Help & Methodology Reference
The Space RHA Ion Beam Planning Tool is a web-based calculator that helps radiation effects engineers plan heavy-ion single event effects (SEE) testing at cyclotron facilities. Given a target linear energy transfer (LET) and minimum range requirement in a specified device material, the tool searches a database of beam cocktails from eight major SEE testing facilities worldwide and recommends specific ions, energies, tilt angles, and degrader thicknesses to achieve the desired test conditions.
The tool handles the full beam transport calculation: energy loss through the beamline exit window (for in-air setups), the air gap between the window and the device under test (DUT), any user-defined overlayer stackup on the device itself, and optional aluminum degrader foils placed upstream. All stopping power calculations are based on SRIM (Stopping and Range of Ions in Matter) tabulated data for 24 ion species across multiple target materials.
The primary workflow is straightforward: specify the beam medium (in-air or vacuum), the target material and any overlayers, the desired LET range and minimum range, and optionally filter by facility. The tool then evaluates every available beam tune and reports which ions can meet the requirements, along with the specific angle and/or degrader settings needed.
Heavy-ion testing is the primary method for characterizing single event effects in semiconductor devices intended for space applications. The goal is to measure the device cross-section — the probability of an SEE occurring per unit particle fluence — as a function of LET. This cross-section versus LET curve is then used to predict in-orbit SEE rates using spectral integration against the space radiation environment.
Cyclotron facilities used for SEE testing provide "cocktail" beams: a set of different ion species accelerated to the same velocity (energy per nucleon, MeV/u). Because different ions have different atomic numbers and masses, each ion in the cocktail delivers a different LET to the DUT. A typical cocktail might include ions from neon (Z=10) through gold (Z=79), spanning a LET range from roughly 1 to 90 MeV·cm²/mg in silicon. By switching between ions in the cocktail, the experimenter can rapidly sweep the LET range without retuning the accelerator.
Linear Energy Transfer (LET) is the energy deposited by an ion per unit path length in the target material, normalized by the material density. It is expressed in units of MeV·cm²/mg. The LET that matters for SEE testing is the LET at the device sensitive region — not the LET at the beamline exit. As the ion traverses material upstream of the sensitive region (exit window, air gap, device lid, passivation, metallization), it loses energy and its LET changes. For most cocktail energies, the LET increases as the ion slows down, until the ion approaches the Bragg peak where LET rises sharply just before the ion stops.
The ion must have sufficient residual range to penetrate through the device sensitive volume. If the ion stops within the overlayer stackup or at the very surface of the device, the test results will be unreliable — the LET will vary dramatically across the sensitive volume depth, and nuclear fragmentation near end-of-range introduces additional complications. ASTM F1192 [2] and JEDEC JESD57A [3] require that the ion range exceed the sensitive volume depth by a comfortable margin. A common rule of thumb is a minimum of 30–40 μm of residual range in silicon, though this depends on the device technology.
Heavy-ion beamlines can deliver ions either in air or in vacuum. Each approach has distinct implications for beam transport and LET at the device:
| Parameter | In-Air | Vacuum |
|---|---|---|
| Beam exit | Passes through a thin metal window (typically Kapton or Havar) to transition from beamline vacuum to atmosphere | DUT is mounted inside the vacuum chamber; no window needed |
| Air gap | Ion traverses several centimeters of air between window and DUT; causes energy loss and straggling | No air gap |
| DUT access | Easier setup; DUT can be on a board outside the vacuum system | DUT must be vacuum-compatible; electrical feedthroughs required |
| LET effect | Energy loss in window + air increases LET at device (ion is slower) | Higher residual energy; lower LET at device for same initial beam |
| Range effect | Reduced range at device due to upstream energy loss | Maximum range at device |
When "In-Air" is selected, the tool includes the facility-specific exit window material and thickness, plus the user-specified air gap distance, in the layer-by-layer energy loss calculation. When "Vacuum" is selected, these layers are omitted.
Each facility in the database has specific beam delivery parameters: the available cocktail energies (MeV/u), the ion species in each cocktail, and whether in-air and/or vacuum testing is supported. The tool stores these parameters for each facility tune and uses them to determine which beams are physically available for a given test configuration.
When the DUT is tilted relative to the beam axis, the effective path length through the air gap increases as 1/cos(θ). At large tilt angles (above ~50°), this can significantly increase energy loss in the air gap and may cause low-energy ions to stop before reaching the device. The tool accounts for this increased path length in all calculations. Users should also be aware that physical clearance between the DUT board and beamline hardware may limit the maximum achievable tilt angle at some facilities.
The overlayer stackup defines the layers of material that the ion must traverse after exiting the beamline (and passing through any air gap) but before reaching the device sensitive region. These layers cause energy loss that changes the LET at the sensitive region relative to what it would be at the device surface.
