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37. EFFECT OF RADIATION DAMAGE – SOFT ERRORS
37.1 Review/Background:
This lecture will focus on radiation-induced reliability issue, which is the fourth reliability mechanism other than NBTI, HCI, and TBBD. In the previous lecture, the importance of radiation related to a large of number of failures of memories as well as logic circuits is covered. Today, how radiation causes soft errors will be discussed. Soft errors refer to reversible errors, which is opposite to hard errors that result from punch- through and is permanent.
37.2 Source of radiation
The source of the radiation determines impact on the transistors. For example, those come from cosmos are very different than those from solar wind or packaging. Thus, the understanding of radiation sources is very important to understand the potential damage.
Figure. 37.1. Four different sources of radiation
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From Figure. 37.1, we have three different types of sources. They are comic ray, solar wind, and packaging process. When we hold our cell phones in classroom, then the source of disturbing our electronics will be comic ray, some of which have enough energy to penetrate to the ground level. Solar wind, which is the radiation from the sun, causes problems to satellites that are out of the atmosphere primarily. Packaging itself has radiative components, such as trace amount of Thorium, which emits alpha particle. A danger situation is the interaction between comic ray and packaging materials. For example, there are two types of p-type doping material Boron: Boron-10 and Boron-11. There is a small fraction of Boron-10 in the packing materials. When Boron 10 absorbs low-energy comic ray, it breaks up as Li(7) and alpha particle – each of which creates a huge number of electron-hole pairs.
Moreover, proton and α-particle are charged particles. According to Columbs law ，they will generate electron-hole pairs through electromagnetic interaction when they come through. Neutron, however, is not a charged particle. So it can penetrate a long distance without anything happening to it at most time. The longest distance it can go is 40 cm on average in Silicon based on Blackwall theory as discussed in the last lecture. So the likelihood of a neutron can hit a silicon atom in a 10-um device is very low. But when it happens, there will be a nuclear reaction between the neutron and silicon atom. The silicon atom will break apart and create three protons, a C-12, and a few α-particles. Therefore, once nuclear reaction happens, the device is guaranteed to fail.
In order to calculate the probability of failure due to particles from a certain source, we must know three things – the flux of particles from the source, and the efficiency of electron/hole pair generation due to each particle, and finally, the critical charge necessary to upset operation. Let us being with calculating the flux. We will derive the Bethe formula for the efficiency of charge generation in the next chapter.
Comic Ray : Let’s first talk about the cosmic ray. It consists of 92% proton, 6% α-particle (or 70% proton, 30% neutron). An important fact to know is that the cut-off of cosmic ray to reach the ground is 1 GeV. Any ray below this energy will be turned around by the earth’s magnetic field. As the plot shown in Figure. 37.2, the part we are primarily interested in is a small region on the top. The letters P, α, L, H and M stand for proton, α-particle, Lithium, Hydrogen, and Magnesium respectively. Interestingly, the
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scattering time for these particles is 300 million years in the space. The reason is that the density of them in cosmos is 1.7 × 10 g/cm . So we may find only single one particle in miles and miles.
Solar Wind . Next, we will take a look at solar wind. Unlike the earth, gas-like materials form the sun. So what actually happens is that the equator of the sun moves faster than the poles by around eight days. It results in tangled magnetic field that allows big holes, which is referred as the black sunspots. These are opening on the sun, through which the gas can escape. The energy density at surface is 1365 W/cm . But only a small portion of the solar wind can reach the earth and the other can deflected by the earth’s magnetic field. The process takes approximately 4 days.
Figure. 37.2. Energy vs. Flux intensity (comic ray)
One of the most interesting curves generated in the last century is shown in Figure. 37.3.
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Figure. 37.3. Radiation Flux Density vs. Altitude
The left side of the curve is the ground and the right side is the surface of atmosphere. The pressure measured by Hg presents the altitude. As shown, there is a peak of the flux near the surface of the atmosphere. The reason is that when the primary particles strike the atmosphere, it generates a creation number of electron-hole pairs with very high energy. Subsequently, a secondary generation that produces even much more pairs occurs due to these high-energy carriers. As the altitude goes down, recombination is dominant. It is the reason why the intensity decreases exponentially as approach the ground. A noteworthy fact is that a flying plane is near the height of the intensity peak, which explains why there is a guaranteed failure in one flight. Moreover, the source of the radiation damaging the satellites is solar wind due to similar reasons. We also can interpret the altitude dependency of radiation flux mathematically.
@ − @ 37.1 = ( )
= 1033 − (0.03648 ) + (4.26 × 10 ) g/cm 37.2
In Eq. 37.1, I stands for the flux intensity. L presents the mean free time before the particles recombine. For example, = 100 g/cm for electron. A is a variable
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depending on the height H of the position where we want to calculate the intensity as shown in Eq. 37.2. The exponential relation in Eq. 37.1 is due to the fact that recombination is exponential with position. Let’s do some simple calculation to demonstrate the formula. The height of Denver is about 5280 ft. So A equals to 1033 g/cm at sea level and 862 g/cm at Denver. The mean free used here is 148 g/cm . So the final number for I at Denver will be 3.4. On the other hand, a plane usually fly at 15 km above the sea level. So after calculation, the intensity will be 100 times larger than Denver. To proceed, let’s discuss about the radiation intensity distribution with respect to energy at the Earth level. On the left side of Figure. 37.4, there are a large number of particles generated by secondary generation so most of them are below 1 GeV and they are the most dangerous particles which will be discuss later. The list in Figure. 37.4 shows the composition of the flux and people are most concerned about neutrons and protons. Similar to the altitude distribution, people also developed mathematical model for energy distribution.
