 Let us now look at two very simple ways of measuring lifetime in a solar cell. The first is the open circuit voltage decay and the second is the reverse recovery transient. Let us first look at open circuit voltage decay. What does it mean? Think of a solar cell. You know that when light is shining on the solar cell, it will generate some voltage. What would happen if the light is suddenly turned off? Well, what would happen is that the carriers which have been generated due to the light eventually will die out and as they die out, the open circuit voltage will decay. How do these carriers die out? They die out by recombination and therefore, if we can measure how the open circuit voltage decays with time after the light is shut off, we will be able to tell what the lifetime is or we will be able to calculate what the lifetime is. So, that is the basis of the open circuit voltage decay measurement. The question is now how can we devise an experiment in which the light is turned off very quickly. For example, could I have a mechanical shutter, the light is shining on my solar cell and then I quickly close the shutter and the light goes off? Will that work? The answer is no, it would not work because the lifetime of the carriers in a solar cell are typically of the order of microseconds and the time taken to close a mechanical shutter will definitely be of the order of fractions of a second. So, it will not be able to capture that very fast turn off or the very fast decay of the carriers if I were to do a mechanical shutter. So, what is the way we can do this? Well, there are various ways and of course, in that setup which I had showed you some time ago, people use very expensive ways of doing it, but actually you can do it in a very simple way. That is to use a light emitting diode to turn off the light very quickly. Fortunately, a light emitting diode turns on and off very fast. So, if I have a light emitting diode shining light on a solar cell, I can turn it off very quickly and thereby capture the open circuit voltage transient. So, that is the first thing which we will do and that is the open circuit voltage decay experiment. The second experiment will be the reverse recovery transient. This is actually a well known experiment for all diodes and what here we would do is to really look at how a diode when it is forward biased and then switch to reverse bias, how long it takes to turn off? I will draw a very simple circuit here which shows the kind of circuit we will be using in the experiment. I will apply a square voltage positive voltage V f negative voltage V r, put it into the diode which is the solar cell and simply put a resistor and I will measure the voltage across the resistor as my output voltage. The voltage across the resistor is really proportional to the current flowing through the circuit. What happens in a case like this? Well, when the positive, when the voltage is positive at plus V f, a positive current will flow through the diode, current will flow through the resistor and I will get some current which I will call I f flowing. Now, plotting the current versus time, here is the current flowing through the solar cell as a function of time. What happens when the voltage goes to a negative voltage V r? Well, initially what happens is that because of the diode really acts like a capacitance, this change of voltage is transmitted through to the resistor out the current goes negative to some value of approximately of value minus I r and now what happens is until, until the diode is turned off, the current stays negative and then only gradually decays to 0. So, here is a reverse recovery transient and how long does it take to recover back to 0 or how long does the current remain at this value minus I r? Well, that is the time we will call the storage time. What is the storage time dependent on? Well, again in this case also the storage time does depend upon the life time because the larger the life time, the more time it will take for the diode to switch off for all of those excess carriers to be removed. So, the larger will be the storage time T s, but in this case there is another thing also and that is the values of I f and I r also determine how quickly the diode turns off. The reason is that this reverse current I r actually pulls out the charge. In other words, there is now two ways of removing the charge firstly by recombination and secondly by the reverse current which pulls out the charge and takes it away. So, both of these things, the life time of the excess carriers as well as the reverse current and for that matter the forward current all contribute to the storage time T s and in fact, you can derive this equation. The storage time T s is tau 0 which is the life time ln of 1 plus I f by I r. So, this is a nice experiment to perform by varying I f and I r and measuring storage time we can actually plot T s versus ln 1 plus I f by I r the slope will give us tau 0. You can see that the kind of experiments we are now looking at the open circuit voltage decay and the reverse recovery transient are really very simple experiments. You just need a simple pulse generator and a very simple oscilloscope to capture this transient and you could actually set up these two experiments total cost of a few hundred rupees really for the solar cell and the LED and probably a few thousand rupees when you include the equipment that is a pulse generator and the oscilloscope which is required. So, these two very simple methods allow us to at least estimate the life time very quickly and very easily. Also because there are two methods we will be able to compare the two results of the life time which we get and that will tell us what the