Radiation effects are mainly caused by electrons and protons trapped in the earth’s geomagnetic field, protons and heavy ions in high energy galactic cosmic rays (GCR), and protons and heavy ions in solar event/flare. Radiation effects include ionizing dose, single event effects (SEE), and spacecraft charging.
TID (Total Ionizing Dose) is the accumulation of the damage from all of the radiation particles. TID is in Krad, which is an energy unit. Particles/energy trapped in SiO2 and Si causes CMOS and bipolar devices to deviate from their normal performance and eventually could cause failure and permanent damage. SEE (Single Event Effect) refers to a gate in an electronic device changes its state from 0 to 1 or from 1 to 0 caused by one single ionizing particle (mainly from heavy ions and protons) striking this gate. SEE causes device malfunction but is normally a soft error and not a permanent damage unless it is SEL (Single Event Latchup).
Galactic cosmic rays (GCR) originate outside solar system and are always present at Earth. GCR consists of about 85% protons, 14% helium, and 1% heavy ions. GCR is a primary source of SEE and a big concern for spacecraft and high-altitude aircraft. Solar wind consists of about 96% protons, 4% helium and heavy ions, and an equal number of electrons. Solar wind is another primary source of radiation in space.
Fig. Van-Allen Belts
Magnetosphere of earth causes radiation particles to be trapped in two belts, called the Van Allen Belts named after the founder, Dr. Van Allen. The inner belt is the so-called the proton belt and outer belt the electron belt. Trapped electrons and protons are omni-directional. These two belts are primary source of for total dose and SEE (mainly proton) for earth orbit satellites.
Next we look at how to model radiation (electrons, protons, and heavy ions) for their effects (TID and SEE).
Fig 1. Electron Flux
Fig 1 shows trapped electron flux vs electron energy. Flux is measured in # of electron particles flowing through cm square area per day. As can be seen,
- electron energy range is from 0.1 to 8 MeV
- there are more low energy electrons and flux decreases sharply with energy going higher.
- high earth orbit like GEO has more electron concentration than medium earth orbit like 1400Km and low earth orbit like 500Km.
Trapped electrons contribute to total dose and deep dielectric charging but are a less concern for SEE due to its low energy.
Fig 2. Proton Flux
Fig2 shows trapped proton flux vs proton energy. Here we show peak flux per sec and not average flux per day. As can be seen:
- proton energy range is from 0.1 to 1000MeV
- there are more low energy protons and flux decrease sharply with higher energy
- GEO has more low energy protons while 1400Km has more high energy protons.
Trapped protons contribute to total dose and SEE.
Fig 3. Total Dose vs Orbit Altitude
Fig 3 shows total dose verse orbit altitude and the curve matches Fig2. Fig2 shows 1400Km has more protons in 100-1000MeV range while GEO has more protons in <100MeV range which is due to Van Allen belt effect. Combined, TID worse case is around 2000Km orbit which is the Van Allen belt region.
Fig 4. Heavy Ion Flux
Both protons and heavy ions contribute to SEE. Fig 2 already shows proton flux. Here fig 4 shows heavy ion flux. Flux goes higher with higher orbit. Most particles reside in low LET section. Here you may ask what is LET and why not just use energy in MeV as in the case of protons and electrons. First, LET (Linear Energy Transfer) is defined as the energy absorbed by the target through which a particle is traveling per unit length of the track of the particle. LET is expressed in units of Mev/mg/cm2. The reason to use LET for heavy ions is related to how we model the relationship between proton / heavy ion flux and number of SEU errors.
Fig 5. Cross-Section from Heavy Ions and Protons
Fig 5 shows we use cross-section to build this relationship. Cross-section defines the sensitivity of a device and it is just (# of SEU errors)/fluence. Fluence unit is # of particles flowing through one cm2 area. So cross-section unit is cm2. Many times we use cm2 per bit to normalize to bit for memory devices. Cross-section fig shows there is a threshold LET (LET_th) for heavy ions and a threshold Mev (Mev_th) for protons that particles with LET or MeV above this value should start causing SEU failures. In addition, cross-section flats out for high LET and high MeV particles. This plateau is also called asymptotic or saturation cross-section.
Cross-section is per chip/device. So theoretically, to calculate SEU, get flux vs LET chart (fig) and cross-section vs. LET chart (fig) for your device, multiply two charts together, and then integrate over LET from 0 to infinity to get the total contribution from all energy particles. Or we can approximate by taking advantage of cross-section saturation. Integrate flux vs LET chart only first. Although LET threshold varies per chip, we can pick a reasonable number here and it won’t affect integral result much. Then multiply this integral with the saturation cross-section of your device and you get # of SEUs for your device.
More about LET. LET depends on the target material (ie. your chip material), ion type such as Helium or Oxygen or Titanium, and the ion energy in MeV. There is an online LET calculator from BNL, http://tvdg10.phy.bnl.gov/LETCalc.html. I did some calculation and result is show as below
|Ion Type||Peak LET (Mev/cm2/mg)||Energy for Peak LET (Mev)||Range for Peak LET (microns)|
Here Peak LET is the maximum value the LET can take with the specified target material and ion type. Range is the distance a particle of a given energy will travel through the target until it is stopped. What is important is peak LET. In other words, LET does not simply go higher with higher energy. Combined with cross-section vs LET chart, you may already realize when heavy ion energy starts going higher, it first causes more SEU errors but when energy goes beyond a threshold (peak LET), higher energy ion actually causes less SEU errors. This is because these ions have so much energy that they just pass through the materials without causing SEU error.
Now back to the question why to use LET for heavy ions while use simple MeV (energy) for protons. Actually we can also use MeV for heavy ions but above cross-section characteristics won’t apply due to peak LET effect. So to apply cross-section concept to both protons and heavy ions, we use LET for heavy ions and MeV for protons.