@ − @ 37.3 = × 1.5 exp ( ) = ln ( )
( ) = −5.28 ± 2.6 + 0.6 ± 0.09 + 0.00369 37.4
With Eq. 37.3and Eq. 37.4, it is convenient to calculate the flux intensity at given height and given energy.
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Figure. 37.4. Energy distribution of different particles at the Earth level
Packaging: Third, let’s move to radiation from packaging. There are several earth sources. For example, boro-phospho-silicate glass contains a certain number of thermal neutron and Lithium will inject proton as well as thermal proton. If taking a close look at Figure. 37.5, we will find the fluxes of α-particle coming from different components. Here, we don’t worry too much about the high-energy particle, which will zip through the device very fast so generate as many as electron-hold pairs as it could. Instead, the low-energy particles are most dangerous to the devices, because it will wander around and create a lot of pairs. Figure. 37.6 can explain it by showing the relation between particle energy and the number of generated charges.
Figure. 37.5. Alpha particle fluxes from a variety of sources
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Figure. 37.6. Charge generated vs. Alpha particle energy
37.3 Charge generation and potential fluctuation
After study the sources of radiation, it is the time to see how radiation influences device. We will start with an intrinsic device. From Eq. 37.5 or Eq. 37.6, it is not difficult to calculate the absorption of the particles. Eq. 37.5 is for direct band materials and Eq. 37.6 is for indirect band.
(2 ) ℎ − 37.5 = ℎ
/ 4 (ℎ − ) 37.6 = 3 ℎ ℎ We can first examine the case when particles strike on intrinsic structure as shown in Figure. 37.7
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Figure. 37.7. Intrinsic structure with particle strike
Figure. 37.8 Post-strike Net charge distribution
Lrad is the radius of the strike and electron-hole pairs are created here. Afterwards, electrons and holes are diffusing toward the two ends of the device. Since they have different motilities, the speed of the diffusion of electron and hole is different then we will have net charge built up along the device as shown in Figure. 37.8. If the mobility of electron and hole is the same such as in graphene, however, the concentration of electron and hole will cancel each other out. As a result, there will not be any petulance on electric field and potential distribution. By solving 37.7, which is the Poisson’s equation, we can have the distribution of electric field and potential as shown in Figure. 37.9
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37.7 − = = ( − + − )
All in all, the imbalance of electron and hole distribution due to particle strike will create asymmetric junction in an intrinsic structure.
Figure. 37.9 Electric field distribution (Left) and potential distribution (Right)
37.4 Junctions and critical charges
Last but not least, it is the time to see how particle will affect a p-n junction. As shown in Figure. 37.10 , it is a simple p-n junction. The doping of both sides is the same 10 18 cm -3. We assume very low lifetime of carriers, which is 10 -12 sec. So the diffusion length will be about 0.025 μm.
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Figure. 37.10. a simple p-n junction
(Right) Namely, the case is very similar to solar cell. With radiation, the current is going the wrong junction so we have the negative junction as same as the photon-generated current.
Figure. 37.11. Electric field distribution (Left) and potential distribution (Right)
(Right) If you look at the right side of Figure. 37.11 , the potential at the bulk region is higher after radiation. Namely, the electric field peak at the junction decreases after the radiation. It indicates the junction disappears. If the junction vanishes, the transistor can’t function anymore.
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People also conduct three-dimensional simulation to find out the total number of charge to upset different kinds of devices as shown in Figure. 37.12 . The total number of charge to destroy a device is called the critical charge.
Figure. 37.12. Critical charge for SEU (Q c) vs. feature size in different devices. From E.L. Peterson and P. Marshall, J. Rad. Eff. Res. And Eng. (Jan 1989)
37.5 Conclusion
In this lecture we discussed different sources of radiation, which are comic ray, solar wind, and packaging, and how they affect the device respectively and interactively. Then we concentrate on soft error and how it is related o generation of electron-hole pairs that perturbs the electrostatics and temporarily destroy the logic state of the devices. It is due the asymmetry of electron hole transport (either due to difference in mobility, doping, or junction). Most importantly, soft error is reversible, since memory can be rewritten and the logic state can be recomputed. Soft errors, however, can be mitigated by clever deice design as well as redundant circuit approaches, which are costly. Hence DARPA and NASA uses special radiation hardened components.
Reference
1. R.C. Bauman wrote a wonderful review on packing related soft-errors, see Soft errors in Advanced Semiconductor Devices, TDMR, 1, 1, 2001.
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2. IBM Journal of Research and Development has published two special issues on radiation-induced damage. They contain wonderful sources of information. 3. The following book gives a very good introductory overview of the physics of soft errors” SER – History, Trends, and Challenges, A guide for designing with memory Ics, J. F. Ziegler and H. Puchner, Cypress. 2004.
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