Help & Methodology Reference
The Space RHA SEE Rate Assessment Tool is a browser-based calculator for predicting in-flight Single-Event Effects (SEE) event rates in space electronics. It computes the expected rate at which SEE events — such as single-event latch-up (SEL), single-event upset (SEU), or single-event functional interrupt (SEFI) — will occur during a space mission by integrating the device cross-section curve against the on-orbit radiation environment spectrum.
The tool combines several established methodologies into a single workflow:
| Capability | Description |
|---|---|
| Spectral Integration | Compute heavy-ion SEE rates by numerically integrating the Weibull cross-section against the differential LET flux spectrum, with IRPP chord-length corrections |
| Proton Rate Calculation | Compute proton-induced SEE rates using proton cross-section data convolved with proton energy spectra |
| Monte Carlo Uncertainty | Propagate uncertainties in Weibull parameters through 10,000 Monte Carlo iterations to produce confidence intervals on predicted rates |
| Ladbury SEL Bounding | Estimate bounding SEL rates for parts without full Weibull characterization, using technology-based susceptibility priors |
| Multi-Part System Analysis | Assess SEE rates for an entire parts list simultaneously, computing per-part and total system-level rates |
| Environment Import | Import custom heavy-ion LET spectra and proton spectra from CREME96 and OMERE output files |
| PDF Reporting | Generate comprehensive PDF assessment reports with rate breakdowns, distribution plots, and methodology documentation |
The tool requires no software installation and runs entirely in the browser. All computations are performed client-side.
The fundamental approach to computing in-flight heavy-ion SEE rates is spectral integration: the device cross-section as a function of LET is convolved with the differential LET flux spectrum of the radiation environment. This is the standard method codified in CREME96 [3] and widely adopted in radiation hardness assurance practice.
The SEE event rate R (events per unit time) is given by the integral:
The integral is evaluated numerically over the LET range from the device threshold LET (Lth) up to the maximum LET in the environment spectrum. The tool constructs a fine-grained LET grid (logarithmically spaced) and computes the differential cross-section dσ/dL at each grid point. The integration is then performed as a summation:
where Δσi = σ(Li+1) − σ(Li) is the incremental cross-section between adjacent LET grid points, and Φ(Li) is the effective flux (with path-length correction) at LET value Li. This formulation, where the integration variable is transformed from LET to cross-section, is numerically efficient because the cross-section changes most rapidly near threshold where the flux is highest.
The SEE rate calculation requires a description of the on-orbit radiation environment in the form of a LET spectrum (for heavy ions) and/or an energy spectrum (for protons). The tool provides several built-in environment models and supports importing custom spectra from CREME96 and OMERE.
The tool includes pre-computed heavy-ion LET spectra and proton spectra for common orbit environments:
| Environment | Description |
|---|---|
| GCR Solar Minimum | Galactic cosmic ray background at solar minimum (worst case for GCR), representing the baseline heavy-ion environment for most missions |
| GCR Solar Maximum | GCR background at solar maximum, with reduced heavy-ion flux due to solar modulation |
| GEO | Geostationary orbit environment including trapped and solar particle contributions |
| LEO | Low-Earth orbit environments at various inclinations and altitudes |
| Solar Particle Events | Enhanced proton and heavy-ion environments during worst-case or design-basis solar energetic particle events |
Users can import custom LET spectra generated by CREME96 or OMERE. The tool supports two input formats:
CREME96 native format: The integral LET spectrum output (.LET files) produced by CREME96, with header lines beginning with ‘%’. The tool automatically converts the integral spectrum (cumulative flux above a given LET) to a differential spectrum (flux per unit LET) by numerical differentiation. The IRPP chord-length distribution correction is then applied across 11 RPP dimension ratios and all LET bins.
Two-column text format: A simple two-column file with LET (MeV-cm2/mg) in the first column and differential flux in the second column. This format is compatible with output from OMERE and other environment tools.
For proton environments, the tool accepts two-column energy-flux spectra (energy in MeV, differential flux in particles/cm2/day/MeV).
When a CREME96 native integral LET spectrum is imported, the tool converts it to a differential spectrum. The integral spectrum Φ(>L) gives the total flux of particles with LET greater than L. The differential spectrum is obtained by computing:
The differentiation is performed using log-log interpolation between adjacent data points, which is appropriate because both flux and LET span many orders of magnitude and the integral spectrum is approximately a power law over most of the LET range.
