# Theory¶

A short academic paper is in preparation which gives an overview of Galore’s applications. Some of that information is repeated here; this section of the user guide aims to provide essential information and refer to the academic literature for those seeking more depth and context.

## Photoelectron spectroscopy¶

### History¶

Photoelectron spectroscopy (PES) is a family of methods used to characterise the chemical nature and electronic structure of materials. PES is based on the photoelectric effect, which was discovered by Hertz. [1] It was explored extensively by Rutherford and colleagues [2] and within a few years researchers including de Broglie [3] and Robinson [4] were using the technique to measure electron binding energies through the relationship

$E_\text{k} = h\nu - E_\text{B}.$

Photons with energies $$h\nu$$ ranging from 5 eV up to 12 keV eject electrons (referred to as “photoelectrons”) from the occupied orbitals of a sample. The kinetic energy $$E_\text{k}$$ of each photoelectron therefore depends on its binding energy $$E_\text{B}$$. The names of various PES methods refer to the photon energy range used:

• ultraviolet photoelectron spectroscopy (UPS): 5–100 eV

• X-ray photoelectron spectroscopy (XPS): 0.3–2 keV

• hard X-ray photoelectron spectroscopy (HAXPES, HE-PES, HXPS, HX-PES): above 2 keV

• While this can play a significant role, the lifetime broadening is energy-dependent and care should be taken when applying it across the full data set.

• This is caused by vibrations in the system which lead to a distribution of accessible photoionization energies.

• In oxides this is associated with as much as 0.8 eV broadening

• Typical values are in the range 0.2–0.3 eV.

### Weighting¶

#### The Gelius model¶

The Gelius model was originally developed to describe molecular systems. [5][6][7]

### References¶

1

H. Hertz. Ueber einen Einfluss des ultravioletten Lichtes auf die electrische Entladung. Ann. der Phys. und Chemie, 267(8):983–1000, 1887. URL: http://doi.wiley.com/10.1002/andp.18872670827, doi:10.1002/andp.18872670827.

2

E. Rutherford. The Connexion between the β and γ Ray Spectra. Phil. Mag., Sept 1914. There are a number of other papers from Rutherford’s group in this volume of Phil. Mag. related to the ejection of β-rays (electrons) from samples exposed to γ-rays (photons). doi:10.1080/14786440908635214.

3

Maurice de Broglie. Les phénomènes photo-électriques pour les rayons x et les spectres corpusculaires des éléments. J. Phys. Radium, 2(9):265–287, sept 1921.

4

H Robinson. The Secondary Corpuscular Rays Produced by Homogeneous X-Rays. Proc. R. Soc. A Math. Phys. Eng. Sci., 104(727):455–479, nov 1923. URL: http://rspa.royalsocietypublishing.org/cgi/doi/10.1098/rspa.1923.0121, doi:10.1098/rspa.1923.0121.

5

U. Gelius and K. Siegbahn. ESCA studies of molecular core and valence levels in the gas phase. Faraday Discuss. Chem. Soc., 54:257, 1972. URL: http://xlink.rsc.org/?DOI=dc9725400257, doi:10.1039/dc9725400257.

6

U. Gelius. Molecular Orbitals and Line Intensities in ESCA Spectra. In D. A. Shirley, editor, Electron Spectrosc., pages 311. North-Holland, Amsterdam, 1972.

7

U. Gelius. Recent progress in ESCA studies of gases. J. Electron Spectros. Relat. Phenomena, 5(1):985–1057, jan 1974. URL: http://linkinghub.elsevier.com/retrieve/pii/0368204874850644, doi:10.1016/0368-2048(74)85064-4.