**4.4. SRAM electrical response module**

320 Numerical Simulation – From Theory to Industry

particles.

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

**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

from a collection of files saved on the machine hard disk during simulation.

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 volume.

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

cases can be distinguished from this pure geometrical analysis, as schematically shown in Figure 8:

Soft-Error Rate of Advanced SRAM Memories: Modeling and Monte Carlo Simulation 323

**I**

( , , ) *<sup>I</sup> <sup>I</sup> <sup>I</sup> x y z*

where n is the carrier density in excess generated in the silicon and D is an ambipolar

**Figure 9.** Left: Schematics of the "diffusion-collection model" used to compute the transient current I(t) resulting from the 3D spherical diffusion and then from the collection by a given reverse-biased drain of the charge in excess generated along a charged particle track. Right: Definition of the different points in

*Track for pMOS*

**P3**

*Si-substrate (P)*

*N-well*

dx×dy

*Contact <sup>I</sup>*(*t*) *<sup>q</sup> <sup>n</sup>*(*dx*,*dy*,*t*)*vdxdy*

The temporal and spatial concentration n(r,t) resulting from the diffusion of a quasiponctual charge δQ in the silicon at the distance r from this charge is thus described by the

*Dt Dt*

<sup>3</sup> (,) exp <sup>4</sup> <sup>4</sup> *Q rt nrt*

where τ is the carrier lifetime, r is the distance from the element δQ, and t is the time.

In the present implementation of the diffusion-collection model, δQ is directly evaluated from Geant4 data, considering the energy lost by the particle in a given geometry volume. Figure 9 (right) illustrates the general case of a given volume impacted by a particle. The particle enters the volume in point I and exits in point F. Because drain and well volumes have reduced dimensions (typically expressed in tenths of a micron), the electrical charge δQ deposited per elementary length dl can be approximated by Qdep × dl / L where L is the length of the segment IF. Considering the Cartesian coordinates of the geometrical points I, F and D defined on Figure 8, the total collected charge at point D due to the contribution of the complete segment IF can be analytically evaluated from the following

2 2

2 / <sup>1</sup> ( ) exp exp 8 4 <sup>4</sup> 2 2 *Q q <sup>l</sup> tK KK n t erf L erf DtL Dt L Dt Dt <sup>L</sup> L Dt*

where quantities L, l0 and K are defined from the Cartesian coordinates of points I, F and D:

0

  2

(2)

**F**

( , , ) *<sup>F</sup> <sup>F</sup> <sup>F</sup> x y z*

*n*(*t*)

**D**

**L Q**

( , , ) *<sup>D</sup> <sup>D</sup> <sup>D</sup> x y z*

(3)

Cartesian coordinates used to numerically evaluate n(t).

**Particle track**

*Track for nMOS*

**P2**

dx×dy

**P1**

*nMOS pMOS*

diffusion coefficient.

Drain contacts (collection area)

following equation:

expression:


**Figure 8.** Schematics of the different cases envisaged in TIARA-G4 for the evaluation of cell upset in the simulated SRAM circuit.

In the diffusion-collection model [39-40], the energy lost by a charged particle in silicon along its track is converted in a succession of elementary carrier densities δQ. The model then assumes that the behavior of these quasi-point charges is governed by a pure 3D spherical diffusion law:

$$\frac{\partial \mathbf{n}}{\partial t} = \mathbf{D} \cdot \Delta \mathbf{n} \tag{1}$$

where n is the carrier density in excess generated in the silicon and D is an ambipolar diffusion coefficient.

322 Numerical Simulation – From Theory to Industry

cell is upset or not.

simulated SRAM circuit.

spherical diffusion law:

Figure 8:

cases can be distinguished from this pure geometrical analysis, as schematically shown in

1. A single or several charged particles directly pass through a sensitive drain volume. In this case, TIARA-G4 directly evaluates from Geant4 data the total energy deposited by these particles in the drain ( ΔE), converts this value into a number of generated electron-hole pairs (Qdep = ΔE/3.6 eV for bulk silicon) and finally compares this value with the critical charge value (Qcrit,P for Pmos, Qcrit,N for Nmos) of the simulated technology. If Qdep > Qcrit, the memory cell is considered to be upset, in the contrary

2. A single or several charged particles impact one or several Nwell, Pwell and/or the silicon substrate. In this case, TIARA-G4 evaluates for each sensitive drain located in the impacted Nwell(s) (for Pmos) or Pwell(s) and substrate (for Nmos) the transient current I(t) resulting from the diffusion of carriers in excess in these regions and the collection of the charge by the sensitive nodes (see also Figure 9). Such calculations are performed using the "diffusion-collection model" detailed in the following. Until the I(t) characteristic is computed for all the considered sensitive drains, TIARA-G4 applies the "Imax-tmax" criterion, also described below, to determine if the corresponding memory

**Figure 8.** Schematics of the different cases envisaged in TIARA-G4 for the evaluation of cell upset in the

In the diffusion-collection model [39-40], the energy lost by a charged particle in silicon along its track is converted in a succession of elementary carrier densities δQ. The model then assumes that the behavior of these quasi-point charges is governed by a pure 3D

*<sup>n</sup> D n*

(1)

*t* 

case, the electrical state of the cell is not changed [19].

**Figure 9.** Left: Schematics of the "diffusion-collection model" used to compute the transient current I(t) resulting from the 3D spherical diffusion and then from the collection by a given reverse-biased drain of the charge in excess generated along a charged particle track. Right: Definition of the different points in Cartesian coordinates used to numerically evaluate n(t).

The temporal and spatial concentration n(r,t) resulting from the diffusion of a quasiponctual charge δQ in the silicon at the distance r from this charge is thus described by the following equation:

$$m(r,t) = \frac{\delta Q}{\sqrt[3]{4\pi Dt}} \times \exp\left(-\frac{r^2}{4Dt} - \frac{t}{\tau}\right) \tag{2}$$

where τ is the carrier lifetime, r is the distance from the element δQ, and t is the time.

