Core level spectroscopy: XPS, XAS, EELS, XES (XSPEC, TELNES)

Transcription

1 Coe level spectoscopy: XPS, XAS, EELS, XES (XSPEC, TELNES) Pete Blaha TU Vienna

2 XPS, coe-level shifts Ionizationpotential of coe-e -, IP= E tot (N) E tot (N-1) gives infomation on chage state of the atom coe-eigenvalues i ae NOT a good appoximation: i =de/dn E Slate s tansition state : coe-eigenvalues i fo half occupancy E secant ~ tangent at N-½ N N-1 occup. -SCF-calculation with and without coe-hole: E tot (N) E tot (N-1) supecells to educe hole-hole inteaction C,N 1s exp.(ev) i -SCF TiC Ti 4 C TiN

3 XAS (XANES), EELS (ELNES), XES: coe electons ae excited into a conduction band Each coe shell intoduces an absoption edge, (they ae indexed by the pincipal numbe of a coe level) K-1s, L 1-2s, L 2-2p 1/2, L 3 -p 3/2 XES: knock out a coe electon, valence electon fills coe hole and hv is emitted L 3 L 2 L 1 K 2p 3/2 2p 1/2 2s 1s SOC coe levels

4 X-ay absoption spectoscopy - XAS Electon enegy loss spectoscopy - EELS X-ay Absoption Nea-Edge Stuctue Extended X-ay Absoption Fine Stuctue Absoption EELS spectum of vaious TM oxides XANES EXAFS Enegy (ev)

5 Diffeence between EELS and XAS

6 XAS vs. EELS: theoy tansition descibed by Femis golden ule between initial (coe) and final (conduction-band) state and the e - o photon double diffeential coss section: E - consevation single diff. coss section momentum tansfe q polaization vecto e

7 dipole appoximation (TELNES3 can also handle non-dipole tansitions + elativistic coections) coe-valence spectoscopies give infomation on the local DOS (because of < coe val >) of angula momentum chaacte l ± 1

8 Final state ule : Final state detemines the spectum: Emission spectoscopy: Final state has filled coe, but valence hole. This is usually well sceened, thus one sees the goundstate. Absoption spectoscopy: Final state has a hole in coe state, but additional e - in conduction band. Coe-hole has lage effect on the spectum electon hole inteaction, excitonic effects.

9 Teating the coe hole within WIEN2k No coe hole (= gound state, sudden appoximation) usually not a good appoximation (maybe in metals?) Z+1 appoximation (eg., eplace C by N) also not vey good Coe-hole (supecell) calculations: Remove 1 coe electon on ONE atom in the supecell, add 1 electon to conduction band Remove 1 coe electon, add 1 electon as unifom backgound chage consides statically sceened e - - h coulomb coelation Factional coe hole (conside diffeent sceening) Explicit teatment of electon-hole inteaction (excitonic effects) using Bethe-Salpete equation (BSE)

10 Final state ule + coe hole: 2x2x2 supecell calculation, with coe hole in one of the Mg atoms. This allows the conduction state to elax (adjust to the lage effective nuclea chage), but also to have static sceening fom the envionment. exp MgO coe hole, no supecell: Z+1 (AlO) goundstate

11 XAS / TELNES in WIEN2k define you stuctue (stuctgen) initialize calculation (init_lapw) un scf-cycle (un_lapw) geomety optimization of you stuctue (min_lapw) geneate supecell (x supecell) initialize supecell stuctue, define coe hole/add valence e - un scf-cycle emove exta valence e - un XSPEC / TELNES3 task

12 XSPEC-task

13 TELNES3 task

14 B-K XANES in h-bn/ni(111) B-K edge in BN and BN/Ni(111) Peobajenski etal, PRB70, (2004): The expeiments contadict ecent DFT calculations by Gad etal. A A

15 aaa Angle dependency of B-K edge in h-bn/ni(111) -bands (they inteact with Ni!) B-p xy B-p z B-p

16 Patial coe hole sceening in the Cu L 3 edge J.Luitz et al., Eu. Phys. J. B 21, 363{367 (2001) 0.5e coehole expeiment without coehole with coehole Unexpected effect of coe-hole!

