SEMM-2: A new generation of single-event-effect modeling tools

The first IBM soft-error Monte Carlo model (SEMM-1) was developed for bipolar technologies and was the result of a large research effort in response to serious challenges of cosmic ray-induced single-event-upset (SEU), or soft-error, problems discovered in mainframe machines in the 1980s and 1990s. A comprehensive review of the IBM SEU work performed in the 1980s is provided in Reference [1].

The SEMM-1 Project was started in IBM in East Fishkill, New York, in 1985. The work has been summarized in a number of papers [2–7]. The original code was written by P. C. Murley and R. R. O'Brien, with important input from colleagues at Fishkill and the IBM T. J. Watson Research Center. I developed the essential nuclear reaction models including the NUSPA (NUclear SPAllation) code [5–7]¹ and the databases that provided the physics inputs required for the SEMM-1 simulations.

The SEMM-1 was the major soft-error simulation tool through the 1990s at IBM. Toward the end of the 1990s, rapid advances in new technologies warranted a new SEU model for soft-error rate (SER) evaluations. Initially, it was thought that creation of a few libraries to improve the accuracy of the physics models would be sufficient. However, it was immediately apparent that because SEMM-1 was designed for older technologies, many features in the code were obsolete. A new code was required to cope with the demands of the new CMOS (complementary metal-oxide semiconductor) technologies. Thus, the SEMM-2 Project was initiated in 2001.

In this paper, we summarize the latest developments in SEMM-2. First, we present an overall view of the SEMM-2 architecture, emphasizing the modular structures of the code organization as well as special computational methods to treat particle transport in arbitrarily complex geometries and material composition. We then describe the major features of the new particle transport module and atomic database, as well as the nuclear physics module and enhancements to NUSPA. Throughout the paper, the major differences between SEMM-1 and SEMM-2 are pointed out wherever appropriate.

Table 1 summarizes the major features of SEMM-1 and SEMM-2. In SEMM-2, these features involve the construction of a realistic back-end-of-line (BEOL) structure² and a front-end-of-line (FEOL) structure,³ special algorithms for particle transport in arbitrarily complex geometries and materials, physics models to simulate the relevant atomic and nuclear processes, generic radiation event generators, and the simulation models of charge collection processes.

The overall architecture of SEMM-2 is outlined in Figure 1. The SEMM-2 design is different from the SEMM‐1 design in one fundamental and important aspect: SEMM-2 is built from a number of independent modules. Each module has a distinct set of functions, and each generates output data for use by another. The modules are structured in such a way that they are only weakly linked with one another. Consequently, the addition of new modules and the implementation of new physics models into SEMM-2 is relatively straightforward. In the following sections, we review the SEMM-2 modules.

Figure 1

Figure 2 shows the simulation options available in SEMM-2, covering a wider range of applications than SEMM-1. Three major categories of particle sources are considered.

Figure 2

Alpha-particle sources in the BEOL structure
Alpha-particles can be emitted from the packaging and chip materials. A well-known example is the alpha-particles emitted from the lead solder bumps located at the top of the BEOL stack. Alpha-particles from thorium foils can be simulated to compare with experiments performed to characterize alpha-particle SEUs. Effects of BEOL structure contamination can be estimated by simulations, as the code can be initiated by specifying alpha-particle sources at various BEOL levels. Effects of alpha-particle emission from hot underfill materials can be simulated. Experimental aspects of SEU issues resulting from underfill materials are described in another paper in this issue [8], and examples of BEOL simulations also can be found elsewhere in this issue [9].

Monoenergetic hadron and ion beam experiments
The simulation options are monoenergetic hadron⁴ (proton, neutron, pion,⁵ and heavy-ion) beams. For a given beam energy, a large ensemble of projectiles is simulated by Monte Carlo procedures. The particle transport starts from the top of the BEOL structure.⁶ In the cases of proton, neutron, and pion beams, simulations of nuclear collisions are automatically activated. The proton option simulates SEU experiments using proton beams, and the neutron option is used to simulate SEUs induced by terrestrial cosmic ray neutrons. The main objective of the heavy-ion option is to simulate tandem experiments in order to 1) check the accuracy of the particle transport algorithms and to benchmark the code (for details, see Reference [9]), and to 2) extract critical charge (Q_crit)⁷ from direct measurements [10]. In a standard heavy-ion simulation, nuclear collisions are not included.

