Not all radiation events are created equal. One of the most commonly used terms in single event effect (SEE) testing and reporting is ion linear energy transfer (LET), expressed in units of MeV-cm2/mg. LET is a measure of the amount of energy, dE, lost by a particle by electronic processes (ionization) in a specific material as it travels an incremental distance, dx, through that material. The LET metric is focused on localized energy loss and does not include the effects of radiative energy loss like Bremsstrahlung (gamma rays emitted due to acceleration of charged particles) or delta-rays (secondary electrons). As a side note, another term, the Stopping Power, accounts for all the energy lost by the particle.
LET is not constant but is dependent on the particle’s energy. LET is also strongly dependent on the particle type (proton, electron, light ion, heavy ion, etc.) and the material through which the particle is traveling. Here are a few simple “rules of thumb” for LET:
- The heavier the particle, the higher the LET.
- At the same energy, lighter particles will usually have a lower LET than heavier particles.
- Consequently, lighter particles will usually have a larger range than heavier particles.
- For the same ion and energy, the LET of particles traversing through denser materials will usually be higher than that of ions traversing less dense materials.
- The range of ions will be shorter in denser materials.
Fig. 1 shows the simulated LET (red) and range (blue) for an iron ion in silicon as a function of its energy. An ion with more energy will go farther (have a longer range). As the ion loses kinetic energy, it moves more slowly and has more time to ionize a greater amount of charge. Thus, in going from high-ion energy to lower energy, the ion LET increases until peaking at low energy. Once the kinetic energy drops to zero, the ion is considered stopped and is no longer an issue from a device upset point-of-view. The LET peak is known as the Bragg peak. This non-linear property as a function of the particle energy implies that unless a shield has a thickness sufficient enough to completely stop a particle, it will reduce the particle energy, which may actually increase its LET and its impact in sensitive circuit areas. This effect was seen in TI DRAMs using a polyimide film serving as an overcoat, mechanical stress relief and “alpha-shield.” Experiments revealed that the industry-accepted practice of using thin shields did not block alpha particles but, instead, stopped them closer to active device layers with a higher LET, thus making alpha particle soft errors worse than in DRAMs without shielding .
LET is physical property independent of the actual trajectory of the ion (ignoring the special case of channeling effects in crystalline materials). However, since the active layers in most semiconductor devices are constrained to a thin layer at the surface, ions with trajectories closer to these layers (higher angles of incidence) will create much more charge in proximity to the active areas. To account for this angle effect, the inverse cosine law is used to calculate the effective LET (LETeff):
LETeff = LET/cos(θ)
where θ is the particle’s angle of incidence (0° for normal incidence) with respect to the surface of the silicon. Fig. 2 shows two identical ion strikes, one at normal incidence and one at a glancing angle of 60°. Since most of the energy is lost at the end of the ion’s path, the glancing ion event deposits much more excess charge near the junction; hence, its ability to disrupt the device function is significantly enhanced.
Fig. 3 shows a stopping and range of ions in matter (SRIM) simulation of LETeff as a function of ion angle. Generally, when LET is mentioned in the context of its effect on electronic devices, you can assume that the angle term is included; thus, LET mentioned in literature is actually LETeff. Understanding LET and LETeff is crucial to be able to read a single-event effects report and papers on the topic. Since the particle fluxes in the space environment are often defined as a function of LETeff, understanding this metric allows you to communicate to space customers and ensure that you understand what is needed for new space product designs.
 The Stopping and Range of Ions in Matter homepage. SRIM software version 2013.
 R. C. Baumann, “Effectiveness of Polyimide for Stopping of Alphas in Memory Devices”, Texas Instruments Technical Activity Report, Sept. 1991. https://www.researchgate.net/publication/280625467_Investigation_of_the_Effectiveness_of_Polyimide_Films_for_the_Stopping_of_Alpha_Particles_in_Megabit_Memory_Devices