**4.3. Interaction, transport and tracking module**

318 Numerical Simulation – From Theory to Industry

**4.2. Radiation event generator** 

view of a 10×20 SRAM cell array covered with the BEOL is shown in Figure 5 (right). For better visibility, BEOL layers have been rendered semi-transparent in this illustration.

To numerically generate the particles with the spectral, spatial and angular distributions mimicking all the characteristics of the natural background, as introduced and defined in section 2, we use the G4 General Particle Source (GPS) [31] which is part of the Geant4 distribution. The module allows the user to define all the source parameters, in particular the energy of the emitted particles from a given energy distribution defined in a separate input file.

**Figure 6.** Differential fluxes of atmospheric muons given by the QARM (top) [22-23] and PARMA (bottom) [33-34] models at the location of the Altitude SEE Test European Platform (ASTEP, latitude North 44° 38' 02'', longitude East 5° 54' 26'', altitude 2555 m, see www.astep.eu). The atmospheric

For atmospheric particles, the energy distributions of neutrons, protons, pions and muons reaching the ground level are available in the literature or on the web as functions of latitude,

proton spectrum calculated with the PARMA model is also plotted (bottom).

Once an incident particle has been numerically generated with the radiation event generator, the Geant4 simulation flow computes the interactions of this particle with the target (the simulated circuit) and transports step-by-step the particle and all the secondary particles eventually produced inside the world volume (the largest volume containing, with some margins, all other volumes contained in the circuit geometry). The transport of each particle occurs until the particle loses its kinetic energy to zero, disappears by an interaction or comes to the end of the world volume.

The G4ProcessManager class contains the list of processes that a particle can undertake. A physical process describes how particles interact with materials. The list of physical processes employed in our simulations is based on the physics lists QGSP\_BIC\_HP [37], one of the standard Geant4 list covering the energy range of particles interacting in low- to medium-energy ranges. This list uses binary cascade, precompound and various deexcitation models for hadrons standard EM, with high precision neutron model used for neutrons below 20 MeV. This list is generally used for simulations in the fields of radiation protection, shielding and medical applications.

Geant4 provides a way for the user to access the transportation process and to obtain the simulation results at the beginning and end of transportation, at the end of each stepping in transportation and at the time when the particle is going into a given sensitive volume of the circuit. Tables 2 and 3 shows two intermediate output results of TIARA-G4 respectively describing a particle interaction event (Table 2, nuclear inelastic event with a silicon atom of the p-type silicon substrate of the circuit, see Figure 5) and the tracking of two secondary particles impact different sensitive volumes of the circuit (Table 3). All these output data are

saved as text files during the simulation and can be used later for event visualization or post-processing. Finally, Figure 7 illustrates the visualization of an interaction event (here a negative muon capture by a silicon atom) using ROOT [38]. Such a 3D perspective view is computed using a dedicated ROOT script which directly imports geometry and event data from a collection of files saved on the machine hard disk during simulation.

Soft-Error Rate of Advanced SRAM Memories: Modeling and Monte Carlo Simulation 321

**Table 3.** Example of the tracking of two secondary particles (28Al and proton) impacting different sensitive volumes (Psub, Pwell and Nmos) of the SRAM circuit. For each particle and each impacted sensitive volume, the (x, y, z) coordinates of the entry and exit points of the particle in this volume are

We detail in this section the model used to calculate the electrical response of the SRAM circuit subjected to the irradiation. Starting a simulation sequence when a primary particle emitted by the particle source enters in the world volume, we already mentioned that Geant4 computes the interactions of this particle with the circuit and transports step-by-step the particle and all the secondary particles (eventually produced) until all these particles loss their kinetic energy to zero, disappear by interaction or come to the end of the world

At the end of the sequence,TIARA-G4 examines the tracks of all the charged particles involved in this simulation step (including eventually the track of the incident primary particle if it is charged) and determine the complete list of the different silicon volumes (drains, Pwells, Nwells, substrates, etc.) traversed by these particles. Two very general

indicated and also the energy deposited by the particle in this same volume.

**4.4. SRAM electrical response module** 

volume.


**Table 2. Table 2.** Example of a TIARA-G4 output in case of particle interaction with the target (circuit). The present example describes a neutron inelastic process (energy of the incident neutron of 56.64 MeV) with a silicon atom of the p-type substrate of the circuit described in Figure 4. This nuclear reaction produces 5 secondary particles at the reaction vertex position; for each produced particle, the particle energy and the three components of the normalized particle momentum (Px, Py, Pz) are indicated.

**Figure 7.** TIARA-G4 screenshot under ROOT visualization tool showing a part of the memory circuit (65 nm SRAM) subjected to a negative muon irradiation. The resulting interaction shown here is a muon capture by a silicon atom in the active circuit region (Pwell) produced a shower of ten secondary particles.

**Table 3.** Example of the tracking of two secondary particles (28Al and proton) impacting different sensitive volumes (Psub, Pwell and Nmos) of the SRAM circuit. For each particle and each impacted sensitive volume, the (x, y, z) coordinates of the entry and exit points of the particle in this volume are indicated and also the energy deposited by the particle in this same volume.
