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SR-NIEL – 7

Screened Relativistic (SR) Treatment for NIEL Dose

Nuclear and Electronic Stopping Power Calculator

(version 10.14)

Proton High AMS02 small

The occurrence probability of events due to large energy depositions in a device - like those commonly referred to as single event effects (SEE) - is usually expressed by means of the cross section as a function of mass electronic stopping power - or mass restricted energy loss - of the device material (e.g., see Sects. 11.4-11.4.9 of [Leroy and Rancoita (2016)] and references therein).
As discussed in this webpage, one can re-express that device cross section as a function of the energy of incoming particles.
Furthermore, incoming particle directions are assumed to be identical to those employed in measuring the SEE cross section, so that the traversed path inside the device is not modified.
One has to remark (see webpage) how the physical mechanism of energy deposition per unit length in a medium is such that the resulting computed value of restricted energy loss depends on the overall traversed path to which W0 is related.The electronic stopping power, on the other hand, does not depend on the incoming particle direction with respect to the medium surface.

Device Materials
Device Material Selection:
N° Elements:
Gas Device:
Device Material Z value Stoichiometric Index or Element Fraction
SEE Cross Section
Saturation cross section - A: [cm2/device]
LET Threshold - x0: [MeV cm2 mg-1]
Width parameter - PW:
Exponent - s:
Selection of Energy Loss type
Energy Loss type:
Incident Particle
Incident Particle:
Mass [amu]:
Spectral Fluence
values:
(use dot "." as decimal separator)
Energy
[MeV]
Spectral Fluence
[cm-2 MeV-1]


EXAMPLE:
Copy and paste the data here to reproduce the following example.
Spectral fluence is calculated for Fe-ions, assuming a 4π solid angle exposure, at 1 AU, from [HelMod (2019)] for Carrington rotations 2148 (see discussion in webpage).

To be remarked about W0
To a first approximation, W0 can be estimated from the electron energies whose corresponding total ranges allow electrons to be fully absorbed inside the medium, i.e., such energies cannot exceed that corresponding to the maximum pathlength inside the device. For electron energies where the radiation energy-loss is not a significant part of the energy-loss process, the practical ranges of electrons in units of g/cm2 are almost independent of the atomic mass-number of traversed absorber (e.g., see Equation (1-21) in Section 1-10 of [Price (1964)] and discussion in Sect. 2.3.2 of [Leroy and Rancoita (2016)]). An example of practical range in g/cm2 of electrons is shown in Figure 9 in this webpage). The curve is obtained using Eq. (2.134) in Sect. 2.3.2 of [Leroy and Rancoita (2016)] (see also, Eq. (1-18) in Sect. 1-10 of [Price (1964)]). Furthermore, values of the CSDA ranges of electrons in materials can be obtained from ESTAR database at NIST. Practical ranges and CSDA ranges of electrons may be employed to roughly estimate the values of W0 for microelectronic devices or semiconductor detectors.

The indicated default-value of 100 keV for W0 approximately corresponds to a practical range (see webpage) of about 0.0135 g cm-2 for electrons in an absorber or in a device active-depth directly exposed to the incoming particles flux. For a correct usage of the present web calculator, the inserted value of W0 should appropriately account for absorber thickness (or device active-depth) and enviromental conditions.

NOTE:
  • The lower energy limit is 1 eV
  • W0 is set to be larger than five times the mean excitation energy of the absorber.
  • Target selection for the results obtained in the EXAMPLE section
    Selection for Protons in Silicon:

    Selection for Protons in GaAs:

    Selection for Protons in Water Liquid:

  • User can select the target as gas only for elemental gas targets: H, He, N, O, F, Ne, Cl, Ar, Kr, Xe, Rn.
  • FINAL REMARK:
  • For few compounds belonging to the ICRU list the parameters employed for the energy loss formula (including those for the densiity effect) are reported in Table II of Sternheimer et al. (1984).
  • For the conversion of the cross section as a function of the incoming particle energy, the input cross section is assumed to be provided as a function of the corresponding type of the selected energy loss (i.e., SRIM Electronic stopping power, SR-Framework Electronic stopping, SR-Framework Restricted energy loss).