Skip to main content
SpringerLink
Log in

Photoelectron Emission Excited by a Hard X-ray Standing Wave

  • Chapter
  • First Online:
Hard X-ray Photoelectron Spectroscopy (HAXPES)

Part of the book series: Springer Series in Surface Sciences ((SSSUR,volume 59))

Abstract

The following chapter describes the basics and some applications for the case that photoelectrons are emitted from a hard X-ray interference field instead of by a travelling wave. The dipole approximation holds astonishingly well even for hard X-rays as far as the magnitude of the transition matrix element is concerned. However, the forward-backward asymmetry caused by higher order multipole terms needs to be considered when the photoelectron is emitted by the coherent action of two X-ray waves travelling in different directions. This has implications on the chosen experimental set-up which will be briefly discussed together with other experimental aspects. Finally, some examples of X-ray standing wave analysis using hard X-ray photoelectron spectroscopy will be presented yielding the geometric and electronic structure of (crystalline) materials with pm resolution.

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Log in via an institution
Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 229.00
Price excludes VAT (USA)
  • Available as EPUB and PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 299.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info
Hardcover Book
USD 299.99
Price excludes VAT (USA)
  • Durable hardcover edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

Notes

  1. 1.

    Note the difference between diffraction plane, i.e. the plane defined by k 0 and k h and diffraction planes, which are parallel to a corresponding set of Miller planes, for example (333), (444), (555), etc. which are all parallel to the (111) Miller planes. Diffraction planes are not necessarily atomic planes. Their spacing \(d_{hkl} /m\) is defined by Bragg’s law \(2d_{hkl} \sin \Theta = m\lambda\) where \(d_{hkl}\) is the spacing of the \((hkl)\) Miller planes.

  2. 2.

    The electron yield \(I_{A}^{h}\) detected in an XSWs experiment is given by \(I_{A}^{h} = I_{A,0} Y_{A,T}^{h}\) where \(I_{A,0}\), called off-Bragg yield, is proportional to the number of sampled atoms and other parameter such as photoelectric cross section, solid angle, beam intensity and more.

  3. 3.

    For details of how the parameters \(S_{R}\), \(S_{I}\) and \(\psi\) are calculated, the reader is referred to the original publication [24].

  4. 4.

    A minor influence by a modified surface layer leading to \(P = \ne 0\) cannot be excluded.

  5. 5.

    If a divergent beam with a wide bandpass is incident on a crystal the different wavelengths are reflected at different angles, they are dispersed. When this rainbow like x-ray beam is incident on a sample crystal, incident wavelengths and angles only match if the crystal has exactly the same diffraction plane spacing (see e.g. [30]).

  6. 6.

    This can easily be understood from Bragg’s law \(2d\sin (\varTheta ) = m\lambda\); at \(\varTheta = 90^\circ\) the sine function is flat and a small change in \(\lambda\) necessitates a large change in \(\varTheta\).

  7. 7.

    As Herbert Kroemer phrased it in his Nobel lecture, December 8, 2000: “Often it may be said that the interface is the device”.

  8. 8.

    This surface distance should not be confused with the bond length.

  9. 9.

    Utilizing additionally the cubic symmetry of the SrTiO3.

  10. 10.

    The absorption probability, i.e. cross section also depends strongly on the shape of the electron wavefunction close to the core.

  11. 11.

    In order to fit with the experimental partial yield, the calculated lpDOS had to be convoluted with a Gaussian significantly wider than given by the experimental resolution, in particular for oxygen.

References

  1. M.V. Laue, Röntgenstrahl-Interferenzen (Akademische Verlagsgesellschaft, Becker & ErlerKolm.-Ges., Leipzig, 1941; Akademische Verlagsgesellschaft, Frankfurt, 1960)

    Google Scholar 

  2. B. Batterman, H. Cole, Rev. Mod. Phys. 36, 681 (1964)

    Article  ADS  Google Scholar 

  3. A. Authier, Dynamical Theory of X-ray Diffraction (IUCr Monographs on Crystallography Oxford Science Publications, 2001)

    MATH  Google Scholar 

  4. B.W. Batterman, Phys. Rev. 133, A759 (1964)

    Article  ADS  Google Scholar 

  5. B.W. Batterman, Phys. Rev. Lett. 22, 703 (1969)

    Article  ADS  Google Scholar 

  6. K. Siegbahn, Nucl. Instrum. Meth. Phys. Res. A 547, 1 (2005)

    Article  ADS  Google Scholar 

  7. J. Zegenhagen, A.Y. Kazimirov (eds.) The X-ray Standing Waves Technique: Principles and Applications (World Scientific, 2013)

