 In last class, we looked at photo detectors. So, in the case of photo detectors, we had an incident light onto your device, which was converted into an electrical signal. Today, we are going to look at solar cells. A solar cell is an example of a photovoltaic device. That is, it is a device where you have a generation of voltage when exposed to light. So, when exposed to light leads to a generation of voltage. Photovoltaics were first discovered by Henry Becquerel in 1839, but the first silicon based PN junction photovoltaic was invented by Ohl in 1940. So, the principle of a photovoltaic, let me just abbreviate this as PV, is similar to the photo detector that we looked at last class, there are just a few crucial differences. So, in the case of a photo detector, we saw that one such example was a photodiode, it could be a simple PN junction or a PIN junction. So, in that case, a photo detector works over a narrow wavelength range. So the maximum wavelength depended upon the energy of the transition that was involved. So, if there was a transition from the valence band to the conduction band, the maximum wavelength was defined by the band gap of the material. The minimum wavelength range depended upon the absorbance of the material, because as wavelength decreases, absorbance increases, so that light is only absorbed very close to the surface. In the case of a solar cell, we need the device to work over a broad wavelength range, and this wavelength range depends upon the solar spectrum. So, that is the first crucial difference between a solar cell and a photo detector. The wavelength range is imposed by the spectrum. Also, in the case of a photo detector, the metric is the quantum efficiency. So we define quantum efficiency as the number of electron hole pairs or the current that is generated to the ratio of the number of photons that are incident on your sample. So the quantum efficiency determines the signal to noise ratio. In the case of a solar cell, the metric that is normally used is the power conversion efficiency. This is the ratio or this is the power delivered per incident solar energy. So solar cells are usually wide area devices, because they need to capture as much as the incident solar energy and then convert it into electrical energy. So to understand the solar cell, we first need to take a look at the solar spectrum. If we look at the solar spectrum, it primarily ranges from the UV to the IR region. So it encloses the visible region. So it goes from UV to IR. The typical wavelength range goes from around 0.2 microns or 200 nanometers to 3 microns. So 3 microns lies in the IR region, 0.2 in the UV region. So this encloses the visible region as well. Of course, the intensity of this radiation is not a constant. The intensity depends upon the wavelength. So we can plot a power spectrum versus wavelength. So I have wavelength lambda on my x-axis. This is in micrometers and then I will plot the power. And the unit is kilowatt meter square per micrometer. So this is your power spectrum, 0.2, 0.8, 0.4, 2. Let me extend the axis a bit to 0.6, 0.8, 0.6, 2.4. So the visible region lies somewhere between 0.2 and 0.8. This is visible. This is IR. This is UV. So if you plot the power spectrum as a function of wavelength, we have a peak and then the intensity decreases at higher wavelengths. So this sort of spectrum can be approximated to a blackbody whose temperature is around 6000 Kelvin. So it's approximated to a blackbody. The area under the curve gives the total intensity of the incoming solar radiation. This area has a value of around 1.35 kilowatts per centimeter square. So this is the intensity of the solar radiation per unit area. Just to be clear, I will say this is area under the curve. Of course, we should also take into account the fact that you have scattering of radiation by the Earth's atmosphere. So the atmosphere has ozone. It also has some water molecules. So these can scatter the solar radiation. They also has dust particles which can scatter radiation. The path length will also change the energy of the spectrum. For example, if you have solar light directly overhead, so when theta is 0, so when we have the solar light directly overhead, the intensity i is around 0.925 kilowatts per centimeter square and when theta is 60, so there is some scattering and the path length is more. The intensity i is lower. It's around 0.691. So there is an energy spread to the spectrum. This energy spread is shown here and the spectrum or the actual intensity that is arriving at the Earth is going to depend upon scattering from the atmosphere and also the incident angle of the radiation. So this radiation needs to be absorbed by your device in order to produce an electrical signal. So let us consider a simple design of a solar cell. So let us look at a solar cell that is based on a simple p-n junction. So last class, we saw that your photo detectors are also based upon a p-n junction or a p-i-n junction. So the basic principle is similar. So we have a solar cell that's based on p-n junction. The n region is heavily doped. So I will call it p-n plus and we also have a thin n region because the light has to penetrate through the n region. So if I were to draw