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Range of Validity - Restrictions

  The energy range of primary electrons, for which the direct model is valid, is approximately 200eV to 50 keV. For energies below 200eV solid state effects are increasingly pronounced. These are not accounted for in the partial wave approach for elastic scattering. Furthermore the dielectric approach is based on an approximation done for electron energies above 200eV.

The main difference between the implementation of the hybrid model and the direct simulation model is the description of inelastic scattering processes. The continuous slowing down approximation (CSDA) (used in both the hybrid as well as the single scattering model) does not localize inelastic scattering events. It only accounts for the mean energy loss for a given flight path. In contrary to this, the direct simulation approach simulates discrete scattering events. This approach leads to following advantages :

  1. Using CSDA there is a rigid relationship between flight path and energy loss. A given electron will always lose the same amount of energy for a certain flight path. In the direct simulation approach the energy losses are subject to random deviations, thus leading to a distribution of energy losses for a given flight path with more realistic results for some applications.
  2. In the CSDA a flight path of an electron is always associated with an energy loss. This approach thus cannot be applied in simulating the escape process of Auger (AES) or photo electrons (XPS) as well as the elastic peak area of backscattered electrons. Due to the stochastic element in the description of inelastic scattering, this problem does not arise in the direct simulation model. Auger and photo electrons have a chance to leave the sample without being subject to a loss of energy. primary electrons can be backscattered conserving their initial energy.
  3. As further advantage, the direct simulation model allows to simulate secondary electrons. Assuming the energy losses to be caused by electron-electron scattering events, energy is transferred from the primary electron to a second electron. The trajectory of this secondary electron can be simulated and its possible emission be detected. The results of the simulation of secondary electrons are not reliable, as the energy of the secondaries usually is in the range of 20-30eV where there is only a limited validity of the physical models used in SESAME. Quantative results cannot be expected.

The main restriction in the application of the direct simulation model is given by the limited availability of dielectric data. The dielectric behaviour of a material is a solid state property and can not be determined using the appropriate elemental dielectric data. The presently available elements and compounds for the direct simulation model is shown in Table A.1.

  
Table A.1: Available elements for the DIR model

Furthermore, the direct simulation approach leads to slightly higher computational effort in both the initialization of the simulation as well as during the simulation itself.



next up previous contents
Next: Applications Up: Direct Simulation Model Previous: Implementation



Horst Wagner
Tue Mar 19 10:24:55 MET 1996