Cosmic ray and other sources
As inputs, one can use a terrestrial cosmic ray neutron flux model, which is derived from recent neutron measurements [11]. Other high-energy proton or neutron fluxes specified by the user can also be used as inputs. There are options that allow user-generated inputs of low-energy neutrons (in the million-electron-volt [MeV] range) and thermal neutrons (in the milli-electron-volt [meV] range).

Figure 3 shows the major components of the nuclear physics module, which is the source that generates the nuclear collision events and the associated nuclear database. In general, there are two classes of nuclear events: inelastic scattering and elastic scattering.⁸ The inelastic processes are simulated by the NUSPA reaction model [5–7], and the elastic processes are simulated by nuclear optical models [12].

Figure 3

NUSPA is a standalone nuclear reaction model that is used to generate a nuclear database consisting of reaction files and cross-section⁹ files. Each reaction file is a table that contains a large number of simulated collision events from a reaction. The use of reaction files results in a computationally efficient scheme of using nuclear models. Significant savings in machine time are possible. More information on the recent enhancements of NUSPA is presented in the section “Nuclear physics module: Reaction models and database in SEMM-2.”

Unlike in SEMM-1, no reaction files are used in SEMM-2 to store elastic events. Instead, short tables of scattering probabilities for the elastic processes are constructed (using nuclear optical models). The elastic events required in SEMM-2 simulations are constructed by fast Monte Carlo sampling algorithms using the elastic scattering probability tables. This amounts to no loss in computational efficiency, and it gains the significant advantage of not having to allocate a large amount of disk space to store the elastic events. Typically, it takes less than 1 CPU second to generate 10⁶ elastic events on an average workstation with the IBM AIX* operating system. For proton–nucleus and neutron–nucleus reactions, the elastic cross-sections at energies less than 100 MeV are large; they are equal to or larger than the inelastic cross-sections.

Certain heavy-ion reactions can be simulated in the latest version of NUSPA (for details, see the section “Nuclear physics module: Reaction models and database in SEMM-2”). Their reaction files, cross-section files, and elastic scattering tables are constructed and processed in SEMM-2 runs in a manner similar to the high-energy hadron–nucleus reactions.

Figure 4 shows the main components of the particle transport module. The Stopping and Range of Ions in Matter (SRIM) code [13] (which is not a part of SEMM-1 or SEMM-2) is the open source used to generate the atomic database in SEMM-2. This database consists of tables of linear energy transfer (LET) and the energy-range relation of a set of charged particles in a number of target media. LET refers to energy loss or energy deposited per particle path length. A convenient unit for LET is MeV/μm. In Si, 1 MeV/μm is equivalent to a linear charge density of 44.5 fC/μm. Hence, multiplying the LET (in fC/μm) of a charged particle at the Si surface by the Si layer thickness (in μm) gives a first-order estimate of the deposited charge in the Si layer. A library of fast table-lookup and interpolation algorithms has been written to use this data in SEMM-2. More details on particle transport are provided in the section “Particle transport module: Simulation methodology and database in SEMM-2.”

Figure 4

The radiation event generator module is a new feature in SEMM-2 that solves a class of transport problems in a general setting. The problems consist of the following major simulation steps. 1) Given the initial conditions of a radiation particle (i.e., its position, velocity, and energy), a basic geometry problem must be solved; that is, the regions and materials intercepted by the particle trajectory must be determined. 2) The energy loss of the particle (if it carries electric charge, as in the case of a proton, pion, or heavy ion) along its trajectory must be computed to determine whether the particle is stopped. 3) In the case of a high-energy particle, whether the particle causes a nuclear collision along its path must be determined. If it does, the location at which the collision occurs must be determined, the secondary fragments produced in the collision must be constructed, and these secondary particles must be transported in the system. In SEMM-1, the BEOL structure is represented by a single Si or SiO₂ block, and hence, transport steps 1 and 2 are simple to compute. The major computations are carried out in step 3.

In an early version of SEMM-2 [14], the BEOL structure is represented by multiple layers of homogeneous materials, and new subroutines were written to handle this more general problem with multiple layers. Although this represents a significant improvement over SEMM-1, the granularity due to metallization and wiring structure in the BEOL structure is not treated explicitly. These details play an important role in certain SEU problems [9] that are relevant to current technologies.