a schematic of this, here's my solar cell. I have electrical contacts at one end. My light is incoming from this direction. So I also have electrodes at the other end. But these electrodes do not cover the entire surface because the light has to penetrate through your device. So this is the interface between the n plus and the p region. So the n plus region is heavily doped. In this case, the depletion region will lie almost entirely on the p side. So I have a very thin depletion region on the n side and it is lot more thicker on the p side. So these are electrodes. So we have solar radiation coming from the left and falling on the n plus region. So now your radiation can have both long wavelength, medium and short wavelength. So a shorter the wavelength, higher the energy. The short wavelengths are usually absorbed by the n plus region because the absorption coefficient is large, hence the penetration depth is small. Whereas the wavelength increases, the penetration depth also increases. So this just depicts three kinds of wavelength, short, medium and large. When the wavelength of light gets absorbed, it generates an electron hole pair. So for example, the medium wavelength region generates an electron hole pair within the depletion region. We have looked at a p-n junction in equilibrium. We know that whenever we have a junction, we always have a contact potential. So we have a plus and a minus. We saw this earlier when we are talking about p-n junctions. This arises because you have the electrons in the holes recombining and getting annihilated to give you a depletion region. So the electric field goes from positive to negative, which means there is a built-in potential or a contact potential v0. So when the incoming radiation generates an electron hole pair, the electron is accelerated towards the n side because it sees the positive potential and the hole is accelerated towards the p side. This means there is now a potential that develops between the p and the n regions. In the absence of any external load, this potential is called voc, which is your open circuit potential. So if you now make the connection between the p and the n, so that instead of an open circuit, you have a short circuit, you have a current that flows through the device and it flows through the outer circuit because of the electron and hole pairs that are generated. This current is called your short circuit current. So let us draw a schematic of that. And I have my n and the p and there is a depletion region. So we have the electrodes on both sides and instead of having an open circuit, we make the electrical connections so that current can flow. So in this particular case, once again you have solar radiation falling on your sample, an electron hole pair that is generated, the electron accelerating towards the n side and the holes accelerating towards the p side so that the current flows from p to n. This current is called your photo current. So it is the current that is generated because you have photo generated carriers. In the absence of any external load, it is also called the short circuit current. So in this particular figure, let W be the width of the depletion region. So your electron hole pairs are generated within this width W. But if you also look more closely, electron hole pairs are also generated within the n and the p regions because all of these regions absorb the light. So electron hole pairs are generated in all of them. So once again you can see that the holes will get accelerated towards the p side and the electrons get accelerated towards the n side. But these electrons and holes are essentially minority carriers. So they can only diffuse within a region which is defined by the diffusion width. So LH is the diffusion width of the holes which are the minority carriers on the n side and LE is the diffusion length of the electrons which are the minority carriers from the p side. So the total region from which current is generated is LH plus W plus LE. So it not only comes from the depletion region but also from the diffusion regions in both the n and the p side. So electron holes generated from this region contribute to the current. So let us now go ahead and calculate the IV characteristics of a solar cell. So let us look at the IV characteristics of a solar cell. In this particular case, we are looking at a solar cell which is a simple p-n junction that is connected to some external load. The external load is defined by a resistor R and you have some incident light of certain intensity which is given by IOP. So in this particular case, there is a built-in voltage within your p-n junction and also a current that flows through the device. So this is a schematic representation of a solar cell that is connected to an external load. Now in the absence of a load where the resistor is 0, we saw that when you shine light, you have a photo current that is generated within. This case the voltage or the voltage difference is 0 because you have a photo current IPH. If we define the conventional direction of current the other way and call it ISC which is your short-circuit current, then ISC is nothing but minus of IPH. So ISC is the short-circuit current which is the current that