Photoelectric effect

Photoelectric Effect and its Application in X-ray Photoelectron Spectrum

Introduction

The photoelectric effect refers to the emission of electrons by the surface of a solid upon its irradiation with electromagnetic waves[1]. Photoelectric effect takes place with photons with energies of about a few eV. If the photon has sufficiently high energy, Compton scattering(~keV) or Pair production(~MeV) may take place[2]. kuotinghas discussed the Compton scattering and min-kong has given detailed information about Pair production. The early observations of photoelectric effect were was intimately linked to the advances in the physics of electromagnetic radiation. Later, photoelectric effect developed into a mature analytical technique[3].

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1. History of photoelectric effect

In 1887, the German physicist Heinrich Rudolf Hertz discovered an interesting property of matter. This property is that physical materials emit charged particles when they absorb radiant energy (eg, light)[4]. He clarified and expanded the electromagnetic theory of light that had been put forth by Maxwell. He was the first to satisfactorily demonstrate the existence of electromagnetic waves by building an apparatus to produce and detect VHF or UHF radio waves[5].

Hertz’s experiments on the photoelectric effect caught the attention of many scientist. Philipp Lenard, studied this phenomenon using a metal plate, and in 1900 concluded that the charged particles emitted were the same as those found in cathode rays. James Clerk Maxwell demonstrated that electricity, magnetism and even light are all manifestations of the same phenomenon: the electromagnetic field. Electric and magnetic fields travel through space in the form of waves, and at the constant speed of light[6].

Einstein proposed that incident light can be considered as individual quanta, called photons, and offered a successful explanation of the observed phenomenon. In 1905, Einstein explained the experimental observations of Hertz and Lenard, and established firmly the corpuscular nature of light proposed earlier by Max Planck. Albert Einstein was awarded the Nobel Prize for the year 1921 for his contributions to Theoretical Physics, especially for his explanation of the photoelectric effect[6,7].

2.Einstein equation

Einstein proposed that the incident electromagnetic energy is absorbed as a corpuscle of energy hν by the metal plate. As a result, an electron is ejected from the plate. A part of the energy absorbed goes to overcome the ‘work function’, φ and the residual energy is carried by the ejected electron as its kinetic energy. Essentially, Einstein expressed the conservation of energy in the following mathematical form[6]:
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The ejected electron is detected at the collector only if its kinetic energy
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A graph between the stopping potential Vs and incident frequency of the electromagnetic radiation would thus be a straight line

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Einstein’s interpretation of the photoelectric effect became a historic building block of the quantum theory. In 1922, Bose and Einstein published together their famous paper about Bose-Einstein Condensation.

3.Three-step model

The photoelectric effect in crystalline material is often decomposed into three steps[8]:
1.excitation from an initial state i to a final state f,
2. transport of the electron to the surface,
3. escape from the surface. The final state is a vacant band whose energy distribution and shape is determined by the crystal and, in the energy region immediately above the band gap or Fermi level. We can refer to coons to find more information about Fermi energy.
And the process can be shown as follows[9]:

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3. X-ray Photoelectron Spectroscopy

3.1 Background

Photoelectron spectroscopy is based on Einstein's photoelectric effect. A photon can ionize an electron from a molecule if the photon has an energy greater than the energy holding the electron in the molecule. Any photon energy in excess of that needed for ionization is carried by the outgoing electron in the form of kinetic energy[10].

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In the mid 1910s -1920s,H. Robinson was able to record the photoelectron spectra, excited by CuKα radiation, of several metals. The positions of the edges of the smears produced were characteristic of the photoelectron kinetic energy. By the mid-1950s the Swedish physicist Kai Siegbahn developed a high-resolution beta-ray spectrometer. It was capable of showing the characteristic peak of electron shell as well as chemical bonding effect[1]. Photoelectron spectroscopy has served as a particularly important basis for the bonding models used to describe organic, inorganic, and organometallic molecules because the energetics of ion formation from the neutral ground state are directly related to orbital electron configurations, oxidation states, charge distributions, and covalency[11].