In the last few years, a number of critical SEU problems arose that were related to critical charge extraction for 65-nm silicon-on-insulator (SOI) technology [10], alpha-particle blocking by BEOL materials, mitigation of alpha-particle-induced SEUs by BEOL designs, and potential SEU impacts of low-LET ionizing particles [15, 16]. It was realized that details of the complex topologies existing in the BEOL structure had to be incorporated in order to produce realistic simulations. As a result, a new, more comprehensive radiation event generator was written, which was then incorporated into SEMM-2. This development became one of the major departures from the SEMM-1 approach. Presently, in SEMM-2 the BEOL geometry can be taken directly from design layouts. In Figure 1, this is illustrated by the block labeled “BEOL geometry interpreters.” In SEMM-1, and in the first version of SEMM-2 [14], the feature of directly passing design structure into the simulation code was not available. Details of this work are described in another paper in this issue [9]. Details of the FEOL geometry and device structure are also constructed and passed as inputs to the radiation event generator (labeled “FEOL and transistor schematics generators” in Figure 1).

The outputs from the radiation event generator consist of two classes of particles: 1) the primary radiation particles, which are energetic enough to penetrate the BEOL region without being absorbed or without encountering nuclear collisions, and 2) the secondary fragments produced from nuclear collisions (between the primary incident particles and the nuclei in the BEOL region).

Taking inputs from the radiation event generator, the charge collection module has two basic functions. The first function is to track the charged particles as they reach the Si surface and follow their transport in the FEOL region. Some of these particles hit sensitive devices and the code computes the charge deposited in their collection volumes on an event-by-event basis. The locations and dimensions of the devices and their collection volumes are defined at the beginning of the simulation run. The charge collection module in SEMM‐2 is designed to handle general device and charge collection volume configurations typical of those encountered in the design of modern technologies.

The second function of the charge collection module is to provide prescriptions to compute fail rates or SEU cross-sections. In order to accomplish this, certain device and circuit parameters are required. In SEMM-1 simulations, field-funneling [17] is the major charge collection mechanism [3, 4]. A post-processor in SEMM-1 simulates the ion track (e.g., which crosses the p–n junction of a sensitive device), partitions the ion track into a number of charge packets, and follows the transport of these charge packets in order to determine which ones will reach the nearby collection node. To determine whether the ion strike will cause a fail, the charge packets collected at the node are compared with a set of precalculated current pulse parameters (which are device and circuit dependent). The simulation proceeds as follows. A radiation-induced current pulse is parameterized as a sum of two exponential functions. By varying the width and the height of the pulse and examining the circuit response to each combination of width and height, a relation between the pulse width and the minimum charge required to flip a bit¹⁰ is constructed by circuit simulations. The SEMM-1 post-processor sums the charge packets collected at the node, and using the precalculated pulse parameters, it determines whether the total collected charge exceeds the circuit critical charge. In addition to the current pulse parameters, the post-processor also uses assumptions about certain key parameters in the calculations, such as the funneling length [3, 4].

In SOI technologies, funneling is not a relevant charge collection mechanism [18], and the SEMM-1 post-processor described above is not used. Instead, a method has been developed with which one extracts Q_crit from experiments. This is accomplished by direct measurements of fails using monoenergetic ion beams, combined with an interpretation of the data using detailed analysis of the ion energy loss in the BEOL materials [9, 10]. In SEMM-2, the charged fragments crossing the collection volumes are analyzed and the experiment-based Q_crit values are used as the fail criteria.

The Q_crit determination technique outlined above is general and is applicable to SOI and bulk technologies. However, its use is limited because it does not provide details of the underlying charge collection mechanisms. These mechanisms involve transport processes that are sensitive to device structure and circuit operating conditions. In order to model the charge collection effects at a fundamental level (for SOI and bulk technologies), inputs from device and circuit simulations must be considered. Ideally, one would use the radiation event generator in SEMM-2 to produce the ion strikes on sensitive transistors and then full three-dimensional (3D) time-dependent device simulations to calibrate the charge collection module in SEMM-2 for each technology. Such detailed simulations are computationally intensive. Hence, for practical calibrations, it is essential to identify the important parameters such as hit angles, hit locations, and distribution of the energy and LET of the hit events in order to optimize the device calculations. Work along this line is now being considered.

An intruding subatomic particle is a potential radiation source. Almost any particle (except for the neutrino, because of its extremely small interaction cross-sections with nuclei) under appropriate conditions can cause fails in a circuit or damage in the materials. However, not all particles are equally important as far as single-event-effect (SEE) impacts are concerned.

