In this video, we will discuss avalanche breakdown. As you increase your reverse bias, the PN junction initially remains like an open circuit, passing very little DC current, in typical reverse bias behavior. But at some point, the PN junction begins to conduct, and the current increases rapidly. And this phenomenon is called a breakdown, and it is important to know that this is not a destructive process. It is a non-destructive and reversible process, that is, if you ramp the voltage down then the current will decrease and if you increase or reverse bias again and then current will increase again. So this is a repeatable reversible process, your diode is not broken, it's part of the normal operation of the diode. And there are two mechanisms that cause breakdown, Avalanche breakdown and Zener breakdown. We're going to look at Avalanche breakdown first. Avalanche breakdown occurs due to a phenomenon called impact ionization. And impact ionization is a process in which electrons gain very high kinetic energy. And it has such a high energy that it can run into on electrons in the valence band or the bonding electrons and break the bond. Knock on electron off of valence band and promote it into conduction band. And that process causes electronal pair amplifying, increasing the number of carriers. So this carrier multiplication process, due to impact ionization, is responsible for the rapid increase of current, and that phenomenon is called the Avalanche breakdown. So here is the energy band diagram. So initially the electron is near the bottom of the conduction band. But due the large electric field within the depression region it get accelerated and it gains large kinetic energy. If you recall, the kinetic energy of an electron was the electron energy minus Ec, the bottom the the conduction band. So these energy difference between this electron and the bottom of the conduction band represents the kinetic energy. If this kinetic energy is high enough, then the electron can collide with an electron down here in the valence band and free that electron. And so it loses it energy in the course, of course, and the electron that was originally in the valence band gains that energy and is promoted to the conduction band, producing an electron and hole pair. So before, you have only one electron. After, you have two electrons and one hole, all of which carry charge and therefore conduct electricity. So, the minimum kinetic energy required to initiate impact ionization is given by this equation here, the threshold energy. Is related to the band gap energy obviously, because that's the energy that these secondary electron needs to overcome in order to be promoted to the conduction band. Well, this is generally higher than the band gap energy. And the pre-factor that goes in front of the band gap energy is related to the effective masses of hole in the valence band and electron in the conduction band. Typically in most semiconductors, this number is anywhere between 1.5 and 2. Now, if you recall in a step junction, electric field varies linearly with position. So it reaches maximum at the junction, this is the boundary between P and N type. And within, it decreases linearly away from it and it reaches zero at the edge of the depletion region. So, in order for impact ionization to occur, this electric field has to exceed the threshold electric field. The electric field that is strong enough to provide the threshold of kinetic energy that electrons need to initiate impact ionization. So let's say that threshold electric field value is this, indicated by the dash line here, then your impact ionization will occur only in this region. Region between X sub a and X sub c, and we call the width of this region X sub 1. Now, to have some more quantitative description, we need some definitions. So again, the region in which impact ionization occur, electric field is high enough. So that the impact ionization occur, this region is between X sub a and X sub b, and so this is X sub a and X sub c right here. And let's say the density of electrons, concentration of electrons, entering this zone is n naught. Now, as these electrons goes through these region of impact ionization, it will multiply, okay? Carrier concentration will increase due to impact ionization process. Let's call the increased amount of concentration due to impact ionization n sub 1. So, for a given position, arbitrary position of interest, let's called that X. So at X, the electron flow or the concentration of electrons coming into this small infinite decimal region is n naught, the initial electron concentration plus n1. This is the increased amount of electron concentration due to impact ionization between Xa and X. Now, after this small infinite decimal width dx, the electron will continue to propogate and will continue to impact ionides, and the electron concentration will continue to increase. The final electron concentration exiting the region of impact ionization, so that boundary's X sub c. Let's call that concentration the final concentration n sub f. So if we can derive an expression for n sub f for a given n naught, then we have a description of this whole impact ionization process. Now, there should be, in general, holes entering this region as well. And the wholes will impact ionize as they propagate in the opposite direction to electrons. And let's called p sub 2 the concentration of holes increased the amount of hole concentration due to impact ionization between X and X sub c. And because impact ionization produces