In this video, we will discuss heterojunction bipolar transistor or HBT. The current gain in a BJT is usually limited by the emitter injection efficiency, and you can try to improve the gain and also the frequency response by reducing the base doping and also reducing the base width. However, too low doping density in the base region could increase the resistance of the base region, and eventually that would hurt the transistor performance. So, is there a way to improve the gain without really increasing the resistance in the base region? One possible way is provided by using the heterojunction. So, in a heterojunction, if you remember, is a junction between a two different semiconductor material that has two different bandgap, among other things. So, you can incorporate heterojunction in two different ways in bipolar transistor because the bipolar junction transistor have two p-n junctions. You could have only one of these two p-n junction replaced with a heterojunction or you can replace both junctions with heterojunction. So, depending on that, you could have a single heterojunction transistor or a double heterojunction transistor. So, single heterojunction transistor, it has a heterojunction for the base-emitter junction, and the typical band diagram is shown here. So, the base-collector junction is the same homojunction with the same bandgap for both base and collector. But in the emitter-base junction, you have this band discontinuity. There is an offset in the conduction band Delta E sub c, and there is also an offset in the valence band Delta E sub v. Now, if you recall, the ratio of the electron current and the hole current across this heterojunction is dependent on the exponential of the Delta E sub G, the bandgap difference. This is the case when the conduction band of the base region, the p-type region, lies higher in energy than the maximum point of the conduction band in the n-type emitter region. So, in that case, the entire current is diffusion current and the hole end electron current density ratio depends only on the total difference between the bandgap. It does not depend on the conduction band offset or the valence band offset specifically but combined difference in the bandgap energy only. You can refer to the lecture on p-n heterojunction to refresh your memory on this. Anyway, so, because the ratio, J sub n to J sub p, depends on exponential Delta E_G over KT, the current gain, the emitter injection efficiency, and therefore, the current gain, increases exponentially with your bandgap difference. So, this can increase because small increase in bandgap difference leads to exponential increase in current gain. This can lead to an increase in gain by several orders of magnitude compared to a homojunction bipolar junction transistor. Alternatively, of course, you can use this fact to increase the current gain, but also if your gain is large enough for your application, you can use this fact to increase the base doping while maintaining the appropriate level of gain that you already have. Either way, you can improve the performance of your bipolar junction transistor. Now, if you keep increasing the base doping however, as you increase the base doping, the band bending on the base region, the p-type region, decreases. So, heavily doped p-n junction, the higher doped side of the p-n junction has a smaller depletion region width and therefore, smaller band bending. The band bending occurs more on the lightly doped side. So, as you increase your base doping, this band bending on the base side will decrease and at some point, you could have a situation where the maximum energy of conduction band of the emitter region exceeds the energy of the conduction band of the neutral base region. So, if that happens, the current no longer depends on the difference between the two conduction band. Rather, the energy barrier for the electrons from the emitter to overcome in order to be injected into the base region really depends on the band bending on the n-type side only or on the emitter region only. So, if that happens, then your current mechanism no longer is a diffusion current, but the current becomes similar to the schottky contact current, which is thermionic emission current. So, in this case, the barrier for the electron flow is usually greater than the diffusion current case. So for the diffusion current, the energy barrier for the electron to overcome should have been determined by E_c2 minus E_c1. Now, the energy barrier is determined by this barrier height, q sub phi Bn, this energy band bending on the n-type side, that is greater than the E_c2 minus E_c1. So, electron injection will decrease and therefore, the electron current to the hole current ratio will decrease and therefore, your transistor gain will also decrease. So, this leads to deterioration of your transistor performance in the screen case where the base is really heavily doped and the entire band bending occurs on the emitter side. So, this side, the base side is flat, your band is completely flat. In that case, the energy barrier height for the electron, the band bending on the emitter side is equal to the total band bending, which is the built-in potential, and naturally, the energy barrier for holes will be the total band bending plus the valence band offset Delta E_G minus Delta E_c. So, that can be easily seen from the band diagram shown here on the right. So, in this case, the electron and hole current ratio depends no longer on the energy band gap difference Delta E_G, but on the difference between the barrier heights for electrons and holes. So, the gain therefore decreases, decreases exponentially, on this quantity. So, this deterioration is related to the fact that the current conduction mechanism changes from the diffusion current to the thermionic emission current. So, in summary, the