Simulations in SEMM-1 were concerned only with the energy loss of alpha-particles and a few typical recoil nuclei produced in Si and SiO₂ because the old technologies were associated with large Q_crit values. For modern technologies, the Q_crit value is on the order of 1 fC and it is expected to decrease further. To capture these technology trends, SEMM-2 is designed to analyze a wider group of particles and to treat more-general transport problems than SEMM-1. Accurate and efficient particle transport algorithms are an essential component of SEMM-2. For a charged particle passing through the packaging materials and eventually hitting the sensitive device regions, the energy loss along its trajectory must be evaluated accurately. This energy loss is converted into direct ionization of the medium around the particle path. At a microscopic level, this involves excitation and de-excitation of atoms responding to the sweeping electric field of the moving charge, the promotion of electrons from lower to higher atomic orbits, and the ejection of certain bound electrons into the vacuum (the delta electrons). Two sets of parameters are central for the transport calculations in SEMM-2: the LET of the particle and its energy range in the medium. (For a general review of the stopping of charged particles, see Reference [19]; some older reviews on the subject can be found in [20–23].)

As mentioned earlier, the particle transport calculations in SEMM-2 use a library of fast table-lookup and interpolation algorithms as well as a precalculated atomic database of LET and energy-range tables of elemental projectiles in a selected set of target media. The atomic database has been constructed using the SRIM (Stopping and Range of Ions in Matter) code [13]. For each set of LET and energy range, the projectile associated with the most abundant isotope of that element is used. For example, the projectile with atomic number (charge number) Z = 1 corresponds to hydrogen, or ¹H isotope, that with Z = 2 corresponds to helium-4, or ⁴He, and so on. The table-lookup and interpolation algorithms were written for general purposes and for flexible table formats. For example, the spacing of the energy grids in the tables can be arbitrary. The algorithms offer options for linear–linear, semilog, or log–log interpolations. Such general computational setups allow for straightforward updates in future work.

The list of projectiles treated by SEMM-2 transport includes protons, heavy ions, charged pions, and leptons [electrons (e⁻), positrons (e⁺), muons (μ⁺, μ⁻) , and tau particles (⁺, ⁻)].

Transport calculations of protons
Proton calculations are performed by using the hydrogen LET and energy-range tables (Z = 1).

Transport calculations of arbitrary ions
The transport of an arbitrary isotope of an element must be taken into account. In high-energy radiation simulations, nuclear processes occur, and one may encounter isotopes that are not found in the precalculated atomic database. For example, among the secondary particles produced in a spallation reaction, one may find the isotopes deuteron (²H) and triton (³H) for Z = 1, helium-3 (³He) for Z = 2, and so on. The LET and energy-range calculations of these isotopes are done by applying a mass scaling rule to the existing tables. The calculations for deuteron or triton apply mass scaling to the ¹H (Z = 1) tables, and that of helium-3, to the ⁴He (Z = 2) tables. Scaling is described in [21–23]. Accuracy is not compromised with the use of mass scaling.

In order to optimize the size of the database (which is read in the code and stored as internal arrays), only a small set of elements must be precalculated, that is, those elements present in the devices, circuits, and packaging materials. In simulations of high-energy protons and neutrons, one may encounter the following situation: The atomic number (Z) of a spallation reaction product produced from a heavy metal such as lead (Z = 82) or tungsten (W) (Z = 74) cannot match the elements in the database. In this case, the LET and energy-range tables of an element whose atomic number is closest to the projectile in question are selected, and the calculations are carried out by using charge and mass scaling. The use of charge and mass scaling offers an option to circumvent the practical problem of having to store a prohibitively large atomic database. In principle, charge scaling is an approximation that works well only when the velocity of the ion is much higher than the orbital velocity of the electrons in the target atoms [i.e., when the ion kinetic energy is at least ~1 MeV/amu (atomic mass unit)]. At low energies, this approximation becomes crude or may even break down.

Transport of pions and other mesons
Pion transport is considered in SEMM-2 because pions are produced as secondary particles in all high-energy proton- and neutron-induced spallation reactions. At very high energies, mesons that are heavier than pions are also produced. Pions are present in terrestrial cosmic rays. In nuclear physics and high-energy physics experiments, protons, neutrons, and pions are common sources of secondary particles produced in (man-made) harsh radiation environments, and they have been found to cause serious SEU problems in detector systems. The database in SEMM-2 does not include pion LET and energy-range tables. Instead, pion transport is treated by applying mass scaling on the proton tables. The rest mass of a proton is approximately 938 MeV, and that of a pion is approximately 135 MeV.  In such  a treatment,  the positive  pion (⁺) and negative  pion (⁻) have the same LET and energy-range relation. This is justifiable because in most of our SEE studies, the effects due to the small differences between ⁺ and ⁻ ranges [24] can be ignored. Similarly, the transport of other mesons heavier than pions is computed by applying mass scaling rules to the proton tables.

