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Fluence to Dose — rad(Si)

Convert photon, proton, or electron fluence to absorbed dose in silicon using NIST cross-section and stopping power data. For total ionizing dose (TID) assessment in space, defense, and HED physics applications. See also: Stopping Power & LET | Displacement Damage

Conversion Parameters

Note: This calculator computes ionizing dose in silicon (TID). For neutron or proton displacement damage, use the Displacement Damage calculator instead.

How It Works

Dose from fluence:

D [rad(Si)] = Φ × C(E) × 1.602 × 10−8

where Φ is the particle fluence (particles/cm²), C(E) is the energy-dependent dose coefficient (MeV·cm²/g), and the factor 1.602×10−8 converts MeV/g to rad (since 1 rad = 100 erg/g = 6.242×107 MeV/g).

Dose coefficient C(E) by particle type:

  • Photons: C(E) = E × μen/ρ(E) — the photon energy multiplied by the mass energy-absorption coefficient for silicon. This uses μen/ρ (not total attenuation μ/ρ) because scattered photons deposit their energy elsewhere in a broad-beam geometry.
  • Protons: C(E) = Sel/ρ(E) — the mass electronic (collision) stopping power. Only the electronic component is used because nuclear stopping produces displacement damage (NIEL), not ionizing dose.
  • Electrons: C(E) = Scol/ρ(E) — the mass collision stopping power. Radiative losses (bremsstrahlung) are excluded because those photons deposit energy elsewhere.

What does “per cm²” mean?

The cm² is in the fluence, not a target area. Fluence is the number of particles crossing a unit area perpendicular to the beam. To get total dose, you multiply fluence (particles/cm²) by the dose coefficient. The dose coefficient already accounts for the energy deposited per unit mass of silicon per particle traversal.

Thin-target approximation:

This calculator assumes the particle energy does not change significantly as it traverses the target. This is valid for electronics die and oxide layers, which are thin compared to the particle range. For thick shielding or deep-dose calculations, transport codes (e.g., MCNP, Geant4) are needed.

Why no neutrons?

Neutrons primarily cause displacement damage in electronics by knocking silicon atoms out of their lattice positions. This is quantified using 1 MeV equivalent neutron fluence (ASTM E722) and non-ionizing energy loss (NIEL), not ionizing dose — see the Displacement Damage calculator. Neutrons do produce some ionizing dose through recoil nuclei, capture gammas, and secondary charged particles, but displacement damage is the dominant damage mechanism and the standard metric for neutron hardness assurance. For more background, see Radiation Effects on Electronics.

Benchmark: For Co-60 gammas (1.25 MeV), this calculator gives ~1 rad(Si) per 1.89×109 γ/cm². This follows from the NIST XCOM value μen/ρ = 0.02652 cm²/g for Si at 1.25 MeV, giving C(E) = 0.03315 MeV·cm²/g and Φ = 1/(C(E) × 1.602×10−8) = 1.89×109 γ/cm² per rad(Si). See ASTM E1249 for Co-60 dosimetry practice in silicon device testing.

References

  1. NIST XCOM: Photon Cross Sections Database — mass energy-absorption coefficients (μen/ρ) for silicon. National Institute of Standards and Technology.
  2. NIST PSTAR: Stopping-Power and Range Tables for Protons — electronic stopping powers for silicon. National Institute of Standards and Technology.
  3. NIST ESTAR: Stopping-Power and Range Tables for Electrons — collision stopping powers for silicon. National Institute of Standards and Technology.
  4. U.S. Department of Defense, “MIL-STD-883, Test Method 1019.9: Steady-State Total Ionizing Dose Test Method.”
  5. ASTM International, “ASTM E1249: Standard Practice for Minimizing Dosimetry Errors in Radiation Hardness Testing of Silicon Electronic Devices Using Co-60 Sources.”
  6. ASTM International, “ASTM E722: Standard Practice for Characterizing Neutron Energy Fluence Spectra in Terms of an Equivalent Monoenergetic Neutron Fluence for Radiation-Hardness Testing of Electronics.”

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