In this video, we will discuss Electronic Transitions and in particular, Radiative Transitions. Electronic transition refers to a process in which electron jumps from one state to another state. In semiconductor, these electronic transitions are important because they can lead to generation in recombination of carriers. So here is an example where electron that was originally in the valence band, jumps up to the conduction band. And this process, this electronic transition, results in a production of one empty state hole in the valence band and one electron in the conduction band. So this is an electron hole pair generation process. And if you can also imagine a process in which electron originally in the conduction band, jumps down to the conduction band- to the valence band, I'm sorry and fill up the empty state hole. So in this process, you lose one electron in the conduction band, one hole in the valence band. And this process is electron hole recombination process and you lose one electron in one hole in this process. Now, there are many different electronic transitions possible in semiconductor and this slide show several of them. So you can have a transition between conduction band and the valence band and this type of transition is called the band-to-band transition. Or, you could also have a transition involving impurity state. So conduction band-to-acceptor, donor-to-valence band, or donor-to-acceptor transition, or you could also have a transition involving deep energy level defect state. Usually, this process leads to carrier recombination. And finally, you could have a transition within the band. So within the conduction band or within the valence band. This type of transition is called the intraband transition as opposed to interband transition that we discussed earlier. Now, all of these transitions can be classified largely into two categories. One, is the radiated transition and the other, is a non-radiated transition. And the distinction here is whether the transition involves photon or not. So you could observe a photon or you could emit a photon. In both cases, you have an optical transition or a radiated transition. And in this case, you must have an energy conservation and the momentum conservation conditions satisfied. So energy conservation says that, "The difference in electronic energy between the final state and the initial state, must equal to the energy of the photon." So here in this case, we're showing emission process. So electron is originally in the conduction band and it jumps down to the valence band, recombine with hole and in the process, it emits a photon. So energy difference between this and this. This is the final stage, this is the initial state. The difference between the two, must equal to the energy of the resulting photon. So that's the energy conservation. Momentum conservation is the same. The difference of momentum between the final and initial state, must equal to the momentum of the photon that's produced. In the momentum of electron and photon, are expressed by its K-vectors, wave vector. Now, the energy conservation is relatively simple because the energy difference determines the photon. So, normally electrons are congregated at the bottom of the conduction band. Holes are congregated at the top of the valence band, so the heist probably transition is the bottom of the conduction band to the top of the valence band. So that energy is equal to the bandgap and the bandgap energy basically, is equal to the energy of the resulting photon. So bandgap energy determines the color of the photon that you produce. Now, momentum conservation you need to look at the K-vector. And the K-vector, wave vector of electron, is determined by the Brillouin zone. And the Brillouin zone boundary defines the maximum K-vector, wave vector that electrons and holes can have and that is basically, two Pie over A. A, being the lattice constant. And the typical lattice constant of a semiconductor, is about 5 angstrom. So this value gives you about 10 to the tenth inverse centimeter. On the other hand, the visible light, the wave number K, is given by two pie over lamda. Lamda being the wave length. And the wave length of a visible light, is several hundred nanometers. So this two pie over lamda gives you a value that's much much smaller than the K value of the electron and hole. So for visible light, is typically of the order of 10 to the seventh inverse centimeter. So for all practical purpose, we can ignore the momentum of light and restate the momentum conservation condition simply like this. So the final momentum of the electron, must equal to the initial momentum of the electron. So what does that mean? That means, if you plop the energy band in the E versus energy versus K diagram, then the radiative transition is represented by a vertical line. In other words, electron and hole must have the same K-value in order to have a radiated transition. If the electron and hole have a two different K-value, then you somehow need to supply these K-difference additional momentum. And that cannot be provided by photon because photon momentum is too small. And typically, you make up this difference by involving phonons lattice vibration quantum. And the phonon momentum is of the same order of magnitude. Roughly same magnitude as the electron momentum. So you can do that. However, this transition then must involve both phonon and photon. And this type of transition is called the second order transition in quantum mechanics and generally have a very low transition probability. So this is a low probability transition and it's a very inefficient process. So now, we can define direct bandgap and indirect bandgap semi-conductor. So, some semi-conductors have the conduction band minimum and this diagram is the energy versus K diagram. So the bottom of the conduction band, top of the valence band, occur at the same K-value. This type of semiconductor is called the direct bandgap Semiconductor. And in this case, when you somehow excite electrons from valence band into conduction band, electrons will thermalize down to the bottom of the conduction band. Holes will be congregated at the top of the valence band and you have a situation like this. And these electrons in these holes have roughly the same K-value and this situation you will have a high probability of having radiative transitions. So direct bandgap semiconductors are generally a efficient light emitter. Because the band structure naturally satisfies the momentum conservation equation, condition, I'm sorry. And many of the 3:5 compounds semiconductors and 2:6 compounds semiconductors, are direct bandgap semiconductors and they are used for a laser and light emitting diodes. You could have a situation where the bottom of the conduction band occur at a different K-value, than the top of the valence band. So in that case, when you excite electrons into the conduction band, the conduction band electrons will be at a different K-value. Majority of the conduction band electron will be located at different K-value than the holes in the valence band. So you must in this case involve phonons to match the difference in K, provides the difference in momentum and this is again, a very inefficient process. So indirect bandgap semiconductors are poor light emitters and silicon and germanium are examples of indirect bandgap semiconductors and they're poor emitters and this is why we don't have silicon laser or germanium laser. You could have an efficient absorption. If you look at the absorption process, if you are to make a transition from the top of the valence band to the bottom the conduction band here, this process again, is an inefficient process because of the momentum mismatch. However, you can make a transition into this band here. Not the bottom of the conduction band, but there is another valley here in the conduction band at a higher energy occurring at the same K-value. So you can do that and this process can be very efficient. So silicon, the second bandgap here of silicon, occurs in the red and infrared edge of the visible spectrum. So silicon is a very efficient light absorber for the visible light. And silicon is commonly used as a photo detector and the detector in your digital camera.
