In this video, we will discuss bipolar junction transistor. A p-n junction under reverse bias normally does not pass current. However, p-n junction on the reverse bias can pass current if there is a large supply of minority carriers injected into the depletion region. Now this can happen in couple of different ways. First, you can shine light onto a reverse bias p-n junction. Then these electron whole pair generation due to light absorption supplies minority carriers. And these minority carriers can then enter the depletion region of the reverse-biased p-n junction and register current and this is how photo detector works. Another possibility is to have a forward-biased p-n junction nearby the reverse-biased p-n junction. In that case, the large minority carrier injection due to the four-biased p-n junction supplies the minority carriers into the reverse files p-n junction and the reverse-biased p-n junction, therefore past his large current. So, in this case, you can control the current across the reverse-biased p-n jnction using the current induced in the for bias p-n junction nearby. So controlling the reverse bias p-n junction current using a nearby for bias p-n junction, that is essentially your transistor action. And this type of transistor is called the bipolar junction transistor. So schematically, the device structure is shown here. It consists of three regions, a meter base and collector. So there is one p-n junction between meter and base, and then on that second p-n junction between base and collector. And you apply voltage between emitter and base to control the first p-n junction, and then bias between base and collector controls the second p-n junction. There are two types of bipolar junction transistor depending on the construction of the device. And you have an n, p, n bipolar junction transisitor. In this case, emitter and collector regions are n type and the base region in the middle is p type. We will primarly focus on n, p, n bipolar junction transistor in this course. But the extension to pnp bipolar junction transistor is very straightforward. pnp would be, of course, emitter and collector being p-type, and the base region being n-type. So a equilibrium energy band diagram, and the carrier concentration looks like this. This is just a standard p-n junction energy band diagram. There is a band bending across the junction here and here, and because it is at equilibrium, from the level, is constant throughout the device. Here in the bottom figure is the electron concentration across the device. Electron is the majority carrier in the meter in base. So it's equal to the doping density, it's a large number. In the base, electron is the minority carrier so the electron density there will be pretty small. Now you apply voltage to these bipolar junction transistor, because you have two P-N junction, and each P-N junction can be biased, either forward or reversed bias. So there are four different biasing combinations you could have, reverse-reverse, forward-forward, forward reverse and reverse forward. So the first case is the reverse reverse case. In this type of biasing condition, it's called the cut-off mode. Because these P-N junctions are reverse biased, the band bending increases in both junctions. And the reverse bias junction tends to pump out the minority carrier, so minority carriers are pumped out of the base region into the emitter and also out of the base region into the collector. So there is a decrease, there will be a decrease in minority carrier concentration in the cut off mode. Now if you apply forward bias on both junction, then of course, the bending will decrease on both junctions, as shown here. And the minority carriers, the electrons, will then be injected into the base from both sides. So there is a large increase in electron concentration in this case. And this type of biasing condition is called a saturation load. If you bias the first p-n juncton with a forward bias and then second p-n junction with a reverse bias, then you will have a carrier injection in the first junction that's forward biased so electrons are injected in today. Second p-n junction is reverse bias. Therefore, this reverse bias p-n junction wants to extract or pump out the minority carriers out of the base into the collector. So the electrons are injected from emitter into base and those electrons will then get pumped out into the collector. So the electron concentration will be high on the emitter side, low on the collector side and there's a large gradient. And if you recall, large gradiant of carrier concentration produces diffusion current, so there is a large electron current flowing through base. So electrons are injected from emitter into base, there is a large diffusion current across the base, and then those electrons that reached the second junction, reverse bias junction, will get swept out of the junction and show up in the collector region. So let's consider the current. In the n, p, n bipolar junction transistor, the current flowing from emitter through base and collector, this current, in general, can consist of electron current and whole current. However, in the npn BJT, both the emitter region and collector regions are n type, so whole concentration will be very low because they are a minority carriers. And so, under any biasing condition, you should expect very small whole current. So whole current J sub p, should be 0 in under any circumstances, and the whole current occurs in general is the sum of the direct current and the diffusion current. Now because this whole current is zero, from this equation you can solve for the electric field and you can express the electric field in terms of the whole current, whole concentration. You can write down the electron current equation in the same way. Some of the drift current and the diffusion current. Now this current is obviously non-zero in general. Now you substitute this expression for the electric field into this electric field here in the electron current equation. Then you can simplify this into this equation readily. And so, the electron current density is q times the diffusion coefficient divided by the whole concentration times the derivative of the np product. Now, if the doping density in the base region is constant, uniform, then your p, the whole concentration will be constant, equaling the doping density. So this p will be a constant. So you can take that out of the derivative, and it cancels with this p. And then, you have a very simple equation for the election concentration which is just the standard diffusion current equation, and the DJT that has a uniform-based opening is called a prototype transistor. Now you futher assume that the base region is