In the present implementation of the diffusion-collection model, δQ is directly evaluated from Geant4 data, considering the energy lost by the particle in a given geometry volume. Figure 9 (right) illustrates the general case of a given volume impacted by a particle. The particle enters the volume in point I and exits in point F. Because drain and well volumes have reduced dimensions (typically expressed in tenths of a micron), the electrical charge δQ deposited per elementary length dl can be approximated by Qdep × dl / L where L is the length of the segment IF. Considering the Cartesian coordinates of the geometrical points I, F and D defined on Figure 8, the total collected charge at point D due to the contribution of the complete segment IF can be analytically evaluated from the following expression:

$$m(t) = \frac{\delta Q / \eta}{8\pi Dt} \times \exp\left(-\frac{l\_0^2}{4Dt} - \frac{t}{\tau}\right) \times \exp\left(-\frac{K^2}{L^2 4Dt}\right) \times \left\{ \text{erf}\left[\frac{1}{2\sqrt{Dt}}\left(L + \frac{K}{L}\right)\right] - \text{erf}\left[\frac{K}{2L\sqrt{Dt}}\right] \right\} \tag{3}$$

where quantities L, l0 and K are defined from the Cartesian coordinates of points I, F and D:

$$\begin{cases} L = \sqrt{\left(\mathbf{x}\_F - \mathbf{x}\_I\right)^2 + \left(y\_F - y\_I\right)^2 + \left(z\_F - z\_I\right)^2} \\ l\_0^2 = \left(\mathbf{x}\_D - \mathbf{x}\_I\right)^2 + \left(y\_D - y\_I\right)^2 + \left(z\_D - z\_I\right)^2 \\ K = \left(\mathbf{x}\_I - \mathbf{x}\_D\right)\left(\mathbf{x}\_F - \mathbf{x}\_I\right) + \left(y\_I - y\_D\right)\left(y\_F - y\_I\right) + \left(z\_I - z\_D\right)\left(z\_F - z\_I\right) \end{cases} \tag{4}$$

The total electrical charge from the particle track collected at the level of a sensitive drain electrode is obtained by integrating Eq. (3) on the total drain surface, as illustrated in Figure 9. Then, the charge is converted into a current by multiplying n(t) by the elementary charge and by the average collection velocity via space charge region of the reverse-biased drain:

$$I(t) = q \iint\_{Contact} n(t) \cdot v \cdot d\mathbf{x} dy\tag{5}$$

Soft-Error Rate of Advanced SRAM Memories: Modeling and Monte Carlo Simulation 325

(6)

<sup>2</sup> 1024 1024 [ ] <sup>9</sup> [FIT/Mbit] [cm] [cm] 10 *X Y*

**5. Simulation results** 

cm-3) and Pmos drains ([B] = 3×1020 cm-3).

*IntFlux cm SER L L TotalUpsetNum CellNum NumPart*

where TotalUpsetNum is the total number of cell upsets obtained during the simulation, CellNum is the number of memory cells of the simulated circuit, LX and LY are the circuit dimensions (in cm), NumPart is the total number of primary particles incident on the simulated circuit and IntFlux is the integral flux (cm-2) of the particle source used to generate the incident particles. For example, considering the atmospheric neutron spectrum of Figure 1, IntFLux = 7.6 n/cm2 for Part #1, 16 n/cm2 for Part #2 and 20 n/cm2 for Part #3 of the spectrum.

In this last section, the capabilities of the TIARA-G4 code are illustrated though a few dedicated studies on the simulation of 65 nm or 40 nm CMOS bulk SRAM circuits subjected to different sources of atmospheric particles. These three examples are independent and respectively concern: i) the impact of thermal and low energy neutrons on a 40 nm SRAM circuit; ii) the SER estimation of a 65 nm SRAM under high energy atmospheric neutrons

Since the 80's, the interaction of cosmic ray induced thermal neutrons with the 10B isotope of the boron has been identified as a major source of soft errors in electronic circuits [41]. 10B only represents 19.9% abundance of natural boron but the very large cross section of the 10B(n,α)7Li reaction at thermal energies combined with the highly ionizing character and the range in silicon of the two nuclei produced by this fission reaction (one lithium nucleus and one alpha particle) can easily explain the danger of 10B when it is present in elevated concentration in close proximity to the sensitive regions of integrated devices [41]. Modern semiconductor processes have thus completely eliminated the presence of 10B in Borophosphosilicate glasses (BPSG) used in the back-end-of-line (or outright the use of the BPSG itself), considered as the principal reservoir of 10B and the dominant source of boron fission in circuits. However, 10B remains present at silicon level, since bulk substrate doping and source/drain implantation are not selective in isotope and continue to use natural boron [41-42]. The issue of thermal neutron sensitivity to current technologies is still relevant and remains open, in particular for ultra-scaled technologies in the natural terrestrial environment at ground level. Recent work demonstrated a substantial SER sensitivity with neutron energies for many SRAM circuits in the 0.25 µm-45 nm technology range [43-44].

Using the new TIARA-G4 code, we propose here to explore the question of thermal and low energy neutron-induced soft errors in state-of-the-art 40 nm SRAMs. Such a study can be only conducted with a code taking into account the real geometry at silicon level, including the silicon doping with natural boron in p-type regions containing 19.9% of 10B. We thus constructed a 40 nm SRAM matrix with exact doping levels at the level of Pwells ([B] = 1016

**5.1. Impact of thermal and low energy neutrons on a 40 nm SRAM circuit** 

and iii) the effects of low-energy muons on the same 65 nm circuit.

Once the I(t) characteristic has been computed for all drains of the sensitive transistors in the SRAM cell matrix, TIARA-G4 applies the Imax-tmax criterion [26] to determine the cell upsets. This criterion is separately obtained from TIARA-G4 simulation and requires the combination of TCAD and PSICE analysis. The calculated Imax(tmax) characteristic delimitates two current-time domains, as illustrated in Figure 10. If the transient current peak is located above this curve, an upset occurs; in the contrary case the extracted transient current from the sensitive node is not able to sufficiently disturb the electrical state of the bi-stable flipflop and consequently to upset the memory point.

