 Last class, we mainly looked at the interaction of light with a semiconductor material. We said that if the energy of the light is less than the band gap, it will not get absorbed and if the energy is more than the band gap, then the light can get absorbed creating electron hole pairs. So, we were able to define an absorption coefficient that is wavelength dependent. Similarly, the absorption coefficient increases as the wavelength goes down or the energy increases, but the actual value depends upon the density of states of the material. We also looked at the interaction of light with say a p type or an n type semiconductor. Under conditions of weak illumination, the increase in the concentration is highest for the minority carriers. So, if you had an n type, then the increase in concentration is maximum for the p type or the hole. We also found that when you shine light, your n p is not equal to n i square. Your system is no longer in equilibrium and when we turn the light off, then the system goes back to equilibrium by the excess carriers recombining. So, today we are going to start to look at optoelectronic devices and the first device we are going to focus on is the LED or the light emitting diode. If you remember, there are mainly two kinds of devices, those in which you have an injection of carriers that recombine in order to give you light. So, this could be in the visible region or in the infrared or UV. You also have a case where you shine light onto a material and get an output in the form of an electric current. So, LEDs and lasers belong to the category of devices, where by injecting carriers, you produce light. Later we will look at a photo detector and a solar cell, where the reverse process happens. So, LEDs belong to the general category of luminescent devices. We can define luminescence as where we have optical radiation that is emitted because of electronic excitation. So, we will just write a working definition of luminescence. So, this is optical emission due to electronic excitation. So, in the case of semiconductors, when we mean electronic excitation, we mean the creation of electron hole pairs. There are different ways of doing this electronic excitation, which leads to different kinds of luminescence. In the case of photo luminescence, you use an optical means in order to create this excitation. For example, if you have a material with a band gap in the visible region, you could shine light in the ultraviolet region, which creates electron hole pairs. So, this creates the electronic excitation. When these electrons and holes recombine, they will give light in the visible region. You can also have cathode luminescence, in which case you have an electron beam incident on your material, which creates the electron hole pairs. There is radio luminescence. Here you use ionizing radiation. And finally, we have electro luminescence, which is what an LED is. In which case, you use an electric field or an external field in order to create an electron hole pair. So, an electric field creates the electron hole pair. And LED is an example of an electro luminescent device. So, we use the external field in order to create electron hole pairs. So, if you have a PN junction, we typically inject the minority carriers. These carriers can then recombine. And we saw that depending upon the type of semiconductor, the recombination can either be dominated by photons or it can be dominated by heat. So, we have seen earlier that semiconductors are essentially two types. So, you have your direct band gap and you have your indirect band gap. So, you have seen that a direct band gap semiconductor is one, in which the electron hole recombination proceeds with the dominant mechanism being the release of electromagnetic radiation or photons. In the case of an indirect band gap semiconductor, the energy is released in the form of heat. So, silicon is an example of an indirect band gap semiconductor. Gallium arsenide is an example for a direct band gap semiconductor. In the case of an LED, since we want a visible light to come out, we preferentially use direct band gap semiconductors. So, the phenomenon of electro luminescence, so I will just call it EL was first discovered in 1907, but until PN junctions were invented in 49, there was not much work done in this area. So, PN junctions came in 1949, but the first LED based on gallium arsenide was only in the 1960. So, what happens in the case of LEDs? By means of injection, we create these electron hole pairs. So, we have electrons in the conduction band and holes in the valence band. These electrons and holes can recombine and typically we want this recombination to give us light. Now, there are different kinds of transitions that are possible. So, if I have a general picture, so this is my conduction band, this is my valence band. So, there are different ways in which transitions can occur between the electrons and holes. So, the first kind are called inter band transitions in which can have an electron and a hole both at the edge of the conduction band and the valence band recombining can also have an electron deep in the conduction band recombining with the hole in the valence band edge or you can have an electron in the conduction band edge recombining with the hole in the bulk of the valence band. So, all of these where the transition occurs from the conduction band to the valence band, it is called your inter band transitions. Now, if you have a material that is doped or has some other impurities, these basically cause defect states in the band gap. So, you could have for example, if you have a donor type impurity that could lead to a donor level that is close to the conduction band, could also have acceptor levels close to the valence band. These are essentially shallow states, if you have other impurity materials or other defects, they could also form states within slightly within the bulk within the