Expressing the sensitivity of electronic circuits to radiation

To make a decision if some electronic device may be sent to space, how to protect it against space radiation and how it may affect the execution of our software, we need to have a set of quantities which describe the device susceptibility to radiation.

Description of radiation environment

Space radiation is a sum of different particles which moves very fast, comes from different sources and carry different energies. To describe the structure of radiation we use models which present a spectrum of fluxes of particles and their energy.

Flux and fluence of particles

Flux is a measure which tells us how densely space is filled with moving particles. We can imagine that we put a square frame in space and starting to count particles which fly through the frame. The intense of appearing particles inside the frame is the flux – number of particles flying through the frame per second. It is usually given in units [\frac {1} {s \cdot cm^2}].

Fluence is a total number of particles which have flayed through the frame in given time, its unit is [\frac {1} {cm^2}].

Resistance for Total Ionization Dose (TID)

During exposition on radiation semiconductors absorbs energy. There is a level of the absorbed energy (TID) which cause permanent failure of the device. TID is defined as an energy absorbed by unit of the material’s mass during its exposition for radiation. The most common unit is rad 1 rad=0,01 Gy  = 0,01 \frac {J} {kg} = 100 \frac {erg} {g}.

Linear Energy Transfer (LET)

When a heavy-ion hits an electronic device, then it loses some energy to ionization while it traverses the device’s matter. Lose of the energy depends on heavy-ion and on the type of hit material. The ion’s lost energy is responsible for parasitic events in the lattice structure. To describe how the radiation particle loses energy in the matter we use quantity named Linear Energy Transfer (in short LET). LET is simply defined as a portion of lost energy per distance on which it happens :LET=\frac{\Delta E}{\Delta x}[N]. Newton is not a convenient unit to describe LET, first of all, it is better to describe lost energy in eV, to be more specific in MeV, what will better correspond with the description of ionization radiation and the energy of its particles. Secondary, when we want to compare different LET levels on the same material it is more practical to use surface field under radiation rays and the mass of the material in which the particle lost its energy, thus helps to better describe radiation treatment during experiments on devices. We can express the length of the partition path in the material using density as follows:
\sigma = \frac{m}{x \cdot y \cdot  z}[\frac{kg}{m^{3}}]
z = \frac {m}{\sigma \cdot x \cdot y } = \frac{m}{\sigma \cdot S}[m]
LET_\sigma =\frac {E} {z} = \frac {E} { \frac{m}{\sigma \cdot S}} = \frac {E \cdot S} {m} \cdot \sigma [ \frac {{}eV  \cdot m^{2}}{kg} \cdot \frac{kg}{m^{3}}=\frac {{}MeV  cm^{2}}{mg} \cdot \frac{kg}{m^{3}}]
Because density is constant for the material we can eliminate it:
LET = \frac {LET_\sigma} {\sigma} = \frac {\frac {E \cdot S} {m} \cdot \sigma} {\sigma} = \frac {E \cdot S} {m} [\frac {MeV  \cdot cm^2} {mg}]

Higher LET means that the material good stops the radiation particles, but then larger amount of absorbed energy may generate parasitic effects. LET for different materials and heavy ions can be computed by calculator like this one.

Cross Section

The cross-section is a general quantity which describes device susceptibility for radiation, it is defined as a ratio of the probability of event occurrence to a fluence of particles:
Cs = \frac {p} {f} [\frac {1} {\frac {1} {cm^2}} = cm^2]

SEU cross section

To describe how the digital device is sensitive for Single Events Upsets, the SEU cross-section is used. If during experiments we treat a device with some fluence of particles, and we detect some number of bits affected with SEU, then the ratio of a number of affected bits to the fluence is named SEU cross-section [cm^2]. We can present the SEU cross-section as a value per device. If we know how many memories are included in the device, then we can divide cross-section per device by a number of bits inside the device to compute SEU cross-section per bit [\frac {cm^2} {bit}].

It was assumed than cross-section characteristic is taken for fluence equals to 10^7[\frac {particles} {cm^2}], what implicates sampling rates during experiments.

For a different type of particles the device my response differently, thus experiments with a different flux of different types of particles are required to find cross-sections for each of them. Especially separated tests for neutrons and protons are required since the response of chips for those particles is different for energy less than 50MeV.

LET Threshold

During experiments on electronic chips, the researchers treat the device with a different flux of particles and measure cross-sections. For experiments, the flux of particles is prepared to cause expected LET in the device material. As a result of experiments, we got characteristic of LET levels vs cross-sections.

cross section vs radiation LET
An example of SEU cross section vs Let: Comparison of SEU cross sections for D-Cache for Motorola PowerPC
7455 with clock frequency of 800 MHz for internal core voltage of 1.6 and

As we can see on the example above, for small LET levels the SEU cross-section tends to be 0[\frac {cm^2} {bit}], it means those levels do not induce effects on the device. The smallest LET level which causes an effect is a crucial element of the device characteristic and is named “LET threshold(LET_t_h)”. In practice it is hard to make experiments which threat the device with a continuous full range of LET level from 0 to hundreds of \frac {MEv \cdot cm^2} {mg}, so the threshold is computed with extrapolation of characteristic taken during the experiment. For example above we can imagine that the curve will reach cross-section 0 for LET about 1 [\frac{MEv \cdot cm^2} {mg}]

SEFI, SEL and other kind of LET_t_h

Apart from study SEU, we can also investigate other kinds of SEE. Similar characteristics may be prepared for SEL or SEFI, and different LET_th may be extrapolated for different kind of events.

Decision about suitability a device to a space mission

We can use LET_t_h to make an assumption about the susceptibility of the device for radiation which is present in the area of the space, in which the spacecraft will work. NASA divides levels of LET_th for three ranges:

Device Threshold [\frac {MeV \cdot cm^2} {mg}]Environment to be Assessed
1LET_t_h < 20Cosmic Ray, Trapped Protons, Solar Proton Events
220 < LET_t_h < 100Galactic Cosmic Ray Heavy Ions, Solar Heavy Ions
3LET_t_h > 100No analysis required

The first group is a set of devices which are very sensitive for radiation, they cannot be considered to use outside the protection of Earth’s magnetosphere, moreover, it must be checked how much they will suffer for SEE even on the relatively benign environment of LEO orbits. The second group is immune for small energy particles, but if the device will be used far away from Earth we need to study its susceptibility for effects caused by heavy ions. The third group contains devices which are immune to the radiation.

Soft error rate (SER)

When exposition on radiation cause change of logical state of logic elements like latches, SRAM cells, or gates, then the logical error occurs. Because this kind of error is not destructive for the circuit it is named soft error.

Soft error rate (also known as SEU rate) is a quantity which describes chip response to a particular type of radiation environment, so for the same device, it is different for a different location (eg. terrestrial vs LEO orbit).

The are two common units of soft error rate:

  • FIT – Failures In Time, which is a number of events per one billion hours
  • MTBF – Mean Time Between Failures in hours

SER Predictions

Soft error rate must be predicted for the device and environment in which it will work. There are models which help to predict SER based on space radiation structure and characteristic of the device. At the moment the best model is CREME96 – The Cosmic Ray Effects on Micro-Electronics (1996 Revision). CREME96 is a set of computer programs to creating numerical models of the ionizing radiation environment in near-Earth orbits, evaluating the resulting radiation effects on electronic systems in spacecraft and in high-altitude aircraft and estimating the high LET radiation environment within manned spacecraft. It requires to known cross-section vs LET characteristics of the devices. CREME96 is available by www here.