In this video, we will discuss the current in heterojunction. So, in a heterojunction, the energy barrier or the potential barrier between the two sides, p and n side is modified by the band offset. So, there is a conduction band offset in the valence band offset as shown here. So, the actual barrier height for electron is given by q sub Phi_ Bn here, which is the total band bending minus this conduction band offset. In the valence band offset also, the Delta E_v valence band offset also modifies the total band bending and determines this actual energy barrier required for holes to overcome to come to the other side. So, this interplay between the total band bending or the built-in potential and the band offset is what actually ultimately determines the current in pn heterojunction. Now, there are two types of current that can flow in pn heterojunction depending on the band alignment. You could have the same old diffusion current as was the case for p and homojunction, but we could also have a thermionic emission current, which is the actual current mechanism that we have in the Schottky contact metal semiconductor Schottky contact. So, let's first consider the case where the spike here, the maximum point, maximum energy point for the conduction band of material one is actually located at lower energy than the conduction band of material two. If that is the case, the energy barrier for electron is determined by the conduction band of material one minus the conduction band of material two. The potential barrier for energy barrier for holes are the conduction band offset plus the band gap difference. Now, the majority carriers on each side is given by the usual equations, n is equal to the doping density and similar. So, for material one, majority carrier is equal to the doping density and the minority carrier in material two is given by the similar equation. So, this is the equation that we derived for non-degenerate semiconductors and you can set up the same equation for hole concentrations. Now, as you apply voltage, you are changing these potential barriers. So, forward bias reduces the potential barrier just as it did for homojunction. So, the minority carrier concentration is given by this diffusion current equation, the same old diffusion current equation. So, this gives you exactly the same equation as we did for the homojunction except that you have to use the intrinsic carrier concentration for material two in this case. So, if you are going to rewrite this equation in terms of the n i, intrinsic carrier concentration of material one, then you have to account for the band gap difference which introduces this extra term here, exponential Delta E_G over kT. So, the injected electron current is the same for the homojunction made of the smaller band gap of material two. However, it is larger than the homojunction made of the larger band gap material, material one because you are going from a larger band gap material to a lower band gap material and therefore the energy barrier is lowered by the band offset, conduction band offset Delta E_C. This is the equation for a long base diode and that's why we use this diffusion length here. For a short base diode, all we have to do is to replace the diffusion length, width, the length or width of the quasi-neutral region in material two. You can do the same exercise for hole current being injected from material two to material one and derive the same equation. It is noted here that both the electron current and hole current are independent of the conduction band offset or the valence band offset, but only depends on the difference in band gap. So, in other words, it does not matter how the bands are aligned relative to each other. The difference in band gap is the only factor that matters here. If you have a situation where the maximum energy point for the conduction band of material one actually is located at a higher energy than the conduction band of the material two, then the total energy barrier for electrons is determined by the band bending on the material one. So, the energy offset or the location of the conduction band of material two is irrelevant in this case. Now, the current depends only on the energy barrier on the n-type side. So, your electron current is proportional to exponential negative q Phi_Bn over kT and this type of current is called the thermionic emission current. If I may go back to the previous slide here, what does that mean? That means electron here needs to overcome this barrier that defined by the band bending on the n-type side, and how do these electron do that? Well, some of these electron have high enough thermal energy to overcome this barrier and only those electrons will come over. That's why it's called a thermionic emission current, and this is the same current mechanism that is at work operative in the metal semiconductor Schottky contact. So, as the forward bias is applied, the voltage is dropped across the entire depletion region, but only a small full portion, only a portion of it that is dropped on the n-side affects the barrier height on the n-side, and those voltage that is dropped on the p-side of the depletion region don't affect the current. So, therefore, that produces a different voltage dependence than the diffusion current case in which case, the entire applied voltage affects the current. So, if you plot the current as a function of voltage in a semi-log plot as shown here, diffusion current and the thermionic emission current has two different slope arising from these different factor inside your exponential function, and therefore they become dominant at different ranges of your applied forward bias.