band gap. So, these are shallow states, this is a deep state. So, if you have electron hole paths that are generated, then these electrons and holes can get trapped in these defect states and then recombine. Those kind of transitions are called defect transitions. So, I can have an electron in the conduction band recombining with a hole in my acceptor state. So, I will call this ED, which is my donor state, EA is my acceptor state. I could have an electron in my donor state recombining with a hole in the acceptor state or I could have an electron in the donor state recombining with an acceptor in the valence band. And sometimes you can have transitions where the electron gets trapped in a deep state and then recombines with a hole. So, all of these transitions which involve some sort of defect states are called your defect transitions. You could also have transitions within the band. These are called intra band transitions. In this particular case, you can have an electron within the bulk of the conduction band and can go to the edge of the conduction band. Similarly, you can have a hole in the bulk of the valence band which goes to the edge of the valence band. So, these are intra band transitions. Now, all of these transitions are radiative only some of them are radiative will depend upon the band gap of the material and also upon the characteristics of these defect states. In the case of LEDs, we want to maximize the radiative transitions and minimize any non radiative components in order to increase the efficiency of the device. For example, if you have defects then defects could act as traps. So, ideally when you want an LED and when we process the material, we have to make sure there are no defect states that can basically cause non radiative recombination. So, the simplest kind of LED is essentially a P N junction based LED. So, let me start with that first. So, consider a simple P N plus junction the N plus means that the N region is heavily doped. So, when we form a junction the depletion region is mostly within the P side. So, I have my P side E f, E v and E c this is my P side and I have my N plus region both my P and the N are the same material. So, the overall band gap is the same. So, now I form a P N junction when this is at equilibrium we know that the Fermi levels line up. So, this is the P that is the N plus. So, this is the P N junction in equilibrium. We have a depletion region that mostly lies in the P side and we also have built in or a contact potential. We can forward bias the P N junction in this particular case if we forward bias the junction we would reduce the contact potential so that we inject the minority carriers on both sides. So, if you draw the band gap or the band diagram of this in forward bias. So, you forward bias the P N junction. So, your new barrier is E v naught minus v. So, when you forward bias we lower the barriers for the electrons and holes to go across these are the holes. So, these electrons and holes can recombine in the depletion region. So, if I have an electron here and I have a hole here the electron and hole can recombine if your material is a direct band gap material then this recombination will dominantly produce light and the energy of the light is just given by the band gap. So, this is the case of a simple LED where we have just forward biased a P N junction in order to produce light. So, this is an example of an injection electro luminescence because we inject carriers. So, electrons and holes in order to generate your light. So, the formation of the light is essentially a spontaneous process. So, your electrons can holes and holes can recombine not only in the depletion region they can also recombine within the bulk of the material. So, the formation of light is a spontaneous process and it occurs randomly in all directions. Now, in the case of any device we always want to improve the efficiency of the device. So, there is some way in which I can trap the carriers within the depletion region. So, that I have a majority of holes and electrons within this and if it is a direct band gap material then I can improve the efficiency of device and also improve the amount of light output. In order to do this we modify the simple P N junction by introducing a hetero structure and you will see that we actually introduce two hetero structures in order to form a double hetero structure device. So, let us take a look at that next. So, we started off with a P N junction and we found that we want to maximize the electron and hole recombination within the depletion region. In order to do that we form a P I N. So, P is your P type, I is an intrinsic and N is an N type and we make the materials different so that you have a double hetero junction. So, let us consider an example for this. Consider a P and N type material that is made of aluminum gallium arsenide and you have an intrinsic material that is made up of gallium arsenide. Now, aluminum gallium arsenide is actually composed of aluminum arsenide and gallium arsenide. Its formula is usually given as Al x gallium 1 minus x and arsenic. So when x is equal to 1 it is aluminum arsenide and when x is equal to 0 it is gallium arsenide. Now, gallium arsenide is a direct band gap semiconductor with an E g of 1.4 electron volts approximately it is more like 1.42 or 1.43. Aluminium arsenide is an indirect band gap semiconductor with E g that is higher on 2.16. So, this is a direct band gap, this is an indirect band gap. This material can be a direct or an indirect band gap depending upon the value of x. For x less than 0.4, this is a direct band gap material and the band gap E g is 1.4325 x. So, this is just an empirical relation. So, we start with aluminum gallium arsenide of band gap 2 electron volts and we have gallium arsenide band gap 1.4 electron volts. So, we are going to form a double hetero junction with these two materials. So, let me first draw the energy