107 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 107 108 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 108 109 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. 109 110 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 − (0.0364 ) + (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 110 111 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 14 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 e(p *+(), = ln (/) +() = −5.2 0 2.6 + 0.6 0 0.01 + 0.00361 2 37.4 With Eq. 37.3and Eq. 37.4, it is convenient to calculate the flux intensity at given height and given energy. 111 112 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 112 113 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. 7 (28) 9:; − /< 37.5 3456 = => : ?@ B / 4 7 8(:; − /<) 37.6 35A456 = 3 => : ?@?C:D We can first examine the case when particles strike on intrinsic structure as shown in Figure. 37.7 113 114 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.