2 N 5 N 4 N 3 N 2 N 1 M M 5 4M M3 2 M 1 L 3 L 2 X-ray lines Lα 1 Lα 2 Lβ1 Lβ 2 Lβ 5 Lγ 3 5d 5/2 5d 3/2 5p 3/2 5p 1/2 5s 1/2 4d 5/2 4d 3/2 4p 3/2 4p 1/2 4s 1/2 3d 5/2 3d 3/2 3p 3/2 3p 1/2 3s 1/2 2p 3/2 2p 1/2 EELS Edges N 6,7 N 4,5 N 2,3 N 1 M 4,5 M 2,3 M 1 L 3 L 2 L 1 K Electron State Notation Principal quantum number Angular momentum state (l) 4 f 5/2 J=L+S quantum number (jj coupling) l=0 s l=1 p l=2 d l=3 f L 1 2s 1/2 Κα 1 Κα 2 Κβ 1 Κβ 3 Κβ 2 K SHELL K EELS transitions are named by the initial state (e.g. 2p 3/2 [3s 1/2 3d 5/2,3d 5/2 ] is just L 3 ) EDX transitions are named by the initial core-hole state, the emission line, and the line strength (1 is the strongest, ) (e.g. 3d 5/2 1s 1/2 is Kα ) 1 AES transitions are named by initial ionization, filling shell, shell of ejected electron (e.g. KL 2 L 3 ) 1s 1/2
Electron Energy Loss Spectrum of SiO 2 Each edge sits on the tails of the preceding edges -> Backgrounds are large 10 8 Intensity (arb. units) 10 7 10 6 10 5 Incident Beam Valence Excitations Si L edge E 0 O-K edge L 3 L 2 L 1 K 2p 3/2 2p 1/2 2s 1/2 1s 1/2 E 0 -ΔE 10 4 0 100 200 300 400 500 600 700 Energy Loss (ev) 5
X-Ray Emission Spectra X-ray Emission Energies for all elements can be found in the X-ray Data Booklet, which is available on line at http://xdb.lbl.gov/section1/sec_1-2.html M 5 M 4 M 3 M 2 M 1 3d 5/2 3d 3/2 3p 3/2 3p 1/2 3s 1/2 L 3 L 2 L 1 2p 3/2 2p 1/2 2s 1/2 K 1s 1/2 X-ray Emission Spectra from Williams and Carter, Electron Microscopy 6
Auger Electrons a small signal on the tails Of the secondary electron peak E M 1 L 3 L 2 L 1 2p 3/2 2p 1/2 2s 1/2 K 1s 1/2 Cross section decreases with Energy multiply by E to compensate 2 nd electron background is slowly varying with E, take derivate to remove it -> Easier to see peaks in E. dn(e)/de (price paid: noise is also amplified) From the Auger tutorial on the Charles Evans website http://www.cea.com/cai/auginst/display.htm 7
Auger vs X-ray Yield 1 ~10 kev Fluorescence Yeild 0.8 0.6 0.4 0.2 ω K ω Auger 0 0 20 40 60 80 100 Z Below ~10 kev, Auger emission dominates and very few x-rays are emitted. X-ray fluorescence is most efficient for detecting high-z elements Eqn 3.13 of Rev. Mod. Phys. 44, 716-813 (1972) 8
X-Ray Absorption e - X-ray detector φ t X t =t/sinφ I esc = I prod exp( -t /λ) (φ should be large to minimize attenuation) X-ray attenuation length λ ~ 10 nm 1 μm Low energy x-rays are strongly attenuated must be corrected for to get quantitative compositions 9
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Bremsstrahlung Radiation + X-rays absorbed in sample Cuts off lower energies e - Accelerating charge produces radiation In thicker films and solids, there is a continuum background to the x-ray spectrum 11
EDX generated by x-rays (XRF) and electrons (SEM) Xray: No vacuum No charging No Bremsstrahlung 100 μm resolution Electron: 0.5 μm resolution Better low energy excitation efficiency Bremsstrahlung 12
Losses in the X-Ray Detector Strong Attenuation for low Z Williams and Carter, Vol 4 13
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Comparison EDS Low collection efficiency (small solid angle) Good peak/background Good for high-z elements SEM (~500 nm) or TEM (~10 nm) Stray x-rays in the column can be mistaken for trace elements EELS TEM only & thin samples High collection efficiency (~90%) Poor peak/background (esp in thick samples) Best for low-z elements (large signals) Bonding information for Z<33 High spatial resolution (0.1 1 nm) 15
