The Solar Cell

Transcript

0:00Introduction

Hello everyone! Let us start with a small puzzle. Think of a rooftop solar panel. There is no battery inside it, and nobody connects any supply across it. Yet the moment sunlight falls on it, current flows out of it and runs your circuit. So who is pushing that current? Soon you will know, and also why a cell never gives all the power its two numbers seem to promise. Solar cell questions do come up in JEE, so let's begin.

0:30Solar cell: light in, emf out

So, first, the solar cell itself. It is a p-n junction, just like a diode, but made with a large area, okay? When light falls on it, it produces an e m f, an electromotive force, all by itself. Right? This is called the photovoltaic effect. And notice the second part: no external bias is applied, no battery at all. Clear? Now the working, in three steps. Light falls on the junction, so what does it make first? Yes, exactly, it makes electron-hole pairs, and that is step one, generation. But only when h nu is greater than E g, the greater-than sign on screen. Here h is Planck's constant, and nu, the Greek letter that looks like a v, is the frequency, so h nu is the energy of one photon. And E g, the E with a small g below it, is the band gap. With me? Now remember, there is no battery. So what pulls the electrons and the holes apart? It is the junction field, across the depletion layer, and this is step two, separation. It sends the electrons, the e with a small minus sign at its top right, to the n-side, and the holes to the p-side, okay? That answers our puzzle: the junction itself does the pushing. Got it? And step three is collection, at the contacts. The holes gather on the p-side, so the p-side becomes positive, and the n-side negative. Connect a load, and current flows through it. Clear?

2:02Fourth quadrant: the cell gives power

Now the course's figure. On both graphs, capital I is the current and capital V is the voltage. On the left is the photodiode from the previous lesson, in reverse bias, with one curve for each intensity, I one, I two and I three. The label below says the intensity for I three is greater than for I two, which is greater than for I one, and the photocurrent is proportional to intensity. On the right, in orange, is our solar cell, with no external bias. Okay? Now look at the orange curve. In which quadrant does it lie? It lies in the fourth quadrant, as the label says: the voltage is positive, but the current is negative. Right? Here is the reason. The p-side is positive, so the voltage is positive. But the current flows out of the p-side into the circuit, opposite to the forward current of a diode. So the cell supplies current to the load; it does not draw it. It delivers power. With me? Two points on this curve matter most. Where it meets the voltage axis, the current is zero. That voltage is the open-circuit voltage, V o c, the V with the small letters o c below it. Clear? And where it meets the current axis, the voltage is zero. That current is the short-circuit current, I s c, the I with the small letters s c below it. Every cell is specified by these two numbers. Got it? So, is the maximum power simply V o c times I s c? It is not, and this is a classic trap. At V o c the current is zero, and at I s c the voltage is zero, so the cell never gives both at once. The maximum power, P max, the P with the small word max below it, is only a fraction of V o c times I s c. On screen, the fill factor in brackets, then the cross, the times sign, then V o c times I s c. That fraction is called the fill factor. Okay?

3:57Choosing the material, and efficiency

Next, the material a solar cell is made of. The best materials have a band gap of one point zero to one point eight electron volts, the e V on screen. And sunlight is strongest near one point five electron volts, the peak of the solar spectrum. With me? So tell me, why not use a material with a much larger band gap? Because then most photons from the sun have less energy than the gap, so most of them go unused. Right? And a much smaller gap is no good either. Then each photon carries far more energy than the gap, and most of that energy is lost as heat. Clear? So the favourites sit near the peak: silicon, S i on screen, with one point one electron volts, and gallium arsenide, G a A s on screen, with one point four three electron volts. Got it? The material also needs strong absorption of light, good conductivity, easy availability and low cost. With me? Finally, the efficiency of a cell. Efficiency is the maximum electrical power, over the light power incident on the cell.

5:03Example 1: max power with Voc, Isc and fill factor 0.75

Okay? Now the first example. This solar cell has V o c of zero point six volts, the capital V for volt, and I s c of forty milliamperes, the m A on screen. Its fill factor is zero point seven five. Find its maximum power. Pause the video and try it first. Done? Okay, let's check. First, forty milliamperes is zero point zero four amperes. Now, many students just multiply V o c and I s c. Is that the answer? Zero point six times zero point zero four gives zero point zero two four watts, the capital W for watt, which is twenty four milliwatts, written m W on screen. But that is not the answer, because it ignores the fill factor. Right? So, P max is the fill factor, zero point seven five, times zero point six, times zero point zero four. Clear? That gives zero point zero one eight watts, which is eighteen milliwatts. That is only three quarters of the twenty four milliwatts the two numbers seemed to promise, just as our puzzle said. Got it?

6:07Example 2: efficiency of a Si cell for 620 nm light

Now a harder one. In a silicon solar cell, each absorbed photon of wavelength six hundred and twenty nanometres, the n m on screen, delivers at most zero point six electron volts of electrical energy to the load. What is the largest possible efficiency for this light? Pause the video and try it first. Done? Okay, let's check, starting with the energy of one photon. The course rule says E in electron volts is one thousand two hundred and forty over lambda in nanometres, where lambda, the Greek letter on screen, is the wavelength. One thousand two hundred and forty over six hundred and twenty gives two electron volts. Okay? Two electron volts is more than E g of silicon, one point one electron volts, so the photon can make a pair. Right? Now the efficiency. Do we divide zero point six by the photon energy, or by the band gap? We divide by the photon energy, two electron volts, because efficiency compares the electrical output with the light that falls on the cell. Zero point six over two gives zero point three, which is thirty percent, the percent sign on screen. Dividing by the band gap is the trap here. Clear?

7:22Quick revision: fourth quadrant, Pmax, best band gap 1.5 eV

So, quick revision. The solar cell needs no bias: light generates pairs, the junction field separates them, and the contacts collect them. Its characteristic lies in the fourth quadrant, and the maximum power is the fill factor times V o c times I s c. The best band gaps sit near one point five electron volts, and efficiency is the output power over the light power. Now try the practice problems on this page. All the best!