narrow, short. In that case, you can ignore any recombination that may happen in the base. And in that case, the carrier concentration will vary linearly just as we have found in the short diode case. So the derivative of the electron concentration is simply the difference between the two end values. The electron concentration on the emitter end, x = 0 represents the emitter side of the base. And x equals x sub b represents the collector side of the base. So now, you can represent these end values, the minority carrier concentration, at the end of the depletion region using the applied bias. So the minority carrier concentrated on the end of the depletion region depends exponentially on the applied bias. And so, the n sub p, the electron concentration in the base, at the end of the depletion region, at the edge of the depletion region on the collector side, depends exponentially on the collector voltage, base collector biased voltage. Likewise, at x equals zero, the emitter side of the base, that concentration will depend exponentially on the base emitter by its voltage. So this here is the general equation for the output current of the BJT and the prefactor here is called the saturation current density, very similar to the saturation current density in the p-n junction case. When the base doping is non-uniform, of course, then you need to consider the variations in doping density. So if you go back, the doping density here, capital N sub A, acceptor density in base, so that's the second subscript B means. So we can't simply use this instead of this, x sub b, the base with times the doping density. We actually have to integrate the doping density across the base. So this denominator here, x of b times n sub ab is replaced by the integration of the doping density. And as you vary the doping density, your diffusion coefficient, d sub n, may change as well. So in general, you would integrate that together as shown here in the base, in the denominator of this new equation. Now, the point is that you have two exponential terms that is subtracting rom each other. So if both of these voltages are large, then the individual exponential terms will be large. But one is subtracted from the other, so the difference will be very small. So this is the case for saturation of both junctions for bias. On the other hand, when both junctions are reversed biased, both the V sub BC and V sub BE will be a large negative number. Then, these exponential terms will be small, and on top of that, they are subtracted from each other, so the current density will be even smaller. This is the case for the cutoff mode. If one of these two voltages are large negative number reverse bias, and the other is a positive number, then you could have a large current. And this is the active mode, when you have a base emitter junction for a bias and the base collector junction reverse bias. Then we call that foward active bias and the opposite case is called the reverse active bias. Typically, transistors they're designed to operate in the forward-active biasd, so in this course when we say active bias, we generaly mean forward active biased. So in the forward active bias, this exponential term containing the base collector voltage can be ignored because the base collector voltage is a large negative number. And that leaves only one exponential term depending on the base-emitter voltage. So if you plot the electron current as a function of the base-emitter voltage, then you have a nice single exponential term. So this plot here is a semi-low plot. And a straight line the semi low plot represents an exponential behavior. And if you extraporate this nice single exponential region and find the y intercept, that will be the value of your saturation current density. Once you know your saturation current density from the equation that we derived before, you can calculate the built-in base charge and built-in base charge is simply given by this equation here. And the built-in base charge represents the total charge due to the whole density or doping density in the base region at zero emitter base bias. People often use a parameter called the Gummel number, which represents a total number of dopants to express the built in base charge, and the Gummel number, which is the integration of the doping density across the base region is simply the total base charge divided by the unit charge. And from this equation above here, that is related to the saturation condensity like this. So the doping density in the base region is inversely related to the saturation current density. And therefore, inversely related to the total current density which is proportional to the saturation current density. So in order to achieve a large current, it is more advantageous to have a lightly doped region. However, if your base doping is too low, then the low level injection condition may become invalid. So minority carrier concentration is no longer small compared to the majority carrier concentration, under large forward bias condition, that is. So if that is the case, then as you inject large number of minority carriers, the majority carrier concentration goes up together in order to maintain charge neutrality. And that leads to a deviation from ideal diode behavior, and subsequently, degradation of your transistor behavior, transistor performance. So in order to avoid this problem, It is common to dope your base region non-uniformly. So the base region is heavily doped on the emitter side and very lightly doped on the collector side. So when you integrate the total doping density and find the Gummel number, the Gummel number is small. However, near the emitter side, emitter region, the base region close to the emitter side is heavily doped. And therefore, the majority carrier concentration is high. And even under large forward bias current, the low level injection condition is maintained. Finally, I'd like to mention Leakage Current before I finish. As shown here in this figure, when your base emitter forward bias becomes very small, then the current deviates from a nice, single exponential behavior. And this is the familiar generation current. Remember, this current, the BJT under active bias has the base collector junction reverse bias. And the reverse bias p-n junction has generation current. This generation current can be small if your forward bias between base and emitter meter is large. But as you decrease your forward bias voltage, that ideal diode current decreases and eventually that becomes smaller than the generation current in that case, generation current dominates. So that is this tail here and the origin of this leakage current is exactly the same as the non-ideal diode under reverse bias p-n junction.