The device SEE cross-section as a function of LET is parameterized using the four-parameter Weibull cumulative distribution function. This is the standard parameterization used throughout the radiation effects community for fitting heavy-ion SEE cross-section data [1, 6].
| Parameter | Symbol | Units | Description |
|---|---|---|---|
| Saturation Cross-Section | σsat | cm2 | The limiting (maximum) cross-section at high LET, representing the full sensitive area of the device. Typical values range from 10−8 cm2 for SEL to 10−3 cm2 for SEU in large memories. |
| Threshold LET | Lth | MeV-cm2/mg | The onset LET below which no SEE events are observed. This is the minimum LET required to trigger the effect. Values range from <1 for sensitive technologies to >40 for hardened parts. |
| Width | W | MeV-cm2/mg | Controls how quickly the cross-section rises from onset to saturation. Larger values produce a more gradual rise. |
| Shape (Exponent) | s | dimensionless | Controls the shape of the transition region. Values near 1 produce an exponential rise; larger values produce a steeper, more step-like transition. |
The Weibull parameterization is flexible enough to fit a wide range of experimental cross-section curves, from gradual onsets (low s, high W) to sharp threshold behaviors (high s, low W). The four parameters are typically obtained by fitting the Weibull function to experimental heavy-ion cross-section data measured at multiple LET values.
The simple rate integral described in Section 2 assumes that all particles traverse the sensitive volume along a single path length. In reality, particles arrive from all directions in the isotropic cosmic ray environment, and the energy deposited depends on the path length through the sensitive volume. The Integral Rectangular Parallelepiped (IRPP) method accounts for this geometric effect by modeling the device sensitive volume as a rectangular parallelepiped (RPP) — a box with dimensions X, Y, and Z — and computing the distribution of chord lengths through it [8].
For an isotropic, omnidirectional particle flux incident on an RPP sensitive volume, the effective flux at a given LET depends on the distribution of path lengths through the box. A particle entering at an oblique angle traverses a longer path through the sensitive volume than one entering normal to a face, depositing more energy for the same LET. Conversely, the projected area of the box (and therefore the probability of being hit) varies with angle.
The IRPP method integrates the rate over all solid angles, accounting for both the path-length variation and the angular dependence of the projected area. The result is a set of effective fluxes that depend on the RPP dimension ratio Z/X, where Z is the depth of the sensitive volume and X is a lateral dimension. The tool pre-computes effective flux tables for 11 RPP ratio values and interpolates between them for the user-specified ratio.
The RPP ratio Z/X characterizes the geometry of the sensitive volume:
| Z/X Value | Interpretation |
|---|---|
| 0.01 | Very thin sensitive volume (pancake geometry). Approximates the cosine-law worst case. Use when device geometry is unknown for a conservative estimate. |
| 0.2 | Moderate depth. A common best-estimate value for many CMOS technologies. |
| 1.0 | Cubic sensitive volume. Represents the isotropic (geometry-independent) limit. |
Smaller Z/X values generally produce higher predicted rates because the thin geometry allows oblique particles with lower LET to deposit enough energy to trigger an event (their longer path lengths compensate for lower LET). The choice of RPP ratio can affect the predicted rate by a factor of 2–5 or more, making it one of the most significant sources of uncertainty in the calculation.
SEE rate predictions carry significant uncertainty due to uncertainties in the Weibull cross-section parameters, the environment model, and the RPP geometry. The tool uses Monte Carlo simulation to propagate these uncertainties and produce confidence intervals on the predicted rates.
The Monte Carlo engine performs N = 10,000 iterations. In each iteration, the Weibull parameters are sampled from their uncertainty distributions, the spectral integration is performed with the sampled parameters, and the resulting rate is recorded. After all iterations, the empirical distribution of rates is used to compute statistics:
| Statistic | Description |
|---|---|
| Mean Rate | Average of all Monte Carlo rate samples |
| 90% Confidence Level | 90th percentile of the rate distribution. The rate has a 90% probability of being at or below this value. |
| 95% Confidence Level | 95th percentile of the rate distribution |
| 99% Confidence Level | 99th percentile of the rate distribution |
The 90% confidence level rate is the most commonly used metric for mission planning, as it provides a conservative but not overly pessimistic estimate.