**Figure 10.** Example of a transient current characteristic superimposed to the Imax-tmax upset criterion. The transient current has been calculated from the "diffusion-collection model" for a 24Mg particle (10 MeV) which perpendicularly impacts a Pwell at the distance of 0.25 µm from the Nmos drain contact.

#### **4.5. Soft error rate calculation module**

At the end of the simulation flow, the last module of the TIARA-G4 code evaluates the Soft Error Rate (SER) of the SRAM circuit from the following expression [32]:

$$SER[\text{HT/Mbit}] = \frac{1024 \times 1024}{\text{CellNum}} \times \frac{\text{IntrFun[cm}^{-2}]}{\text{NumPart}} \times L\_X[\text{cm}] \times L\_Y[\text{cm}] \times 10^9 \times TotalUpsetNum} \tag{6}$$

where TotalUpsetNum is the total number of cell upsets obtained during the simulation, CellNum is the number of memory cells of the simulated circuit, LX and LY are the circuit dimensions (in cm), NumPart is the total number of primary particles incident on the simulated circuit and IntFlux is the integral flux (cm-2) of the particle source used to generate the incident particles. For example, considering the atmospheric neutron spectrum of Figure 1, IntFLux = 7.6 n/cm2 for Part #1, 16 n/cm2 for Part #2 and 20 n/cm2 for Part #3 of the spectrum.

### **5. Simulation results**

324 Numerical Simulation – From Theory to Industry

0

*FI FI FI*

2 22

*Kxx x x yy y y zz z z*

The total electrical charge from the particle track collected at the level of a sensitive drain electrode is obtained by integrating Eq. (3) on the total drain surface, as illustrated in Figure 9. Then, the charge is converted into a current by multiplying n(t) by the elementary charge and by the average collection velocity via space charge region of the reverse-biased drain:

Once the I(t) characteristic has been computed for all drains of the sensitive transistors in the SRAM cell matrix, TIARA-G4 applies the Imax-tmax criterion [26] to determine the cell upsets. This criterion is separately obtained from TIARA-G4 simulation and requires the combination of TCAD and PSICE analysis. The calculated Imax(tmax) characteristic delimitates two current-time domains, as illustrated in Figure 10. If the transient current peak is located above this curve, an upset occurs; in the contrary case the extracted transient current from the sensitive node is not able to sufficiently disturb the electrical state of the bi-stable flip-

**Figure 10.** Example of a transient current characteristic superimposed to the Imax-tmax upset criterion. The transient current has been calculated from the "diffusion-collection model" for a 24Mg particle (10 MeV) which perpendicularly impacts a Pwell at the distance of 0.25 µm from the Nmos drain contact.

**tmax**

100 101 10<sup>2</sup> 103 104 105

Time (s)

At the end of the simulation flow, the last module of the TIARA-G4 code evaluates the Soft

Error Rate (SER) of the SRAM circuit from the following expression [32]:

*I DF I I DF I I DF I*

() () *Contact I t q n t v dxdy* (5)

**Imax-tmax criterion** (4)

*DI DI DI*

2 22 2

*L xx yy zz*

flop and consequently to upset the memory point.

**Imax**

**No Upset**

**Upset**

**4.5. Soft error rate calculation module** 

Collected Current (µA)

*l xx yy zz*

In this last section, the capabilities of the TIARA-G4 code are illustrated though a few dedicated studies on the simulation of 65 nm or 40 nm CMOS bulk SRAM circuits subjected to different sources of atmospheric particles. These three examples are independent and respectively concern: i) the impact of thermal and low energy neutrons on a 40 nm SRAM circuit; ii) the SER estimation of a 65 nm SRAM under high energy atmospheric neutrons and iii) the effects of low-energy muons on the same 65 nm circuit.

#### **5.1. Impact of thermal and low energy neutrons on a 40 nm SRAM circuit**

Since the 80's, the interaction of cosmic ray induced thermal neutrons with the 10B isotope of the boron has been identified as a major source of soft errors in electronic circuits [41]. 10B only represents 19.9% abundance of natural boron but the very large cross section of the 10B(n,α)7Li reaction at thermal energies combined with the highly ionizing character and the range in silicon of the two nuclei produced by this fission reaction (one lithium nucleus and one alpha particle) can easily explain the danger of 10B when it is present in elevated concentration in close proximity to the sensitive regions of integrated devices [41]. Modern semiconductor processes have thus completely eliminated the presence of 10B in Borophosphosilicate glasses (BPSG) used in the back-end-of-line (or outright the use of the BPSG itself), considered as the principal reservoir of 10B and the dominant source of boron fission in circuits. However, 10B remains present at silicon level, since bulk substrate doping and source/drain implantation are not selective in isotope and continue to use natural boron [41-42]. The issue of thermal neutron sensitivity to current technologies is still relevant and remains open, in particular for ultra-scaled technologies in the natural terrestrial environment at ground level. Recent work demonstrated a substantial SER sensitivity with neutron energies for many SRAM circuits in the 0.25 µm-45 nm technology range [43-44].

Using the new TIARA-G4 code, we propose here to explore the question of thermal and low energy neutron-induced soft errors in state-of-the-art 40 nm SRAMs. Such a study can be only conducted with a code taking into account the real geometry at silicon level, including the silicon doping with natural boron in p-type regions containing 19.9% of 10B. We thus constructed a 40 nm SRAM matrix with exact doping levels at the level of Pwells ([B] = 1016 cm-3) and Pmos drains ([B] = 3×1020 cm-3).