band gap of these materials when they are far apart and then when they come together in order to form the junction. So, I have my n type. So, I have my n Al gas. So, this band gap is 2 electron volts. We then have intrinsic gallium arsenide can either have an intrinsic material or a very lightly doped material. So, either way the band gap is smaller and the Fermi level is close to the center of the gap and then finally, I have p type gallium arsenide or p type aluminum gallium arsenide. So, this is intrinsic gallium arsenide p Al gas. So, now we form a junction. So, we have two junctions and these are different materials. So, it is a hetero junction because we have two of these this forms your double hetero junction. So, once again at equilibrium the Fermi levels must line up. So, that this is your P i n at equilibrium most of the depletion region will be within the gallium arsenide. So, these are your two junctions and you essentially have two depletion regions. We then bias this P i n. So, we bias this in such a way n is connected to negative and p is connected to positive. So, in both cases we bias this junction and forward bias. So, this is an example of a forward bias. When we forward bias the n region is shifted up and similarly the p region is shifted down. So, we can just take the example of two p n junctions and then just shift them when we do that. So, the bands bend up between the n region and the intrinsic and the bands bend down between the p region and the intrinsic. So, let me just mark. So, this is n al gas that is my intrinsic gallium arsenide that is p al gas. So, this is the case of the band diagram when the junction is in forward bias. So, we are injecting the electrons from the n side and we are injecting the holes from the p side. Now, because of the difference in band gaps we create these potential wells. So, we have a potential well where electrons can accumulate in gallium arsenide. We also have a potential well in the valence band side. So, holes can accumulate. These electrons and holes can recombine and then give you light. So, the energy of the radiation that comes out depends upon the band gap of the gallium arsenide region. So, it has a value of around 1.4, but by using a double hetero junction we can make sure that most of the carriers are located in the intrinsic region. So, that we increase the efficiency of the recombination and then produce more light. We can repeat this with another material. For example, instead of aluminum gallium arsenide where the aluminum actually substitutes for gallium you can have another material where you have gallium arsenide and phosphide. So, that instead of substituting in gallium the phosphorous substitutes for arsenic. So, this is formed by combining gallium phosphide GAP and gallium arsenide. So, I can have gallium phosphide and gallium arsenide. So, gallium phosphide is an indirect band gap semiconductor. Gallium arsenide is direct. So, this gives you gallium again depending upon the value of x you can have a direct or an indirect band gap material. So, once again using this you can form a double hetero junction with gallium arsenide even there the energy of the radiation that comes out will be equal to the band gap of gallium arsenide. In the case of an LED transitions occur from the valence band from the conduction band to the valence band. Now, most of the electrons and the holes are located at the edges of the conduction band and the valence band. But at any given temperature there will always be some thermal excitation which means that we will always have some broadening of the peak that comes of the radiation that comes out there always be some thermal excitation. This leads to a broadening of the intensity. So, that there is some line width. So, the line width depends upon the number of states that are available for the electrons and holes to occupy that is your density of states and also the probability of the occupation. So, that is your Fermi function. So, H mu is the energy of the photon and this is because of recombination of an electron in the conduction band with some wave vector k with a hole in the valence band having a some other wave vector k in the photon energy is nothing but e c plus h bar square k square over 2 m e star. This represents the energy of the electron minus the energy of the hole e v minus h bar square k square over 2 m h star. So, this is the energy of the electron this is the energy of the hole. So, these values of k can be different but for simplicity let me just take them to be the same in this case this equation simplifies to e g plus h bar square k square over 2 m r star. So, this equation is called the joint dispersion relation m r star is called the reduced effective mass and 1 over m r star is called the reduced effective mass. We can similarly define a joint density of states. So, again if we assume a solid with a uniform potential then the joint density of states is 4 pi 2 m r star. We also need the occupation probability can assume that the occupation is a simple Boltzmann function. So, that p of e is just exponential minus e over k T. So, this is Boltzmann approximation. So, the line width which is the spread of the light that comes out from the LED because of thermal excitation depends upon the density of states and the probability of occupation. So, we can show this in a graphical fashion. So, let me plot the intensity versus the energy y axis I have intensity x axis I have energy. Now, we would not have any light whose energy is less than e g because you cannot have any states in the gap. So, the minimum energy is e g. Now, the density of states function increases as square root of the energy. So, this is the density of states proportional to e minus e g square root. Then we have the occupation probability we said that goes as a Boltzmann function which means as the energy increases the occupation probability decreases. So, this is p