I'm testing your ability to listen to me for a few hours, and also my ability to speak

for a few hours, but I'm switching subjects now, so we're going to talk about something completely different, we're going to talk about solar cells, so we have a few different faces in the audience, including some experts like Professor Agarwal in solar cells, so it'll be a little more challenging, but what I'm going to try to do is to give a very basic

introduction to solar cells. So some of this material, for some of you, will seem a little too basic, because I'm going to explain what an energy band diagram is, and if you didn't know what an energy band was, you probably haven't been following the last few days, but there won't be a lot of that, and I mentioned to my wife this morning that

I had 69 slides, and she said, oh those poor people, but you know, this is a high level, it's a high level look, and we have four more lectures where we're going to delve into it in a little more detail. So it's an introduction to solar cells, and

so let me start out by thanking my students, some of whom I see in the audience here, they've been working very hard over the last few days to get my plots for me, so I want to thank them for all of their help in putting this together. Okay, so you know, the idea

of a solar cell has a long history, you know, in the 1800s people discovered the photovoltaic effect, you could shine light on materials and get a current to flow, and Albert Einstein got a Nobel Prize for figuring out what the photoelectric effect was, how the absorption of photons translated into electrical current, but it really wasn't until

the 1950s, after the invention of the transistor and semiconductor technology was perfected at Bell Labs, that people started to make reasonably good solar cells and the field started to be taken seriously as a means of generating electricity. So the first work

was done in 1954 by a team at Bell Labs, oh I forget now, this solar cell was five or six percent efficient I think, basic silicon solar cell, and there were high hopes for the technology. Now if you're interested you can see what's happened in efficiencies,

if you go to the, this is a plot that's maintained by NREL, the National Renewable Energy Lab, so you can find this somewhere on their webpage or you can go to the Wikipedia site on solar cells, this is a plot showing efficiencies over time, and I don't have a laser pointer here, but you know, you can see what's happened there, there's an interesting

plot down there about 1976, it says IBM T.J. Watson Research Center, and efficiency of about 22 percent, so that was a record efficiency done by Jerry Woodall, who's now a professor here in Purdue, some of you know about, and that efficiency was not

exceeded for something like 15 or almost 20 years by other technologies, that was a gallium arsenide, aluminum gallium arsenide solar cell with a heterojunction, it was very nice work. Let's see, if we look at crystalline silicon, so crystalline silicon is still the mainstream technology, and when I do examples and things I'm going to be talking

about crystalline silicon because it's just the easiest to explain what this is all about. Crystalline silicon, single crystal are the black squares, and you can see around 19, late 70s, 1980, that blue line is about 15 percent or so, that's when I left my job

at Hewlett-Packard and came back to do a Ph.D. on solar cells, and a lot of very good work got done then, people really dove into the device physics, at that time people thought it was a mature technology, it had been developed from 5 or 6 percent for when Bell

Labs first demonstrated it, it had been increased to 15 percent or so when it was used to power satellites, the efficiency gains had saturated, and then there was our first energy crisis in the late 1970s and people got serious about solar cells, and a lot of very good work was done, we dove in not only in crystalline silicon but other materials

and figured out ways to raise the efficiency, and you can see from that blue line with the rectangles there, that the efficiency, the record efficiencies now are up around 24 percent, so that's a very big increase from 15 percent, what was thought to be relatively mature to 24 percent, it'll be very hard to keep going on that, we've

extracted almost every percentage point of efficiency that we can get out of crystalline silicon, now, but you do see some lines, you see a, what is that, 42.4 percent up there, how's that done, that's a material, that's a solar cell that uses a combination

of band gaps, we'll talk about this a little later, so it uses different band gaps that are optimized to different parts of the solar spectrum, and if you can hook those all in series appropriately and take out the photons that need to go to the right band gap semiconductor, they're much more expensive to produce, but the efficiencies

can be remarkably high. And then there are a whole variety of other techniques in there, various types of thin film and polycrystalline which have respectable efficiencies but are much lower cost, and we'll talk a little bit about that later on. So if you would like a recent view from industry, Mark Pinto is at Applied Materials and he has a very

nice talk from an industrial perspective about what the future prospects look like for photovoltaics, so you can find that on the nanoHUB, so I would refer you to his talk, I'm going to be talking by and large about some, just some very basics,

how do these devices work? And they're incredibly simple, so you might think there's not much to say, it's just a p-n junction with light shining on it, or some kind of junction with light shining on it, but you need a very good knowledge of p-n junctions to figure out how to extract every percentage point of efficiency out of it. So we have

sunlight shining on a diode, we make a solar cell, and if we want to understand how this works, we first of all have to understand how a p-n junction works, so we can talk about that in the dark first, and then we have to understand a little bit about how you absorb light in a semiconductor, and then we can put the two together and talk

about how a solar cell works. So let's do, you know, we treat p-n junctions in about the first third of a course here in semiconductor devices, but let's just talk very briefly about what a p-n junction is and how it works, because it's not too difficult to understand the basic principles. So you remember if you have silicon, you have

atomic number, what is it, 14, you have these discrete energy levels. If you put silicon atoms together in a crystal and all of their wave functions overlap, then all of those energy levels broaden into a band, and each one of them has one for every atom that it originally came from. So we have a band of energy levels that are so closely

spaced that the electrons can move between energy levels without thinking about discrete hops. Now the only bands that really matter to us are the ones near the top. The topmost filled level or band, which is called the valence band, and the topmost empty band,

because under operating conditions, we can take a few electrons out of the valence band or we can put a few electrons into the conduction band. The deeper levels, the core levels are just going to remain unperturbed and shielded from us and nothing is going to change there. So if we draw an energy band diagram, we only worry about the bottom

of the top band, which at 0 degrees is empty, and the top of the filled band, and at 0 degrees, all of those states below the top of the band are filled. And the

one point one electron volts for gallium arsenide is one point four, depends on what semiconductor we use. Alright, and then just to acquaint you with some basic terminology in semiconductors. If we just have pure silicon, you know, and silicon these days

is probably the purest material that human beings make. It's been refined to enormous precision, very small densities of defects. If we take an intrinsic pure piece of silicon, ideally, we shouldn't have any empty states in the valence band and we shouldn't have any electrons in the conduction band. But at room temperature, there's some thermal

energy that can break some bonds and can promote an electron from the valence band to the conduction band. Now we've got a missing, an empty state in the valence band that we think of as a positive charge carrier or a hole, and we have an electron in the conduction band. That's an intrinsic semiconductor, equal numbers of electrons and holes. If we

crank the temperature up, we have more thermal energy to break bonds, we get more holes in the valence band and more electrons in the conduction band. Okay, now what's an n-type semiconductor? So if I intentionally introduce an impurity in a semiconductor

like phosphorus, which has a valence of five, silicon has a valence of four, then there's one electron left over, and it's weakly bound into the phosphorus atom, and at room temperature we can easily break that bond. So for every phosphorus atom that I put in, if I put in nd of them, I break a bond and that extra electron is now a free