Typical overlayer materials encountered in SEE testing include:
| Layer | Material | Typical Thickness |
|---|---|---|
| Package lid | Kovar, ceramic (Al2O3), or removed (delidded) | 0 (delidded) to 500+ μm |
| Die attach / epoxy | Epoxy, silver-filled epoxy | 25–75 μm |
| Passivation | Silicon nitride (Si3N4), SiO2 | 0.5–2 μm |
| Metallization (BEOL) | Aluminum, copper, tungsten | Effective 2–15 μm (technology dependent) |
| Polyimide tape | Kapton | 25–50 μm (if used for beam monitoring) |
Users define the stackup by adding layers with a specified material and thickness. The tool calculates energy loss through each layer sequentially, starting from the outermost layer (closest to the beam) and proceeding inward to the device sensitive region. The order of layers matters because energy loss is energy-dependent — the ion LET changes as it traverses each layer.
As the ion loses energy in the overlayer stackup, its LET generally increases (the ion is slowing down on the rising portion of the Bragg curve). This means the LET at the sensitive region is typically higher than the surface LET. However, the residual range decreases. If the overlayer is too thick, the ion may stop before reaching the sensitive region, or the remaining range may be insufficient for a valid test.
All energy loss and range calculations in the Beam Planner are based on stopping power data from SRIM (Stopping and Range of Ions in Matter) [1], the standard reference for ion-matter interactions in the radiation effects community.
SRIM calculates the electronic and nuclear stopping powers of ions in matter using a quantum-mechanical treatment of ion-atom collisions. For each ion–target combination, SRIM produces tables of:
| Quantity | Units | Description |
|---|---|---|
| Electronic stopping (Se) | MeV·cm²/mg | Energy loss due to interactions with target electrons |
| Nuclear stopping (Sn) | MeV·cm²/mg | Energy loss due to elastic collisions with target nuclei (small at high energies) |
| Total LET | MeV·cm²/mg | Se + Sn |
| Projected range | μm | Mean distance the ion travels before stopping |
The tool stores pre-computed SRIM tables for 24 ion species commonly used in SEE testing cocktails, covering target materials including silicon, gallium arsenide (GaAs), silicon carbide (SiC), aluminum, copper, Kapton, Mylar, air, and others.
SRIM tables are provided at discrete energy points. To obtain LET and range at arbitrary energies, the tool performs log-log interpolation — that is, linear interpolation in ln(energy) vs. ln(LET) and ln(energy) vs. ln(range) space. This is physically motivated: stopping power curves are approximately power-law functions of energy over broad energy ranges, so log-log interpolation produces significantly more accurate intermediate values than linear interpolation, particularly on the steep portions of the Bragg curve.
where E1 and E2 are the nearest tabulated energies bracketing the energy of interest, and LET1, LET2 are the corresponding tabulated LET values. The same approach is used for range interpolation.
SRIM stopping power data is calculated for specific isotopes. When a facility cocktail uses an isotope for which SRIM data is not directly available (e.g., Xe-126), the tool maps to the nearest available isotope in the SRIM database (e.g., Xe-129). Because stopping power depends primarily on the atomic number Z and only weakly on the mass number A (through velocity scaling at the same MeV/u), this approximation introduces negligible error for the isotope differences typically encountered in cocktail beams. The energy is scaled by the mass ratio (Aactual/ASRIM) to maintain the correct velocity.
Tilting the DUT relative to the beam axis is a standard technique for increasing the effective LET without changing the ion species. When an ion enters the device at an angle θ from normal incidence, it traverses a longer path through the sensitive volume, depositing more energy per unit vertical depth.
For a thin, planar sensitive volume (the standard assumption for most modern CMOS technologies), the effective LET and effective range are related to the normal-incidence values by:
The physical interpretation is straightforward: the ion path through the sensitive volume is longer by a factor of 1/cos(θ), so more charge is deposited per unit depth. Conversely, the vertical component of the ion's remaining range is reduced by cos(θ), so the effective penetration depth is less.
Tilting also increases the path length through all overlayer materials. The tool accounts for this by dividing each layer thickness by cos(θ) before computing energy loss. This is important because increased path length through the overlayer means more energy loss before the ion reaches the device, which further modifies the LET (and reduces remaining range) beyond the simple cosine correction.