flows through at the device when it is short-circuited. So when there is no external load. This in turn depends upon the photo current IPH. Now IPH depends upon the intensity of solar light that is shining on your device. So IPH is usually some constant K times IOP which is the intensity of the solar radiation shining on the device. So K here is a constant and this is the intensity of incident radiation. So we take this and now add on an external load in the form of a resistor. So then you have a potential now, you have IOP. So once again there is a photo current IPH but this photo current generates a voltage across the resistor. This voltage across the resistor is IR and this voltage opposes the inbuilt voltage of your PN junction because any PN junction has an inbuilt potential or an inbuilt voltage which is your contact potential and the photo current basically generates external potential that opposes this. So this is equivalent to saying that you are forward biasing your PN junction so that now it is easier for the minority carriers to diffuse so that you have a forward bias current. So the forward bias current goes the other way I am going to call it ID. So ID which is your forward bias current and you can write the standard diode equation for this is IS0 where IS0 is the reverse saturation current exponential EV over KT-1. So IS0 is your reverse saturation current which we have seen earlier in the context of a regular PN junction. So we have a forward bias current that goes in one way. We have a photo current due to the radiation that falls on your sample that goes the other way. So the net current is nothing but ID-IPH which is just IS0 exponential EV KT-1-IPH. So it is possible to draw an equivalent circuit for your solar cell which is nothing but a PN junction under illumination. So we have a solar cell connected to an external load and you have some incident radiation shining on it. So it is possible to draw an equivalent circuit for that. So in that case you have a constant current source which is your photo current generated because of the incident light. You have your PN junction that is now under forward bias. So that there is a forward bias current ISO and this forward bias current opposes the constant current source or your photo current and then there is your resistor R. So the equivalent circuit for a solar cell is just a constant current source and a PN junction under forward bias which opposes each other. So you can also draw an IV characteristics for the solar cell. If there is no radiation, so in the case of a dark solar cell, the IV characteristics will just resemble a PN junction under bias. So we have the current which increases exponentially with the voltage just given by this expression. So this is in the case of dark. We found that when we shine light we have a photo current that opposes the forward bias current so that the net current is ID-IPH. So the effect of this is to shift your IV current below so that when you have some photo current shining you no longer start at 0 but you are shifted below because of the –IPH. If you increase the value of the incident radiation intensity so that IOP is higher then IPH will be even higher and then you are shifting this even further below. So in this particular case we can calculate the voltage at which current is 0. So when current I is equal to 0 the voltage is called your open circuit voltage. So in that case I which is I s0 exponential E VOC over kT-1 this is 0. So when the voltage is VOC which refers to this point the current is 0. So we can rearrange this expression to give you VOC to be approximately equal can neglect this factor – 1 to be kT over E ln of IPH over ISO. So let me rewrite this expression and we can look at the two parts of it. So we have written down the expression for the open circuit voltage VOC approximately kT over E ln of IPH over ISO. IPH is your photo current which depends upon the intensity of the light and ISO is your reverse saturation current which depends upon the intrinsic carrier concentration Ni square and also on the diffusion coefficients, diffusion lengths and the concentration of the P and the N regions. There is a term E here. So if you increase the value of photo current so if IPH is higher VOC will increase. Similarly if you go for a material with a higher band gap so if EG is higher then Ni will be lower so ISO will be lower and that will also increase VOC. So in the case of a solar cell we saw that the important parameter was the power conversion efficiency. The power is nothing but I times the voltage which is ISOV exponential EV over kT – 1 – IPHV. In order to have the maximum power so for maximum power DP over DV should be equal to 0 so we are just differentiating this expression. So in that case the corresponding voltage is Vm and we can write a recursive relationship that relates Vm to VOC. So this is a recursive relationship because Vm is on both sides but it can be solved in order to get the maximum voltage or the voltage corresponding to maximum power. So once we know the value of Vm we can plug in this expression and get the maximum power. So let us once more look at your IV curve. You just redraw this. So this is your dark current. This