**2.2. Telluric radiation sources**

312 Numerical Simulation – From Theory to Industry

40

0

10

20

30

neutron flux is 43.6 neutrons per cm2 and per hour.

France (Latitude 43.18' N, Longitude 5.22' E, sea-level).

10-12 10-11 10-10 10-9 10-8 10-7 10-6 10-5 10-4 10-3 10-2

**MARSEILLE, France** *Sea-level*

Differential Flux (cm-2

s


)

able to disrupt electronics.

Neutron fluence rate

Cumulated integral

flux (cm-2 h-1)

per lethargy (x10-4 cm-2 s-1)

technologies, the small amount of electrons and gamma-rays having very low energy are not

**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

Total flux (NYC, quite Sun) **: 43.6 n cm-2**

**Part #1** 7.6 n cm-2

h-1

10-10 10-8 10-6 10-4 10-2 100 102 104 106

Neutron energy (MeV)

16 n cm-2 h-1

**Part #2**

 **h-1**

**Part #3**

20 n cm-2 h-1

> Neutrons Protons Muons Pions

**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,

0.1 1 10 100 1000 10000 100000

Energy (MeV)

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


**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].

in silicon vary from 19 to 46 µm and their initial Linear Energy Transfer (LET) from 0.47 to 0.68 MeV/(mg/cm²), as summarized in Table 1.

Soft-Error Rate of Advanced SRAM Memories: Modeling and Monte Carlo Simulation 315

converted into electron-hole pairs, the remaining energy being converted into heat and a very small quantity in atoms displacement. It was experimentally shown that the energy necessary for the creation of an electron-hole pair depends on the material bandgap. In a Silicon substrate, one electron-hole pair is produced for every 3.6 eV of energy lost by the

As already mentioned, neutrons of the terrestrial environment do not interact directly with target material since they do not ionize the matter on their passage. However, the products resulting from a nuclear reaction can deposit energy along their traces, in the same manner as that of direct ionization. Since the creation of the column of electron-hole pairs of these secondary particles is similar to that of ions, the same models and concepts can be used.

*Charge transport*: When a charge column is created in the semiconductor by an ionizing particle, the released carriers are quickly transported and collected by elementary structures (e.g. p-n junctions). The transport of charge relies on two main mechanisms [Figures 3(b) and 3(c)]: the charge drift in regions with an electric field and the charge diffusion in neutral zones. The deposited charges can also recombine with other mobile carriers existing in the

*Charge collection*: The charges transported in the device induce a parasitic current transient [Figure 3(d)], which could induce disturbances in the device and associated circuits. The devices most sensitive to ionizing particle strikes are generally devices containing reverselybiased p-n junctions, because the strong electric field existing in the depletion region of the p-n junction allows a very efficient collection of the deposited charge. The effects of ionizing radiation are different according to the intensity of the current transient, as well as the number of impacted circuit nodes. If the current is sufficiently important, it can induce a permanent damage on gate insulators (gate rupture, SEGR) or the latch-up (SEL) of the device. In usual low power circuits, the transient current may generally induce only an

This section describes in details the TIARA-G4 code developed these last years conjointly at Aix-Marseille University (IM2NP laboratory) and at STMicroelectronics (Central R&D, Crolles). TIARA-G4 is a general-purpose Monte Carlo simulation code written in C++ and fully based on the Geant4 toolkit for modeling the interaction of Geant4 particles (including neutrons, protons, muons, alpha-particles and heavy ions) with various architectures of electronic circuits. TIARA stands for Tool Suite for Radiation Reliability Assessment. The primary ambition of TIARA is to embed in a unique simulation platform the state-of-the-art

The initial version of TIARA [26-27] was a standalone C++ native code dynamically linked with IC CAD flow through the coupling with a SPICE solver. The code has been developed such that the addition of new radiation environments, physical models or new circuit architecture should be quite simple. On one hand, this first version was able to treat the

particle.

lattice.

eventual change of the logical state (cell upset).

knowledge and methodology of SER evaluation.

**4. The TIARA-G4 Monte Carlo simulation code** 