Soft-Error Rate of Advanced SRAM Memories: Modeling and Monte Carlo Simulation 327

 MCU5 MCU4 MCU3 MCU2 SBU

**Figure 12.** Event multiplicity distributions obtained for the 40 nm SRAM subjected to thermal neutrons and deduced from both experiment and numerical simulation, respectively conducted at LLB facility

Experiment Simulation

**Figure 13.** Convergence of the soft-error rate as a function of the number of incident primary neutrons obtained from TIARA-G4 simulation. The upper and lower limits of the SER confidence interval for 90%

Figure 13 illustrates the convergence of the soft-error rate during the TIARA-G4 simulation as a function of the number of incident primary neutrons. The code asymptotically converges towards a unique SER value, demonstrating the invariance of the extracted SER when the statistics become satisfactory, typically above 1.5×109 primary neutrons in this

Finally, Figure 14 shows a synthesis of both experimental and simulation results obtained for the soft-error rate (expressed in bit flips) of the 40 nm single-port SRAM. "Simul. Part #1", "Simul. Part #2" and "Simul. Part #3" correspond respectively to the SER extracted from

and obtained with the new release of the TIARA/Geant4 code.

Events (%)

based on the χ2 distribution are also plotted.

case.

**Figure 11.** TIARA-G4 screenshots under ROOT illustrating the results of 2×109 thermal neutrons incident on the 40 nm single-port SRAM (20×20 memory cell block). White points correspond to the reaction vertex (only localized in the Pmos drain volumes); colored segments to the trajectories of the secondary ions produced (red for alpha, yellow for 7Li). For clarity, BEOL and substrate have been removed from the perspective view in b). c) Detail a 10B fission reaction occurring in the volume of a Pmos drain (note that the alpha-particle and the lithium nucleus are emitted in opposite directions to conserve momentum).

Figure 11 illustrates the simulation results obtained on a 20×20 SRAM matrix. This circuit was irradiated with thermal and low energy neutrons generated by the Geant4 GPS source considering Part #1 of the reference atmospheric spectrum shown in Figure 1. In order to obtain a sufficient event statistic (interaction events are relatively rare), we pushed the number of incident particles up to 2×109 thermal neutrons. A total 116 single bit upsets (SBU) and 24 multiple celle upsets (MCU) have been detected: they are exclusively the result of 10B fission events localized in the drain volumes of the Pmos transistors (see Figure 11(b), the vertex of the reactions are indicated by the white dots).

Figure 12 shows that both the SER value and the event multiplicity distributions are in excellent agreement with experimental data performed at the LLB facility, located at CEA Saclay, France [45]. The experiment was conducted on the G3-2 beam line under a thermal neutron flux reduced to 7.88×108 n/cm2/s (beam surface area of 25×50 mm2, neutron energies in the range 1.8-10 meV). For the purposes of the study, we considered a 7 Mbit 40 nm SRAM array with a layout cell area of 0.374 µm2). We obtained an experimental thermal neutron-induced SER of 4 FIT/Mbit for the SRAM, with 75% of SBU, 17% of MCU with a multiplicity of 2 and 8% of events with multiplicities ranging from 3 to 5. All these MCU events correspond to physical adjacent bit cells in the memory plan. For comparison, results obtained with TIARA-G4 give a SER equal to 4.5 FIT/Mbit with 83% of SBU, 14% of MCU with a multiplicity of 2 and 4% of events with multiplicities ranging from 3 to 5.

**Figure 11.** TIARA-G4 screenshots under ROOT illustrating the results of 2×109 thermal neutrons incident on the 40 nm single-port SRAM (20×20 memory cell block). White points correspond to the reaction vertex (only localized in the Pmos drain volumes); colored segments to the trajectories of the secondary ions produced (red for alpha, yellow for 7Li). For clarity, BEOL and substrate have been removed from the perspective view in b). c) Detail a 10B fission reaction occurring in the volume of a Pmos drain (note that the

Figure 11 illustrates the simulation results obtained on a 20×20 SRAM matrix. This circuit was irradiated with thermal and low energy neutrons generated by the Geant4 GPS source considering Part #1 of the reference atmospheric spectrum shown in Figure 1. In order to obtain a sufficient event statistic (interaction events are relatively rare), we pushed the number of incident particles up to 2×109 thermal neutrons. A total 116 single bit upsets (SBU) and 24 multiple celle upsets (MCU) have been detected: they are exclusively the result of 10B fission events localized in the drain volumes of the Pmos transistors (see Figure 11(b),

Figure 12 shows that both the SER value and the event multiplicity distributions are in excellent agreement with experimental data performed at the LLB facility, located at CEA Saclay, France [45]. The experiment was conducted on the G3-2 beam line under a thermal neutron flux reduced to 7.88×108 n/cm2/s (beam surface area of 25×50 mm2, neutron energies in the range 1.8-10 meV). For the purposes of the study, we considered a 7 Mbit 40 nm SRAM array with a layout cell area of 0.374 µm2). We obtained an experimental thermal neutron-induced SER of 4 FIT/Mbit for the SRAM, with 75% of SBU, 17% of MCU with a multiplicity of 2 and 8% of events with multiplicities ranging from 3 to 5. All these MCU events correspond to physical adjacent bit cells in the memory plan. For comparison, results obtained with TIARA-G4 give a SER equal to 4.5 FIT/Mbit with 83% of SBU, 14% of MCU

with a multiplicity of 2 and 4% of events with multiplicities ranging from 3 to 5.

alpha-particle and the lithium nucleus are emitted in opposite directions to conserve momentum).

the vertex of the reactions are indicated by the white dots).

**Figure 12.** Event multiplicity distributions obtained for the 40 nm SRAM subjected to thermal neutrons and deduced from both experiment and numerical simulation, respectively conducted at LLB facility and obtained with the new release of the TIARA/Geant4 code.

**Figure 13.** Convergence of the soft-error rate as a function of the number of incident primary neutrons obtained from TIARA-G4 simulation. The upper and lower limits of the SER confidence interval for 90% based on the χ2 distribution are also plotted.

