Ultraviolet Photoelectron Spectroscopy

In photoelectron spectroscopy, electrons are released from the solid by photons. At photon energies between 3 and 100 eV  this refers to UPS. Our source generates He I photons with an energy of 21.2 eV. The photons add energy to the electrons in the valence band of the solid body, so that they are excited to states above the vacuum level. These excited electrons of characteristic kinetic energy leave the surface and can then be detected. The surface sensitivity depends on the mean free path of the emitted electrons, since the penetration depth of the UV photons is up to 1000 Å, while electrons with energies of up to 100 eV have a mean free path length of less than 15 Å. This results in an information depth of 2 to 3 atomic layers for UPS. For the number of electrons that are excited by the UV photons the following applies:

(3.1)

Di and Df denote the local density of states in the initial and final state. μ fi denotes the matrix element of the dipole transition between initial and final state. Since the final state densities usually have much less structure than the initial state densities, UPS spectra mainly deliver information about the initial state density.


Fig. 3.1: UPS energy level diagram (EF,Pr = EF,Sp = EF, because of a conductive connection between sample and spectrometer.)

Fig. 3.1 shows a schematic representation of the energy levels on excitation of the electrons by UV photons. A valence electron excited by a photon of the energy ħω has after emerging from the surface a kinetic energy of     

(3.2)

EB denotes the binding energy of the electron in the solid. The electron is detected in the spectrometer with the kinetic energy     

(3.3)
(3.4)

The Fermi levels of the sample, EF,Pr and the spectrometer EF,Sp are equal (EF,Pr = EF,Sp = EF), since the sample and the spectrometer are conductively connected. Electrons emitted directly from the Fermi level (EB = EF), have the maximum kinetic energy:

(3.5)

The position of the Fermi levels of the sample therefore only depends on the work function of the spectrometer which can be assumed as constant and the photon energy ħω. The low-energy use of the spectrum gives the minimum kinetic energy

(3.6)

For the entire width of the spectrum one obtains from (3.5) and (3.6)   

(3.7)

From the width of the measured spectrum and the known photon energy of 21.2 eV, the work function of the sample can be calculated from (3.7). It is given by the low energy slope of the spectra when the kinetic energy is used as scale and the Fermi level is placed on the photon energy of 21.2 eV. The spectra are plotted as a function of binding energy EB, which is obtained by subtraction of the kinetic energy from the photon energy of 21.2 eV.

  (3.8),

thus the work function of the sample is 21.2 eV - EBmax.

For more information see here.

 

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