**2.1. Atmospheric radiation environment**

The cascades of elementary particles and electromagnetic radiation are produced in the Earth's atmosphere when a primary cosmic ray (of extraterrestrial origin) enters the atmosphere [20]. The term cascade means that the incident particle (generally a proton, a nucleus, an electron or a photon) strikes a molecule in the air so as to produce many high energy secondary particles (photons, electrons, hadrons, nuclei) which in turn create more particles, and so on.

Among all these produced secondary particles, neutrons represent the most important part of the natural radiation constraint at ground level susceptible to impact electronics. Because neutrons are not charged, they are very invasive and can penetrate deeply in circuit materials. They can interact via nuclear reactions with the atoms of the target materials and create (via elastic or inelastic processes) secondary ionizing particles. This mechanism is called "indirect ionization" and is potentially an important source of errors induced in electronic components. One generally distinguishes thermal neutrons (interacting with 10B isotopes potentially present in circuit materials, but progressively removed from technological processes [5]) and high-energy atmospheric neutrons (up to the GeV scale). Figure 1 (top) shows the typical energy distribution of atmospheric neutrons, ranging from thermal energies to 1 GeV, as measured by Goldhagen et al. [21] using a Bonner multi-sphere spectrometer at the reference location (New-York City, NYC). The integration of this spectrum, also shown in Figure 1 (bottom), gives the total neutron flux expressed in neutrons per square centimeter and per hour: this flux is equal to 7.6 n/cm2/h for the lower part (thermal and epithermal neutrons below 1 eV), 16 n/cm2/h for the intermediate part (between 1 eV and 1 MeV) and 20 n/cm2/h for the upper part (high energy neutrons above 1 MeV).

Atmospheric muons also represent an important part of the natural radiation constraint at ground level [20]. Muons belong to the meson or "hard" component in the atmospheric cosmic ray cascades and are the products of the decay of charged pions (instable particles with a short lifetime of 26 ns) via the weak interaction. They are easily able to penetrate the atmosphere down to sea level and they constitute the only secondary cosmic radiation able to penetrate significant depths underground. In spite of a lifetime of about 2.2 µs, most of them survive to sea level and constitute the most preponderant charged particles at sea level. But despite this abundance, muons interact extremely few with matter, excepted at low energies by direct ionization (see subsection 5.3).

In contrast and while strongly interacting with matter, pions are not enough abundant at ground level to induce significant effects in components. Furthermore, for modern technologies, the small amount of electrons and gamma-rays having very low energy are not able to disrupt electronics.

Soft-Error Rate of Advanced SRAM Memories: Modeling and Monte Carlo Simulation 313

Finally, protons, although they interact with silicon as neutrons above a few tens of MeV, are one hundred times less numerous than the latter at ground level. Their low abundance allows us to consider their impact as negligible compared with that of neutrons, except at low energies (< 1 MeV) for which certain advanced technologies show an exacerbated

Figure 2 shows a typical energy distribution of the differential flux for atmospheric neutrons, protons, muons and pions at ground level. Such a collection of spectra, characteristic of a given location (latitude, longitude and elevation), constitute a set of input data of primary importance for any simulation code dedicated to the evaluation of the soft

Natural radioisotopes contained in the Earth's crust are the principal natural sources of α, β and γ radioactivity but only the alpha-particle emitters present a reliability concern in microelectronics. Beta and gamma processes are indeed not able to deposit a high enough amount of energy susceptible to significantly impact the microelectronic circuit operation. The presence of alpha-particle emitters in electronic devices can be classified as materials that are naturally radioactive (they contain a fraction of radioactive nuclei) or materials that contain residual trace of radioactive impurities [24]. Currently, several types of alphaparticle emitters have been identified at wafer, packaging and interconnection levels, including lead in solder bumps, uranium and thorium in silicon wafers and in molding compounds, more recently hafnium in new high-κ gate and platinum in silicide materials.

Considering the activity of radioisotopes in the calculation of the soft error rate of a circuit thus requires to accurately modeling the alpha-particle source mimicking the presence of these alpha-particle emitters in the circuit materials. For example, considering traces of uranium in a given material (silicon for example) requires to take into account the complete uranium disintegration chain composed of 14 daughter nuclei with 8 alpha-particle emitters. Energies of the alpha-particle are ranging from 4.20 to 7.68 MeV; their corresponding ranges

> **Range in Si (μm)**

**Corresponding initial LET (MeV/(mg/cm²))**

**Alpha Energy (MeV)**

**238U 1.40×10+17 4.19 18.95 0.677 234U 7.76×10+12 4.68 22.17 0.634 230Th 2.38×10+12 4.58 21.49 0.642 226Ra 5.05×10+10 4.77 22.78 0.627 222Rn 3.30×10+05 5.49 27.94 0.575 218Po 1.86×10+02 6.00 31.86 0.545 214Po 1.64×10-04 7.68 46.22 0.468 210Po 1.20×10+07 5.31 26.61 0.588**

**Table 1.** Main characteristics (half-life, mean energy, range in silicon and initial linear energy transfer of the emitted alpha-particle) of the eight alpha-emitters of the disintegration chain of 238U [25].

error rate induced by the atmospheric radiation environment (see section 4).

sensitivity due to charge deposition by direct ionization.

**2.2. Telluric radiation sources** 

**T1/2 (s)**

**Figure 1.** Top: Reference atmospheric neutron spectrum measured on the roof of the IBM Watson Research Center main building [21]. Numerical data courtesy from Paul Goldhagen (U.S. Department of Homeland Security). Bottom: Cumulated integral flux corresponding to the above spectrum. The total neutron flux is 43.6 neutrons per cm2 and per hour.

**Figure 2.** High energy (> 0.1 MeV) differential flux for atmospheric neutrons, protons, muons and pions at ground level. Data computed using the Qinetic Atmospheric Radiation Model [22-23] for Marseille, France (Latitude 43.18' N, Longitude 5.22' E, sea-level).

Finally, protons, although they interact with silicon as neutrons above a few tens of MeV, are one hundred times less numerous than the latter at ground level. Their low abundance allows us to consider their impact as negligible compared with that of neutrons, except at low energies (< 1 MeV) for which certain advanced technologies show an exacerbated sensitivity due to charge deposition by direct ionization.

Figure 2 shows a typical energy distribution of the differential flux for atmospheric neutrons, protons, muons and pions at ground level. Such a collection of spectra, characteristic of a given location (latitude, longitude and elevation), constitute a set of input data of primary importance for any simulation code dedicated to the evaluation of the soft error rate induced by the atmospheric radiation environment (see section 4).
