**1. Introduction**

308 Numerical Simulation – From Theory to Industry

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Single-event-effects (SEE) are the result of the interaction of highly energetic particles, such as protons, neutrons, alpha particles, or heavy ions, with sensitive regions of a microelectronic device or circuit [1-2]. They may perturb the device/circuit operation (e.g., reverse or flip the data state of a memory cell, latch, flip-flop, etc.) or definitively damage the circuit (e.g. gate oxide rupture, destructive latch-up events).

With the constant downscaling of microelectronic devices, the sensitivity of integrated circuits to natural radiation coming from the space or present in the terrestrial environment has been found to seriously increase [3-5]. In particular, ultra-scaled memory integrated circuits are more sensitive to single-event-upset (SEU) and digital devices are more subjected to digital single-event transient (DSETs). The problem has been well-known for space applications over many years (more than forty years) and production mechanisms of single-event effects (SEE) in semiconductor devices by protons or heavy ions well apprehended, characterized and modeled [6]. In a similar way for avionic applications, the interaction of atmospheric neutrons with electronics has been identified as the major source of SEE [7]. For the most recent deca-nanometers technologies, the impact of other atmospheric particles produced in nuclear cascade showers on circuits has been clearly demonstrated (protons [8-9]) or is still under exploration for some exotic particles (pions and charged muons [10-14]).

With respect to such high-altitude atmospheric environments, the situation at ground level is slightly different. Of course, atmospheric neutrons are always the primary particles but, with a flux approximately divided by a factor ~300 at sea-level with respect to the flux at avionics altitudes, the Soft-Error Rate (SER) of circuits can be now affected by an additional source of radiation, usually neglected because completely screened by

© 2012 Autran et al., licensee InTech. This is an open access chapter distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/3.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. © 2012 The Author(s). Licensee InTech. This chapter is distributed under the terms of the Creative Commons Attribution License http://creativecommons.org/licenses/by/3.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

neutrons in avionics: the alpha particles generated from traces of radioactive contaminants in CMOS process or packaging materials [1,15]. As a consequence of these multiple sources of radiation, the accurate modeling and simulation of the SER of circuits at ground level is rather a complex task because one can clearly separate the contribution to SER of atmospheric particles (the external constraint) from the one due to natural alpha-particle emitters present as contaminants in circuit materials (the internal constraint).

Soft-Error Rate of Advanced SRAM Memories: Modeling and Monte Carlo Simulation 311

As briefly stated in the introduction, natural radiation that causes soft error in digital circuits may come from various sources. At ground level, one can distinguish two major sources of radiation described in the following: i) the 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

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

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

**2. Natural radiation at ground level** 

**2.1. Atmospheric radiation environment** 

low energies by direct ionization (see subsection 5.3).

and ii) the telluric radiation sources,.

particles, and so on.

Modeling and simulating the effects of ionizing radiation has long been used for better understanding the radiation effects on the operation of devices and circuits [16-19]. In the last two decades, due to substantial progress in simulation codes and computer performances which reduce computation times, simulation reached an increased interest. Due to its predictive capability, simulation offers the possibility to reduce radiation experiments and to test hypothetical devices or conditions, which are not feasible (or not easily measurable) by experiments. Physically-based numerical simulation at devicelevel presently becomes an indispensable tool for the analysis of new phenomena specific to short-channel devices and for the study of radiation effects in new device architectures for which experimental investigation is still limited [19]. In these cases, numerical simulation is an ideal investigation tool for providing physical insights and predicting the operation of future devices expected for the end of the microelectronic roadmap. Last but not least, the understanding of the soft error mechanisms in such devices and the prediction of their occurrence under a given radiation environment are of fundamental importance for certain applications requiring a very high level of reliability and dependability [1].

In this framework, this chapter describes in details a complete general purpose simulation platform we have developed these last years for the numerical evaluation of the sensitivity of advanced semiconductor memories (static RAMs) subjected to natural radiation at ground level. The physical modeling approach we developed as well as the object-oriented programming implementation are very general and can be used to simulate both external or internal radiation constraints, i.e. the bombardment of the memory circuit by heavy-ions, neutrons, protons, muons, etc. or the generation of alphaparticles inside the circuit materials due to the presence of traces of radioactive contaminants.

The chapter is organized as follows. After introducing the natural radiation environment at ground level and the different types of radiation constraints in section 2 and the basic mechanisms of single-event effects on microelectronic devices in section 3, section 4 will present in details the different modules of our multi-scale and multiphysics numerical simulation chain, including some important precisions related to the modeling of the circuit architecture, the generation of particles mimicked a given radiation environment and the physical-based modeling of the circuit/cell electrical response. Finally, in section 5, we will illustrate various capabilities of our code to estimate the soft-error rate of different SRAM circuits representative of advanced technological nodes.
