X-ray photoelectron spectroscopy#Hemispherical Electron Energy Analyzer
A hemispherical analyzer, a detector for high-resolution measurement of particle energies, especially of electrons in the photo-electron spectroscopy or Auger electron spectroscopy. An ideal hemispherical analyzer consists of two concentric electrodes between which an electrical voltage is applied. Depending on the applied voltage only particles can pass through the detector with a certain energy.
If the potentials are respectively applied to the inner and outer semi- spherical, the electric potential and the electric field strength in the space between the electrodes is determined by the Laplace equation:
There are and the radii of the hemispheres. From the condition that the electrons (or negatively charged ions) followed by the kinetic energy of a circular path having a radius, it follows that the action of force by the electric field is equal to the centripetal force (). Hence the condition on the potentials:
With the energy of the electrons in eV. From this equation, we obtain the potential difference between the two half-spheres:
This equation determines the potential that must be applied to the electrodes, so that electrons can pass through the detector with the energy. This energy is called the pass energy ( engl. pass energy ).
The energy resolution of the detector depends on the geometric parameters of the analyzer and the angular distribution of the incoming electrons.
With the aperture size and the angle of incidence of the electrons.
While a low pass energy, the energy resolution improves, it reduces the number of electrons that pass through the detector, so that the signal -to-noise ratio deteriorates and longer measurement times are necessary. The number of transmitted electrons is approximately proportional to the pass energy. A disadvantage of the detector is that the probability that an electron passes through the detector depends on the initial energy of the electron. For comparing the intensity signals are far apart, the detector must be calibrated. Upstream of the analyzer are electrostatic lenses with two main functions: to collect and focus the electrons approaching the entrance aperture of the analyzer and they slow down the electrons, so that lower pass energies can be used with better resolution.
To determine the energy spectrum of the incident electrons, the pass energy is normally ( and thus ) is kept at a constant value, and the braking voltage of the electrostatic lens varies, this results in a constant resolution in the entire energy.