electron to move around in the conduction band. So we would say that that material is doped n-type and the number of electrons is equal to the number of phosphorus atoms that we put into the silicon. If we cool it down, they might freeze out because it might

not be enough thermal energy to break that weak bond to the phosphorus atom. We could do this, we could also make it p-type, so we could introduce a material like boron. Boron has a valence of three. In a silicon lattice, it wants to be surrounded by four nearest neighbors, so it's got one too few electrons. So in the boron atom, then what

we can do is to satisfy its bonding to its four nearest neighbors, we can pull an electron out of the valence band and satisfy that bond, and now we've introduced a hole in the valence band. So for every boron atom that goes in, we have one empty

state in the valence band, and the energy to do that is very weak, so the number of holes is equal to the number of boron atoms that we put in. So now the concept of a Fermi level, and those of you that have been with me for

the previous lectures, you know all about Fermi levels and Fermi functions, but for those of you that are brand new to this lecture, let me remind you of what it is. We sort of think the Fermi level tells us how the states are filled up. It's like you can think of it as a liquid water level. Things below the level are filled, things

above are empty. So if the Fermi level is up near the conduction band, it means that at t equals zero, there's an abrupt drop off. All the states below the Fermi energy are filled, all the states above the Fermi energy are empty. But if there's some thermal energy, then it means there's a small probability of the states above the Fermi level to be

occupied, so that gives us electrons in the conduction band. There's a small probability of states below the Fermi level to be unoccupied, but the valence band is way down below it, so there's virtually none. So in my p-type semiconductor, I would draw the Fermi

level down near the valence band. It means that most of the states below it are filled, but close to the Fermi energy, there's some probability that a few of them will be empty. So the Fermi level is near the conduction band for n-type, near the valence band for p-type. The Fermi function is given by this expression, and you can see that if the

energy is equal to the Fermi energy, the probability that the state will be occupied is exactly one half. But if the Fermi energy is located in the band gap where there are no states, then it's probability of one half times zero, so there's nothing there.

Alright, and if you go, if you look at that expression and you go to energies that are way less than the Fermi energy, that expression will go to one. If you go to energies that are way above the Fermi energy, that expression will go to zero. Okay, so now back to intrinsic semiconductors again. If I don't have any of those boron

or phosphorous atoms, then I've got an equal number of electrons in holes, just thermal energy that has broken a bond, gives me one electron in the conduction band, one hole in the valence band. That number we'll call n sub i, it's the intrinsic density of carriers, so that's an important number for semiconductors. And the product of

the number of electrons times the number of holes is ni squared, because each one is equal to ni, each one came from that same broken bond. And you might guess that the energy that it takes to do that is related to the band gap, and the probability

that you'll break one of those bonds is e to the minus band gap over kT. So in silicon the band gap is 1.1 electron volts, and kT at room temperature is 0.025 electron volts, so the probability that you'll break one of those bonds is e to the minus

40th, so it's very small. But there are a large number of silicon atoms, 10 to the 22nd per cubic centimeter or something. So what you'll find is that the number of electrons in holes is almost very close to 10 to the 10th per cubic centimeter in

the intrinsic silicon. Minuscule fraction of the total number of atoms that are there. If you heat it up to a very high temperature, you can get much more thermal energy and you can break many more and you can get lots of carriers. Now this is the interesting, so I'm giving you a synopsis of semiconductor physics in

a whirlwind and then we'll talk about solar cells. What if we dope this by n-type? Then the number of electrons at room temperature is about equal to the number of phosphorous atoms that we put in, nd. Now the thing that we need to remember is this law, n times p is equal to ni squared, that always holds in equilibrium.

That's like a chemistry law of math action. So I know what the number of electrons is. If I want to find out what the number of holes is, it's just n naught is nd so it's just the number of holes, p naught, is ni squared over nd. So if you take a

look at this, in this example if I put 10 to the 17th phosphorous atoms per cubic centimeter in, that's a moderate doping, not too heavy, not too light. If we put that in, ni is about 10 to the 10th, so the number of holes is 10 to the 10th

squared over 10 to the 17th, so the number of holes is 10 to the third. Now we've got even fewer than we did in equilibrium. And it works the same way if I have a p-type semiconductor. Now I know that the number of holes is equal to the number of boron atoms that we intentionally put in, but np is

still ni squared, so if I put in 10 to the 17th boron atoms, I'll end up with 10 to the third electrons such that the product of the two is equal to ni squared. Okay, so now we can get to a p-n junction. A solar cell is a p-n junction. So we have to talk about what a p-n junction is. So a p-n junction

we just bring an n-type and p-type semiconductor together. So this isn't the way you make a p-n junction, but it's a nice way to conceptually think about it. We have an n-type semiconductor, we have a p-type semiconductor, we bring the two together, and we ask what will happen. Well, this Fermi level,

if we think about this as like the level of a liquid that's filling up the states, and the top surface is the Fermi level. If I bring the two together, it's like you've got two separate lakes at different levels. You dig a channel between the two, the water will flow, and the water level will equalize. In equilibrium, there's only one Fermi level in one position.

So when I bring these two together, I can only have one Fermi level. When they're separate, I have two isolated systems, I have two different Fermi levels. So if we bring them together, that's what happens. So if we want to draw the energy band diagram for this p-n junction,

we start by drawing a straight line for the Fermi level because we know it's constant. And I'll just ground it over here, and I need some reference somewhere, it can be arbitrary. So I'll say it stays where it did. What was that side? Was that my p-side of the semiconductor? Okay, now if I draw the energy band diagram, I'll draw something like this.

If I get way to the right, then I won't know that I've made a junction, and it'll just be a p-type semiconductor with the Fermi level down by the valence band. If I get way to the left, it's just an n-type semiconductor that doesn't know that there's a p-n junction over there to the right somewhere. So the Fermi level has to be by the conduction band.

And then I just smoothly draw a line from one to the other. That's the energy band diagram of my p-n junction. So you can see that in the transition region, the Fermi level is a long way from the conduction band, which means there are very few electrons, and it's a long way from the valence band, which means there are very few holes,

so people call that a depletion region. And physically you can think that the holes have diffused in one direction, and the electrons have diffused in another direction, and they've left behind this depletion region where there aren't very many carriers. Now, how did this all happen?

What we had for an electron, an electron has a minus charge, so if you apply a potential, you'll lower the electron energy by minus Q times the voltage. So this movement of charge set up an electric field that set up a potential difference between the n-type and p-type that lowered the energy on the n-side

and pulled the n-side down so that the conduction band will come down and be where it's supposed to be with respect to the Fermi energy. So there must be a positive voltage that developed on the n-side. That positive voltage is called the built-in potential of the p-n junction.