While the cosine law allows arbitrarily high effective LET in principle, practical considerations limit the useful tilt angle range:
| Angle Range | 1/cos(θ) | Considerations |
|---|---|---|
| 0°–30° | 1.00–1.15 | Minimal complications; standard operating range |
| 30°–45° | 1.15–1.41 | Moderate LET increase; increased path through overlayers |
| 45°–60° | 1.41–2.00 | Significant LET increase but reduced range; beam spot broadens on DUT; physical clearance may be an issue |
| > 60° | > 2.00 | Generally not recommended; cosine law validity becomes questionable for thick sensitive volumes; beam uniformity concerns |
An aluminum degrader foil placed in the beam path upstream of the DUT is a standard technique for increasing the LET at the device beyond what the undegraded beam provides. By passing through the degrader, the ion loses energy and slows down, increasing its LET in the subsequent target material.
The physics is identical to overlayer energy loss: the ion's energy after the degrader is calculated using the SRIM stopping power tables for the ion in aluminum, accounting for the degrader thickness. The tool then recalculates the LET and remaining range in the target material at the reduced energy.
Adding degrader thickness has a monotonic effect: as the degrader gets thicker, the ion emerges with less energy, higher LET, and less remaining range. There is a maximum achievable LET for each ion corresponding to the Bragg peak — beyond this, adding more degrader simply stops the ion. The tool searches for the degrader thickness that produces the target LET while maintaining sufficient residual range.
In practice, degrader foils are placed between the beamline exit and the DUT. For in-air setups, the degrader is typically positioned just after the exit window, before the air gap. The tool models the degrader as the first layer the ion encounters after exiting the beamline, followed by the air gap (if in-air), then the overlayer stackup, and finally the target material.
The recommendation engine is the core of the Beam Planner. Given the user's target LET, minimum range, maximum acceptable LET, and tilt angle range, it evaluates every beam tune in the database and classifies each ion into one of three categories: Pass (meets requirements as-is or with angle adjustment), Achievable (can meet requirements with degrader and/or angle), or Fail (cannot meet requirements).
The engine uses three strategies, applied in order of preference:
The simplest approach. If the ion's normal-incidence LET at the device (after all upstream material) is less than the target LET, and the target LET can be reached by tilting within the allowed angle range, the engine solves for the exact tilt angle:
This analytical solution assumes that LETnormal does not change with angle, which is only approximately true because tilting also increases path length through the overlayers. The engine therefore refines the angle using a binary search: it recalculates the full layer-by-layer energy loss at each candidate angle, accounting for the increased overlayer path length, until the LET at the device converges to the target value within tolerance.
Angle-only solutions are preferred because they preserve the full beam range (no degrader-induced straggling) and are operationally simple at the facility. The engine also verifies that the effective range at the solved angle meets the minimum range requirement.
If angle-only cannot achieve the target LET (e.g., the required angle exceeds the maximum allowed, or the normal-incidence LET already exceeds the target), the engine searches for an aluminum degrader thickness that produces the target LET at normal incidence (or at the minimum allowed angle). The search is performed by binary search over degrader thickness, evaluating the full beam transport calculation at each thickness.
The engine checks that the residual range after degradation meets the minimum range requirement. If the range falls below the minimum before the target LET is reached, the ion is marked as unable to achieve the target via degrader alone.
For hard-to-reach LET values — where neither angle alone nor degrader alone can achieve the target while maintaining sufficient range — the engine combines both techniques. A degrader is used to bring the LET close to the target, and then a tilt angle is applied to reach the final target value. This two-parameter optimization searches over degrader thickness and angle simultaneously, subject to the constraints on maximum angle and minimum range.
Combined solutions are the most operationally complex (requiring both degrader foil installation and DUT rotation), but they extend the achievable LET range for ions that would otherwise be unable to meet requirements.
The LET vs Range plot is the primary visualization in the Beam Planner. It shows how LET varies with remaining range in the target material for each beam, following the TAMU-style convention used widely in the radiation effects community.
In this convention, the x-axis represents remaining range in the target material (in μm), with zero on the left (the Bragg peak, where the ion stops) and increasing range to the right (corresponding to higher initial energies and the ion being farther from end-of-range). The y-axis is LET in MeV·cm²/mg.
Each curve on the plot traces the LET vs. range relationship for a particular ion. The rightmost point of each curve corresponds to the surface LET (the LET when the ion first enters the target with its full remaining range). As the ion penetrates deeper (moving left on the plot), it slows down, its LET increases, and its remaining range decreases. At the far left, the ion reaches the Bragg peak — the maximum LET — just before it stops.
For a given beam arriving at the device surface with a known energy, the operating point on the plot is determined by the remaining range. The vertical position gives the surface LET, and the horizontal position gives the available penetration depth. When you tilt the device, the effective LET increases (you move up on the plot) while the effective range decreases (you move left). When you add degrader, the ion arrives with less energy and less range, so the operating point shifts to the left along the curve, to a point with higher LET and lower range.