and that will tell us whether the experiments are working and the two values of tau 0 should be approximately the same. So, let us now go and have a look at the experimental setup and see what is happening. So, here is the solar cell. So, solar cell made by Bharat electronics limited and here is the LED it is a small LED bank. You can see that it is being the LEDs are flashing on and off as controlled by the pulse generator. If I change the frequency of the pulse generator I can increase the frequency of the flashing. What I am going to do really for my open circuit voltage decay now is to adjust the frequency to what I need put the LED bank in close proximity to the solar cell and then try and measure the open circuit voltage decay. The solar cell is just open circuited and I can measure the open circuit voltage decay. What we have done now is put the solar cell and the LED in here. The LED is being driven by this simple function generator at about 2 kilo hertz. The solar cell is just open circuited. I am taking the output voltage here and feeding it into the scope. Here is the input voltage which is driving the solar cell. It is just a square voltage going from about 0 volts to about 10 volts or so. Of course, at the input of the circuit I do have a resistor here about a 100 ohm resistor which limits the current, but it drives the LEDs and the LEDs are flashing on and off as we had seen some time ago. I am measuring now the output voltage. Here is the output voltage. You can see that the output voltage is decaying with time slowly as the carriers which are generated finally disappear. You can see incidentally that when the light turns on, here is the light turning on when the voltage goes positive. When the light turns on, the transient is really very fast because the carriers get generated very rapidly. Lifetime really does not come into the picture there, but now when the light goes off which happens on this transient, you can see that the output voltage which is the open circuit voltage decays rather slowly and that is the open circuit voltage decay which we have to capture. So, by looking at this output voltage, we can estimate what the slope of this open circuit voltage decays and from that we can measure the lifetime. If I look at this, I should measure the slope in the initial part of the characteristic and it is approximately if I look at this, it is at about 0.2 volts per division. So, it is about 0.2 volts just trying to measure the time. It is 0.2 volts and this is about, it is about 100.1 millisecond per division or 100 microseconds per division. So, this is about 90 microseconds. So, the initial slope is about 200 millivolts upon divided by 90 microseconds and we will use this data to calculate the lifetime. We know that the lifetime is given by this equation. You can try to derive it, not very difficult to do. Tau 0 is kT by Q, that is a thermal voltage into 1 upon dV OC by dt, which is dV OC by dt is the slope of the transient which we have just measured. So, in our case kT by Q of course is 25 millivolts, 1 upon dV OC by dt we have just measured, it turned out to be 200 millivolts in 90 microseconds. So, I would write it down like this, so that this becomes 25 millivolts into 90 microseconds upon 200 millivolts. I can cancel this out, this goes 8 times. So, you can see I get about 11.2 microseconds. So, according to this measurement the lifetime of the carriers in this solar cell is about 11.2 microseconds. Let us now compare this measurement with the value of tau 0 which we will get from the reverse recovery transient. Here is the simple reverse recovery transient set up, basically I have a function generator which is feeding a square wave which is captured here to the circuit which is the solar cell and the resistor. It is driving that circuit and the output voltage which is the voltage across a resistor and therefore, the current flowing through the solar cell is captured here. You can see that when the input is positive, there is some positive current I f which is flowing when the input goes negative, the output current goes negative goes through the transient and then comes to 0. It is not very easy to find out where is exactly the storage time, but we will try to estimate this the best as we can. For that let me do this, I will just change the oscilloscope settings a little bit. Let me make sure first of all where is the 0 of this? Here is the 0, let me put the 0 at this point. Let us put the 0 here, here is the 0, put the 0 here that will make it convenient. So, in this case you can see that here was the 0, here is a pretty large forward current, here is a large reverse current. The value of the resistor is 100 ohms, I am measuring the voltage on 2 volts per division. So, you can see that this is about 2 for about 4.8 volts divided by 100 ohms. So, that gives me about 48 milliamps is the forward current. So, let me write that down in this case reverse is about 1.6 volts divided by 1.6 volts. So, this divided by 100 that is 16 milliamps. What I can now do is to change IF and IR and try to see how the storage time changes. For this particular case how much is the storage time? Well, I estimated to be approximately half a division here and half a division because this is at 50 micro seconds per division, half a division gives me about 25 micro seconds. So, I am writing down 25 micro seconds. Now, I can change IF and IR, easiest way to do that is to change the DC offset of the function generator. So, for example, I can put it at about 4 volts which gives me 40 milliamps in the forward direction. The reverse is about 2.4 volts that is 24 2.3 volts. So, say 23 milliamps. So, this is about 40 milliamps and the storage time