And this is a really interesting voltage, you know, that we talk about a bit when we do semiconductor courses. You have a p-n junction, you own the lab, you put your voltmeter across the p-side and the n-side, what do you measure? Nothing. But the voltage is there. And this takes a little bit of discussion that,

you know, that maybe we can do at the break or something. What you argue is that what the voltmeter really measures is the difference in Fermi levels. It doesn't measure the difference in the electrostatic potential. What it really measures is the difference in the Fermi energies. And in some cases those are the same things,

but when you have junctions and you have built-in voltages in equilibrium, they're not the same thing. You can see what would happen if that was a real voltage. I would just attach a resistor across there, there would be voltage across that resistor, current would flow, it would be given by Ohm's law, I would be delivering power to a load, I'd have a perpetual motion machine.

Something would be wrong. But there is a potential drop there, and it's central to the operation of this device, and we can measure it with special techniques and things. And another thing to think about is you can see that that potential drop

is about the band gap divided by Q, the band gap in electron volts. Because the Fermi level in the p-side was near the valence band, the Fermi level in the n-side was near the conduction band, I have to establish a voltage that lines those two, so it's roughly the band gap that it takes to move those two into alignment.

And you can get this simple little expression if you derive exactly what it is. And one of the other things that we teach students in beginning semiconductor courses is that the variation of that energy band

is occurring because there's a variation in the local electrostatic potential. So the slope of that is the gradient of the electrostatic potential, it's the electric field. So if you look at the gradient of that, you can get the electric field, you can see it's positive there. So you can think of the electric field as exerting a force on holes to the right, which stops them from diffusing and stops current flowing,

and it exerts a force on electrons to the left which stops them from diffusing away from the n-region, that's what establishes equilibrium and stops the current from flowing. And then we draw this little circuit diagram here where the arrow points from the p-side to the n-side. Alright, that's our convention.

Now let me look about this in equilibrium a little bit more. So I have this potential barrier that got set up, this is what keeps the electrons on the n-side and keeps the holes on the p-side, that when this charge sloshed around and moved apart and set up an electric field, it set up a potential energy barrier that holds all the electrons on the n-side

and all the holes on the p-side. But still things are happening at a microscopic basis. If I look at what's really happening, electrons have a probability of hopping over that potential barrier. And then some of them will just drop down the potential barrier. And those two processes just balance in equilibrium so that

we get the right number of electrons in equilibrium on the p-side and the right number of holes on the n-side. Now what is that probability? Well, you know there are lots of problems in physics where you ask what's the probability that you can get over a barrier. Or you ask the things like, if you know the density of

oxygen molecules on the surface, what's the density 50,000 feet higher? Well it's e to the minus gravitational potential, mgh, e to the minus barrier height over kt. In this case the barrier height is that q times vbi. So the probability that an electron will get over that

is e to the minus 40 because vbi is about one electron volt. Very small, but a few of them will get over there, a few of them will drop down, just enough to balance everything out and keep it all in equilibrium. Okay, now we go on to forward bias

because our solar cell is going to develop a voltage and deliver power. So if we apply a positive voltage to the p-side, a positive voltage lowers electron energy and these are electron energy band diagrams. So a positive voltage on the p-side is going to pull everything down and

if I pull everything down it means that that potential energy barrier is not as high as it was in equilibrium. It's the built-in potential of about one volt minus whatever forward bias I put on it. If I put on a half a volt then the potential energy barrier is a half a volt. Okay, now the probability of getting over that barrier is much higher.

It's still e to the minus barrier height over kt but the barrier is much smaller so the probability is exponentially bigger. So in fact the probability is the equilibrium probability times e to the q applied voltage over kt. Which, kt is small so you apply just a few tenths of a volt, that can be a

very big number. What it means is it's much easier now for electrons to get over that barrier so we're going to be out of equilibrium on the n-side. We're going to have many more minority carrier electrons on the n-side than we did in equilibrium because they can hop over that barrier from the n-side and get to the p-side.

Same thing, we'll have many more holes on the n-side than we did in equilibrium because the hole energy goes down so the hole energies hop over a barrier by going down. Okay, so the important point here then is that there is a lot of what we would call excess charge on the n-side. There are excess electrons that weren't there in

equilibrium and we're going to ask the question what is the total concentration of excess electrons in the p-region? So we would just integrate from the beginning of the p-region to the end, that total concentration.

And if I want to find how much current flows, current is charge divided by time. So that excess carriers, the current, I know it's going to be charge divided by some time and I'll have to figure out you know what is that time mean? But current is always charge divided by time

so I'll just have to figure out what the time means. Now at the same time I'm injecting excess holes onto the n-side so there's some excess hole charge q sub p and it will give me current also when I just add the two up. Now as we'll discuss in a minute here, this time is actually the average time it takes for one of these electrons or holes to recombine

and I'll talk about that in a minute, or it's the average time that it takes to diffuse to a contact where it will recombine quickly. So I'm kind of suggesting that every time an electron hole pair recombines I get current through my diode. So let's see how that works.

So this is an important point that I use to try to understand solar cells. Its recombination leads to current. So we have a forward bias diode. We've lowered that barrier, electrons can get injected over and now we have a population of excess minority carrier electrons in the p-side. Now

they can recombine you know in a number of different ways but one way they they could recombine is that there could be a defect even though silicon is very very pure. Well for solar cells you like to use less expensive silicon so it's not as pure as it could be but it's still very good. But there are

defect energy states inside the band gap. An electron could hop down into that and then hop down again and fill up a whole state. That's a dominant way. You know it could just hop directly from the conduction band to the valence band and that happens more more in some semiconductors that's the dominant way.

In semiconductors like gallium arsenide and 3,5 that's the way most of them occur and then that extra that energy that they lost in dropping down energy is given off as light. That's how you make a light emitting diode. In materials like silicon that's not the strongest recombination path it's through these defects

and the excess energy is given up to phonons and it just heats up the lattice. Okay so let's let's see what happens you know when that happens. The electron drops down fills up the hole. We've now lost a hole. The p-side was happy. It was electrostatically neutral.

You know it had just the right number of holes and just the right number of boron atoms that were ionized that's where the holes came from. Everybody was happy. Now we've destroyed a hole. There's an electrostatic imbalance. The system doesn't like that. So it reacts immediately by kicking an electron out of the valence band

to create a hole. Now the p-side is happy again. You know but the n-side isn't happy because it was electrostatically neutral. It had just the right number of electrons to be electrostatically neutral and balance the charge of the phosphorus atoms that were ionized to give us that electron.

Well that one electron flows through the power supply around the other side comes in the conduction band of the n-side and replaces the missing electron. So you can see anytime an electron or a hole recombine one electron flows in the external circuit. So diode current is all about recombination. Now

the electron might be able to diffuse all the way to the contact and the contact is usually a highly defective region. There's a lot of traps and interface states and a lot of ways it can recombine. If an electron gets to the contact and recombines quickly there the same thing happens. It doesn't matter whether it recombines in the bulk or whether it recombines at the contact.

