Inelastic soft x-ray scattering, fluorescence and elastic radiation What happens to the emission (or fluorescence) when the energy of the exciting photons changes? The emission spectra (can) change. One can usually distinguish easily the following contributions to the spectra: Elastic contribution (same energy as incoming photons). Inelastic features (energy changes and tracks excitation energy). Fluorescence features (at fixed energy). Note: When approaching the Fluorescence threshold, the inelastic scattering features evolve into fluorescence. The spectra in the graph are offset in y-direction for clarity. 6000 5000 4000 Counts 3000 RIXS 153.1 ev XAS TEY PFY calc. 150 155 160 165 2000 1000 155.2 ev 0 140 145 150 155 160 165 Emission Energy [ev]
Emission Energy axis versus Energy loss axis 4000 3d 10 4f 0 3d 9 4f 1 excitations for LaAlO 3 (single crystal): 834.85 ev 851.6 ev 16.3 ev 4000 3000 Counts 2000 1000 819.4 ev 813.1 ev 866 ev 871 ev 866 ev 861 ev 856 ev 851 ev 848.5 ev 846 ev 841 ev 836 ev 831 ev 826 ev 0 760 780 800 820 840 860 880 900 Emission energy [ev] Note that on the new energy loss scale: Energy losses appear at fixed energy. Elastic features appear at 0 ev. Fluorescence features track energy. Electron loss scale: hν loss =hν exc -hν emission 3000 858.9 ev Counts 2000 7.5 ev 853.9 ev 848.9 ev 846.4 ev 843.9 ev 1000 838.9 ev 833.9 ev 828.9 ev 823.9 ev 0-70 -60-50 -40-30 -20-10 0 Energy loss [ev]
From emission (XES) to Resonant Inelastic X-ray Scattering (RIXS) Conduction band Valence band hω Photon in E F E Photon out hω = hω - E Advantages of RIXS: charge-neutral probing low-energy excitations site selectivity bulk and buried structures band dispersion no core state lifetime broadening ultra-fast dynamics Core level Formalism of scattering as a one-step process is described by Kramers-Heisenberg formula: F(ω,ω ) = Σ Σ f m <f D m><m D g> E g + hω -E m -iγ m 2 δ(ε g + hω Ε f hω ) Any possible transition that can be excited directly can also occur as an energy loss E. The transitions are only governed by (1) Selection rules. (2) Energy and momentum conservation.
XES Resonant Inelastic Scattering of Dy 2 O 3 TEY Moewes et al., PRB 60, 15728 (2000) 1x10 4 2x10 4 hν exc = 150.8 ev 6 K 17/2 hν exc = 150.8 ev PFY calc. Counts 5x10 3 153.1 ev 155.2 ev 150 155 160 165 Counts 1x10 4 153.1 ev 6 I 15/2 ; 4 M 17/2 155.2 ev 4 I 15/2 ; 4 M 17/2 ; 4 L 17/2 161.7 ev 161.7 ev 165.4 ev 0 140 145 150 155 160 Emission Energy [ev] 165 Electron configuration Dy: 0 9 8 7 6 5 4 3 Energy loss [ev] 2 1 0-1 Strong and resonant loss features. Intensity depends on selected intermediate state (Kramers-Heisenberg formula). 4d 10 5p 6 4f 9 ( 6 H 15/2 ) 4d 9 5p 6 4f 10 4d 10 5p 6 (4f 9 ) * Net transition 4f 9 (4f 9 ) * 6 H 13/2 Dy core levels Dy bands 10 2 6 10 2 6 9 1 2... 3d 4s 4 p 4d 5s 5p 4 f 5d 6s
Bandmapping in Graphite with XES absorption 0.6 0.4 0.2 Experiment XAS 280 285 290 295 300 C Kα XES Absorption (Excitation) Counts (arb. units) Energy (ev) 15 10 5 0 Calculation Graphite E exc 292.7 291.9 291.3 288.0 285.6 285.0 299 292.7-5 265 270 275 280 285 Emission Energy (ev) 284.3 285.0 288.0 285.6 291.3 291.9 Emission (Relaxation) Excitation Energy (ev) -10-15 -20 Γ M K Γ A L Soft x-ray emission spectroscopy can map the band structure (for light elements).
One example of hard X-ray fluorescence Fluorescence spectroscopy (10 kev) of impurities on a Si wafer. From energy and intensity of the spectrum the type (element) and concentration of impurities can be determined (Ni: 10 fg). Due to I fluo ~Z 4 this is less feasible for lighter elements. In the graph Si Kα (1740 ev) is not in the detector window. For energetically not too deep core holes the exact energy of the core hole depends on the exact chemical environment. In this case even more details about the chemical structure can be obtained (like the chemical valence of the elements).
Photo Electron Spectroscopy (PES)
The principle of PES Tunable photons are used for excitation and the emitted electrons are monitored and their kinetic energy is determined. Other ways of excitation are photons from an X-ray source (XPS), ultra-violet photons (UPS) [or even electrons (EELS or electron energy loss spectroscopy)]. Due to the short attenuation length of electrons (~10Å), PES is a strongly surface sensitive technique.
Reminder: Electron processes are dominating (for lighter elements) Radiative transitions are competing with non-radiative transitions (Auger and Autoionization). In soft x-ray range radiationless transitions (Auger) are dominant.
PhotoElectron Spectr. (PES) or X-ray Photoelectr. Spectr. (XPS) T. Greber, 4 th PSI Summer School, 2005
The principle of PES T. Greber, 4 th PSI Summer School, 2005
Auger versus photoelectrons How can one distinguish Auger electrons and Photoelectrons?
Band structure and density of states of three semiconductors