Intuition The one idea behind this whole topicSpace is full of tiny fast bullets (particles) that fly through your satellite's electronics and dump energy where they land. That dumped energy either scrambles a signal, shifts how a transistor behaves, or physically breaks the crystal — and the whole subject is just three names for those three outcomes.
Before you can read the parent note without tripping, you need the vocabulary of the bullets and the target . This page builds every symbol from nothing. We never use a letter before we have drawn its picture.
Everything starts with one fast particle entering one solid material . Picture a marble fired into a slab of clear jelly.
A tiny piece of matter moving fast: an electron , a proton , or a heavy ion (a whole atomic nucleus, like iron, stripped of electrons). "Fast" means it carries kinetic energy — the energy of motion.
Definition Material / targetThe solid the particle flies into. In electronics this is mostly silicon (Si, the semiconductor) and silicon dioxide (SiO₂, the glassy insulator that sits on top of it).
Why we need both: radiation effects are always a conversation between what flies in and what it hits . Change either one and the damage changes.
Definition Energy — measured in electron-volts (eV)Energy is the "how much punch" of the particle. We measure it in electron-volts : 1 eV 1 volt 1 keV = 1 0 3 eV 1 MeV = 1 0 6 eV
Picture: a bigger, faster marble = more eV. A space proton is often "1 MeV
Each E different "energy of what?" question — that is why they carry subscripts.
A fast particle drags on the electrons of the atoms it passes, ripping some loose. Each freed electron leaves behind a "hole" — an empty spot that acts like a positive charge.
Definition Ionization and the electron–hole pairIonization = knocking an electron loose. The freed electron (negative) plus the hole it left (positive) is one electron–hole pair . This is the core event of TID and SEE.
E pair 3.6 eV 18 eV E deposited E deposited / E pair
Why we need it: it is the exchange rate between "energy left behind" and "charge created" — the bridge from physics to circuit trouble.
Definition Electric charge —q Charge is the electrical "stuff" carried by electrons and holes. The smallest chunk is q = 1.6 × 1 0 − 19 C pico-coulombs 1 pC = 1 0 − 12 C femto-coulombs 1 fC = 1 0 − 15 C
A particle does not dump all its energy at one point — it leaves a trail , losing energy step by step along its path.
d x d E d E d x rate of loss along the path . If you know the loss-per-step everywhere, adding up all the steps gives the total:
E deposited = ∫ d x d E d s
Intuition Why an integral (∫ same everywhere . It usually is not — the particle slows down, so its loss-per-step changes along the track. The symbol ∫ total energy left = sum of all the little losses. No other tool answers it.
Definition LET — Linear Energy TransferLET is d x d E ρ MeV ⋅ cm 2 / mg
ρ g/cm 3 ρ = 2.33 g/cm 3
One bullet is an event . A mission is trillions of bullets over years. To describe the slow pile-up we measure dose .
D rate D rate per day . The running total is the Total Ionizing Dose :
TID ( t ) = ∫ 0 t D rate ( t ′ ) d t ′
cumulative ; LET is per-event
Do not mix them. LET tells you how bad one particle is (SEE). Dose/TID tells you how much has piled up over the whole mission (TID). Different questions, different symbols.
TID and SEE both attack a switch called a MOSFET. You need three of its numbers.
Definition Threshold voltageV th V th voltage you must apply before it turns on . Trapped charge from radiation shifts this on-point; we write the shift Δ V th Δ
Definition Oxide capacitanceC ox capacitor is two conductors with insulator between — it stores charge. Its capacitance C Q Q = C V t ox ϵ ox C ox = t ox ϵ ox C ox Δ V th = − Q trap / C ox
Definition Critical chargeQ crit smallest charge a single particle must dump to flip a stored bit: Q crit = C node ⋅ V crit C node
To predict how often errors happen we need the language of "how many particles, how big a target."
Φ Flux = how many particles cross one square centimetre per unit time. Picture rain: flux is raindrops per second hitting a fixed patch of ground. Φ ( LET )
σ effective target area of a device for getting hit, in cm 2 / bit hit rate :
R = σ ⋅ Φ
Intuition Why "cross-section" and not just "area"?The real transistor has fuzzy edges — some hits flip it, some do not, depending on angle and LET. σ equivalent perfectly-sharp bullseye that reproduces the observed error rate. It is a measured number, not a ruler measurement.
The third mechanism is different: sometimes the bullet strikes an atomic nucleus head-on and knocks the whole atom out of its lattice spot.
Definition Crystal lattice and displacementLattice = the neat repeating grid of silicon atoms, like oranges stacked in a crate. A displacement = one orange punched out of its slot, leaving a gap plus a loose orange elsewhere. These defects trap charges and slowly ruin the device (this is Displacement Damage).
E recoil M p , M Si M p M Si E recoil θ
Ionization: electron-hole pairs
Nuclear collision: recoil
Flux Phi and cross-section sigma
Where these live in the vault: the orbit that sets Φ D rate Spacecraft Orbits and Van Allen Belts ; how those levels rise and fall comes from Solar Activity Cycles ; the transistor physics behind V th C ox Semiconductor Physics ; the fix for upsets is Error Correcting Codes ; the mission-level risk maths is Reliability Engineering ; power-side effects touch Photovoltaic Systems and the Power Budget . All of this feeds back into the parent, the main radiation-effects note .
Cover the answer, say it out loud, then reveal.
What does one electron-volt (eV) mean physically? The energy one electron gains crossing a 1-volt difference; 1 MeV = 1 0 6 eV
What is an electron–hole pair? A freed electron (−) plus the positive "hole" it left behind; made by ionization.
How many pairs does deposited energy E deposited About E deposited / E pair E pair ≈ 3.6 eV
What does d x d E Energy lost per tiny step of distance along the particle's track.
Why is E deposited Because the loss-per-step changes as the particle slows, so you must sum many tiny slices.
What is LET and its unit? Linear Energy Transfer, d x d E MeV ⋅ cm 2 / mg
What is dose, and rad vs Gray? Ionizing energy deposited per kilogram; 1 Gy = 1 J/kg 1 rad = 0.01 Gy
What is V th The voltage needed to switch a MOSFET on; radiation shifts it by Δ V th
What is Q crit The minimum charge that flips a stored bit, Q crit = C node V crit
What do flux Φ σ The error/hit rate R = σ Φ
Difference between LET and dose? LET = per-single-particle severity (SEE); dose/TID = mission-total pile-up (TID).
What is displacement damage at the atomic level? A nucleus knocked out of the crystal lattice, leaving defects that trap carriers.