All that matters is that it recombines and we send one electron around the external circuit. Okay so here's a summary of how the forward bias diode works. We lower the potential energy barrier by applying a positive voltage on the p-side. That allows us to

more easily, electrons can more easily hop over the barrier. We now have an excess population of electrons on the p-side. Those excess electrons, now the system always reacts. It's out of equilibrium. It always reacts by trying to restore equilibrium which means the system will try to promote recombination to get rid of

those excess electrons. When they recombine then one electron flows in the external circuit. So now we can develop an equation for the I-V characteristic. So current is charged divided by time. That q sub n

is the total number of excess electrons on the p-side. q sub p is the total number of excess holes on the n-side. And tau is the characteristic time. This is either the time it took to recombine through the defect or the time it took to diffuse to the contact and immediately recombine at the

contact. Whichever one is shorter. So the charge is going to be exponentially proportional to e to the qv over kt. In equilibrium, and we have this relation n p is equal to n i squared, the equilibrium charge of electrons on the p-side was

n i squared over the p-type dopant concentration. When I lower the barrier I increase that by e to the qva over kt. The minus one is so that when I'm in equilibrium I don't have any excess charge. q is only the extra charge

not the equilibrium charge. So my ideal diode equation, you can see that if I just take t or q and divide it by some t I'm going to get an equation that has some constant out front times e to the qv over kt minus one. So people call that either the Shockley diode equation or the ideal diode

equation. That's the simplest form of the description of the ideal diode equation. Now more generally if you work with p-n junctions a little bit you know that more generally you put a factor n in the denominator and you write the diode current as e to the qva over n kt.

So we've described a process that leads to a current that has an n equals one. There are other processes that lead to n equals two and I don't remember whether I discussed that in this talk but I surely discuss it in the next one. I'll have to remind myself about what's on board here.

So in practice if you measure a diode you should expect to see a diode ideality factor between n equals one and n equals two. If you get something that's like n equals one you say I have an ideal diode. Okay so dark iv, let's see.

Okay so let's take a quick look at here. This is a generic solar cell. So this is a generic you know not a record efficiency silicon solar cell but something that might be manufactured at reasonable cost so that dimensions and doping are fairly reasonable. It's built on a p-type layer.

It has a very heavily doped p-type layer on the back and I'll discuss that in a minute and then a bottom ohmic contact. It has a very thin n-type layer on the bottom actually 0.3 microns is not all that thin but it's relatively thin. The whole wafer is about 200 micrometers thick and you know it has I can't put a top contact

I can't put a metal contact across the whole top surface where I can't get I wouldn't let light in. I'm trying to make a solar cell. So there's a metal grid of fingers and you try to design the grid such that you obscure less than 10 percent of the

of the area with the metal grid. If you get it too fine you'll start adding some resistances and things. Okay so if I draw an energy band diagram if I look near the front region it's just like that energy band diagram that I sketched. This is a simulated one with a program called ADEPT and you'll hear about that tomorrow. Professor Gray will talk about it.

But you can see it looks just like the one we sketched. The n-type layer is doped pretty heavily so the Fermi level is actually inside the conduction band the p-type layer is doped moderately. Now if I go way back to the end remember that there was this heavily doped p-type region at the end so if I go way back at the end you know the whole structure is 200

microns thick if I go back in the final one micron or eight-tenths of a micron you can see that when the valence band gets closer to the Fermi level it means that I have more holes. So you can see the heavily doped region right at the back and then you can see it's a little bit more lightly doped there.

And actually this is something that we'll talk about in my lecture tomorrow. You can see an energy barrier there. We're going to insert excess electrons in the conduction band and you can see that there's an energy barrier there that they have to hop over if they are going to get to the contact. That's designed to keep them

from getting to the contact because the contact is a defect where they recombine. It's called a minority carrier mirror. So if you look at the IV characteristic again this is a simulated one using realistic material parameters and lifetimes and things.

If you look to the left you're on a linear plot and you might remember it takes about six-tenths of a volt to turn a silicon diode on and for significant current to start to flow. But if you look at it on a log plot that's the green plot you can see even below six-tenths of a volt there's a lot of current flowing and you can see it on a log plot. If you look very

carefully here you'll see that there's a region in the middle where n is almost exactly one and I explained the physics of what that was with those simple arguments earlier. If you look down near at lower voltages you can see a region where it's starting to increase

you know and depending on the band gap and the lifetimes and things it could go all the way to two. In this case it's just you just beginning to hint see a hint that something else is going on. We'll talk about that tomorrow. And then you see the dip down and what you're seeing there is just that minus one in the e to the qv over kt minus one. If you go up

to higher voltages you can see it starting to roll off just a little so n is a little bit bigger than one and that can happen for a couple of reasons the most common one is that there's a series resistance and we'll talk about that later on also. Okay so these are plots that I'm going to go through carefully tomorrow

but I just want to make a point here that I argued that the current is related to recombination so in order to understand the device you'd like to understand recombination inside the device so the blue line is the recombination rate. Now

you'd also like to know where are those carriers recombining because if you want to change the performance or improve the performance you might want to go in and re-engineer the cell to shut off some recombination mechanisms. The green line is the integrated total. Now you can see that there's a bunch of stuff happening right at the

beginning at that first three-tenths of a micron that you can't see you know so and there's a bunch of stuff happening at the end where it looks like the green line plot goes from 0 to 1 that's a hundred percent of the recombination. You can see that an awful lot of the recombination is occurring at that back contact

you know that little barrier we put there isn't keeping the electrons away and if I look in the front I can see that there's a significant amount of recombination in the front two orders of magnitude bigger than what's happening in the p-region that's because the lifetime is very very short in that very heavily doped material

recombining very quickly. So there's a lot of information that we can get out of that and that's sort of the subject of the talk tomorrow. I will mention that roll-off region I described this ideal diode but you put metal contacts on PNN type silicon you're going to introduce some contact resistance

so really any real device that you measure in the lab you'll have a series resistance and you'll only be able to apply your voltage to those two white terminals there. Meaning that when some of the current flows it'll be lost across that series resistance and the actual voltage that

gets applied across the diode V sub A the applied voltage across the junction will be less than the voltage that you apply across the terminals of the diode and as you get higher and higher in current you'll get more you'll lose more and more of that voltage you're applying in that series resistance and that's what causes things to roll off.

So here's a simulation of that same solar cell when you have a series resistance of no ohms you get that red dashed line that we showed earlier if you put a hundred ohms in you'll get that blue line and you can see it starting to roll off. So one of the things that people try to do in solar cells is to minimize that series resistance as much as possible.

So we'll talk about that later on too. So that's how the I-V characteristic works in the dark. When I did my PhD thesis I basically worked on dark current of solar cells and I would go home and my wife would say what did you do in the

lab all day and I said I'm working on the dark current of a solar cell and she thought this was the silliest thing to do. You shine the whole point of a solar cell is to shine light on it and why are you working on the dark current? Now I'll explain in a minute here. But let's talk about optical absorption so

just a few fundamentals. So you know the idea is this, light comes in it's got some wavelength it's got some energy that is Planck's constant times its frequency. If the energy is bigger than the band gap it can promote an electron from the valence band to the conduction band that will leave behind an empty state in the valence band

so now I've got a hole and it will give me an electron in the conduction band. So whether or not that happens will depend on the energy of the light that comes in so the energy must be big enough or the wavelength must be short enough such that I've got enough energy to create an electron hole pair.

