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SR-NIEL – 7

Screened Relativistic (SR) Treatment for NIEL Dose

Nuclear and Electronic Stopping Power Calculator

(version 11.0)

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NIEL Dose Calculator for electrons spectral fluence

Form Factor Model:
Target Materials
Target Selection:
N° Elements:
Target Material Z Stoichiometric Index or Element Fraction Displacement Threshold Energy [eV] *
Spectral Fluence
values:
use dot "." as decimal separator;
at least, a pair (energy and spectral fluence) of values are required
Energy
[MeV]		Spectral Fluence
[cm-2 MeV-1]


EXAMPLE:
Copy and paste the data here to reproduce the following example.
Electrons NIEL in Si (red) and protons spectral fluence (blue) assuming an orbit around Jupiter, at Europa altitude, during 1 year mission:

Spectral fluence data are calculated with JOREM Model implemented in SPENVIS
assuming a 4π solid angle exposure.

NOTE:
  • *Experimentally determined Ed values:
    1. Ga: 21.5 eV, As: 21.5 eV as reported in [Campesato et al. (2019)] from proton, electron and neutron irradiations of solar cells. In Triple Junction solar cells, in which the dominat damage mechanism is that one due to the GaAs middle junction, a commonly effective value of Ed was 24 eV [Campesato et al. (2018), Campesato et al. (2019)].
    2. Ge: 40.5 eV as reported in [Campesato et al. (2019)].
    3. In: 43 eV, Ga: 21 eV, P: 21 eV as reported in [Campesato et al. (2018)] for In0.49Ga0.51P single junction solar cells irradiated with electrons and protons. In [Campesato et al. (2019)] with electron, proton and neutron irradiation, it was shown that a commonly effective value of Ed=38 eV can be employed in an equivalent way.
  • In the present treatment, screening effects are factorized in the expression for the differantial cross section (Boschini et al. (2011)). However, it has to be remarked - as derived by Zeitler and Olsen (1956) - that for electron energies above 200 keV the overlap of spin and screening effects is small for all elements and for all energies; for lower energies the overlapping of the spin and screening effects may be appreciable for heavy elements and large angles.
  • User can suggest an "ad hoc" form factor by contacting us using This email address is being protected from spambots. You need JavaScript enabled to view it. . In fact (see discussion in Boschini et al. (2011)), a further work is likely to be needed for the most suited parametrization of the nuclear form factor, particularly for high-Z naterial.
  • NIEL for compounds can be determined by means of Bragg's rule, i.e., the overall NIEL in units of MeV cm2/g is obtained as a weighted sum in which each material contributes proportionally to the fraction of its atomic weight. An example for selection, with GaInP2 as target, follows:

    or equivalently

  • The Total Cross Section is not affected by the Form Factor term. This because the Differential Cross Section is larger by several orders of magnitude with respect to the corresponding values at the very low angles, where the form factor is relevant. The effect of different form factors on differential cross section for 184 MeV electrons in In (Z=49) is in the following images, with the same experimental data set from B.Hahn et al. (1956). Our calculation is on the left and the graph from Fernandez-Varea et al. (1993) is on the right.:

    However the transferred energy is several order of magnitude larger at high scattering angles.

    The overall results is that the NIEL and the Nuclear Stopping power are affected by the form factor. Numerical results for 183 MeV electrons in In are presented in the following table:

    • Details
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