Transport of leptons
In a 1996 review in the IBM Journal of Research and Development [5], it was estimated that the potential SEUs caused by muons are not significant for terrestrial applications. This analysis remains valid for current IBM products. However, in going beyond terrestrial applications, one may find exceptions. For example, in space environments, and in high-energy physics experiments, the circuits and devices can be exposed to high fluxes of electrons, positrons, and muons.

The transport codes in SEMM-2 offer options to compute the LET and energy-range relations of all types of leptons. For electrons and positrons, because their masses are small (0.511 MeV), their transport must be calculated using special methods [20, 25]; the algorithms formulated in [26] are adopted in SEMM-2 for electrons and positrons. For muons and tau particles, their masses are much larger (105.66 MeV and 1,784 MeV, respectively) than those of the electron and positron, and their LET and energy-range relations are computed by applying mass scaling to the proton tables.

Nuclear reaction models play a central role in modeling of radiation effects whenever high-energy incident particles are involved. This is a major theme in a 1996 review of SEMM-1 [5]. In general, both elastic and inelastic nuclear collisions must be considered. In older technologies, elastic processes of proton–nucleus, neutron–nucleus, and pion–nucleus collisions play only a minor role, because older technologies are characterized by large Q_crit values and elastic scattering is dominated by forward scattering events that involve only small recoil energies. (Large-angle scattering leads to large recoil energies but is rare.) This point has been analyzed in detail in Reference [5]. However, the arguments in [5] must be modified when we consider heavy-ion reactions.

For current technologies, because the Q_crit has decreased, both elastic and inelastic reactions must be considered in rigorous SEE modeling such as NUSPA and nuclear optical models. These reaction models generate the critical databases required by the event generator. The fundamental physics and applications of NUSPA have been described in a number of papers [5–7, 27–32]. Here, the main points are summarized for the benefit of readers who are not familiar with the earlier work. Some of the major enhancements introduced in NUSPA in the last few years are reviewed in the sections “New nuclear databases” and “NUSPA-2: Physics enhancements,” later in this paper.

NUSPA simulates proton–nucleus, neutron–nucleus, and pion–nucleus spallation reactions, which are inelastic processes. It assumes that the nuclear reaction takes place in essentially two distinct stages: 1) a fast intranuclear cascade (INC) stage (of the order of 10⁻²² to 10⁻²¹ seconds) that involves nucleon–nucleon or pion–nucleon collisions, and 2) a slower stage (of the order of 10⁻¹⁹ to 10⁻¹⁶ seconds) that involves the statistical decay of the compound nucleus formed at the end of the first stage. Both stages produce secondary particles, which include secondary protons, neutrons, light ions (e.g., deuteron, triton, and helium), and heavy-recoil nuclei. (In high-energy reactions, secondary pions can be produced in the INC stage.) Any charged secondary particle can be a source of an SEE. Symbolically, these reactions are given as

In Equation (1), the hadron projectile can be a proton, neutron, or pion (⁺, ⁻). The secondary reaction products X₁, X₂, …, X_n can be protons, neutrons, light ions (e.g., He, Li, or Be), or pions.

NUSPA has been checked by a large quantity of nuclear data [5, 6, 29]. It has several important features that are particularly useful for SEE applications:

1. Absolute cross-sections are calculated. The simulations do not depend on any arbitrary normalization with respect to prior measurements, or other theoretical calculations. Hence, the model can be directly checked by basic nuclear experiments.

2. All of the exclusive exit reaction channels—which are compatible with energy-momentum conservation and the assumed underlying reaction mechanisms—are simulated and treated on an equal footing. In a general reaction represented by Equation (1), if the energies and momenta of all reaction products on the right side are measured in coincidence in an experiment, the experiment is said to be exclusive. In contrast, if particle X₁ is observed while all the others are not, the measurement is said to be a single-particle inclusive experiment. Similarly, if particles X₁ and X₂ are observed in coincidence while the others are not, the measurement is said to be a two-particle inclusive experiment. In principle, the set of all possible exclusive cross-sections contains the maximum information of the reaction. Any inclusive cross-section can be deduced from the exclusive cross-sections. However, in general, the exclusive cross-sections cannot be constructed from the inclusive cross-sections alone, because the inclusive cross-sections do not contain the complete information of the reaction dynamics. This feature (i.e., treating exclusive exit channels on an equal footing) is particularly important in the analysis of multiple-bit, multiple-cell fails in new technologies, caused by hits from several secondary fragments produced by the same nuclear event (see the examples described in [31, 32]).