So we have to think about this spectrum, you know, the solar spectrum is roughly I think a black body of about 6,000 degrees Kelvin I guess roughly approximately. If you go in outer space and measure the solar spectrum, so this is the amount of solar power

in each little wavelength integral, this is called air mass zero because there's no atmosphere for it to go through and be absorbed. So the solar spectrum will look like this. You can see some sharp lines here that have to do with things in the solar atmosphere

and if you integrate the power you get a hundred and thirty six milliwatts per square centimeter of solar power and when you make a solar cell you want to compare that to the electrical power that you get out and maximize the efficiency. Now if you look on the on the surface of the earth you'll get a slightly different solar spectrum

and it will depend on how much atmosphere you have to go through so that's going to depend on the latitude that you're at and what angle the sun is at. So people measure this thing, call it air mass, it's one over cosine of the angle to the normal and air mass

1.5 is sort of a typical condition for mid-latitudes in the US or mid-latitudes anywhere and it corresponds to a latitude of 42.8 degrees. So if you're at the equator and you're going directly through

you don't have to go through as much atmosphere. If you're up here at our latitude you have to go through and there are various gases, species, water vapor in the atmosphere that have absorption at particular frequencies so if you look at the blue line you can see that we have these notches where the solar spectrum that came in is

strongly absorbed in certain bands. So it's the blue line that's going to be the incident power for our solar cell if we're making a terrestrial solar cell and the G there means global so when people do these measurements there's a lot of diffuse scattering in the atmosphere so the beam that's coming down is not just a direct beam

there's some diffuse scattering too so when they do these measurements they include that so AM 1.5 G means it includes all of those global and diffuse effects as well and the total integrated power is exactly 100 milliwatts per square centimeter

so you may ask how can it be exactly 100 milliwatts per square centimeter? Well it isn't but it's just a standard so people have adjusted this spectrum so that it's exactly 100 milliwatts per square centimeter and everybody compares their efficiencies to a spectrum like this its intensity has been adjusted so it's exactly 100 milliwatts per square

centimeter so if you get 10 milliwatts out of your solar cell you know you have a 10 percent efficient solar cell okay so then you can ask yourself well how many photons can be absorbed? so if your solar cell is made out of silicon the band gap is 1.1 eV

so only photons with an energy above 1.1 eV can be absorbed or that means only photons with a wavelength below something that turns out to be close to 1.1 micrometers so if I look at that same solar spectrum I can only absorb the photons that have a short enough wavelength those are the ones in yellow

the rest of them are totally wasted they contain power they contain part of that hundred milliwatts per square centimeter but I can't take advantage of that in silicon just goes through so the total number of photons per square centimeter per second that I can get if I collect every one of those is 2.761 times 10 to the 17th

and that corresponds to a current of 44.24 milliamps per square centimeter these high efficiencies silicon cells are getting remarkably close to that okay so what happens to all of those a lot of those photons have an energy more than the band gap

so they put an electron way up in the conduction band somewhere then what happens? well what happens is it emits optical phonons sheds that energy and it just heats up the solar cell that's all wasted so that's one of the problems that you have in these solar cells is that you're just wasting the energy of any photon that has

more energy than the band gap so there are a lot of people that think about you know are there ways to prevent this from happening one way is to use a lot of different band gaps and just take a slice of the solar spectrum and use the right band gap for that right part of that spectrum that's how those over forty percent efficiency solar cells are made but people also

think about you know is there some scheme that I could get that electron out before it loses all of its energy and then I wouldn't waste it you know those are ideas that fall under this category of third generation PV okay now the question we have potentially

every photon with an energy above the band gap could be absorbed but if I have some finite thickness of solar cell not everyone will actually get absorbed some of them won't have a chance to so here I'm just pointing out that the incident flux is going to decay as e to the minus alpha x

so it will decay exponentially with position and alpha is the optical absorption coefficient if it's greater than zero it means electrons are being absorbed so I can compute the generation rate because as the flux decays the reason it's decaying is because electron hole pairs or photons are being converted into electron hole pairs

so I can just differentiate that position dependent flux and I get an expression for the generation rate versus position now that's at a specific wavelength so then I have to integrate over that complicated solar spectrum but all of that's easy to write a MATLAB script

these are things that my students did for me in a few of these plots that I'm going to show you now so your question is what determines alpha and this gets into some semiconductor physics that we won't be able to go into deeply but this gets into the details of the band structure so remember for a classical particle

energy is momentum squared divided by two times math now in a semiconductor crystal the momentum is really the crystal momentum h-bar k and we have some complex band structure but it oftentimes looks something like that now when the minimum of the conduction band and the maximum of the

valence band occur at the same momentum at zero we call that a direct band gap semiconductor now it turns out photons carry very little momentum so I can make vertical transitions there come in with an energy bigger than h nu I can make a transition up and I can conserve momentum and it's no problem materials like this

absorb light very efficiently now if you have silicon it's what's called an indirect gap semiconductor the minimum in the conduction band is at a different momentum than the maximum in the valence band the photon doesn't have much momentum so

in conserving momentum in exciting electron from the valence band to the conduction band what you have to do is to find a lattice vibration with the right momentum so that it's a it's an extra interaction with a lattice vibration that's less probable so the absorption coefficient is going to be weaker

so it's not going to be as efficient in absorbing as a direct band gap semiconductor is so here's an example so CIGS is a material copper, indium, gallium, diselenide is a material that is widely used for photovoltaic applications Professor Agarwal's lab does a lot of work on that over

here at Purdue silicon is also the most common commercial technology still today although some thin film materials are making significant inroads if you look at the percentage these are the percentage of photons absorbed you look at just the photons above the band gap what percentage of those are absorbed

versus thickness of the absorbing layer you can see that for CIGS that's a direct gap material one micron will absorb ninety percent of all photons that can possibly be absorbed for silicon you know I have to get closer to 10,000 microns of silicon if I want to absorb every photon because the absorption coefficient is much

weaker it's an indirect gap semiconductor so if you're looking to minimize material costs for low-cost photovoltaics you'd like to use a direct gap semiconductor because a very small amount of material can absorb all of the photons silicon it takes a very much thicker layer so to get as many electron hole pairs generated we have to get the light in

so people do things like anti-reflection coatings to make sure you get as many photons in and then you want to make the solar cell as thick as possible but sometimes there are tricks that you can use to make it effectively thick and this is one of the ways so this is a record efficiency silicon cell

from Martin Green's group at University of New South Wales it was over 24 percent efficient it's only got three to four hundred microns of thickness of silicon so it can't absorb all the photons but if you look at the structure it has a set of