Scanning Transmission Electron Microscopy 200 kv Incident Electron Beam (ΔE=0.1-0.5 ev) 1 atom wide (0.2 nm) beam is scanned across the sample to form a 2-D image ADF Signal Er M 4 Edge x y 3 Å Elastic Scattering ~ "Z contrast" 0 0.5 1 1. Distance (nm) Annular Dark Field (ADF) detector Electron Energy Loss Spectrometer Increasing energy loss Single atom Sensitivity: P. Voyles, D. Muller, J. Grazul, P. Citrin, H. Gossmann, Nature 416 826 (2002) U. Kaiser, D. Muller, J. Grazul, M. Kawasaki, Nature Materials, 1 102 (2002) 16
Energy Filtered Electron Microscopy image 1 energy at a time (as opposed to STEM 1 pixel with all energies at a time) 200 kv Incident Electron Beam ΔE = 100 500 mev Point Spread Function 10 sec. acquisition time Specimen 150 mv Entrance aperture -1.0-0.8-0.6-0.4-0.2 0.0 0.2 0.4 0.6 0.8 1.0 Energy (ev) Magnetic prism CCD Camera Energy-Selecting Slits 17
Energy Filtered TEM: Image at a fixed Energy Loss Ratio maps cancel most of the diffraction contrast (elastic scattering is same for both energy losses) Ti L edge ratio map (post/pre) 18
Energy Loss Spectrum of a 100 kev Electron Beam in Si Plasmon mean free path λ~ 120 nm 10 5 Zero Loss Peak 17 nm 210 nm t/λ = 0.14 t/λ = 1.75 10 4 CCD Counts 1000 100 1 st Plasmon 2 nd Plasmon 3 rd Plasmon 10 0 20 40 60 80 100 Energy Loss (ev) In the thinner film (17 nm thick), only single scattering has occurred, and there is a single peak at the plasma energy (~17 ev) this is also called a plasmon. In the thicker film (210 nm), a significant portion of the electron beam has undergone inelastic scattering many times. In each scattering event it loses ~ 17 ev so those electrons that have scattered twice show up as a peak at 2x17 = 34 ev, those that scattered 3 times at 3x17=51 ev and so on. 19
Effect of Thickness on the Si L 23 Edge at 100 kv CCD Counts 5 10 4 3 10 4 10 4 8000 6000 4000 4 th Plasmon 5 th Plasmon 6 th Plasmon Si L 2,3 Edge 210 nm 174 nm 148 nm 114 nm 78 nm 38 nm 17 nm Increasing Thickness Plasmon Mean Free Path in Silicon λ p 120 nm. When the thickness t/λ p > 1 multiple plasmon scattering dominates the EELS spectra. At 210 nm, a ratio map at the 100 ev will measure the 6th plasmon, not the Si L edge! 2000 50 100 150 200 Energy Loss (ev) Moral: EELS needs thin samples! 20
Effect of Increasing the Illumination Angle ( (α) (by reciprocity: increasing the collector angle in STEM) α<<θ obj α θ obj Phase contrast No Phase contrast Diffraction contrast Diffraction contrast 31 mr 10 2 mr α>>θ obj No Phase contrast No Diffraction contrast 80 3 mr ADF 4 30 nm The incoherent BF image is the complement of the ADF image 21
Effect of Increasing the Illumination Angle (by reciprocity: increasing the collector angle in STEM) 1.5 mr 80 mr Si 17 ev (Si Plasmon) Si 23 ev (SiO2 Plasmon) SiO 2 Coherent Illumination: Condenser < Objective Aperture Thickness fringes Fresnel Contrast Incoherent Illumination: Condenser > Objective Aperture Diffraction contrast suppressed 22
Core-Level Electron Energy Loss Spectroscopy E Fermi EELS measures a local density of states partitioned by site - as the probe is localized, element - the core level binding energy is unique Dipole transition: s p - probes the conduction band - provides local electronic information O 1s 23