3.2 Physics and application

Consider the photoemission process. Equating the total energies before and after photoemission, and by comparison with the Einstein equation it can be seen that the “binding energy” Eb of the electron (orbital) is just the difference between the final state and initial state energies of the target atom Ef - Ei[1].

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hυ: the energy of the X-ray photon
Ei: the energy of the target atom in its initial state
Ef: the ionized atom in its final state
Ek: the kinetic energy of the photoelectron
Eb: binding energy

Here is an X-ray photoelectron spectrum, obtained from a Ti6Al4V sample previously[11].This is a “survey scan” spectrum, obtained at low resolution and covering the entire useful range of binding energies accessible with the X-ray source employed.

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The spectrum is dominated by three photoelectron peaks, corresponding to electrons originating in the 1s orbitals of the carbon, titanium and oxygen atoms in the sample surface. The “O KLL” structure results from the excitation of Auger electron emission. Auger electrons are emitted with a kinetic energy that is independent of the X-ray energy, so in cases where Auger peaks are superimposed on photoelectron peaks.

The binding energies are characteristic of specific electron orbitals in specific atoms. It should be related to the orbital energy resulting from a quantum mechanical calculation (the Hartree-Fock energy). We will express this energy as the energy for the orbital on an isolated atom, plus a shift to allow for bonding in a molecule.

For atoms and molecules aggregated in the solid state, there are following considerations.

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“Madelung potential” represents for the shift in orbital energy resulting from the insertion of our target atom into the solid state. The term “extra-atomic” relaxation energy represents the reaction of the electron density in surrounding atoms to the ionization of our target atom. Electrons formally “belonging” to neighbouring atoms can “screen the core hole” we create in ejecting the photoelectron.

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The “atom-like” terms will not change, and the binding energy shift will be determined by those terms that reflect the presence of neighbouring atoms. We can use a charged-shell model to think about Va and Vea. The formation of an atomic bond is regarded to be equivalent to the displacement of charge from a shell at the orbital radius of the valence electrons to another shell whose radius is characteristic of the Madelung potential. The extra-atomic relaxation energy isdetermined principally by the polarizabilities of the neighbouring atoms[1].
Here is an examples of chemical shifts in titanium oxide obtained from UV irradiated Ti6Al4V discs(dotted line) and discs without UV irradiation(solid line)[12].

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It is well-known that the binding energy of XPS spectra is very sensitive to the environment around atomic.The observed changes in XPS line shape indicate an electron transfer from the reactive overlayer to the substrate Ti ions or is oxygen phisically extracted from TiO2 and incorporated in the overlayer. The shoulder at the lower binding energy side is due to the appearance of lower oxidation states, which indicate a reduction of the substrate [13].

Reference
[1]http://csacs.mcgill.ca/francais/docs/CHEM634/XPS_Paynter_t.pdf
[2]http://en.wikipedia.org/wiki/Compton_scattering
[3]H.P. Bonzel and C.H. Kleintt, On the History of Photoemission, Progress in Surface Science. Vol. 49(2), pp. 107-1.53. 1995.
[4]http://www.play-hookey.com/optics/photoelectric_effect.html
[5]http://en.wikipedia.org/wiki/Photoelectric_effect#Equations
[6]http://www.physics.iitm.ac.in/~labs/amp/EPEE_PCD_SV.pdf
[7]R.H. Pratt, Akiva Ron and H.K. Tseng, Atomic Photoelectric effect above 10 kV, Reviews of Modern physics, 45(2), 273-325,1993.
[8]Jennifer C. Green,Photelectron Spectroscopy Study of Valence Bands in Solids,Ann. Rev. Phys. Chem,28,161-83,1977.
[9]http://dissertations.ub.rug.nl/FILES/faculties/science/2007/m.popinciuc/c2.pdf
[10]D. W.Ball. Photoelectron Spectroscopy, Spectroscopy, 18(11), 36-37,2003,
[11] http://www.chem.arizona.edu/facilities/pes/facility/PES_description.htm
[12] Z.M. Xia, and M. Mei, Biomimetic Collagen-Hydroxyapatite Coating on UV Irradiated Ti6Al4V Discs.
[13] U. Diebol, The Surface Science of Titanium Dioxide, Surface Science Reports, vol. 48, pp. 53-229, 2003.

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