Figure 13 illustrates the convergence of the soft-error rate during the TIARA-G4 simulation as a function of the number of incident primary neutrons. The code asymptotically converges towards a unique SER value, demonstrating the invariance of the extracted SER when the statistics become satisfactory, typically above 1.5×109 primary neutrons in this case.

Finally, Figure 14 shows a synthesis of both experimental and simulation results obtained for the soft-error rate (expressed in bit flips) of the 40 nm single-port SRAM. "Simul. Part #1", "Simul. Part #2" and "Simul. Part #3" correspond respectively to the SER extracted from TIARA-G4 simulations considering the parts labeled #1, #2 and #3 of the reference atmospheric spectrum (Figure 1) as the primary sources of particles. Note that the contributions of parts #1 and #2 of the neutron spectrum in the SRAM SER are very small with respect to the high energy part #3 and only represent 3% of the total SER value. "Simul. 1+2+3" is equal to the sum of these three SER simulated values and corresponds to the SER estimation for the full atmospheric spectrum, estimated around 500 FIT/MBit. The "Exp. real-time ASTEP" value (682 FIT/Mbit) corresponds to the neutron-SER extracted from a real-time experiment (conducted on the ASTEP platform at the altitude of 2252m, see www.astep.eu) and corrected from the contribution of internal chip radioactivity (alphaparticle emission). The comparison of these results evidences a ~30% discrepancy between simulation and experimental results. Such an underestimation of the total SER by simulation in such ultra-scaled technology can be easily explained by the fact that the bipolar amplification mechanism has not been yet included in the SRAM electrical response module of the simulation code. In the next validation example (see subsection 5.2) considering a less integrated technology (65 nm), the impact of bipolar amplification will be significantly reduced and its impact on SER value quasi negligible.

Soft-Error Rate of Advanced SRAM Memories: Modeling and Monte Carlo Simulation 329

Figure 15 shows the comparison of the neutron-induced SER computed with the different versions of TIARA for a 20×20 65 nm SRAM array. The atmospheric neutron source considered for these simulations corresponds to the Part #3 of the reference neutron spectrum of Figure 1 (high energy neutrons below 1 MeV). Very close values are obtained with TIARA and TIARA-G4 without taking into account the complete BEOL structure (a single SiO2 layer is used as a simplified BEOL stack in this case): respectively 266 and 251 FIT/MBit, evidencing the equivalence of the two approaches in terms of global SER values. For memory, the initial version of TIARA computes neutron-silicon interactions from precalculated databases using Geant4 while TIARA-G4 is a full Geant4 application. Taking into account the complete BEOL structure (defined in Figure 5) in the new code TIARA-G4 results in a significant increase of the SER (337 FIT/Mbit). This +30% variation of the SER can be attributed to additional secondary particles produced by the interactions of incoming neutrons with the different BEOL materials (mainly SiO2, Cu and Al), these secondary

particles being able to deposit electrical charges in the active silicon regions.

**GEANT4/TIARA** simulations 65nm SRAM

**Figure 15.** Comparison of simulation results obtained with the initial (TIARA) and new (TIARA-G4) versions of the code for the evaluation of the neutron-induced SER in the 65 nm SRAM architecture. Data are also plotted for TIARA-G4 with and without taking into account the real

without BEOL

**TIARA TIARA-G4**

**TIARA-G4** with BEOL

A more detailed analysis, reported in Figure 16, evidences slight differences in the distributions of the events as a function of the event size or event multiplicity (which corresponds to the number of simultaneous cell flips induced by a single primary particle interaction with the circuit). TIARA-G4 is found to generate more single bit upsets and, inversely, less multiple cell upsets than the initial TIARA code. The presence of the complete BEOL structure above silicon is also found to induce more single bit upsets and high multiplicity events than the simplified BEOL structure. This can be attributed to the production of new nuclei and recoil nuclei up to the atomic number Z = 74 corresponding to the tungsten, precisely present in the BEOL at the level of the plugs for the interconnection of drains with the first metal layer. The detailed analysis of this new produced nuclei shows that the majority of those inducing an upset are the result of neutron-cupper interactions in

BEOL structure.

the first metal layers close to the active silicon.

Neutron SER (FIT/MBit)

**Figure 14.** Synthesis of both experimental and simulation results obtained for the soft-error rate (expressed in bit flips) of the 40 nm single-port SRAM subjected to atmospheric neutrons.

#### **5.2. SER estimation of a 65 nm SRAM under high energy atmospheric neutrons**

In this second example, we simulated the complete 65 nm SRAM architecture previously defined in Figure 5. The objective was to compare neutron-induced SER results obtained by TIARA-G4 with simulation data previously obtained from the initial code TIARA [26,30] (see the introduction of section 4). Another objective was to perform simulation with and without taking into account the complete BEOL stack in order to evidence the impact of this BEOL on the neutron SER.

Figure 15 shows the comparison of the neutron-induced SER computed with the different versions of TIARA for a 20×20 65 nm SRAM array. The atmospheric neutron source considered for these simulations corresponds to the Part #3 of the reference neutron spectrum of Figure 1 (high energy neutrons below 1 MeV). Very close values are obtained with TIARA and TIARA-G4 without taking into account the complete BEOL structure (a single SiO2 layer is used as a simplified BEOL stack in this case): respectively 266 and 251 FIT/MBit, evidencing the equivalence of the two approaches in terms of global SER values. For memory, the initial version of TIARA computes neutron-silicon interactions from precalculated databases using Geant4 while TIARA-G4 is a full Geant4 application. Taking into account the complete BEOL structure (defined in Figure 5) in the new code TIARA-G4 results in a significant increase of the SER (337 FIT/Mbit). This +30% variation of the SER can be attributed to additional secondary particles produced by the interactions of incoming neutrons with the different BEOL materials (mainly SiO2, Cu and Al), these secondary particles being able to deposit electrical charges in the active silicon regions.

328 Numerical Simulation – From Theory to Industry

reduced and its impact on SER value quasi negligible.