electron-hole pair, this P sub 2 should be equal to the number of electrons produced between this region as well, withing this region, between X and X sub c as well. So, this P sub 2 represents the increased amount of electron concentration between here and here, the difference between n sub f and n naught plus n1. So, putting all that together, we define a constant called alpha, which we call impact ionization coefficient. And it is a multiplicative factor describing the number of impact ionization events per unit distance. That is, how many times? What is the multiplicative factor that describes the increase in carrier concentration for a given distance of propagation? So the unit of this coefficient has an inverse length and dimension. And if you're familiar with optics, this has basically the same definition as the absorption coefficient. Or yeah, absorption coefficient, which represents the number of photons absorbed per unit distance of light propagation. So, using this alpha, we can write down the concentration of secondary electrons produced by the impact ionization within the small infinite decimal width dx. And that is basically the initial electron density entering the region, which is n naught + n1, times alpha 4 electron. Alpha sub n, this is the impact ionization coefficient for electron, times the distance, which is dx. So this whole thing should be equal to the number of electrons generated or the concentration of the electrons generated. Which should be equal to the concentration of holes generated because they're always generated together. Now, there should be holes entering the region from the right and the hole concentration produced by the impact ionization event should be the initial hole concentration times the impact ionization coefficient for hole. Times the width of the region dx, and this should again, be equal to the number of electrons or concentration of electron generated by the process. So we call that dn double prime. So this dn prime is the electron produced by electron impact ionization, and dn double prime is the electrons generated by hole impact ionization. So the total increase in electron concentration dn, should then be the sum of the two dn prime plus dn double prime. And we basically plug in these expressions for the n prime and dn double prime down here, and we get a simple first order differential equation. So the rate of change of electron concentration is the electron impact ionization plus the rate of electron impact ionization plus the rate of whole impact ionization. Now, as I said, the final electron concentration is the initial concentration plus n1. This is the electron produced by impact ionization between xa to x and p2 which is the hole concentration produced by impact ionization between x and x sub c. So that's the total final electron concentration exiting the region impact ionization. So plug that into the equation in the previous slide, we get this first order differential equation. Now, in order to evaluate this, we need to know the impact ionization coefficient. We consider the two extreme cases, one is the impact ionization coefficient for electron is equal to their holes. So alpha sub n is equal to alpha sub p, in that case this first term here goes away. And you get a very simple equation, dn dx is simply equal to alpha sub p times nf. And so you can simply integrate the impact ionization coefficient across the region where impact ionization occurs. And you can then define these multiplication factor. This multiplication factor is a ratio of the final electron density to the initial electron density. So this tells us how many electrons are generated by impact ionization and that from this equation here is simply given by this. So now you can see that there is a singularity. If this integral, here, integral of alpha across the region is equal to 1, then you have singularity m diverges, and that is the condition for breakdown. What does that mean? That means you have an indefinite uncontrolled increase in carrier concentration. In other words, insert a single electron in to the depletion region. That single electron will produce infinitely large current, and this is the condition for a break down. Now, let's consider the other case where the whole impact ionization rate is 0, whole impact ionization coefficient is 0. So holes do not impact ionize, only electrons do. In this case, the alpha p here goes away, alpha p here goes away. And so you get a simple expression of dn dx is equal to alpha 7 times n. And once again, you can define the multiplicative factor here, which is simply given by the exponential of these integral of alpha across the regional impact ionization. Now there is no singularity, m is always finite under all circumstances. And so you do have carrier amplification, but you do not get uncontrolled increase in current,. So this is something that you can take advantage of and, in fact, this is the condition that people are trying to achieve when designing avalanche photo diode. Avalanche photo diode is something that we will discuss later, but it is a photo detector that has a large gain. So it is very effective in detecting very low intensity light signal, because impact ionization mechanism provides gain. So one photon produces one electron-hole pair and then those electron will then undergo avalanche breakdown, or the impact ionization process. And will give you many, many electrons, which will contribute to your photo-current. And in that way, you can detect a very, very low intensity light signal.