is your current under illumination. This point is VOC. Here we can calculate the Vm which corresponds to the maximum power and also the Im. So this is Vm corresponds to Im. The area under the curve or the area between these two points gives you the maximum power that is delivered to the system. So Vm times Im is the maximum power delivered. If you do the calculation we find that Vm will increase as VOC increases. So higher your open circuit voltage higher the value of Vm. So one way of increasing VOC is to increase the intensity of the radiation and the other way we saw was to have a p-in junction with a higher band gap. The drawback in that case is that as your band gap increases the region of the solar spectrum that is being absorbed will decrease because as EG increases the corresponding wavelength for the transition will decrease. So there is a trade off on what material you choose in order to get the maximum value of the power. So conventional silicon based solar cells have efficiencies of around 22%. So in this case these are single crystal silicon based devices. Instead of single crystal if you have a polycrystalline silicon your efficiency let me just call this eta. Your efficiency will be around 15%. You could also go for amorphous silicon based solar cells. The advantage is that the cost is reduced because you can directly deposit these on a glass slide. So you can have amorphous silicon based solar cells but the efficiency will drop even further. There are other materials that are used for solar cells. Some of the typical materials we already saw silicon have cadmium telluride, cadmium sulfide and then copper indium diselionide. This is a material with a band gap of around 0.7 electron volts and the variation of this is copper indium gallium diselionide. So it is usually written as Cu Inx gallium 1-x Se2. The band gap in this case depends upon the value of x. All of these have efficiencies somewhere between 10 to 20% depending upon the processing route which is used in order to make these devices and also the quality of the films that are produced. The solar cells we have seen so far are simple PN junction based solar cells. You could also have a hetero junction solar cell. So in this case you can increase the efficiency of the device. For example, consider a hetero junction where you have P aluminum gallium arsenide which is a thin layer that is deposited on top of PNN gallium arsenide. So in this case your PN junction is still between the same material but the aluminum gallium arsenide layer helps in passivating the surface bonds or the surface defect states. It also has a higher band gap than gallium arsenide so that it allows the radiation to pass through it and be absorbed by the gallium arsenide. So this in turn leads to a higher efficiency. So you can also have other designs for PN junctions. So you can also have a PN junction between different materials. So you have N aluminum gallium arsenide and P gallium arsenide. So aluminum gallium arsenide has a higher band gap. Once again it acts as a window in order to allow the radiation to reach the junction. So that we no longer need the N layer to be really thin as in the case of a homo junction based PN junction. So here you have different band gaps. So this again makes carrier separation easy. So this is your gallium arsenide with the band gap of 1.4 electron volts. This is aluminum gallium arsenide with 2 electron volts. So any electron hole paths that are generated can be easily separated and this gives rise to a current. You can have also solar cells that are in tandem which means you have one solar cell on top of the other. So you have 2 PN junctions and you choose your material in such a way that the band gap of the first material is greater than the band gap of the second. So if you look at the design you have the first material which has its PN junction and you have the second material with its PN junction. So this has a band gap EG1 which is greater than EG2. The advantage of having this type of arrangement is that the shorter wavelengths will get absorbed by the first material because it has a lower absorption distance or a lower penetration distance while the longer wavelength will get absorbed by material true. The problem of course is that making the devices more complex also adds on to the processing cost and the processing complexity because if you have tandem cells like these then they have to be grown with no defects between them because defects will again act as straps for carriers and will reduce the efficiency of the device. So these last few classes we have looked at electronic devices. So we started with a simple metal semiconductor junction then we moved on to a PN junction and then we looked at transistors. We also looked at some examples of optoelectronic devices like LEDs, lasers, photo detectors and then solar cells. So in the last part of the course we are going to focus on fabrication of these devices. We will look at some of the terminology that I used, some of the processes that I used in fabrication and also the challenges. We will also look at some alternate methods of fabrication then your standard micro fabrication processing that is currently being practiced.