3. The model automatically satisfies certain fundamental sum rules [5, 6, 33] that set rigorous constraints on the reaction cross-section and the partial cross-sections of all exit channels. Since the model gives good predictions of the reaction cross-section and those of the light fragments (proton, neutron, helium), the sum rules imply that the model predictions of the heavy recoils stay within reasonable bounds. The recoil nuclei, each carrying more charge than a secondary ⁴He, are a dominant source of radiation energy. Figure 5 shows examples of the double differential spectra of several heavy-recoil fragments from 80-MeV protons on Si. The histograms are NUSPA simulations, and the measured data (symbols in Figure 5) was taken at the National Superconducting Cyclotron Laboratory of Michigan State University using an inverse kinematics measurement technique [29]. The agreement between the model and the measured data is good. These experiments provide stringent checks on nuclear reaction models. A brief discussion of the basic concepts of this experimental method is given in the Appendix.

4. The model can be justified from the theoretical framework of a fundamental reaction theory that is based on a formal many-body theory [34]. This basic point was raised and emphasized in [5, 6].

Figure 5

In order to support SEMM-2 developments, a new nuclear database was created. This was necessary because the database used by SEMM-1 was constructed using early versions of NUSPA. Also, in the previous database, only secondary alpha-particles and recoils were tabulated, because large Q_crit values were of concern for the older technologies. In the new nuclear database, all charged secondary fragments produced—proton, deuteron, triton, pion, light ions (He, Li, Be)—and heavy recoils are processed.

Extension to low-energy reactions
The NUSPA model has been shown to work down to an incident nucleon (proton or neutron) energy of about 50 MeV (a critique of NUSPA applications to nuclear reactions can be found in [6]). This seems to contradict the notion that INC models are not valid at energies less than 100 MeV. This view was commonly held in the nuclear physics literature prior to the 1980s. The INC models were originally developed for reactions at energies well more than 100 MeV. Such a pessimistic viewpoint is based on the alleged argument that for an incident proton or neutron at less than 100 MeV, its de Broglie wavelength becomes comparable to the linear dimension of the target nucleus. Hence, the wave mechanical nature of the projectile becomes more significant, and the classical prescriptions in the INC model break down. In such an argument, however, certain nuclear medium effects have been ignored. For example, when the nucleon enters the nucleus, it experiences an attractive nuclear mean field (from the target nucleus) of about 45 MeV, which would accelerate the projectile, increase its kinetic energy, and hence decrease its de Broglie wavelength somewhat in the nuclear interior.

The nuclear mean field and the Pauli exclusion principle govern the most important features of nuclear structure [35–37] and play crucial roles in reactions at less than 100 MeV. In INC simulations in NUSPA, these features are already incorporated into the Monte Carlo simulations.

Since the publication of the 1996 review [5], NUSPA has been extended approximately to the Coulomb barrier.¹¹ For proton reactions on Si, the Coulomb barrier is approximately 4.5 MeV. At proton or neutron incident energies of less than 30 MeV, the INC processes are not expected to be effective in producing secondary particles (i.e., via nucleon–nucleon collisions). In the new version of NUSPA, the INC is switched off at less than 30 MeV. The incoming nucleon is assumed to fuse with the target to form a compound system. After the recoil energy of the compound system has been accounted for, the kinetic energy of the incident particle is converted into an excitation energy and statistical decays of the composite system follow, producing secondary particles. One parameter in this treatment that must be fixed is the fusion cross-section of the nucleon + target system. Prescriptions that are based on semi-classical methods [38] are used to compute this fusion cross-section, which is then equated to the reaction cross-section.

Extension to heavy-ion reactions
In ion beam experiments, if the beam energy is above the Coulomb barrier, the projectiles can induce nuclear reactions within the BEOL or packaging materials. Questions arise about whether the secondary debris from these reactions can cause significant SEUs in the underlying circuits. With the Q_crit of newer technologies decreasing to less than 1 fC, these questions must be answered quantitatively.

A new heavy-ion reaction option has been developed, invoking ideas similar to the low-energy reaction option described in previous section. The model is assumed to be valid for energies up to about 30 MeV/amu. First, the incoming ion is fused with the target, according to a fusion cross-section computed by a semi-classical method. Second, the excitation energy of the composite (projectile + target) system is computed, and finally, the statistical decay of the composite system follows.