17 L 2,3 specta: failue of the single paticle appoach In paticula ealy 3d TM-compounds show a non-standad L 2 /L 3 banching atio (1:2) sometimes a completely diffeent lineshape (TiO 2 ) wong SOC o CF splittings utile TiO 2 CaF 2 L 3 L 2 soc exp. exp. CF gound state calc. coe-hole calc.

18 Beyond IPA ab-initio configuation inteaction (solid is appoximated by finite cluste) Y. Kumagai, H. Ikeno, and I. Tanaka, J. Phys.: Condens. Matte 21, (2009). H. Ikeno, F. M. F. de Goot, S. E., and I. Tanaka, J.Phys.: Condens. Matte 21, (2009). H. Ikeno and I. Tanaka, Phys. Rev. B 77, (2008). linea esponse in time dependent DFT (TDDFT) J. Schwitalla and H. Ebet, Phys. Rev. Lett. 80, 4586 (1998). A. L. Ankudinov, A. I. Nesvizhskii, and J. J. Reh, Phys.Rev. B 67, (2003). Bethe- Salpete equation (BSE) E. L. Shiley, J. Electon Spectosc. Relat. Phenom , 1187 (2005). E. L. Shiley, Phys. Rev. Lett. 80, 794 (1998). J. A. Soininen and E. L. Shiley, Phys. Rev. B 64, (2001). W. Olovsson, I. Tanaka, T. Mizoguchi, P. Puschnig, and C. Ambosch-Daxl, Phys. Rev. B 79, (2009). R. Laskowski, P. Blaha, Phys. Rev. B, 81, (2010)

19 fully elativistic electon-hole inteaction (BSE) Bethe-Salpete-equation: L(12;1 2 ) solving a 2-paticle (e - - h) equation of lage dimension ( N v N c N k ~ ) Excitons in LiF ) ( ) ( ), ( ) ( ) ( ) ( ) ( ), ( ) ( ) ( ) ( 2 * * 3 3 * * 3 3,, v d d H W d d H E E H H H H H k c k v ck vk x k c vckv k c k v ck vk di k c vckv kk vv cc k c k v diag x di diag eh eigenvalue diffeence between hole (v) and electon(c) state attactive sceened static Coulomb inteaction W; W~ -1 e-h exchange with bae Coulomb potential v

20 gound-state DOS Ca-L 23 edge in CaF 2 coe-hole calc.(atio 2:1) BSE fo L 2 and L 3 sepaately expeiment BSE with p 1/2 and p 3/2 togethe BSE without diect tem H eh di BSE without exchange tem H eh x

21 L 2,3 edge fo Ca in CaF 2 L 3 L 2 Decomposition of є 2 into the excitation fom p 1/2 and p 3/2 states coss tems suppess the L 3 banch and enhance L 2

22 Ti L 2,3 in utile-tio 2, anatase-tio 2, STiO 3 L 3 L 2 t 2g e g The expeimental Ti L 2,3 edges ae athe well epoduced. intensity atio L 3 /L 2 (not 2:1) t 2g /e g atio (not 3:2) left/ight shoulde in L 3 - e g peak of utile/anatase

23 Ti L 2,3 in STiO 3, decomposition of є 2 Decomposition into excitations fom p 1/2 and p 3/2 L 3 L 2 coss tem suppesses the L 3 banch and enhances the L 2 Decomposition into excitation into the e g and t 2g bands the fist peak of L 2 o L 3 is elated to excitations into t 2g, the second peak is associated with e g the coss tem stongly modifies the atio between these peaks S Ti O t 2g e g

24 3d metal L 2,3 banching atio Ti L 2,3 banching atio in utile-tio 2 (SOC splitting is set to values fom 5eV to 25eV) The size of spin obit splitting is a main facto detemining the banching atio (deviating fom 0.5)

25 fcc Ca, L 2,3 edge L 3 L 2 L 2 L 3

26 Acknowledgement Pactical aspects of unning the WIEN2k code fo electon spectoscopy, C.Hebet, Micon 38 (2007) Acknowledgement: TELNES: P.Schattschneide, M.Nelhiebel, C.Hebet (TU Vienna) K.Joissen (Univ. Washington) BSE: R.Laskowski (TU Vienna) C.Ambosch-Daxl WIEN2k: K.Schwaz, J. Luitz Thank you fo you attention!