In this video, we will discuss non-ideal behavior of bipolar junction transistor. So, the first non-ideal behavior that we want to discuss is the Early effect. In the previous discussions on active bias, the current is entirely determined by the base emitter voltage. The role of the reverse bias on the base-collector junction is simply there to make sure that the minority carriers arriving the base-collector junction gets swiftly swept away by the built-in electric field of the reverse bias junction, and gets collected in the collector terminal. However, we all know that a reverse biased PN junction has this bias-dependent depletion region width. So, if you increase the reverse bias, the depletion region width will increase, and as the depletion region width on the base-collector junction increase, that will subsequently decrease the neutral base region width. The decrease in the neutral region width will then increase the current that flows across the base. This effect is called the Early effect. If you recall, the collector current expression that we derived was as shown here. So, it depends on the total built-in charge on the base. That is represented by this integration from zero to X sub b. So, zero is the depletion region edge on the emitter side, and X sub b is the depletion region edge on the collector side. So, the Early effect says that X sub b here that goes into the upper limit of the integral will decrease as you increase the reverse bias on the collector. That would lead to increasing collector current as a function of the collector voltage. So, you can calculate how much increase there is by simply taking the derivative of this collector current with respect to the collector voltage. You can express this expression using this voltage factor V sub A which is called the Early voltage. From this equation, you can see the definition of Early voltage is given by this equation here. Now, you can have an analogous description for the effect of the depletion region changing voltage dependent depletion region width on the emitter side, and that leads to another voltage, V sub B, which describes the effect of the emitter base reverse bias voltage, which is important in the case of reverse active mode operation. But in most cases, the transistors are designed to operate in the forward active mode and therefore V sub A is really the relevant parameter in most cases. So, the bottom line is, when the base-collector junction is reverse biased, the derivative here is negative. Therefore, the Early effect leads to increase of the collector current with increasing the collector-base reverse bias voltage. You can see that very easily because as shown in this diagram here, this plots the minority carrier concentration as a function of position within the neutral base region. So, as the neutral base region with X sub B decrease, you can see that the slope of this minority carrier profile increase and that leads to higher diffusion current. This gives you the physical explanation of why the current goes up as you increase the reverse bias on the collector-base junction. The collector-base junction change is associated with change in the total charge within the base region. So, that will be this Q sub B here which is really due to the majority carrier density in the base region. Now, that change is as a function of your reverse bias voltage and the change in charge as a function of reverse bias voltage fundamentally is a capacitance. So, this gives rise to a capacitance. This is related to the junction capacitance on the collector side. So, the Early voltage V sub A can be written simply as the total base charge divided by the junction capacitance on the collector side. So, the large Early voltage V sub A means that the ratio of the stored charge in the base region to the junction capacitance is very large, so large V sub A means slower increase in the collector current as a function of the collector voltage. As I explained in the previous slide, the same effect can be described by the changes in the carrier concentration profile slope as a function of your collector voltage which leads to larger diffusion current as as the collector voltage is increased. So, if you consider this simple circuit in common emitter configuration, if you plot the collector current as a function of collector voltage, now in the active region, you will have a finite slope. If you ignore Early effect, then the current in the active region is independent of the collector voltage, depends only on the base voltage. So, the I-V curve will be perfectly horizontal, but with the Early effect, you now have a finite slope which means that there is a finite output resistance on your collector terminal. The Early voltage can be found by extrapolating this I-V curve in the active mode and find the intercept with the x-axis that represents your Early voltage V sub A. So you can see that the large V sub A means lower smaller slope and larger output resistance on the collector terminal. Now, I want to talk about emitter bias dependence. Normally, both the collector current and the base current will be a simple exponential function of the forward bias voltage VBE. However, experimentally, you will find that the base current will deviate often from the ideal behavior. This is due to the recombination in the space-charge region between emitter and base. If you calculate the expression for the recombination current, you will find that the ideality factor that goes into the denominator of this exponent to be two. So, if you have a combination of recombination current and ideal diode current, the actual ideality factor that you observe in your device will be a number between one and two. Now, notice that the space-charge region recombination current flows only between base and emitter. The injected electrons are lost to recombination within the space-charge region between base and emitter. Therefore, these electrons never reach collector. So, the collector current are not affected by this. So, if you plot the collector current and the base current for large forward bias voltage, of course the effect of these recombination current is minimal, and therefore both collector current and the base current behave ideally. But as you decrease the forward bias voltage, the base current begins to deviate and begins to show this non-ideal behavior due to the recombination. However, the collector current continues to behave ideally. For this reason, you can see that the ratio between the collector current and the base current decrease in this region down here, and therefore, the current gain decrease in your transistors. So, this leads to a deterioration of the transistor performance. So, if you plot Beta sub F, the current gain, as a function of the collector current at very low current, your base current behaves non-ideally. For that reason, the current gain deteriorates in this region. Now, we can look at the opposite case where the emitter current is very high, you have a high-level Injection. If you have a high-level Injection condition, then of course, the low-level injection assumption breaks down. What that means is that your minority carrier concentration is so high that it becomes comparable to the majority carrier concentration in the base region. If that's the case, then in order to maintain the charge neutrality, the majority carrier concentration in the base region will increase also. This leads to a deterioration of the bipolar junction transistor performance as well. So, under high-level Injection condition, the majority carrier concentration, P, is a combination of the doping density which is what was originally used to produce these majority carriers, and plus N prime. This is the excess minority carrier concentration due to the injection by the forward bias. Now, this is so large you have to add this so that you can maintain the charge neutrality. So, the majority carrier concentration is the sum of doping density and the excess carrier concentration. Now, because the carriers are injected from the emitter side, the excess minority carrier concentration at X equals zero, the depletion region edge on the emitter side, that value dominates in this integral. So, in order to evaluate that integral, you can recall that the PN product is equal to the NI squared, the intrinsic carrier concentration squared and the exponential factor containing the forward bias. Now, if you use this general equation, generalized law of mass action which remains valid even under high-level Injection condition, then, you can estimate the carrier concentration at X equals zero, the emitter side of the depletion region edge and then you will find this expression here. So, under high-level injection condition, this equation predicts that you have a q times VB over two K T behavior just like the non-ideal behavior due to the recombination current that we discussed before. So, this leads to the decrease in gain in the high-level injection conditions. So, to see this, if you go back to this I-V curve, then you look at this high-end when the forward bias voltage is very high, then both IC and IB begins to deviate from nice exponential behavior, and this deterioration is due to the breakdown of low level injection condition in this creation of majority carrier due to high level injection. So, this also leads to the decrease in gain, so this same plot that I've shown you, the current gain Beta sub F as a function of collector current, the high end, the gain decrease and this is due to the breakdown of the low-level injection conditions. So, the [inaudible] spot for BJT operation will be in the middle obviously, where you avoid high-level injection and you also avoid those significant deterioration of the base current due to the recombination of electrons in the depletion region.