For parts with full Weibull characterization, the tool applies a beta-distribution scaling factor to the computed spectral rate. The beta distribution parameters are derived from the threshold LET, with lower-threshold devices having broader uncertainty distributions reflecting the greater difficulty of characterizing their cross-section behavior in the steep part of the LET spectrum.
For parts without full characterization (see Section 9), additional uncertainty is introduced through technology-based susceptibility priors, lognormal cross-section distributions conditioned on threshold LET, and random sampling of Weibull width and shape parameters from empirically observed ranges.
The tool supports simultaneous analysis of multiple parts, computing per-part SEE rates and aggregating them into a total system-level rate. This is the standard workflow for mission-level SEE rate assessments, where the total system SEL rate determines the overall latch-up risk and the required latch-up mitigation strategy.
Each part in the analysis is defined by its name, quantity (number of instances in the system), data category, and the appropriate cross-section parameters. The tool supports four data categories:
| Category | Required Data | Rate Method |
|---|---|---|
| Full Weibull | σsat, Lth, W, s | Spectral integration with the specified Weibull parameters |
| Partial | Measured Lth and/or σ at one LET | Monte Carlo sampling of missing parameters using empirical prior distributions |
| Null Result | Test LET and fluence (no events observed) | Upper-bound rate from Poisson statistics on zero observed events |
| No Data | Technology type only | Ladbury bounding method using technology susceptibility priors (Section 9) |
The total system SEE rate is the sum of the individual part rates, accounting for part quantity. In each Monte Carlo iteration, the system rate is:
The tool reports per-part rate contributions sorted by magnitude, allowing the analyst to identify the dominant SEE risk drivers in the system. The Mean Time Between Events (MTBE) at the 90% confidence level is computed as MTBE = 1 / R90% and expressed in days and years.
The space radiation environment includes both heavy ions (from galactic cosmic rays and solar particle events) and protons (from trapped radiation belts and solar events). These two particle populations induce SEE through different physical mechanisms and require different rate calculation approaches.
Heavy ions deposit energy primarily through direct ionization along their track. The cross-section is parameterized as a function of LET using the Weibull model, and the rate is computed by spectral integration against the differential LET flux spectrum as described in Sections 2–5.
Protons induce SEE primarily through nuclear reactions that produce short-range, high-LET secondary particles (recoiling nuclei) within the device sensitive volume. Because the SEE-causing mechanism is indirect, the proton cross-section is parameterized as a function of proton energy rather than LET. The proton SEE rate is computed by integrating the proton cross-section against the proton energy spectrum:
When direct proton test data is not available, the tool estimates the proton cross-section from the heavy-ion Weibull parameters using a Bendel-type convolution model. This model integrates over all possible nuclear reaction products weighted by their probability, producing an estimated proton saturation cross-section. The proton threshold energy is related to the heavy-ion onset LET, and the cross-section is assumed to rise linearly from threshold to saturation.
Parts with Lth > 15 MeV-cm2/mg are generally classified as proton-immune, since the maximum LET achievable by proton-induced nuclear reaction secondaries in silicon is approximately 15 MeV-cm2/mg.
Not all parts in a spacecraft have been tested for SEE susceptibility. The Ladbury SEL bounding method provides a framework for estimating worst-case SEL rates for untested or partially characterized parts using technology-based priors derived from historical SEE test databases [5].
For parts with no SEE test data, the method assigns a probability of SEL susceptibility based on the semiconductor technology. This probability is derived from the historical fraction of parts in each technology family that have exhibited SEL in heavy-ion testing. The tool includes default susceptibility priors for common technology families:
| Technology | P(SEL Susceptible) |
|---|---|
| Bulk CMOS | 70% |
| CMOS SOI | 10% |
| BiCMOS | 50% |
| Bipolar | 30% |
| GaAs | 5% |
| SiGe | 25% |
| FPGA | 60% |
| Flash | 55% |
| DRAM | 55% |
These default values can be adjusted by the user based on project-specific knowledge or updated database statistics.