EELS Theory Some subtleties as to which density of states is measured see Muller, Singh and Silcox, Phys Rev B57, 8181 (1998) This is very important if you want to measure charge transfers (you don t there is no unique definition). Dipole selection rules: Δl = ± 1, Δj = 0, ± 1 K-edge: 1s p L-edge: L1 : 2s p; L2, 3 : 2 p d, s; 24
EELS as a Local Density of States (LDOS) If we project the total density of states on to a local set of states and examine the overlap of each eigenstate with the local state. The probability of finding an electron in the eigenstate at site is, so the local contribution to the density of states from site is The basis set chosen for { i } is not unique, so the amount of charge at site i is also not Unique. (e.g. a sphere of arbitrary size). For EELS, the oscillator strength is proportional to a LDOS with a basis set of Muller, Singh and Silcox, Phys Rev B57, 8181 (1998) 25
Don t compare EELS to calculations of charge transfer The charge-transfer problem: Since there is no unique definition of a local density of states, there is also no unique definition for charge transfers between local states To caution against directly comparing EELS whitelines against calculated charges, we show the charge transfer from an atomic sphere surrounding a Ni atom in the B2 NiAl compound, calculated in the LMTO-ASA approximation. The choice of the relative sphere sizes for the Ni and Al sites are a matter of computational convenience, rather than being a physically measurable property of the system. By altering the ratio of the Ni/Al sphere sizes we can change not only the magnitude, but also the sign of the Ni-Al charge transfer. Muller, Singh and Silcox, Phys Rev B57, 8181 (1998)
Dipole Approximation is good for Core Level EELS (except when the probe < core orbital size can happen during channeling) K Edge 1s->p dipole 1s->s monopole 1s->d quadrupole L Edge 2p->d dipole 2p->p monopole 2p->s dipole P. Rez, Ultramicroscopy 28 1989 16-23 27
Dipole Approximation is good for Core Level EELS Si L 23 edge for a 100 kev incident electron Collection angles of 12.5 mrad (q=20 nm -1 ), The solid line is the full calculation, the dashed line is the dipole contribution, and the light dotted line is the nondipole 2p-3p term Collection angles of 100 mrad (q= 167 nm -1 ) P. Rez, Ultramicroscopy 28 1989 16-23 28
EELS Fine Structure is Visible in Individual Spectra Ti L 2,3 Edge 0 Intensity (a.u.) La-M 4,5 Distance (nm) 1 2 3 Ti-L 2,3 Mn-L 2,3 440 450 460 470 480 490 500 400 500 600 700 800 Energy Loss (ev) Energy Loss (ev) 29
Chemical Imaging in 2D (Integrated counts above background) La Ti EELS map Of LaMnO 3 /SrTiO 3 recorded on the Nion SuperSTEM Mn 28 seconds live time (10 seconds overhead) 30
EELS Fine Structure of Transition Metals Ground state interpretation of spectra as a LDOS (ignore core hole) EELS edge L 2 d DOS L 3 L 2 L 3 Pearson, Fultz and Ahn, Phys Rev B47 (1993) 31
EELS Fingerprints of Oxidation States Leapman, Grunes, Fejes,Physical Review B26 614-635 (1982) Ti L 2,3 Edge Cu L 2,3 Edge 32
Fingerprint EELS from our website www.weels.net : EELS spectra of common semiconductor materials Identify the local environment from the shape of the spectrum (e.g. Cu vs. CuO vs. Cu 2 O) 33
