**4.1. Circuit architecture construction module**

316 Numerical Simulation – From Theory to Industry

radiation at ground level.

transport and energy deposition of charged particles (heavy ions and alpha particles) without the need for a nuclear code as Geant4 [28]; only SRIM [29] tables were used as input files to compute the transport of the particles in silicon and in a simplified Back-End-Of-Line (BEOL) structure reduced to a single layer. On the other hand, for neutrons, it used separate databases compiled using a specific Geant4 application to generate nuclear events in the

The new version of TIARA, described here, is called TIARA-G4, in reference to the fact that it is totally rewritten in C++ using Geant4 classes and libraries and compiled as a full Geant4 application [28]. The main improvement of TIARA-G4 with respect to the first version of the code comes precisely from this transformation of the code in a Geant4 application, allowing the use of Geant4 classes for the description of the circuit geometry and materials (now including the true BEOL structure) and the integration of the particle transport and tracking directly in the simulation flow, without the need of external databases or additional files. Figure 4 shows a schematics of the TIARA-G4 simulation flow structured in several independent modules. In the following, we present the content of the main modules of the code and illustrate (also in Section 5) their capabilities for the soft error rate evaluation of different SRAM CMOS bulk circuits (65 nm and 40 nm technologies) subjected to natural

**Figure 4.** Schematics of the TIARA-G4 simulation flow showing the different code inputs and outputs and the links with Geant4 classes, libraries, models or external modules and visualization tools.

simulation flow resulting from the interactions of incident neutrons with the circuit.

The first step of the TIARA-G4 simulation is to construct a model of the simulated circuit from Geant4 geometry classes and libraries of elements and materials. In the framework of Geant4, the circuit under simulation is considered as the "particle detector". The structure creation in TIARA is based on 3D circuit geometry information extracted from GDS formatted data classically used in the Computer-Aided Design (CAD) flow of semiconductor circuit manufacturing. To perform such an extraction from the GDS layout description, a separate tool has been developed [30]. It parses the GDS file, obtains coordinate points of CAD layers and using geometrical computations tracks the positions and dimensions of the transistor active areas, cell dimensions, p-type and n-type and Back-End-Of-Line (BEOL) stack geometry. Based on this information and additional data concerning the depth of the wells, junctions, STI regions (obtained from TCAD or SIMS measurements) and BEOL layer composition, TIARA creates a 3D structure of the elementary memory cell and, by repetition, of the complete portion of the simulated circuit. The real 3D geometry is simplified since it is essentially based on the juxtaposition of boxes of different dimensions, each box being associated to a given material (silicon, insulator, metal, etc.) or doped semiconductor (p-type, n-type).

**Figure 5.** Left and Center**:** ROOT screenshots illustrating the geometry of the complete 65 nm SRAM architecture considered in TIARA-G4 simulation. Right: 3D perspective view of a 10×20 SRAM cell array covered with the BEOL.

Figure 5 (left) illustrates the geometry of a complete 65 nm SRAM architecture considered in TIARA-G4 simulation. Sensitive Pmos and Nmos drains regions are connected to the first metal layer (Cu) of the BEOL stack with tungsten plugs. The BEOL structure is composed of 18 uniform stacked layers with exact compositions and thicknesses. The 3D perspective 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.

Soft-Error Rate of Advanced SRAM Memories: Modeling and Monte Carlo Simulation 319

longitude and altitude. They are obtained from direct measurements and/or from Monte Carlo simulations. For the neutron flux, we use the experimental atmospheric spectrum presented in Figure 1, which is actually the reference curve (for high-energy neutrons above 1 MeV) for the JEDEC Standard JESD89A [32]. For the other atmospheric particles (mainly muons and protons), we adopted the QinetiQ Atmospheric Radiation Model (QARM) [22-23] and the PARMA model [33-34], which are specifically developed for prediction of the radiation in the atmosphere for a given location and date. Figure 6 shows the differential fluxes of atmospheric

Another important issue in Monte-Carlo simulation is the strong zenith angular dependence of atmospheric showers. To make our Geant4 GPS primary particle sources more realistic, we introduce in simulations the angular dependence of the primary flux intensity in the form I(θ) ~ cosn (θ) where θ is the zenith angle and n a parameter fixed to n=3.5 for neutrons

For the simulation of alpha-particle emitters present in the IC materials, we directly generate in the code the random positions and emission directions with uniform probability densities

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

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

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

for each daughter element of the considered decay chain (uranium or thorium).

muons (resp. protons) given by these two models (resp. by PARMA).

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

or comes to the end of the world volume.

protection, shielding and medical applications.

[35], and for muons n=2 [36].