etchings there along 111 planes so it gets inverted pyramids it creates this structure in silicon such that when the light comes in if it doesn't get absorbed if it doesn't get transmitted into the silicon it gets bounced off into another one it's got a chance to get transmitted there so it has a very low reflection

coefficient once the light gets in if it goes all the way to the back and hasn't been absorbed yet you can see that most of the on the back surface there's a thin layer there labeled oxide that oxide layer is about a half wavelength thick so that when the photons go down reflect off the metal back contact and

come back they interfere in phase so it's a layer that's designed to maximize reflection they go back through and they make a second pass when they make a second pass they hit most of those inverted pyramids at an angle that's above the critical angle so they're internally reflected and they stay in

and they go back down and they reflect out again that's called light trapping so it can make a physically thin layer of silicon appear to be very very thick so we get a chance to absorb the photons okay so we've generated the electron hole pairs we have to collect them if we collect them then we have a p-n junction

so the way we collect them is we just see that if we create a minority carrier electron on the p-side near the junction it'll just fall down in energy and go over to the n-side so the p-n junction collects the carriers that's why we use a p-n junction. So we have a

layer usually the top layer is relatively thin that was three-tenths of a micron in my example the absorbing layer is thicker so we can absorb all of the photons and what we want to be careful of is that the photons that we absorb, the minority carriers that we generate have to diffuse to the junction so that they can be collected and go out to

contact now some of them might recombine at a defect before they get to the junction some of them might diffuse backwards to the back contact where they can recombine so you want to engineer the structure so that most of them diffuse towards the front and are collected so a parameter that people will talk about is the collection efficiency

so it's the if JL max so if I know how many electron hole pairs are generated I multiply that by the charge on the electron that's the maximum current I could ever get the current that I actually get out J light is a little bit less than that and that ratio is called the collection efficiency for a high efficiency solar

cell you want that to be well over ninety percent and I'll just mention one of the nice things about a silicon cell is that you don't expect this collection to have much to do with the voltage it's just gonna fall down that barrier you know

if I apply a forward bias and I make the barrier a little smaller it'll still fall down that smaller barrier and go out the n-type so the collection is relatively insensitive to the voltage that I apply across the diode and I'll just mention briefly these electrons that are generated away from the junction

they typically diffuse before they recombine they can diffuse on the order of a diffusion length which is the square root of diffusion coefficient times time so we want a material that has a high diffusion coefficient or high mobility or material that has a very long lifetime so it has plenty of time to diffuse to the junction get collected now that's one of the reasons that you

can't make the layer as thick as you want because if you make it too thick it'll be more than a diffusion length away from the junction and it won't get there so that's one of the reasons that when people design cells like this you try to keep the absorbing layer physically thin

so that once you generate an electron hole pair it can diffuse to the junction and get collected. Okay so now we can talk about a solar cell. We've done it in the light and we've done it in the dark. So here's how it works the light creates an electron hole pair the p-n junction collects the electron hole pair

the electron goes out the end contact an electron going out the end contact runs around the external circuit and comes back in the p-type and that gives us a current that flows opposite to the direction of the arrow so the direction of the arrow tells us the direction

that the current flows when we apply a positive voltage to the p-side that's a forward bias junction the light generated current flows in the opposite direction so current flows it's flowing in the opposite direction of the arrow it flows through that resistor R which is the load that we're delivering the power to we're trying to do something useful with it

that creates a positive voltage that gets applied to the positive side that forward biases the diode and gives me a current that goes in the other direction so the net result is that I get some combination of those two so that forward bias lowers the barrier and now some electrons are being collected but other electrons are hopping

over the barrier in the opposite direction going to the to the p-side so what I get is the combination of the two and the simplest way I can think about this is it just behaves like a superposition so I had the current in the dark we discussed where that comes from now we have a current in the light and I discussed that it's more or less

independent of voltage it doesn't matter how big that barrier is once an electron gets close to it it just falls down the barrier goes out the n-type contact if I want the total IV characteristic of the solar cell I just add the two and I'll get a characteristic that looks like that

so that's why I've worked on dark current for my PhD thesis because then if somebody tells me what the light current is I just have to add it to the dark current and we can understand how the solar cell works so if we look at this again you can see that first of all you can see that the current is negative the voltage is

positive that means that the power which is the product of the two is negative what does a negative power mean it means I'm not dissipating power in the diode I'm generating power now if you look down at V equals zero the power is zero we have a lot of current so the power is zero if I look at

the open circuit voltage where no current flows I have a lot of voltage but no current so there's no power there somewhere in between I get maximum power that's where you want to operate the device and that's called the max power point and you can see that it's less than the product of the short circuit current and the open circuit voltage and it's less by a factor people call the fill

factor and the fill factor is something that you can't do a whole lot about it depends on the shape of the diode characteristic which is the Shockley diode equation you can make it worse but you can't make it better very easily and then the efficiency then is just to power out which is a short circuit current times the open circuit voltage times the fill factor

divided by the power in so I'll just mention briefly I told you I was going to fly through these and I'll do it a little more slowly tomorrow but this idea of superposition it's not immediately obvious why this should work you know so the idea is we take this light-generated current

we take this dark IV characteristic of the diode and we just add the two and we say that's how the solar cell works so I'll say a little bit more about that in a minute or two now there are going to be some non-idealities you know we're going to have a large p-n junction because we want to collect a lot of

sunlight and generate a lot of power there may be shorts here and there, shunt-passes, leakage mechanisms defects in the diode so that would be a resistor a shunt resistor that's in parallel with the junction that's not good it's going to lower the performance the contacts themselves are going to introduce some extra

resistance. That's RS, the series resistance. So if you do that, you can see here's the effect of taking that blue curve as the simulation of the device without any extra series resistance. If you add some extra series resistance in, you can see that it's lowering the current and the voltage at the max power point or it's lowering the fill

factor. So it's bad. People worry a lot about that. The shunt resistance does the same thing. So you worry about these kind of defects a lot when you're trying to make high efficiency solar cells. Okay, so we run a simulation so you can see what the IV characteristic

looks like. This is not a record 24 percent efficient cell, but it's not bad. It's 20 percent efficient. This is a typical thing you could do without lots of fancy expensive processing. Open circuit voltage is about 616 millivolts. Short circuit current, remember, what was that number? Anybody remember that? We said the maximum current that you could get if you absorbed

every photon above the band gap and collected every one of those was 42 or something? 44. Okay, so we get 39. So if we had a better design, we might be able to get a higher current. Fill factor is 0.83.