    Google Scholar 

  8. N. Hertel, G. Materlik, J. Zegenhagen, Z. Phys, B 58, 199 (1985)

    Google Scholar 

  9. J. Zegenhagen, Surf. Sci. Rep. 18, 199 (1993)

    Article  ADS  Google Scholar 

  10. Y. Shvyd’ko, X-ray Optics: High-Energy-Resolution Application (Springer, Berlin, Heidelberg, 2004)

    Book  Google Scholar 

  11. T. Ishikawa, Nucl. Instr. Meth. A 547, 42 (2005)

    Article  ADS  Google Scholar 

  12. E.A. Sozontov, M.V. Kruglov, B.G. Zakharov, Phys. Stat. Sol. A 66, 303 (1981)

    Google Scholar 

  13. P.L. Cowan, J.A. Golovchenko, M.F. Robbins, Phys. Rev. Lett. 44, 1680 (1980)

    Article  ADS  Google Scholar 

  14. G. Materlik, J. Zegenhagen, Phys. Lett. A 104, 47 (1984)

    Article  ADS  Google Scholar 

  15. P. Funke, G. Materlik, Solid State Commun. 54, 921 (1985)

    Article  ADS  Google Scholar 

  16. J.R. Patel, P.E. Freeland, J.A. Golovchenko, A.R. Kortan, D.J. Chadi, G.-X. Quian, Phys. Rev. Lett. 57, 3077 (1986)

    Article  ADS  Google Scholar 

  17. S.M. Durbin, L.E. Berman, B.W. Batterman, J.M. Blakeley, J. Vacuum Sci. Technol. A 3, 973 (1985)

    Article  ADS  Google Scholar 

  18. T. Ohta, Y. Kitajima, H. Kuroda, T. Takahashi, S. Kikuta, Nucl. Instr. Meth. A 246, 760 (1986)

    Article  ADS  Google Scholar 

  19. In the dipole approximation, the exponential e 2πikr of the E-field operator in the Matrix element, describing the photoelectric process, is simply replaced by 1, the first term of its corresponding representation in a Taylor series (1 + 2πi kr–π 2(kr)2–…)

    Google Scholar 

  20. T.W. Barbee, W.K. Warburton, Mater. Lett. 3, 17 (1984)

    Article  Google Scholar 

  21. M.J. Bedzyk, D.H. Bilderback, G.M. Bommarito, M. Caffrey, J.S. Schildkraut, Science 241, 1788 (1988)

    Article  ADS  Google Scholar 

  22. I.A. Vartanyants, J. Zegenhagen, Solid State Comm. 113, 299 (1999)

    Article  ADS  Google Scholar 

  23. Z. Zhang, P. Fenter, L. Cheng, N.C. Sturchio, M.J. Bedzyk, M.L. Machesky, D.J. Wesolowski, Surf. Sci. 554, L95 (2004)

    Article  ADS  Google Scholar 

  24. J. Zegenhagen, Surf. Sci. 554, 77 (2004)

    Article  ADS  Google Scholar 

  25. J. Zegenhagen, in Surface Science Techniques, eds. by G. Bracco, B. Holst, Surface Structure Analysis with X-ray Standing Waves (Springer Series in Surface Science, Springer, Berlin, 2013), p. 249

    Google Scholar 

  26. A. Jablonski, F. Salvat, C.J. Powell, NIST Electron Elastic Scattering Cross-Section Database-Version 3.0 (National, Institute of Standarts and Technology, Gaithersburg, MD, 2002)