you can see has reduced a little bit. My estimate is that it has gone down to about 20 micro seconds. I admit that it is not very easy, but you will have to do the best as you can. Change the offset voltage even more. The forward current is now 24 milliamps. The reverse current is now about 40 milliamps and the storage time has now become I would say about 15 micro seconds or so. And then reduce, change the IF and IR even further. In this case, now the forward current is, I have to adjust the level to trigger it. The forward current is about 12 milliamps. The reverse current is about 54 milliamps and the storage time now has become very small at about 10 micro seconds. So, these are the data which we have got. Now, we can just try to see what results we get from this data. So, here is the data we have got. IF and IR we have taken from the oscilloscope and of course, the storage time TS also we have taken from the oscilloscope. I have now calculated IF by IR and ln of 1 plus IF by IR. So, this completes our data and the best thing now to do is to plot TS the storage time versus ln 1 plus IF by IR and the slope of this plot should give us tau 0. Let us do that. Here is the plot of the storage time TS versus ln of 1 plus IF by IR from the table. I have plotted the points here. You can see that it is a reasonable straight line as expected from the theory. I have got the straight line here and here is the slope I am calculating and the slope turns out to be 13 micro seconds divided by 1 and that turns out to be about 13 micro seconds. So, from this I get the value of tau 0 to be about 13 micro seconds. Compare that with the value which we got for the from the open circuit voltage decay which was 11.2 micro seconds. You can see that these two are comparing quite well with each other. Given the simplicity of these two experiments, it is really very good that the values of tau we get by the two methods are within about 10 to 20 percent of each other and that gives us confidence at the value of lifetime that we are measuring is quite correct. It should be noted that these are typical values about some tens of micro seconds, typical values which we would see for a solar cell. So, that also actually confirms that our measurements are probably correct. So, this completes our experiment now. This experiment has to do with the measurement of lifetime in a solar cell. The lifetime is one of the most important parameters for a solar cell and basically it tells us how rapidly the excess carriers, the electrons and holes generated by the shining light, how rapidly they can recombine. Why is this important? Well even a simple qualitative understanding of the operation of a solar cell tells us why lifetime is important. For example, just imagine I have a solar cell, light is shining on it. What is the effect of the light shining on the solar cell? Well first of all of course, light shining on the solar cell what it does is generates electron and hole pairs. As light continues to keep shining of course, the holes and electrons keep getting generated, but this process cannot go on indefinitely otherwise the number of electrons and holes in the solar cell will become infinitely large. What happens obviously is that the generation of electrons and holes is actually reduced by the recombination which takes place. So, as the carriers are getting generated they are also recombining, the recombination annihilates the electrons and holes and eventually causes them to reach a steady state where the generation and the recombination just match with each other. In a solar cell would I like the lifetime of the carriers, the lifetime by lifetime I mean how long does it take for the electrons and holes to recombine. Would I like this lifetime to be large or small? The answer is I would like it to be as large as possible because if the lifetime is large then the recombination does not take place very easily. In other words when the carriers are generated they stay alive for a long time and this gives a chance for many more carriers to be generated. If more carriers exist in the solar cell I will get larger current short circuit currents, larger open circuit voltages. So, I would like to have as large a lifetime as possible in a solar cell. Of course there are some other types of devices for example think of a switching transistor where I want the lifetime to be very small because I want things to switch back and forth rapidly and that could only happen if the lifetime is small. But anyway coming back to the solar cell you can see that the lifetime is important and I must try to increase the lifetime in the solar cell to get better and better performance of the solar cell. So, measurement of lifetime becomes very important whenever I am fabricating a solar cell and of course one of the key parameters which the manufacturer of the solar cell will keep monitoring is indeed the lifetime in the solar cell. So, lifetime measurement is important and this experiment really will tell us how to measure the lifetime in an existing solar cell. There are actually many fairly expensive and complex equipments available to measure the lifetime I will show you some of them two of them here. Here are two lifetime measurement setups can either use if you look see this is basically the photo conductance lifetime tester and it has an optional suns VOC stage and I can measure the lifetime in a wafer or in a fabricated solar cell using this fairly sophisticated setup. Unfortunately the problem with this is that it is sophisticated but also it is quite expensive this costs about 20 lakhs or so and therefore it is really not very easy to replicate when I want to get some simple estimate of the lifetime.