Interpreting Experimental Data 1400 1400 1200 1200 1000 1000 Intensity (a.u.) 800 600 400 Is this real? Intensity (a.u.) 800 600 400 200 200 0 0-200 530 540 550 Energy (ev) -200 520 530 540 550 560 570 Energy (ev) Always show the pre-edge background. Gives noise level & confidence in background subtraction 34
What Happens when Al is added to Ni x Al 1-x? 50.0 40.0 30.0 Ni L 2,3 Edge After Deconvolution with Low Loss Ni Ni 3 Al NiAl Area (barns) 514±20 508±20 508±20 20.0 B 10.0 A 0.00 845 850 855 860 865 870 875 880 885 Energy Loss (ev) The Total Areas under each curve are very similar (no charge-xfer). Ni d is broadened, shifting states from the main band, to the tails increased Ni-Al bonding (Ni p-d hybridization) 35
EELS: Final State Effects Initial State Electrons relax to screen core hole metal Excited electron couples to core hole insulator δe ex δe rel δe rel 36
Comparison of the Ni L 3 Edge measured by EELS with the calculated, unoccupied d DOS of Ni 0.20 NiAl Measured NiAl Calculated 0.10 G.O.S. (e - /ev/atom) 0.00 0.20 0.10 0.00 0.30 Ni 3 Al Ni Ni 3 Al Ni More Ni-Al bonds 0.20 0.10 0.00-5 0 5 Energy (ev) 10 15 0 5 10 15 Energy (ev) [D.A. Muller, D.J. Singh, J. Silcox, P.R. B57 (1998) 8181] 37
Comparison of the Measured Si-L L Edge with ab-initio Calculations Intensity (arb. units) 0.2 0.15 0.1 0.05 Experiment Z+1 (core hole) (ground state) 0 0 5 10 15 20 Energy (ev) Strong core-hole effects on the silicon-l Edge (it does not reflect the ground state) Neaton et al, Phys. Rev. Lett. 85 1298(2000) 38
When are core holes important? When you have good energy resolution (<1 ev) When screening is poor Metals (small), semiconductors(medium), ionic (huge) The effect is larger on anions than cations More noticeable in nanoparticles and clusters than bulk Batson s Rule: core hole effects are more pronounced when the excited electron is confined near the core hole. (It shouldn t work, but it does.) Atoms surrounded by strong scatterers (often nodeless valence wavefunctions 1s, 2p, 3d ) (e.g Si in SiOx, Al in NiAl, TiB 2 out of plane) 39
Core Hole Lifetimes Resolution Limits: 0.1 ev Z~14 (Si L 3 Γ i =0.15 ev) 0.2 ev Z~21 (Sc L 3 Γ i =0.19 ev) 0.3 ev Z~25,14 (Na K Γ i =0.30 ev) Better than 0.1 ev is still useful for valence EELS -image electrically active defects, - -Doesn t require sub nm probe Krause and Oliver, J. Phys. Chem. Ref. Dat. 8 (1979) 329. 40
20 ev above the edge, no feature can be sharper than 3 ev 41
XAS of the Si L 2,3 Edge at 15 mev Energy Resolution 50 mev Photon Energy Photon Energy Vibrational modes are important at 100 mev resolution Core hole lifetimes are measured at 50-80 mev (~ 50 100% larger than theory) R. Puttner et al, Phys. Rev. A57 297(1998). 42
XAS of N-K in N 2 N 2 gas N 2 in Oxidized TiAlN Instrument resolution is 70 mev Vibrational states are resolved, but core-hole lifetime depends on the environment F. Esaka et al, J. Elec. Spectr. and Rel. Phen. 88-91 (1998) 817-820 43
Calculation of the Final States Cluster Methods: good for defects & clusters, often easier to run Muffin-Tin Potential (OK for Metals, bad for semiconductors) FEFF7 no self-consistency: must guess charge transfers FEFF8 self consistent: good for metals Full Potential FDMNES no self-consistency, but it can input potentials from WIen2k Bandstructure methods: (3D periodic structures or supercells) Almost all bandstructure codes are self-consistent now Muffin-Tin Potential LMTO good for close-packed structures, esp. metals Full Potential FP-LAPW Wien2k easy to calculate matrix elements & core hole effects Plane-wave codes (faster and less prone to artifacts than APW codes ABINIT (free, open-source and downloadable from abinit.org) VASP (commercial) CASTEP (commercial, fancy user interface) 44