heterojunction bipolar transistor with a single heterojunction, the emitter injection efficiency can be generally written like this in equation here. So, here in the exponential factor, you have these Delta E sub X and when the current conduction mechanism is diffusion current, this Delta E sub X is equal to Delta E sub G, the band gap difference. But, if the current conduction mechanism becomes thermionic emission current due to the fact that the energy band bending on the emitter side is so large, that the top of the spike caused by the band bending exceeds in energy that of the conduction band of the base region. When that happens, you have to change this Delta E sub X into Delta E sub V, the valence band offset only. So, the conduction band offset doesn't count and that leads to the deterioration of the bipolar junction transistor performance. Now, double heterojunction. So, in the double heterojunction BJT, you have in addition to the base emitter junction, you also have the base collector junction as heterojunction as shown here. So, now you have a band offset on the base-collector junction as well, and this band discontinuity will obviously decrease the hole injection from base into collector and hole injection from base to collector being diminished is important if you are operating the saturation regime, where the base collector junction is forward-biased. Under active mode, there is a conduction band discontinuity, this impedes the electron flow from base to collector. This barrier may be reduced if you apply a large reverse bias and integrated doping in the base region. But, in either case, the presence of this band offset leads to decrease in the electron current and therefore leads to decrease in collector current. If the dopant happen to diffuse from base into collector, which happens, then you can form a mini pn junction across a base collector junction as shown here on the right figure here. In this case, the potential barrier forms once again and that impedes the electron transport once again, and therefore deteriorates the transistor performance. So, instead of having an abrupt interface as shown before, you could have a gradual change in energy band gap by, for example, using a alloy material such as this aluminum gallium arsenide, and as you increase the aluminum fraction, the band gap increases. So, if you gradually change from gallium arsenide to aluminum arsenide, you can create a material with a continuously changing band gap. So, when you do that, these energy band gap change as a function of position. Leads to a built-in electric field in much the same way that a gradual doping profile leads to built-in electric field. So, if you have a material looking like this, where on the left side you have a larger band gap. On right side you have a smaller band gap, that leads to a electric field building from the smaller band gap side to the larger band gap side here as shown here. So, this supposed to be E field here. The resulting profile of the majority and minority carrier concentration is shown here. The majority carrier concentration doesn't change as long as you have a uniform doping, but because your energy band gap changes, your minority carrier concentration changes gradually. So, minority carrier concentration becomes smaller, much smaller, in the large band gap region compared to the smaller band gap region. Now, this electric field which is determined by the gradient in your band gap energy. That electric field will lead to a drift current. So, without full derivation, we will give you this electron current density in this situation. So, this compare to the homogeneous BJT case, where in the denominator you have simply the total doping density in the base region, N sub AB times X sub B. Simply represents the total doping density in the n-type region. So, that is replaced by this integral here. So, N sub AB and the D sub N, the diffusion coefficient may no longer be constant because you're gradually changing the host material itself. N sub I square here, the intrinsic carrier concentration depends on band gap. So, your N sub I squared also now changes as a function of position. So all of those things should be lumped into this integral here in the denominator. So, the denominator contains this integral of doping density divided by diffusion quotient times NI squared, and that will give you the generalized expression for the electron current. Now, notice the NI squared, intrinsic carrier concentration, depends exponentially on the band gap and if the band gap changes linearly with position, it will be a linear function as shown here, and then if you plug that into this integral, that leads to this simple expression. So now, if you look at the electron current density, you have this additional term which gives you delta E_G, which is the change in band gap from one end to the other end. So, you can increase the electron current density due to this band gap gradient. So, compared to the homogeneous material, your J sub N electron current density is increased by this factor. Whereas J sub P, the hole density, is not significantly affected because the energy band for the valence band doesn't really change much. So, that leads to a subsequent increase in the ratio between J sub N and J sub P and therefore improvement in the emitter injection efficiency. You can rewrite the electron current density in terms of the built-in electric field because this band gap gradient is related to the electric field. The electric field not only increases the current itself, but also it increases the electron transit time. Electron no longer relies on diffusion to traverse the base region. It is now drifted by a built-in electric field and therefore they move faster and therefore it improves the switching speed. So, you can achieve faster switching speed this way as well.