We haven't added any extra series resistance in this simulation. One ohm, so one ohm, people worry, you know, even one ohm is a significant series resistance for a solar cell and that lowers the fill factor a little bit. We could get a little bit higher if we didn't have any. Okay, then I'm just gonna wrap up here

and say a few things and, you know, we'll get a chance to discuss these in more detail in some of the other talks. So this idea of superposition, you know, I told you that this was not maybe intuitively obvious as to why this should work. It really works well for silicon, and I'll show you this in my lecture tomorrow,

but it's not so easy to explain why, you know, and we just take this light current, we take the dark current, we add the two and we say superposition says that this will give us the response when it's illuminated. Now, you know, how can you justify this? If you have a

system that's described by a differential equation, if the differential equation is linear, you can add solutions. Okay, let's look at the differential equation to describe a semiconductor device or a solar cell. Here they are. The first one is divergence D is equal to rho, the charge density, this is

Gauss's law. The second one is divergence current density is equal to generation minus recombination. The third one is divergence of hole current is generation minus recombination. You know, the currents are given by drift diffusion equations. We have expressions for the recombination rate. The point is we have three

coupled nonlinear partial differential equations. It is really not obvious that you could take the solution in the light, you could take the solution in the dark and add them. There's no reason to expect that that would happen from these equations. Now it turns out that you can, and I'm still searching for a simple explanation of why this works so well in

silicon. We'll show you some simulations that show how beautifully it works, but to try to explain why it works takes a little bit of work. There have been a few papers about this. I haven't been able to boil it down to a one-line explanation. You know, they can establish some conditions under which

if these conditions hold, you can expect to see superposition. But there are many solar cells, especially thin-film solar cells that contain more defects than high-quality crystalline silicon for which superposition does not apply. Now we should talk briefly about efficiency limits.

You know, what determines the limit efficiency? So we have only three things to think about. Short-circuit current, open-circuit voltage, and fill factor. We can understand those three factors. We can understand efficiency. The fill factor is just determined by the shape of the IV characteristic, which is the diode characteristic. That's pretty fundamental. We can't

change that very much. We can make it worse if we have too much series resistance. So we'll spend a lot of time trying to reduce series resistance. Now the short-circuit current, well, the smaller the band gap, the more photons I can absorb from the

solar spectrum. So the short-circuit current strongly depends on the semiconductor that I've chosen. If I've chosen a given semiconductor, then I have to work hard to minimize the reflection of photons from the top surface, to maximize their absorption in the layer, and to minimize their recombination. Now the open-circuit voltage. So the open-circuit voltage has something to

do with Vbi, and Vbi goes as proportional to the band gap. So what you'll find is that as you increase the band gap, the open-circuit voltage increases. So there's a very classic paper that if you work on solar cells, everyone needs to study the Shockley-Kweezer paper.

This is a very famous paper where back in 1961, they did a calculation to try to determine the theoretical upper limit efficiency of a solar cell. And they did it so well that everybody has used it ever since. But the results are kind of intuitively easy to see.

If you have a smaller band gap, the smaller your band gap, the higher the short-circuit current. So what you're seeing on the bottom axis, on the bottom that's a normalized band gap, on the top you can see it in electron volts. As you increase the band gap, the efficiency gets better and better because you have

more and more photons that you can absorb. Now larger band gaps give higher voltage. As you increase the band gap, you have fewer and fewer photons that you can absorb, but the open-circuit voltage is increasing.

So that's why the efficiency goes up. As you keep increasing the band gap, the voltage keeps going up, but the number of photons that you can absorb goes down, so the current drops. So there's some peak there, there's some optimum band gap, where you're extracting for that particular band gap, you're getting the most photons that you can get

at the highest voltage that you can get. It turns out that that peak, look how nice that is, that peak is just a little above one electron volt. That's silicon. It turns out that silicon is very very close. You just calculate it a little more carefully, it might be a little bit above. Gallium arsenide is also very close to the optimum. So if you're going to pick

one band gap, you'd pick something around just a little above one volt to give you the best efficiency. And you can see the numbers here. The best that you could possibly get is a little over 40%. I think people have refined these calculations and the optimum is felt to be a little bit lower than that now.

But it's up around 40%. So when you're doing solar cells, you know there are three things you're trying, you're basically trying to reduce the cost of producing electricity because that's what's needed in order to make solar cells economically viable. So one thing you can do is to have very high efficiencies.

But it's usually very expensive. You saw that Martin Green cell that I showed you. Processing that is very expensive. You can try to produce cells that have good enough efficiency but at very very low cost. And then you would use cheaper materials,

thin film materials, polycrystalline materials that you don't have to epitaxially grow and that are very expensive and take high temperature processing. A third approach which is really related to the first is you could use concentration. And the idea there is you spend a lot of money on a very high efficiency small cell and then you have a very big set of optics to collect lots of solar energy

and focus it down on that. So most of your expenses is in the optics to focus it down onto a smaller cell that you can afford to make more expensive. So those are the three general approaches. The thing that people are after these days in trying to solve energy challenges is something you call grid parity.

And they go through these economic analyses and in order to get electricity that's at five to six cents per kilowatt hour, you need to have a system that you can, you need to install a PV system at about a dollar a watt. So if you build a

hundred megawatt system it will cost you a hundred million dollars. And if you can do that then all of the costs will translate. You can charge five to six cents per kilowatt hour and it can be competitive with other sources. And the system includes more than just the solar cell. So you package all of these solar cells and you wire them up into a module

and then you have to have power conditioning electronics to take that fluctuating DC that comes out and put it into AC and put it onto the grid. And you have all of these, you have to install them and you have to clean them and you have to do everything else that it takes to maintain them and operate the system.

Now the current costs, 2011, are about three dollars and forty cents per watt. So that's a long way from where it needs to be in order to be economically competitive. If you just look at what's happening and the improvement in manufacturing processes, by 2016 it should be down to two dollars and twenty cents a watt.

But that's still more than double where it needs to be to be competitive. So this is a big research challenge that people are looking at. These are some numbers from the Department of Energy and they're sort of showing you in 2010 this is where we're at. In 2016 that's where we're projected to be and this is where we need to be to start being competitive.

And you can see how it's broken down into the power conditioning electronics are very efficient. That only contributes ten cents or contributes twenty two cents now and it has to drop in half. But the cell part has to get down to fifty cents per watt

for the module. So that's not just one cell, you hook a whole set of cells together in a module, you package them, encapsulate them so that they'll last for thirty years. The efficiency drops a bit after you do all of that. You've got to be able to do that module at fifty cents per watt. We're at a dollar seventy a watt now. So more than a factor of three reduction is needed.

So that's the challenge. It's different from those of us who work on integrated circuit chips and things where you know the value added comes because you put it in an expensive product, the cost of the chip is not that much. The manufacturing, you know you add the value in the design of a complex

microprocessor or something and the manufacturing costs are a relatively small fraction of the overall cost. We're just dealing with a p-n junction here. The manufacturing costs are really crucial. Okay, so summary. The solar cell is really very simple.

Light is absorbed, produces electron hole pairs. The junction separates those electron hole pairs, sends the electron out the n contact, the hole out the p contact. That current source as it's flowing in the external circuit induces a forward bias voltage that reduces the total current. The output power is short circuit current times open circuit voltage times fill factor

and as I just mentioned, everything is about cost in photovoltaics. Okay, so I can point you to a couple of references if you want to get a broader overview of the field and I'll stop there and see if we,

if I haven't warned you out, if there's a question or two, I'll try to answer it. We have one down here in the front. Thank you, and I wonder if it's possible to go to slide 24?

