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Quick DFT tour of Electron Energy Loss Spectrum (EELS)

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Transmission electron microscopy (TEM) is important tools for surface and interface study. Electron Energy Loss Spectroscopy (EELS) belongs to the TEM family, I added some know-how about DFT simulation of EELS spectrum. I showed some tricks and caution which I found important. Please send me a note for questions and comments

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Quick DFT tour of Electron Energy Loss Spectrum (EELS)

  1. 1. By Shruba Gangopadhyay Email: shruba@gmail.com
  2. 2. Basics of EELS  Material exposed to a beam of electrons with a known, narrow range of kinetic energies  Electrons will undergo inelastic scattering, which means that they lose energy  Inelastic interactions include  phonon excitations,  inter and intra band transitions  plasmon excitations  inner shell ionizations 2
  3. 3. Atomic & Electronic Structure  STEM + EELS makes essential connection between physical & electronic structure, both at atomic resolution Electron Energy Loss Spectrometer Annular Dark Field (ADF) detector y x Atomic Diameter Electron Probe Increasing energyloss  We can have an estimate of beam energy ranges from  http://people.ccmr.cornell.edu/~davidm/WEELS/index.html  http://pc-web.cemes.fr/eelsdb/index.php?page=search.php
  4. 4. EELS …(Theory) THEORY OF EELS : The EELS (and XAS) spectral shape is given by the Fermi golden rule. The core electron is excited to an empty state, where at the edge the lowest empty state (allowed by the selection rules) is reached. As such, one essentially probes the empty density of states in the presence of the core hole. Calculations to obtain a quantitative picture of the empty states can be performed with DFT based codes. A double differential scattering cross-section is calculated by summing over all possible transitions between initial and final states, each described by a Fermi’s golden rule. 4
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  6. 6. When we need core hole approximation  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, TiB2 out of plane) 6 In Wien 2k we can only simulate electron loss near- edge structure (ELNES) ”: features in the spectrum with energy loss E = Ec to Ec + 50 eV (by definition). It contains information on local density of empty states, oxidation state.
  7. 7. How to simulate Core Hole in Wien2k No core hole (= ground state, sudden approximation) 􀂄 Z+1 approximation (e.g., replace C by N) 􀂄 Remove 1 core electron, add 1 electron to conduction band 􀂄 Remove 1 core electron, add 1 electron as uniform background charge More localized the core hole, the bigger the error 7
  8. 8. How to simulate EELS in in Wien2k (TELNES) Construct a supercell and perform an SCF (need good amount of K points) If excited states required prepare another input by reseting energy range and recalculate valence bands Compute Valence electron densities from eigenvectors Calculate eigenvalues and corresponding partial charges Prepare input for EELS use of beam energy and other angular parameters This results : The differential cross section is either a function of energy (ELNES ( the output of Wien2k) integrated over impulse transfer); or a function of impulse transfer (ELNES integrated over energy loss E), which shows the angular behavior of scattering. 8
  9. 9. Available softwares and pros and cons Wien2k Quantum ESPRESSO (External suite SaX) Telnes (code) SaX external code Double differential scattering cross section on a grid of energy loss Macroscopic dielectric tensor within the Random Phase Approximation with or without excitonic effects as a function of energy Computationally less expensive Very expensive Applied to various systems Not too many published papers Band structure codes PARATEC (Cabaret et al.,2007;Gaudryetal.,2005), PWSCF(Cabaret et al.,2010;Juhin et al.,2010), CASTEP(Gao et al.,2008) WIEN2K(Schwarz et al., 2002), Real space multiple scattering codes FDMNES (Joly, 2003) FEFF(Rehr andAlbers,2000) Molecular DFT codes STOBE(Kolczewski andHermann,2005) ORCA (George etal.,2008) 9
  10. 10. Literature Review As per my understanding the advantages of Wien2k is Can handle large system No need to worry about core hole pseudopotentials Applied to TM and Lanthanide including Magnetic transitions Parallel implementation Option of using relativistic correction User friendly interface for generating input files Extremely active user forum 10 Wien2k VO2 (crystal), LiMn2O4, TiO2, ZrO2, Nb1-xMgxB2, LixTiP4 (x=2- 11), LiK edge in Li, Li2O, and LiMn2O4 , Si layers ferroelectric transition in BaTiO3 ………………………………………… TiC , TiN Quantum ESPRESSO Boron, Nitrogen doped graphene, different phases of Al2O3 VASP No direct implementation (derived from DOS), C60
  11. 11. Simulated EELS for K edge EELS of Carbon in TiC using (2x2x2) supercell 1000 k points 100 k points I did not use any core hole approximation in this calculation 11
  12. 12. Sources  Wien2k manual, Tutorial from 2007 PSU workshop  SaX manual  Presentation from David Mullers summer school pdf  Calculations are performed in NERSC using Wien2k v10.1 and Telnes2 12

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