BEOL on the neutron SER.

**Simul.** Part #1

SER in bit flips[FIT/Mbit]

TIARA-G4 simulations considering the parts labeled #1, #2 and #3 of the reference atmospheric spectrum (Figure 1) as the primary sources of particles. Note that the contributions of parts #1 and #2 of the neutron spectrum in the SRAM SER are very small with respect to the high energy part #3 and only represent 3% of the total SER value. "Simul. 1+2+3" is equal to the sum of these three SER simulated values and corresponds to the SER estimation for the full atmospheric spectrum, estimated around 500 FIT/MBit. The "Exp. real-time ASTEP" value (682 FIT/Mbit) corresponds to the neutron-SER extracted from a real-time experiment (conducted on the ASTEP platform at the altitude of 2252m, see www.astep.eu) and corrected from the contribution of internal chip radioactivity (alphaparticle emission). The comparison of these results evidences a ~30% discrepancy between simulation and experimental results. Such an underestimation of the total SER by simulation in such ultra-scaled technology can be easily explained by the fact that the bipolar amplification mechanism has not been yet included in the SRAM electrical response module of the simulation code. In the next validation example (see subsection 5.2) considering a less integrated technology (65 nm), the impact of bipolar amplification will be significantly

**Figure 14.** Synthesis of both experimental and simulation results obtained for the soft-error rate (expressed in bit flips) of the 40 nm single-port SRAM subjected to atmospheric neutrons.

**Exp.** LLB

*thermal neutrons*

4.5 4

**Single-port 40 nm SRAM** Standard density

**5.2. SER estimation of a 65 nm SRAM under high energy atmospheric neutrons** 

**Simul.** Part #2

10

In this second example, we simulated the complete 65 nm SRAM architecture previously defined in Figure 5. The objective was to compare neutron-induced SER results obtained by TIARA-G4 with simulation data previously obtained from the initial code TIARA [26,30] (see the introduction of section 4). Another objective was to perform simulation with and without taking into account the complete BEOL stack in order to evidence the impact of this

 **Exp.** real-time ASTEP

682

**Simul.** 1+2+3

*Atmospheric (full spectrum)*

482 500.5

**Simul.** Part #3

**Figure 15.** Comparison of simulation results obtained with the initial (TIARA) and new (TIARA-G4) versions of the code for the evaluation of the neutron-induced SER in the 65 nm SRAM architecture. Data are also plotted for TIARA-G4 with and without taking into account the real BEOL structure.

A more detailed analysis, reported in Figure 16, evidences slight differences in the distributions of the events as a function of the event size or event multiplicity (which corresponds to the number of simultaneous cell flips induced by a single primary particle interaction with the circuit). TIARA-G4 is found to generate more single bit upsets and, inversely, less multiple cell upsets than the initial TIARA code. The presence of the complete BEOL structure above silicon is also found to induce more single bit upsets and high multiplicity events than the simplified BEOL structure. This can be attributed to the production of new nuclei and recoil nuclei up to the atomic number Z = 74 corresponding to the tungsten, precisely present in the BEOL at the level of the plugs for the interconnection of drains with the first metal layer. The detailed analysis of this new produced nuclei shows that the majority of those inducing an upset are the result of neutron-cupper interactions in the first metal layers close to the active silicon.

Soft-Error Rate of Advanced SRAM Memories: Modeling and Monte Carlo Simulation 331

(9)

(12.4 ) (14.2 ) (15.5 ) (18.4 )

28 27

kinetic energy.

incident muons.

27 24 26

 

*Al Al n MeV*

In contrast to the first version of TIARA, TIARA-G4 is now capable of simulating the impact of muons on SRAM circuits. For this first study, we considered low energy (< 1 MeV) negative and positive muons susceptible to directly deposit charge by ionization or to be captured (negative muons) after they stop in silicon. The Geant4 general particle source was then used to generate mono-energetic muons incident on the well-known 65 nm SRAM architecture (with complete BEOL) previously defined in Figure 5. Figure 17 illustrates different possible scenarios of negative and positive muon interactions with the structure. Figure 17(a) shows a negative muon decay in the top layers of the BEOL structure, this cannot lead to an upset since the muon disintegrates in light particles not able to deposit any significant charge in silicon. Figure 17(b) shows a similar event but occurring in the silicon substrate. In this case, the incoming positive muon traverses the complete BEOL structure and, statistically, can cross a sensitive drain. If the charge deposited in the impacted drain is higher than the critical charge for this transistor type and for this technology, the corresponding memory cell is upset. Figures 17 (c) and (d) show two negative muon capture events occurring in the BEOL and in silicon, respectively. These events produce large secondary particle showers, containing one or more charged particles susceptible to reach the active silicon region and to induce an upset or even a multiple cell upset. Of course, the probability to induce an upset is maximum when the muon capture-induce shower is produced in the immediate vicinity of the sensitive drain layer, as illustrated in Figure 17(d). This case corresponds to a reduced energy interval for the incoming muons in so far as the penetration depth of the muons in the structure and then the capture location primarily depends on the muon

In order to illustrate this effect, we plotted in Figure 18 the distribution inside the SRAM structure of the vertex positions related to the negative muon capture reactions for three different values of the incident muon kinetic energy: 0.1, 0.3 MeV and 0.5 MeV. We clearly evidence in this figure such a dependency of the capture position (depth) with the muon kinetic energy. As a result, the soft error rate induced by negative muon irradiation presents a maximum when precisely muon captures occurs at the depth of the layer containing sensitive drains. This behavior is illustrated in Figure 19 which also plot the percentage of cell upsets induced by muon capture reactions or directly by muon impacts on sensitive drain (i.e. direct charge deposition in drain volumes). When increasing the kinetic energy of primary particles, the fraction of upsets induced by muon capture rapidly decrease as soon captures occur deeper in silicon, below the active layer. In this case, upsets become mainly induced by direct charge deposition from

*Al n MeV Na MeV Mg d MeV* 

**Figure 16.** Event multiplicity distributions obtained with the initial (TIARA) and new (TIARA-G4) versions of the code for the evaluation of the neutron-induced SER in the 65 nm SRAM architecture. Data are also plotted for TIARA-G4 with and without taking into account the real BEOL structure.