Which slide? Slide 24. Let's take a look at slide 24. See, I got through all 69 of my slides. And most of you are here. I'm going to tell my wife that.

Oh, that's not the one. Which slide? Oh, I might have done some editing since I passed that out. Yeah, okay. You said this equation is provided for your equations. Yes. And you have no idea, you know,

how do you treat the ideality and what kind of ideality you have? Yeah, so what, you know, I will say a little more about this in my next lecture. Yeah, you know, I'm not, so this is what people, I mean, this is what people call the ideal diode equation and you know, what they mean by that is that all of the recombination processes

are the kinds of recombination processes that I talked about. Carriers are recombining in the neutral N or P region. Carriers could also recombine in the depletion region. And that gives an N equals 2. Now there are lots of other non-idealities that we could talk about

tunneling through defects and things and things could get very complicated, but... You see how much it would really affect our simulations, how much it would be changed? 10%, 5% or 50%? Oh, no, I mean, you know, especially when you look at these low-cost photovoltaic materials

where you have thin films of polycrystalline material processed at low temperatures, there can be high levels of defects and there can be many of these non-idealities and it can be impossible to see an N equals 1 component anywhere. I mean, that can be the whole game.

Well, we'll see, maybe we'll come back to you if we have some... Yes, we have a...

Yeah, so I guess the question is, you know, what role does the charge collection efficiency play?

And if it's less than a, so we can easily take the solar spectrum and we can say, we can compute from that solar spectrum how many electron hole pairs are generated inside the solar cell.

So the best we can do is to collect every one of those and that would give us a short circuit current of 44 milliamps per square centimeter or something for silicon. Now in practice, you know, we lose some by recombination. And I'm going to say a little more about that in my next lecture. So different types of cells, you know, sometimes people design a cell where all of the generation

comes in this junction region where there's a strong electric field, which can take everything and quickly sweep it out to the right contact. There are other things you do to try to have minority carrier mirrors, so you make sure that the electrons don't diffuse to the contact and recombine there, you turn them around and have them diffuse towards the front.

But there's a lot of, a lot of solar cell design is all about trying to maximize that collection efficiency. That's going to be my message on my next lecture. It's just recombination and generation. That's all there is to the solar cell.

Alright, I'm not sure if I exactly, solar energy is free. I heard that, right?

Yeah, so I, you know, I may ask Professor Agarwal to comment on here because I think he's more of an expert than I am.

But I know people that do this economic analysis, they'll make some assumption for what is the lifetime of this solar array. And you know, and when you back all of that out, they say, okay, if we can build the initial system for one dollar per watt, we can build a hundred megawatt system for a hundred million dollars, and if it has their assumed lifetime, which is going

to be 20 or 30 years, and they do all of the other cost analysis, then they can make an economic case that they could charge electricity for five to six cents per kilowatt hour. So there are a lot of assumptions. Reliability is a really important factor in these solar cells. Because if it lasts for 30 years instead of 20 years, it's much easier to make

the economic case. You know, you just made that one time investment, and then the longer it lasts, the cheaper the electricity you produce is. Is that on?

Yes, it is, if you hold it close enough to your mouth. So, when energy photons are absorbed by a photovoltaic cell, some of the energy is lost to photons, right? And that's basically heat inside the device, right? Do people work on using thermoelectric principles to extract some of that excess heat?

Well, you should know that. You're from MIT, right? I just saw, didn't I just, I just saw a paper in, what was it, Nature or Nature Maybe Last Week from the Geng Chen Group, which is on my laptop to try to read. So, my understanding, I just looked at the title and I thought, oh, this sounds interesting.

So my understanding is that he's trying to take this waste heat, that for a solar cell, this is just waste, right? And to take that waste heat and couple the solar cells to a thermoelectric device and convert that into electricity and get a little more power out of it. I don't know.

I'm a little, you know, the efficiency of thermoelectric devices is not that great, but if you get it for free, you know, you've got that heat there and if it doesn't increase your manufacturing cost by much and you can get another 1% or even 2% out

of it, that would be very useful, yeah. So that's a good question, right? So it connects this lecture with the previous two lectures on thermoelectric devices.

Yeah, so you know what happened, we talked about energy relaxation time in the last lecture. So what happens is these carriers very quickly in picoseconds or a few tenths of a picosecond shed all of this excess energy and just relax down to the bottom

of the conduction band and you know generally that happens so fast that when we think about current flow we don't even have to account for those processes when we're looking at steady state currents and things. They very quickly thermalize.

Yeah, you get the electrical current but you don't get all of the energy because they've dropped down, you know, they've dropped down to the band gap, right? Now you've lost all of that, you've lost some portion of that energy that they had. You know, that's the whole idea of using tandem junction solar cells, multiple band gaps.

The size of the PN junction, well, I mean, so you need large-

Well, I mean, basically you want to collect light from as big an area as possible so that you would tend to think I want as big a PN junction as I can get. So there is-

No, not that I know of. But you know there's something related to that, maybe I could point out it might come up in the lecture tomorrow.

I'm looking for my Martin Green cell here. Now this is really a nice example of solar cell engineering. You'll notice how small, there's a small P-type contact on the end.

There's also another variety of solar cell that also gets near record efficiencies where the end layer is a small thing like that, they call them point contact cells. So there's a big piece of silicon that might be either N-type or P-type but the PN junctions, the N region and the P-type contact are very small

so they're trying to minimize the size of the PN junction so it's mostly absorbing materials. These PN junctions are very small so the carriers can diffuse to them and get collected but there's a lot of recombination and things that happen in the PN junction so if you can minimize that, those are called point contact cells.

Now I mean the area of the cell can still be very big but the area of the PN junction itself can actually be quite small. Alright, are we ready for a break?

See you're keeping all of these people from a break so I don't want to put pressure on you but it better be a great question. Slide 38? Alright, let's take a look at slide 38.

Now is that the right one? Because it generates heat when we have higher energy photons, when it's absorbing, it makes it a little bit warped, it makes the solar cell warp, yes?

That kind of heat could help this kind of solar cells to work better or the direct band gap will work better? Yeah, I'm not sure I exactly understand that question. You know, there actually is a direct band gap in silicon, right? There is a conduction band that's up there in higher energy

and the higher energy photons can be absorbed by that direct process. Oh, I think direct band gap would be better, yeah. Because it would take less, you know, everything is about cost.

You know, even if you can minimize the materials cost and you can absorb all of the photons in a very thin layer, it's always best to have a direct gap. You know, it is some parallel current flow path.

You know, it might be a defect. You know, you might have a crystal defect that goes right to the junction and just kind of shorts it out. You might have had a pinhole in your process so when you deposited the metal contacts, a little bit of metal went down and shorted out. You know, there can be all kinds of extraneous current paths that are, you know, can only be bad, right?

Thank you. Yeah.