For Monte Carlo iterations where a part is determined to be susceptible, the tool samples a threshold LET from a weighted distribution derived from the historical SEE database and then samples a saturation cross-section conditioned on the threshold LET using an empirical power-law relationship:
Weibull width (W) and shape (s) parameters are randomly selected from a library of empirically observed W-s pairs spanning the range typically seen in SEE test data. The spectral integration is then performed with these sampled parameters to produce a rate for that iteration.
For parts that have been tested but showed no SEE events (null result), the tool computes a bounding rate based on the test LET and fluence. The upper-bound cross-section from Poisson statistics on zero events is used together with an empirical power-law model that relates the bounding rate to the test LET:
The tool generates comprehensive PDF assessment reports that document the complete analysis for archival and review purposes. The exported report includes:
Executive Summary: Risk classification (Low / Medium / High / Very High) based on the 90% confidence level MTBE, along with the total system SEE rate broken down by heavy-ion and proton contributions.
Analysis Configuration: The selected heavy-ion and proton environments, RPP ratio, mission duration, and number of Monte Carlo iterations.
Summary Statistics: Mean and 90%/95%/99% confidence level rates for heavy-ion, proton, and total system SEE rates.
Parts List: Complete table of all analyzed parts with their category, Weibull parameters, proton cross-section, and technology type.
Per-Part Rate Contributions: Sorted breakdown of each part's contribution to the total system rate, with bar charts showing the relative magnitude of heavy-ion vs. proton contributions.
Distribution Plots: Rate distribution histograms and mission likelihood (survival probability) plots captured from the tool's interactive charts.
SEL Susceptibility Priors: Table of the technology-based susceptibility probabilities used in the Ladbury bounding analysis.
Methodology Notes: Summary of the computational methods and key assumptions for traceability.
Users should be aware of the following assumptions and limitations when interpreting SEE rate predictions from this tool.
The IRPP chord-length correction assumes that the device sensitive volume is a rectangular parallelepiped. Real device sensitive volumes may be irregularly shaped, multi-layered, or distributed across multiple nodes. The RPP approximation is a first-order geometric model that can introduce systematic errors, particularly for devices with non-planar sensitive volumes or when the sensitive depth is comparable to the lateral dimensions.
The accuracy of the rate prediction is strongly dependent on the quality of the Weibull fit to the experimental cross-section data. Common issues include:
Insufficient data near threshold: If cross-section data is sparse near the onset LET, the Weibull threshold and width parameters may be poorly constrained. Since the rate integral is most sensitive to the cross-section behavior near threshold (where the environment flux is highest), this can lead to large errors.
Non-Weibull behavior: Some devices exhibit cross-section curves that are not well described by a single Weibull function, such as devices with multiple sensitive volumes that produce a stepped cross-section curve. In such cases, the single-Weibull fit may not adequately capture the true behavior.
Temperature and bias dependence: SEE cross-sections can depend on device temperature and operating voltage. The Weibull parameters used should correspond to the worst-case operating conditions expected in flight.
The on-orbit radiation environment is inherently variable and uncertain. GCR flux levels vary with the solar cycle, and solar particle events are stochastic and unpredictable in timing, duration, and intensity. The built-in environment models represent statistical descriptions (e.g., solar-minimum GCR, worst-case solar event) rather than precise predictions of what a specific spacecraft will encounter. Shielding effects are incorporated into the environment spectra and depend on the assumed shielding geometry and material thickness.
The SEE rate during a solar particle event can be orders of magnitude higher than the quiet-time GCR rate, particularly for proton-induced effects. Mission planning should consider both the average quiet-time rate (for estimating total event count over the mission) and the peak rate during design-basis solar events (for assessing worst-case instantaneous risk and sizing mitigation strategies such as power-cycling or safe-mode entry).
When direct proton SEE test data is not available, the tool estimates the proton cross-section from the heavy-ion Weibull parameters using a simplified Bendel convolution. This is an approximation; actual proton cross-sections can differ from the estimate by an order of magnitude or more, particularly for devices where the proton SEE mechanism is not purely nuclear-reaction driven.
The Monte Carlo uncertainty analysis uses parameterized uncertainty models (beta distributions, lognormal distributions) that are calibrated to historical data. These models may not fully capture the true uncertainty for all device types and technologies. The Ladbury bounding method relies on historical database statistics that may not be representative of newer technologies or specialized processes.