In this video, we will discuss the frequency response of bipolar junction transistor. So, in order to discuss the speed or frequency response, we need to look at various components, that contributes to the delay. The first component is the Base Transit Time. So, this is the time it takes for the injected minority carriers to traverse the neutral base region. So, when the electrons are injected from emitter interface, that electron has to go across the base and reach the collector. So, base transit time is just that, and so in order to calculate that, you first need to consider the total excess charge in the base, due to the injected minority carriers. So, you just basically integrate the excess carrier concentration across the base, then that leads to your base current, I'm sorry, base charge. If you look at the ratio of the base charge, divided by the collector current. Collector current, if you remember, is determined by the rate of arrival of these minority carrier from the base. So, if you take that ratio, you get the time constant. This time constant tells us b, represents the base transit time, the time for a minority carrier to traverse the neutral base region. For a prototypical transistor with a uniform doping, you can easily get an expression for the base transit time, which is related to the base width obviously and the diffusion coefficient, because the current mechanism is diffusion. So, the diffusion coefficient will determine how fast these guys are moving. So, to give you some idea, here are some numbers. So, for a doping density of 10 to the 16th and one micron width, the transit time is about 140 picosecond. Now, if you incorporate non-uniform doping, then of course, the transit time changes. Why? Because non-uniform doping creates electric field, electric field drift carriers, and that leads to a faster transit time. Now, if you consider the high level injection condition, then the low level injection assumption breaks down. Low level injection assumption, once again, means that the injected excess minority carrier concentration is small compared to the majority carrier concentration. So, under low level injection assumption, majority carrier concentration does not change. It always remains the same as the doping density. However, under high level injection condition, in order to maintain charge neutrality, the majority carrier concentration increases together with the minority carrier concentration. So, if we assume a uniformly doped short base, you can calculate the minority carrier concentration, varying linearly with position, because in the short base there is no recombination. The carrier concentration varies linearly. So, under the high level injection condition, you can see that the majority carrier concentration, p, varies linearly, just the same as the minority carrier concentration, n, here. So, from this carrier profile, you can recalculate the base transit time, as shown here, and what the result shows is that, in the low level injection condition, your base transit time goes as the base width square, divided by two times the diffusion coefficient. But, in the high level injection condition, your base transit time goes as, xB squared divided by four times the diffusion coefficient. So, this reduction in the transit time under high level injection condition is called the Webster effect. So, under high level injection condition, the transistor becomes faster. The carriers moves faster across the base region, and why is that? Because there is a non-uniform majority carrier concentration, and that non-uniform majority carrier concentration results in a non-zero built-in electric field within the base region, and that electric field contributes to higher speed for the carriers to move through the base region. The next component that we will look at is the Collector Transit Time. The carriers, once they complete the travel across the base region, they reach the depletion region between base and collector, and there is a large built-in electric field within this depletion region, so the carriers get swept away by this large built-in electric field. However, that speed is not infinite and therefore, there is a finite time associated with this. That's the collector transit time. Ideally, the carriers travel at the limiting velocity, and the limiting velocity will be the saturation velocity in that material. So, the transit time across the base collector depletion region or the space charge region can be simply written as, the depletion region with x sub DC divided by the the saturation velocity of the carrier, which is the maximum velocity allowed for the carriers. You can reduce these transit time further by increasing the collector doping. But if you increase the collector doping too much, then your breakdown voltage decreases, and therefore, there is a greater risk that you may experience a junction breakdown on the collector side. The next component that I want to look at is the Emitter Transit Time. This is the time delay associated with the charge traversing the neutral emitter region, and just like the base transit time, the emitter transit time can be found by the ratio of the total charge within the emitter region divided by the current density. Now, the current density here is the electron current density in the base, which is related to the hole injection current density with the beta factor here, the current gain. Then, for a uniformly doped devices, this expression can be written as this. So, very similar expression to the base transit time, except that you now have a neutral emitter region width x sub E, and the hole diffusion coefficient D sub p, and the additional factor here is the ratio of the doping density in the base versus the emitter region. Now, there is these ubiquitous time delay due to these capacitive effect, RC time constant. There are two junctions in the bipolar junction transistor, and therefore, two junction capacitances, first associated with the BE junction. You have this junction capacitance on the emitter side. The associated resistance will be the dynamic resistance in the emitter region, which is defined as the change in the collector current as a function of the base emitter for bias voltage. That is equal to the inverse of the trans conductance of your transistor. Now, the second component of the RC time constant is related to the base collector junction. In this case, you multiply two these base collector junction capacitance with a resistance, which is the dynamic resistance, plus the R sub E and R sub C. These R sub E and R sub C are geometric resistances in the emitter and collector regions respectively. If there is any contact resistance, series resistance, there should be added here as well. So, the frequency response is determined by all of these components. So, all of these time constants, well, we have this so far. You add them all up, and that should be related inversely to the cutoff frequency. So, if you define a unity gain frequency to be f sub t, and this is the frequency at which your short circuit current gain becomes unity, and therefore the name unity gain frequency. That is related to the time delays as shown here, and at low current density, you will find that the dynamic resistance in the emitter region, R sub E dominates, and therefore, it becomes the limiting factor for this unity gain frequency at high currents, your base transit time tau sub B becomes very large and is the limiting factor for your bandwidth.