    Google Scholar 

  27. I. Vartanyants, T.-L. Lee, S. Thiess, J. Zegenhagen, Nucl. Instr. Meth. A 547, 196 (2005)

    Article  ADS  Google Scholar 

  28. S.K. Andersen, J.A. Golovchenko, G. Mair, Phys. Rev. Lett. 37, 1141 (1976)

    Article  ADS  Google Scholar 

  29. T.-L. Lee, C. Bihler, W. Schoch, W. Limmer, J. Daeubler, S. Thiess, J. Zegenhagen, Phys. Rev. B. 81, 235202 (2010)

    Article  ADS  Google Scholar 

  30. J. Zegenhagen, G. Materlik, W. Uelhoff, J. X-ray Sci. Technol. 2, 214 (1990)

    Article  Google Scholar 

  31. M.B. Trzhaskovskaya, V.I. Nefedov, V.G. Yarzhemsky, At. Data Nucl. Data Tables 77, 97 (2001)

    Article  ADS  Google Scholar 

  32. M.B. Trzhaskovskaya, V.I. Nefedov, V.G. Yarzhemsky, ibid. 82, 257 (2002)

    Google Scholar 

  33. M.B. Trzhaskovskaya, V.K. Nikulin, V.I. Nefedov, V.G. Yarzhemsky, At. Data Nucl. Data Tables 92, 245 (2006)

    Article  ADS  Google Scholar 

  34. L.E. Berman, M.J. Bedzyk, Phys. Rev. Lett. 63, 1172 (1989)

    Article  ADS  Google Scholar 

  35. M.J. Bedzyk, Q. Shen, M.E. Keeffe, G. Navrotski, L.E. Berman, Surf. Sci. 220, 419 (1989)

    Article  ADS  Google Scholar 

  36. T. Ohta, H. Sekiyama, Y. Kitayima, H. Kuroda, T. Takahashi, S. Kikuta, Jpn. J. Appl. Phys. 24, L475 (1985)

    Article  ADS  Google Scholar 

  37. D.P. Woodruff, D.L. Seymour, C.F. McConville, C.E. Riley, M.D. Crapper, N.P. Prince, Phys. Rev. Lett. 58, 1460 (1987)

    Article  ADS  Google Scholar 

  38. C. Bocchi et al., J. Vac. Sci. Technol., B 20, 1436 (2002)

    Article  Google Scholar 

  39. C. Bocchi et al., J. Vacuum Sci. Technol. B 23, 1504 (2005)

    Article  ADS  Google Scholar 

  40. S.M. Durbin, L.E. Berman, B.W. Batterman, J.M. Blakely, Phys. Rev. Lett. 56, 236 (1986)

    Article  ADS  Google Scholar 

  41. D. Pacilé, M. Papagno, A. Cupolillo, G. Chiarello, L. Papagno, J. Electron Spectrosc. Related Phenom. 135, 201 (2004)

    Article  Google Scholar 

  42. I.A. Vartanyants, J. Zegenhagen, Nuovo Cimento 19D, 617 (1997)

    Article  ADS  Google Scholar 

  43. M. Sugiyama, S. Maeyama, S. Heun, M. Oshima, Phys. Rev. B 51, 14778 (1995)

    Article  ADS  Google Scholar 

  44. G.J. Jackson, J. Ludecke, D.P. Woodruff, A.S.Y. Chan, N.K. Singh, J. McCombie, R.G. Jones, B.C.C. Cowie, V. Formoso, Surf. Sci. 441, 515 (1999)

    Article  ADS  Google Scholar 

  45. G. Heimel et al., Nature Chem. 5, 187 (2013)

    Google Scholar 

  46. J.D. Emery, B. Detlefs, H.J. Karmel, L.O. Nyakiti, D.K. Gaskill, M.C. Hersam, J. Zegenhagen, M.J. Bedzyk, Phys. Rev. Lett. 111, 215501 (2013)

    Google Scholar 

  47. A.J. Van Bommel, J.E. Crombeen, A. Van Tooren, Surf. Sci. 48, 463 (1975)

    Article  ADS  Google Scholar 

  48. J.C. Woicik, T. Kendelewicz, K.E. Miyano, P.L. Cowan, C.E. Bouldin, B.A. Karlin, P. Pianetta, W.E. Spicer, Phys. Rev. Lett. 68, 341 (1992)

    Article  ADS  Google Scholar 

  49. A. Herrera-Gomez, J.C. Woicik, T. Kendelewicz, K.E. Miyano, W.E. Spicer, Phys. Rev. B 75, 165318 (2007)

    Article  ADS  Google Scholar 

  50. J.C. Woicik et al., J. Vacuum Sci. Technol. A 11, 2359 (1993)

    Article  ADS  Google Scholar 

  51. J.C. Woicik, T. Kendelewicz, A. Herrera-Gomez, K.E. Miyano, P.L. Cowan, C.E. Bouldin, P. Pianetta, W.E. Spicer, Phys. Rev. Lett. 71, 1204 (1993)

    Article  ADS  Google Scholar 

  52. J.C. Woicik, T. Kendelewicz, S.A. Yoshikawa, K.E. Miyano, G.S. Herman, P.L. Cowan, P. Pianetto, W.E. Spicer, Phys. Rev. B 53, 15425 (1996)