Option to include hadron-induced fission processes
In SEMM-1, Si and SiO₂ are the major material types considered. However, the high-Z materials present in current and future technologies can contribute to radiation sources via nuclear spallation reactions. A significant portion of the BEOL region consists of metals. The wires are made of copper (Z = 29, A = 63). The solder contacts at the top of the BEOL stack consist of lead (Z = 82, A = 208). In addition, close to the active nodes in the FEOL region, there can be tungsten (Z = 74, A = 184) contacts. In SEMM-2, these high-Z materials have been included in the nuclear and atomic databases. Several research groups [39–41] have raised questions about the potential impacts from the heavy metals.

When high-energy protons or neutrons collide with the heavy metals, in addition to the usual spallation reaction products of secondary protons, neutrons, light ions, and recoil nuclei, there are certain probabilities for producing fission¹² fragments. The fission cross-sections for sub-actinide metals such as Cu, W, and Pb are typically small fractions of their reaction cross-sections [42, 43]. However, it is important to note that the fission fragments are energetic because of the large Coulomb repulsion at the scission point, and that each fragment, carrying a large charge (roughly half that of the parent nucleus),¹³ is much more ionizing than a secondary ⁴He or recoil nucleus produced from a lighter nucleus such as Si or O. Hence, even though fission events are rare compared to typical spallation events (see Footnote 12), their potential SEE impacts should not be ignored. Their effects should be quantified in future designs.

In order to address these issues in SEMM-2 analysis, a new feature in NUSPA has been developed to simulate the proton- and neutron-induced fission reactions. The simulations of the fission events are based on phenomenological prescriptions that are constrained by fission cross-sections and calibrated with the fragment energy systematic observed in experiments [42, 43].

In Table 2, the reaction cross-sections are compared with the fission cross-sections for the reactions of protons on tungsten target at 50, 150, and 500 MeV. The reaction cross-sections computed by the NUSPA code and the corresponding experimental reaction cross-sections [44] are shown. The NUSPA reaction cross-sections are within 5–8% of the experimental values, which is considered to be very good agreement given that the NUSPA reaction cross-sections are calculated without any free parameter adjustment. The last column shows the experimental fission cross-sections [42, 43]. In the proton + tungsten system, the fission cross-section rises to a saturation value of approximately 30 mb at proton energies of more than 1 billion electron volts (GeV). At less than 100 MeV, the fission cross-section decreases rapidly with energy so that there is no significant cross-section at less than 50 MeV. (The fission cross-section at 50 MeV is estimated from a neutron-induced reaction.)

To illustrate the salient features of a conventional spallation reaction versus a fission reaction, consider the following Monte Carlo-generated events from the generalized NUSPA code (for 150-MeV protons on tungsten [W]):

and

In Equation (2), a neutron is knocked off by the incident proton, and the compound system fissions into a ⁹²Sr fragment (Z = 38) and a ⁹²Rb fragment (Z = 37). In this particular simulated event, the Sr and Rb fragments fly apart with kinetic energies of 61.54 MeV and 64.19 MeV, respectively. In Equation (3), a proton, ten neutrons, and an alpha-particle are produced via nucleon–nucleon quasi-free scatterings and compound nucleus decays. In this spallation event, a ¹⁸⁰Hf recoil is formed. The secondary ⁴He has a kinetic energy of 20.92 MeV, whereas the Hf recoil moves with a kinetic energy of 1.38 MeV.

This paper describes the development of SEMM-2, a new simulation system designed for the analysis of SEEs in advanced CMOS technologies. The code is built on a number of modules. By exploiting generic simulation techniques for the event generators, particle transport in arbitrarily complex BEOL and FEOL geometries can be treated in SEMM-2. Hence, SEMM-2 can treat radiation problems far more complex than those routinely analyzed with SEMM-1.

Most conventional nuclear physics experiments are performed with a projectile beam impinging on a stationary target. To measure heavy-recoil spectra using a stationary target imposes serious experimental challenges. Heavy fragments often have small velocities and are easily stopped in the target region and hence escape detection. As a remedy, one can use a thick target to make up for the lost events and apply corrections to account for the absorbed fragments. These procedures tend to make the analysis difficult and increase the uncertainties in the data.