Beam curves are color-coded by their status relative to the user's requirements:
| Color | Status | Meaning |
|---|---|---|
| Green | Pass | Ion meets the target LET and minimum range requirements (with angle or as-is) |
| Amber | Achievable | Ion can meet requirements with degrader and/or angle adjustment |
| Red | Fail | Ion cannot meet the requirements (insufficient range or LET not achievable) |
Both axes support log and linear scale toggles. Log scale is useful for viewing the full dynamic range of LET values across all ions. Linear scale is useful for examining a specific LET region in detail. The plot can be zoomed and panned interactively.
The tool includes beam data from eight major heavy-ion SEE testing facilities. Each facility entry specifies the available ion species, beam energy (MeV/u), and surface LET in silicon for each tune. Users can enable or disable individual facility tunes using the facility filter.
| Facility | Tunes (MeV/u) | Notes |
|---|---|---|
| TAMU K500 | 15, 25, 40 | Texas A&M University Cyclotron Institute. Three cocktail energies covering a broad LET range. Widely used for SEE testing per ASTM F1192. In-air and vacuum operation [8]. |
| TAMU K150 | Various | Lower-energy cyclotron at TAMU. Provides additional ion species and energies complementary to K500 [8]. |
| LBNL 88-Inch | 4.5, 10, 16 | Lawrence Berkeley National Laboratory 88-Inch Cyclotron. Three standard cocktail energies. Historically one of the most widely used SEE test facilities [10]. |
| BNL NSRL | Up to 1000 | Brookhaven National Laboratory NASA Space Radiation Laboratory. High-energy beams suitable for testing through thick shielding and for simulating GCR spectra. Energies up to 1000 MeV/u available [9]. |
| NASA GSFC | NSRL-based | NASA Goddard Space Flight Center program using NSRL beams. High-energy ions for deep penetration testing. |
| GANIL | 9.3 | Grand Accélérateur National d'Ions Lourds, Caen, France. European SEE testing facility with a 9.3 MeV/u cocktail. |
| RADEF | 10, 16.3 | University of Jyväskylä Accelerator Laboratory RADiation Effects Facility, Finland. ESA-supported SEE testing with two cocktail energies. |
| TRIUMF | Various | TRIUMF, Canada's particle accelerator centre, Vancouver. Provides various ion species and energies for SEE characterization. |
Because different cocktail energies at the same facility produce different LET ranges and penetration depths, the tool allows filtering at the individual tune level. For example, you can enable the TAMU K500 40 MeV/u cocktail while disabling the 15 MeV/u and 25 MeV/u tunes. This is useful when you know which specific beam time you have been allocated, or when you want to compare what different energies can achieve for your test requirements.
While the Beam Planner provides useful estimates for test planning, users should be aware of the following limitations inherent in the calculation approach:
SRIM stopping power predictions are generally accurate to within ±5% for heavy ions at energies above 1 MeV/u in elemental targets, and within ±10% for compound targets [1]. At very low energies (near end-of-range) and for the heaviest ions, accuracy may degrade further. The tool uses SRIM 2010 data, which incorporated substantial improvements over earlier versions, but users should treat all LET and range values as estimates with inherent uncertainty of at least ±5–10%.
The tool calculates electromagnetic (electronic and nuclear) stopping power only. It does not model nuclear fragmentation reactions, in which the projectile ion or target nucleus breaks apart, producing secondary fragments with different Z, A, and LET. Nuclear reactions become increasingly important at high energies (above ~100 MeV/u) and can cause the primary beam to lose intensity with depth. For high-energy facilities like BNL NSRL, nuclear reaction losses should be considered separately [5].
Statistical fluctuations in energy loss (straggling) are not modeled. The tool reports only the mean energy loss and mean LET. After passing through thick degraders or overlayers, the actual energy distribution of the beam broadens, resulting in a spread of LET values at the device. Straggling is typically small for undegraded cocktail beams but can become significant for heavily degraded beams (where the residual range is a small fraction of the initial range). Users should consult SRIM full Monte Carlo simulations or Geant4 for straggling estimates when using thick degraders.
The tool assumes a perfectly uniform beam with a single energy. Real beams have finite spot size, spatial non-uniformity, and energy spread from the accelerator. These effects are facility-specific and can affect the actual LET distribution across the DUT. Beam uniformity is typically characterized by the facility and should be verified during dosimetry.
Actual beamline parameters (exit window material and thickness, air gap distance, available degrader thicknesses, maximum tilt angle) vary by facility and may differ from the default values in the tool. Users should confirm these parameters with the facility before testing and adjust the tool inputs accordingly.
For compound target materials (GaAs, SiC, etc.), SRIM uses the Bragg additivity rule with corrections for chemical bonding effects. The accuracy for compounds is generally ±5–10% but can be larger for certain material combinations [1]. The tool uses SRIM compound calculations directly without additional corrections.