    Article  ADS  Google Scholar 

  53. T. Haage, J. Zegenhagen, J.Q. Li, H.-U. Habermeier, M. Cardona, Ch. Jooss, R. Warthmann, A. Forkl, H. Kronmüller, Phys. Rev. B 56, 8404 (1997)

    Article  ADS  Google Scholar 

  54. C. Jooss, R. Warthmann, H. Kronmüller, T. Haage, H.-U. Habermeier, J. Zegenhagen, Phys. Rev. Lett. 82, 632 (1999)

    Article  ADS  Google Scholar 

  55. H.Y. Hwang, Y. Iwasa, M. Kawasaki, B. Keimer, N. Nagaosa, Y. Tokura, Nat. Mater. 11, 103 (2012)

    Article  ADS  Google Scholar 

  56. T.-L. Lee, S. Warren, L. Cao, S. Thiess, B.C.C. Cowie, J. Zegenhagen, Nucl. Instrum. Meth. A 547, 216 (2005)

    Article  ADS  Google Scholar 

  57. J. Zegenhagen, T. Siegrist, E. Fontes, L.E. Berman, J.R. Patel, Solid State Commun. 93, 763 (1995)

    Article  ADS  Google Scholar 

  58. T. Haage, Q.D. Jiang, M. Cardona, H.-U. Habermeier, J. Zegenhagen, Appl. Phys. Lett. 68, 2427 (1996)

    Article  ADS  Google Scholar 

  59. T. Haage, J. Zegenhagen, H.-U. Habermeier, M. Cardona, Phys. Rev. Lett. 80, 4225 (1998)

    Article  ADS  Google Scholar 

  60. Sebastian Thiess, Ph.D thesis, University Hamburg (2007)

    Google Scholar 

  61. J. Zegenhagen, B. Detlefs, T.-L. Lee, S. Thiess, H. Isern, L. Petit, L. André, J. Roy, Y. Mi, I. Joumard, J. Electron Spectrosc. Related Phenom. 178–179, 258 (2010)

    Article  Google Scholar 

  62. J.C. Woicik et al., Phys. Rev. B 64, 125115 (2001)

    Article  ADS  Google Scholar 

  63. E. Nelson, J. Woicik, P. Pianetta, J. Synchr. Rad. 6, 341 (1998)

    Article  Google Scholar 

  64. S. Thiess, T.-L. Lee, F. Bottin, J. Zegenhagen, Solid State Comm. 150, 553 (2010)

    Article  ADS  Google Scholar 

  65. J.H. Scofield, Theoretical photoionization cross-sections from 1 to 1500 keV, Lawrence Livermore Report UCRL-51326(1973)

    Google Scholar 

  66. D.B. Fischer, Phys. Rev. B 5, 4219 (1972)

    Article  ADS  Google Scholar 

  67. J.C. Woicik, E.J. Nelson, Leeor Kronik, Manish Jain, James R. Chelikowsky, D. Heskett, L.E. Berman, G.S. Herman, Phys. Rev. Lett. 89, 077401 (2002)

    Article  ADS  Google Scholar 

  68. R. Ovsyannikov, P. Karlsson, M. Lundqvist, C. Lupulescu, W. Eberhardt, A. Föhlisch, S. Svensson, N. Mårtensson, J. Electron Spectrosc. Related Phenom. 191, 92 (2013)

    Article  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Diamond Light Source Limited, Diamond House, Didcot, Oxfordshire, OX11 0DE, UK

    Jörg Zegenhagen & Tien-Lin Lee

  2. Deutsches Elektronen-Synchrotron, Notkestraße 85, 22607, Hamburg, Germany

    Sebastian Thiess

Authors
  1. Jörg Zegenhagen
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Tien-Lin Lee
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Sebastian Thiess
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Jörg Zegenhagen .

Editor information

Editors and Affiliations

  1. Brookhaven National Laboratory, National Institute of Standards and Technology, Upton, New York, USA

    Joseph Woicik

Rights and permissions

Reprints and permissions

Copyright information

© 2016 Springer International Publishing Switzerland

About this chapter

Cite this chapter

Zegenhagen, J., Lee, TL., Thiess, S. (2016). Photoelectron Emission Excited by a Hard X-ray Standing Wave. In: Woicik, J. (eds) Hard X-ray Photoelectron Spectroscopy (HAXPES). Springer Series in Surface Sciences, vol 59. Springer, Cham. https://doi.org/10.1007/978-3-319-24043-5_12

Download citation

Publish with us

Policies and ethics

Search

Navigation