In the inverse kinematics method, the roles of projectile and target in the conventional setup are reversed. In the Michigan State University experiment quoted in the text, a ²⁸Si beam with energy of 80 MeV/amu impinges on a stationary CH₂ target. The experiment is repeated with the ²⁸Si beam impinging on a stationary C target. The measured spectra of the heavy fragments produced by the C target are then subtracted from those produced by the CH₂ target. This yields the desired spectra of the heavy recoils. By applying a coordinate transformation, one obtains the heavy-recoil spectra in the conventional setup. The important point is that the physics in both experiments (using the stationary target and inverse kinematics) is the same. In the inverse kinematics method, the heavy fragments produced in the collisions are beam-like and move with higher velocities than if they were produced in the conventional experiment. They are not stopped by the target; they move in the Si beam direction with a small angular spread and are detected.

The IBM SEMM-1 Project began more than 2 decades ago. I have the unique privilege of being a member of the original group that delivered SEMM-1 in 1986. Among my former IBM colleagues, Phil Murley and Red O'Brien (both retired) should be specifically thanked for their dedication. Their work in SEMM-1 has become a legacy in the field of SER modeling. Without their pioneering work, the SEMM-2 Project probably would not have taken place. In the past few years, people who have had positive impacts on SEMM-2 development include the following: David Heidel, whose methodical thinking has helped to clarify many confusing technical issues; Kenneth Rodbell, who has been a strong advocate of rigorous physics-based modeling and who favors experimental measurements over arbitrary circuit parameterizations; and Conal Murray and Giovanni Fiorenza, who have shown me powerful techniques to analyze BEOL material composition. Tim Collopy, Robert Dennard, Mark Hakey, Russ Lang, and Tak Ning are to be thanked for their constant and keen interest in all aspects of SER work. For helpful discussions in radiation physics, I am indebted to Phil Oldiges, H. Takai (Brookhaven National Laboratory), J. L. Romero (University of California, Davis), D. Röhrich, K. Ullaland, and K. Røed (University of Bergen and CERN), C. Foster (Indiana University Cyclotron Facility), and F. Faccio, A. Ferrari, and M. Huhtinen (CERN). For guiding me through the literature on the recent measurements on high-energy hadron-induced fission reactions, I am thankful to Professor A. V. Prokofiev of the The (Theodor) Svedberg Laboratory at the University of Uppsala and Professor V. E. Viola of the Indiana University Cyclotron Facility.

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¹One of the major causes of SEUs from terrestrial neutrons is the secondary charged fragments produced from neutron–nucleus reactions.
²Back-end-of-line structure is that portion of the integrated circuit fabrication that includes the contact, insulator, metal interconnect levels, and bonding sites for chip-to-package connections.
³Front-end-of-line structure is the first portion of the integrated circuit fabrication where individual devices (e.g., transistor and resistor) are patterned, except for the metal interconnect levels.
⁴A hadron is a strongly interacting subatomic particle.
⁵Pion (or pi–meson) is a short-lived particle that is produced in high-energy nuclear reactions. It interacts with a nucleus via the strong nuclear force. Pions are known to cause SEUs for the same reasons that protons and neutrons cause SEUs. In the context of the Standard Model of modern particle physics, a pion is a composite system that is made up of a quark–anti-quark pair.
⁶We always assume in the text that the primary particle starts from the top of the BEOL stack. In practice, the transport algorithms in SEMM-2 treat arbitrary initial position and direction for the particle.
⁷The parameter extracted from a monoenergetic beam experiment is a critical deposited charge that causes fails. It is a parameter that is derived from a broad ion beam [9, 10].
⁸In an inelastic scattering event, the internal states of the projectile, the target, or both are changed. In an elastic scattering event, the internal states of the projectile and target remain unchanged. Typical spallation events involve the production of secondary particles.
⁹In atomic, nuclear, and particle physics, a cross-section is a fundamental quantity for a reaction. A typical unit of nuclear cross-section is barn (b): 1 b = 10⁻²⁴ cm². Another unit is millibarn (mb): 1 mb = 10⁻²⁷ cm².
¹⁰The minimum charge required to flip a bit is the circuit critical charge, which is dependent on the shape of the pulse.
¹¹Between a charged projectile (such as a proton or an ion) and a target nucleus, there is a repulsive Coulomb force. In order for a nuclear reaction to occur, the kinetic energy of the projectile must be large enough to overcome this repulsive force. The threshold value of this energy is the Coulomb barrier.
¹²In this paper, fission refers to the breakup of a heavy nucleus into two fragments of equal or roughly equal masses. The general class of spallation reactions given by Equation (1) does not include fission products.
¹³For sub-actinides, fission is dominated by symmetric breakup of the parent nucleus.

Received August 21, 2007; accepted for publication November 7, 2007; Published online February 27, 2008.