#### **5.3. Effects of low-energy muons on a 65 nm SRAM circuit**

This last example concerns a preliminary study of the effects of low-energy muons on SRAM memories. As already introduced in subsection 2.1, atmospheric muons represent an important part of the natural radiation environment at ground level [1,20]. The muon is an elementary particle similar to the electron, with a unitary negative electric charge and a mass about 200 times the mass of an electron. The muon, denoted by µ and also called "negative muon", has a corresponding antiparticle of opposite charge and equal mass: the antimuon, often called "positive muon" (µ+). Because they are charged, both negative and positive muons can loss their kinetic energy by ionization process when they travel through matter. But this interaction with matter is tenuous and muons can travel large distances in matter, thus deeply penetrating into material circuits.

Another particularity of muons is that they are unstable particles with a mean lifetime of 2.2 µs. They spontaneously decay into three particles:

$$
\mu^- \to e^- + \overline{\nu}\_\epsilon + \nu\_\mu \quad \mu^+ \to e^+ + \nu\_\epsilon + \overline{\nu}\_\mu. \tag{7}
$$

Finally, when negative muons (and only negative muons) stop in silicon, about 35% decay following the previous reaction scheme and the remaining 65% are captured. If an intermediate state is assumed, the capture reaction can be written as:

$$
\mu^- + \text{Si}^{28} \rightarrow \text{Al}^{28} + \nu + 100.5 \text{ MeV} \tag{8}
$$

The excited 28Al nucleus can decay from the following modes, thus producing secondary heavy nuclei that can deposit important charge in silicon:

$$\begin{aligned} Al^{28} &\rightarrow Al^{27} + \text{\textquotedblleft (12.4 MeV)}\\ &\rightarrow Al^{27} + \text{\textquotedblright} \text{\textquotedblleft (14.2 MeV)}\\ &\rightarrow Na^{24} + \alpha \text{\textquotedblleft (15.5 MeV)}\\ &\rightarrow Mg^{26} + d \text{\textquotedblright} \text{\textquotedblleft (18.4 MeV)} \end{aligned} \tag{9}$$

In contrast to the first version of TIARA, TIARA-G4 is now capable of simulating the impact of muons on SRAM circuits. For this first study, we considered low energy (< 1 MeV) negative and positive muons susceptible to directly deposit charge by ionization or to be captured (negative muons) after they stop in silicon. The Geant4 general particle source was then used to generate mono-energetic muons incident on the well-known 65 nm SRAM architecture (with complete BEOL) previously defined in Figure 5. Figure 17 illustrates different possible scenarios of negative and positive muon interactions with the structure. Figure 17(a) shows a negative muon decay in the top layers of the BEOL structure, this cannot lead to an upset since the muon disintegrates in light particles not able to deposit any significant charge in silicon. Figure 17(b) shows a similar event but occurring in the silicon substrate. In this case, the incoming positive muon traverses the complete BEOL structure and, statistically, can cross a sensitive drain. If the charge deposited in the impacted drain is higher than the critical charge for this transistor type and for this technology, the corresponding memory cell is upset. Figures 17 (c) and (d) show two negative muon capture events occurring in the BEOL and in silicon, respectively. These events produce large secondary particle showers, containing one or more charged particles susceptible to reach the active silicon region and to induce an upset or even a multiple cell upset. Of course, the probability to induce an upset is maximum when the muon capture-induce shower is produced in the immediate vicinity of the sensitive drain layer, as illustrated in Figure 17(d). This case corresponds to a reduced energy interval for the incoming muons in so far as the penetration depth of the muons in the structure and then the capture location primarily depends on the muon kinetic energy.

330 Numerical Simulation – From Theory to Industry

0.0 0.5 1.0 1.5 2.0 2.5

Fraction of events (%)

**Figure 16.** Event multiplicity distributions obtained with the initial (TIARA) and new (TIARA-G4) versions of the code for the evaluation of the neutron-induced SER in the 65 nm SRAM architecture. Data are also plotted for TIARA-G4 with and without taking into account the real BEOL structure.

80 TIARA

123456789

Event multiplicity

 TIARA-G4 without BEOL TIARA-G4 with BEOL

This last example concerns a preliminary study of the effects of low-energy muons on SRAM memories. As already introduced in subsection 2.1, atmospheric muons represent an important part of the natural radiation environment at ground level [1,20]. The muon is an elementary particle similar to the electron, with a unitary negative electric charge and a

"negative muon", has a corresponding antiparticle of opposite charge and equal mass: the antimuon, often called "positive muon" (µ+). Because they are charged, both negative and positive muons can loss their kinetic energy by ionization process when they travel through matter. But this interaction with matter is tenuous and muons can travel large distances in

Another particularity of muons is that they are unstable particles with a mean lifetime of 2.2

28 28

. *e e e e*

 

> 

The excited 28Al nucleus can decay from the following modes, thus producing secondary

Finally, when negative muons (and only negative muons) stop in silicon, about 35% decay following the previous reaction scheme and the remaining 65% are captured. If an

*Si Al* 100.5 *MeV* (8)

 (7)

and also called

**5.3. Effects of low-energy muons on a 65 nm SRAM circuit** 

matter, thus deeply penetrating into material circuits.

intermediate state is assumed, the capture reaction can be written as:

heavy nuclei that can deposit important charge in silicon:

µs. They spontaneously decay into three particles:

mass about 200 times the mass of an electron. The muon, denoted by µ-

In order to illustrate this effect, we plotted in Figure 18 the distribution inside the SRAM structure of the vertex positions related to the negative muon capture reactions for three different values of the incident muon kinetic energy: 0.1, 0.3 MeV and 0.5 MeV. We clearly evidence in this figure such a dependency of the capture position (depth) with the muon kinetic energy. As a result, the soft error rate induced by negative muon irradiation presents a maximum when precisely muon captures occurs at the depth of the layer containing sensitive drains. This behavior is illustrated in Figure 19 which also plot the percentage of cell upsets induced by muon capture reactions or directly by muon impacts on sensitive drain (i.e. direct charge deposition in drain volumes). When increasing the kinetic energy of primary particles, the fraction of upsets induced by muon capture rapidly decrease as soon captures occur deeper in silicon, below the active layer. In this case, upsets become mainly induced by direct charge deposition from incident muons.