of e is proportional exponential e minus k T. So, the theoretical spectrum depends upon the product of these two. So, that I of some energy equal to h mu is proportional to square root of e minus e g exponential minus e over k T. So, if I were to plot this. This will be the spectrum of the intensity the peak usually lies k T over 2 above e g and then there is a line width. This line width delta lambda is approximately 1.8 k T over h c lambda square. So, for example, if you have an LED which gives light at 400 nanometers. So, 400 nanometers is in the visible region and calculate a delta lambda this is just by substituting this here and we take temperature to be room temperature. So, delta lambda is approximately 6 nanometers at room temperature. So, if we have different LED materials we can basically have light of different wavelengths the wavelength is going to depend upon the band gap of the LED material. So, we can summarize this in the form of a plot. So, just like to look at the different LED materials. So, plot the visible region wavelength form of nanometers this is 400 500. We also plot the energy energy is in electron volts somewhere around 3 2.8 0.4 2. So, depending upon which region in the spectrum you want you choose the corresponding LED material we already saw that if you had gallium arsenide. Then gallium arsenide with a band gap of 1.4 actually gives you light in the IR region. So, within the blue region so, if I just were to mark this violet. So, within the blue region typically you can use an indium gallium arsenide, indian gallium nitride based material for a slightly lower band gap indium based with aluminum gallium phosphide. So, it is an indium phosphide doped with aluminum and gallium already saw al gas that has an energy around 2 electron volts depending upon the value of x. You also have gallium phosphide based materials this is gallium. So, if you see most of these materials are based upon 3 5 can also have 2 6 based materials with different values. So, they are all based off of gallium arsenide. So, gallium arsenide is a direct band gap material and you can also use it as a substrate for growing many of these LEDs. In order to avoid defects these LEDs are usually grown by some vapor deposition means like chemical vapor deposition or atomic layer deposition or even a simple physical vapor deposition like sputtering or laser processes. So, this enables to grow different layers with minimum defects again you have to choose your materials in such a way that there is a lattice match. So, that if there is any lattice mismatch that can also lead to defects. When we talk about LEDs we usually talk about a factor called the quantum efficiency I am going to abbreviate this as Q E. Now, there are different metrics for the quantum efficiency the first one is called the internal quantum efficiency I am going to denote this as eta i n. So, this is the number of photons which are generated internally divided by total number of carriers. So, eta i n is the number of photons emitted or generated internally divided by the number of carriers. So, this is nothing, but the ratio of the recombination rate which is radiative to the total recombination. So, R R which is the radiative recombination rate divided by the total. So, this is radiative this is non-radiative. For a highly efficient device we want the internal quantum efficiency to be high which means the radiative recombination rate must be much higher than the non-radiative part. We can also define an external quantum efficiency this is nothing, but the number of photons emitted externally divided by the number of carriers. So, eta external depends upon the internal quantum efficiency times the optical efficiency of the device. This is related to the device geometry the reflectivity or the absorbance or the transmittance of the various layers and so on. We also define something called a power efficiency eta p which is the optical power output divided by the input power. So, eta p the optical power divided by the input power the optical power output is nothing, but the number of photons. So, this is number of photons times the energy h mu divided by the input power which is usually just I v. So, far we have looked at LED materials that are mainly based upon semiconductors. We can also have LEDs based upon organic materials these are called OLEDs. So, we will not talk much about them here because we mainly deal with inorganic semiconductor materials, but OLEDs or OLEDs also work on a similar principle. In this case you have an organic material which is your active material sandwiched between two electrodes carriers are injected into this organic material which then recombine to give you light. So, usually OLEDs because they are organic materials we do not talk about valence band or conduction band, but we talk about molecular orbitals. So, we have something called a highest occupied molecular orbital which is similar to a valence band and a lowest unoccupied molecular orbital which is similar to a conduction band. So, that when electrons and holes recombine against this you will get light. So, there are different OLED materials that are available again you choose the material based upon the region of wavelength which you are interested in. So, OLEDs are useful mainly for display devices they can easily be thermally evaporated on to a substrate, but one of the problems with OLEDs is of course, the cost that is involved and the life span of these organic materials. Stability of the organic material is another issue. So, water damage is an issue there, but OLEDs are again another type of LEDs which are based upon organic materials. So, today we have looked at LEDs the next class we will focus on lasers. So, lasers work on a similar principle to LEDs, but there are some important differences because we also need to create population inversion in lasers. So, we will look at lasers in the next class.