Ionising radiation can release charge in the semiconductor in different ways. SEEs can occur through the impact of the incident particles themselves (e.g., direct ionisation from galactic cosmic rays (GCRs) or solar particles). SEEs can also occur as a result of secondary particles generated via inelastic or elastic nuclear reactions (Howe et al., 2005; Reed et al., 2006; Warren et al., 2005) and Coulombic (Rutherford or inelastic Coulomb) scattering (Wrobel et al., 2006) between the incident particles and the stationary targets in the struck material (indirect ionisation).
An incident particle can experience a number of interactions before its kinetic energy is expended. In every interaction the path of the particle can be altered and can lose some of the kinetic energy. To measure the energy transferred to the material the terms Linear Stopping Power and Linear Energy Transfer (LET) can be used. Equation 4.1 describes the rate at which a particle loses energy while moving through an absorber. The incremental energy (dE) may be expressed in units of MeV while the path length (dx) may be expressed in units of cm.
𝑆(𝐸) = −𝑑𝐸 𝑑𝑥
Equation 4.1. Linear stopping power
From these interactions, two types of stopping power can be distinguished (ECSS, 2007; Podgorsak, 2009):
Nuclear stopping power (also called radiation stopping power) resulting from energy loss per unit path length due to inelastic Coulomb interactions between the charge particle and the nuclei of the absorber. Only light particles, such as electrons and positrons, experience significant energy loss via nuclear stopping power. For heavier charged particles, such as protons and α particles, this type of loss is insignificant.
Electronic stopping power (also called ionisation or collision stopping power) resulting from inelastic Coulomb interactions between the charge particle and orbital electrons of the absorber. Electronic stopping power describes the energy lost due to direct ionisation. Unlike nuclear stopping power, heavy and light particles experience this type of interaction that results energy transfer from the incident particle to the orbital electrons via excitation and ionisation (ECSS, 2007).
Figure 4-5. Electronic, nuclear and total stopping power of protons in silicon, computed with PSTAR from NIST laboratory (Berger et
al., 2005)
The electronic, nuclear and total stopping energy of different particles are presented in Figure 4-5 (for protons) and Figure 4-6 (for electrons). Figure 4-5 shows that at all energies the electronic stopping power of protons dominates and that the nuclear stopping power is insignificant. Figure 4-6 shows that the nuclear stopping power of electrons dominates at higher energies.
Figure 4-6. Electronic, nuclear and total stopping power of electrons in silicon computed with ESTAR from NIST laboratory (Berger et al.,
2005)
The total stopping power (S(E)tot) for a charged particle with Ek energy passing
through an absorber of atomic number Z is in general the sum of nuclear stopping power and electronic stopping power as shown in Equation 4.2 (Podgorsak, 2009):
𝑆(𝐸) = 𝑆(𝐸) + 𝑆(𝐸)
Equation 4.2. Total stopping power for a charged particle
Charge deposition is often characterized by mass stopping power, instead of Linear stopping power. Mass stopping power is defined as the Linear Energy Transfer (LET) (not equal to Linear Stopping Power, but approximated) and can be obtained by dividing S(E) (expressed in MeV/cm) by the density of the material p (expressed in mg/cm3). Nearly independent of the density of the material, LET (Equation 4.3) describes the linear rate of energy transfer to the
𝐿𝐸𝑇 = 1 𝑝
𝑑𝐸 𝑑𝑥
Equation 4.3. Linear energy transfer
The LET of an incident ion and thus the density of ionisation, typically increase to a maximum immediately before the particle comes to rest. This peak, the Bragg peak, occurs due to the increasing cross section as the particle loses energy.
Figure 4-7. Bragg peaks: LET (MeV/cm2) of the standard components of a 16MeV/nucleon cocktail versus depth in silicon
(μm) (McMahan et al., 2004)
Incident particles can cause different nuclear reactions depending not only on the striking energy but also on the target mat erial. Figure 4-7 shows a plot of the LET of the standard components of a 16MeV/nucleon cocktail as a function of depth in silicon. The LET of a given ion is dependent on its energy and the target material, and therefore is an important parameter to quantify the sensitivity of electronic devices. Theoretical and experimental values of LET for most ions in different materials have been published (Northcliffe and Schilling, 1970). In addition, stopping power for different particles can be calculated using the TRIM code (Ziegler et al., 2010), and the ESRAR, ASTAR and PSTAR programs (Berger
The LET can be converted into charge per unit length (fC/μm or pC/μm). This is more suitable to situations that take into account the physical dimensions of the device and the charge stored at the critical nodes. For example, in silicon based technologies a particle with a LET of 97 MeV-cm2/mg corresponds to a charge deposition of approx. 1 pC/μm.
Figure 4-8. Energetic particle strike and generation of electron hole pairs: a) direct ionisation due to heavy strike; b) indirect ionisation
due to proton strike
In passing through a semiconductor material, high energetic particles (direct ionisation Figure 4-8a) can deposit energy in the absorber through a one step process involving Coulomb interactions with the electrostatic field electrons in the target atom (Podgorsak, 2009). The energy introduced allows bound electrons to leave their atoms, releasing free electron hole pairs and converting their energy into charge (part b of Figure 4-8b). The particle rests in the semiconductor material once almost all its energy is lost. The formation of an electron hole requires an average energy of 3.6eV. The energy lost due to direct ionisation can be referred as the electronic stopping power.
The total path length or total distance travelled is referred as particle’s range and is highly dependent on the type of particle, its initial energy and the properties of the semiconductor material.
At sea level, direct ionisation is the main charge deposition mechanism for upsets caused by heavy ions and alpha particles, emitted due to the contaminants in packaging materials. Traditionally, since protons and neutrons are lighter, the charge released by them is not enough to produce upsets via direct ionisation.
As suggested in 1997 the technological shrink model would soon be affected by direct ionisation of low energy particles (Duzellier et al., 1997). Recent experimental evidence (Heidel et al., 2008) of 65nm SOI SRAM sensitivity to direct ionisation from protons supported the latter suggestion with results that the low energy proton for the 65nm technology is different to those from previous generations.
However, the most significant upset rates due to light particles are caused via indirect ionisation mechanisms. In fact, in today’s semiconductor technology, high-energy neutrons derived from cosmic rays are the primary contributor to soft error rates at sea level.
In those mechanisms, the highly energetic particles (protons or neutrons) do not directly interact with the material. The three indirect ionisation mechanisms are:
Inelastic nuclear reactions that take place when the incident particle hits a target nucleus causing fragmentation and ejection of secondary particles; Elastic nuclear reactions that take place when the incident particle transfers some of its energy to a target nucleus that recoils (Figure 4-8) with extra energy transferred from the incident particle;
Coulombic scattering, similar to elastic nuclear reactions, takes place when the incident particle gets close to a target nucleus that recoils due to Coulomb force with less momentum and smaller angle than with elastic nuclear reactions.
significant indirect mechanism in the formation of SEE. If an inelastic nuclear reaction takes place, a collision with a target nucleus leads to the emission of reaction products that can, in turn, deposit energy via direct ionisation.
Those resulting particles are much heavier than the incident particle, which involves higher charge deposition that may result in a SEE. Since the incident particles do not directly interact with the semiconductor material, the number of counts or neutrons per cm2 is used to measure the effect rather than the LET.