Soft-Error Rate of Advanced SRAM Memories: Modeling and Monte Carlo Simulation 333

**µ- SER** 65 nm SRAM

**Figure 19.**Estimated negative muon-induced soft error rate versus muon kinetic energy for the 65 nm SRAM. The percentage of cell upsets induced by the secondary particles produced by muon capture reactions or directly by muon impacts on sensitive drain (i.e. direct charge deposition in drain volumes) are also plotted.

**Direct ionization**

**Muon capture**

0.0 0.2 0.4 0.6 0.8 1.0

Kinetic Energy (MeV)

In conclusion, we described in this chapter a new simulation platform, named TIARA-G4, 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. Based on the Geant4 toolkit, the application is sufficiently general and modular to simulate a user-defined circuit architecture subjected to the external irradiation by heavyions, neutrons, protons, muons or directly by alpha-particles generated inside the circuit materials. After defining the natural radiation environment at ground level and the different types of radiation constraints, we presented in details the different modules of our code, including the methods and approximations adopted to model the circuit architecture, to generate particles mimicking a given radiation environment and to model the circuit/cell electrical response. Finally, we illustrated the capabilities of our code to estimate the softerror rate in deca-nanometer SRAM circuits subjected to atmospheric thermal and high energy neutrons and to mono-energetic positive and negative muons, investigating and illustrating for the first time, some unconventional physical effects, such as the 10B thermal neutron capture at the level of the Pmos drains or the negative muon capture and its consequences on the SER in the SRAM circuit structure. TIARA-G4 should be used in the future to more deeply investigate the radiation response of ultimate MOS circuits and

alternate nanoelectronic devices in the natural (terrestrial) environment.

Jean-Luc Autran, Sergey Semikh , Daniela Munteanu and Sébastien Serre

*Aix-Marseille University & CNRS, Marseille, France* 

SER (FIT/Mbit)

Upsets (%)

Gilles Gasiot and Philippe Roche *STMicroelectronics, Crolles, France* 

**6. Conclusion** 

**Author details** 

**Figure 17.** TIARA-G4 screenshots under ROOT of four events illustrating the interactions of low energy negative and positive muons with the complete 65 nm SRAM structure. From left to right: µ- decay in the BEOL (Al layer), µ+ upsetting a drain by direct charge deposition though the structure followed by the muon decay in the substrate, µ- capture on an aluminum atom in the BEOL, µ- capture on a silicon atom in the active circuit region (Pwell) leading to a drain upset via a direct impact by a secondary particle (proton in this case).

**Figure 18.** 3D distribution inside the SRAM circuit of the vertex positions related to the negative muon capture reactions for three different values of the incident muon kinetic energy: 0.1 MeV (white dots), 0.3 MeV (yellow dots) and 0.5 MeV (green dots).

**Figure 19.**Estimated negative muon-induced soft error rate versus muon kinetic energy for the 65 nm SRAM. The percentage of cell upsets induced by the secondary particles produced by muon capture reactions or directly by muon impacts on sensitive drain (i.e. direct charge deposition in drain volumes) are also plotted.

## **6. Conclusion**

332 Numerical Simulation – From Theory to Industry

particle (proton in this case).

0.3 MeV (yellow dots) and 0.5 MeV (green dots).

**Figure 17.** TIARA-G4 screenshots under ROOT of four events illustrating the interactions of low energy negative and positive muons with the complete 65 nm SRAM structure. From left to right: µ- decay in the BEOL (Al layer), µ+ upsetting a drain by direct charge deposition though the structure followed by the muon decay in the substrate, µ- capture on an aluminum atom in the BEOL, µ- capture on a silicon atom in the active circuit region (Pwell) leading to a drain upset via a direct impact by a secondary

**Figure 18.** 3D distribution inside the SRAM circuit of the vertex positions related to the negative muon capture reactions for three different values of the incident muon kinetic energy: 0.1 MeV (white dots),

In conclusion, we described in this chapter a new simulation platform, named TIARA-G4, 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. Based on the Geant4 toolkit, the application is sufficiently general and modular to simulate a user-defined circuit architecture subjected to the external irradiation by heavyions, neutrons, protons, muons or directly by alpha-particles generated inside the circuit materials. After defining the natural radiation environment at ground level and the different types of radiation constraints, we presented in details the different modules of our code, including the methods and approximations adopted to model the circuit architecture, to generate particles mimicking a given radiation environment and to model the circuit/cell electrical response. Finally, we illustrated the capabilities of our code to estimate the softerror rate in deca-nanometer SRAM circuits subjected to atmospheric thermal and high energy neutrons and to mono-energetic positive and negative muons, investigating and illustrating for the first time, some unconventional physical effects, such as the 10B thermal neutron capture at the level of the Pmos drains or the negative muon capture and its consequences on the SER in the SRAM circuit structure. TIARA-G4 should be used in the future to more deeply investigate the radiation response of ultimate MOS circuits and alternate nanoelectronic devices in the natural (terrestrial) environment.

#### **Author details**

Jean-Luc Autran, Sergey Semikh , Daniela Munteanu and Sébastien Serre *Aix-Marseille University & CNRS, Marseille, France* 

Gilles Gasiot and Philippe Roche *STMicroelectronics, Crolles, France* 
