9.5.2 Predictions of SEE rates for ions

a. Calculation of the ion contribution to SEE rates shall be performed as follows:

1. By using the LET spectra for cosmic rays and heavy ions from solar particle events given by the radiation environmental specification, obtain the cross section experimental curve giving at least LET threshold and saturation cross-section, or the Weibull parameters.

2. If using RPP approach:

(a) Assume that the sensitive volume is a parallelepiped of the same volume as the sensitive one.

(b) Calculate the error rate using one of the following formulae:

- Bradford formula:

with

- Pickel formula:

- Blandford and Adams formula:

where:

A = total surface area of the SV;

l, w and h = length, width and height of the SV;

dΦ/d(LET) = differential ion flux spectrum expressed as a function of LET (shortened to “differential LET spectrum”);

P_CL(>D(LET)) = integral chord length distribution, i.e. the probability of particles travelling through the sensitive region with a pathlength greater than D;

LET_Min = minimum LET to upset the cell (also referred to as the LET threshold);

LET_Max = maximum LET of the incident distribution (~10⁵ MeV×cm²/g).

Figure 9‑1: Procedure flowchart for hardness assurance for single event effects.

3. If using IRPP approach:

(a) Use the real sensitive volume for the integration.

(b) Calculate the error rate using the following formula:

with

where:

dF/d(LET) = differential LET spectrum;

P_CL(>D(LET)) = integral chord length distribution;

ds_ion/d(LET) = differential upset cross section;

A = total surface area of the sensitive volume;

S = surface area of the sensitive volume in the plane of the semiconductor die;

l, w and h = length, width and height of the sensitive volume;

D_Max = maximum length that can be encountered in the SV;

LET_Max = maximum LET of the LET spectrum;

LET_i,Min = lower bin limit in the differential upset cross section ds_ion/d(LET);

LET_i,Max = upper bin limit in the differential upset cross section ds_ion/d(LET).

NOTE For a detailed discussion of the RPP and IRPP approaches, see ECSS-E-HB-10-12 Sections 8.5.2 to 8.5.4. References can be found in [6], [7], [8], [9] and [10].