The Muffin-Tin Approximation This is a shortcut that makes it easier to solve Schrödinger's equation by approximating the potential From Joly A good approximation for close-packed structures like metals (DOS inside spheres looks like an EELS final states) 45
Wien2k vs FEFF8 TiC 0.8 N 0.2 expt FEFF8 Wien2k expt FEFF8 Wien2k 46
Many-Body Calculations Strongly-correlated systems, and materials with large core-hole effects cannot be calculated using DFT codes. The options are limited GW : Correct bandgap, but only a few atoms/supercell Configuration-Interaction (CI): very accurate for 1-6 atoms -good for transition metal oxide clusters Multiplet: (de Groot, van der Laan) single-atom in a crystal field good for transition metal oxide crystals. - like CI, except it has adjustable parameters 47
Many-Body Corrections for the Ti-L Edge in SrTiO 3 Intensity (arb. units) t 2g 450 455 460 465 470 475 Energy (ev) a a L 3 e g t 2g L 3 L 2 L 2 e g Single Particle Theory: (Ogasawara, PRB 2001) includes core-hole self-consistently L 3 : 2p 3/2 Ti 3d (t 2g, e g ) L 2 : 2p 1/2 Ti 3d (t 2g, e g ) Wrong oscillator strengths and positions Configuration-Interaction Theory: (Ogasawara 2001) 4 main peaks analogous to SP theory Peak a is multiplet of the 2p 3/2 t 2g No lifetime broadening (gaussian used) 2p spin-orbit splitting is too small Experiment: XAS: van der Laan 1990 (2 ev too high) EELS: Muller 2002 100 mev resolution 50 mev absolute accuracy 48
Spatial Resolution in EELS For E 0 =100 kev electrons, λ=0.037 Å, v=1.64x10 8 m/s 2 d dωde For dipole scattering, the cross section is α f r i ρ ( ΔE) with the characteristic angle at energy loss ΔE of 2 θ 1 + θ σ 2 E 2 E ΔE 2E 0 By analogy with the Raleigh resolution criterion, we might expect a resolution of r inel λ θ (this would assume that all the scattering lies inside θ E, which is not true). E θ f For an energy loss ΔE=20 ev, we get r inel = 6. 5 nm 49
How Delocalized is an EELS Signal? Diamond Nanoparticle in ZnS 18 ev 25 ev 34eV An upper limit to the cutoff angle is the maximum momentum transfer in the small-angle approximation. This is also the peak of the Bethe Ridge at Which gives Muller & Silcox, Ultramicroscopy 59 (1995) 195. r min θ B 2θ E λ E ΔE 0 or 0.26 nm for ΔE=20 ev which is a little too small. The real answer seems to lie between r inel and r min (and closer to r min ) 50
Dipole Theory Calculations of Inelastic Resolution 4 3 θ θ E R. F. Egerton, Journal of Electron Microscopy 48 (1999) 711. 51
Comparison of Dipole and Full Atomic Calculations For a free atom, agreement is ~10% or better. Crystal channeling could cause problems dipole dipole 52
Comparison Nickel Oxide EDS Low collection efficiency (small solid angle) Good peak/background Good for high-z elements SEM (~500 nm) or TEM (~10 nm) EELS TEM only & thin samples High collection efficiency (~90%) Poor peak/background (esp in thick samples) Best for low-z elements (large signals) Bonding information for Z<33 High spatial resolution (0.1 1 nm) 53