1 00:00:05,770 --> 00:00:11,040 How can we determine the performance of a solar cell? Or in other words, 2 00:00:11,040 --> 00:00:17,500 how much of the energy in the solar spectrum can be converted into electrical energy? 3 00:00:17,650 --> 00:00:22,340 This is the first important question which will be addressed this week. 4 00:00:22,340 --> 00:00:29,660 First, in this block I will present a simple electrical circuit and corresponding current-voltage curves, 5 00:00:29,660 --> 00:00:36,660 which are able to describe the behavior and the performance of solar cells under illumination 6 00:00:36,690 --> 00:00:42,320 and under voltage bias, as we have discussed in detail last week. 7 00:00:42,320 --> 00:00:47,020 Before I do that, I will quickly summarize last week's important highlights 8 00:00:47,020 --> 00:00:51,630 concerning the physical working principle of a solar cell. 9 00:00:51,730 --> 00:00:56,560 Last week we have shown that we can dope semiconductor materials n-type and p-type. 10 00:00:56,960 --> 00:01:05,180 In p-type the holes are the majority charge carriers and in n-type the electrons are the majority charge carriers. 11 00:01:05,299 --> 00:01:10,679 If we have semiconductors in which one part is doped p-type and another part is doped n-type, 12 00:01:10,679 --> 00:01:14,350 we have created a so-called p-n junction. 13 00:01:14,350 --> 00:01:21,650 We have also seen that two different mechanisms control the transport of charge carriers in semiconductors: 14 00:01:21,650 --> 00:01:24,010 diffusion and drift. 15 00:01:24,310 --> 00:01:30,420 Diffusion is controlled by a density gradient, whereas drift is controlled by electric fields, 16 00:01:30,420 --> 00:01:36,679 which you can build in the p-n junction or apply externally. 17 00:01:36,679 --> 00:01:41,649 In a p-n junction the diffusion of majority charge carriers through the p-n interface, 18 00:01:41,649 --> 00:01:48,069 followed by recombination creates a space charge region or depletion zone at the p-n interface. 19 00:01:48,069 --> 00:01:54,179 In the dark and in thermal equilibrium drift of minority charge carriers and diffusion 20 00:01:54,179 --> 00:01:58,130 of majority charge carriers are in balance. 21 00:01:58,130 --> 00:02:03,479 If we apply a reverse bias on such p-n junction in the dark, the depletion zone gets wider, 22 00:02:03,479 --> 00:02:08,489 the diffusion of majority charge carriers is suppressed and only an extreme small current 23 00:02:08,489 --> 00:02:13,400 related to drift of minority charge carriers is generated. 24 00:02:13,400 --> 00:02:18,730 If we apply a forward bias on such p-n junction in the dark, the width of the depletion zone 25 00:02:18,730 --> 00:02:24,090 is getting smaller, the diffusion of the majority charge carriers is significantly enhanced 26 00:02:24,090 --> 00:02:27,560 and overrules the drift of minority charge carriers. 27 00:02:27,560 --> 00:02:33,340 The p-n junction becomes conductive and is able to generate a current. 28 00:02:33,340 --> 00:02:37,590 If we illuminate the p-n junction, the density of the minority charge carriers is increased 29 00:02:37,590 --> 00:02:41,800 many orders of magnitude and as a result the drift becomes dominant 30 00:02:41,800 --> 00:02:44,890 and the p-n junction generates a large current. 31 00:02:45,090 --> 00:02:53,070 Now, we are going to construct first an equivalent circuit in which we can describe the behavior 32 00:02:53,070 --> 00:02:55,960 of a p-n junction solar cell. 33 00:02:55,960 --> 00:02:59,970 We have discussed that in the dark a p-n junction behaves like a diode. 34 00:02:59,970 --> 00:03:04,600 A diode is an electrical element that if you apply a forward bias on it, 35 00:03:04,600 --> 00:03:10,200 it becomes conductive in one direction, whereas if you apply a reverse bias on it, 36 00:03:10,200 --> 00:03:15,890 a diode is hardly conductive and basically blocks the current in the opposite direction. 37 00:03:15,890 --> 00:03:23,560 P-n diodes are electrical elements used in many electrical circuits and their main function 38 00:03:23,560 --> 00:03:30,320 is to allow an electrical current in one direction and block an electrical current in the other direction. 39 00:03:30,430 --> 00:03:37,040 A p-n junction is represented by the electrical symbol shown here. 40 00:03:37,040 --> 00:03:41,430 It's a triangle with on top of its vertex a line. 41 00:03:41,430 --> 00:03:46,560 The triangle points in the direction in which the diode allows an electrical current to flow 42 00:03:46,560 --> 00:03:49,340 under forward bias conditions. 43 00:03:49,340 --> 00:03:53,819 In the opposite direction the diode blocks the current. 44 00:03:53,819 --> 00:03:59,660 So now we put the p-n junction in the dark and apply a reverse bias. 45 00:03:59,660 --> 00:04:05,690 The p-n junction generates an extreme small current in the block direction of the diode. 46 00:04:05,690 --> 00:04:10,120 The current direction in electrical circuits in general points in the direction in which 47 00:04:10,120 --> 00:04:12,310 the positive charges flow. 48 00:04:12,310 --> 00:04:18,940 It means that the electrons, which are negatively charged, flow in the opposite direction of the current direction. 49 00:04:18,940 --> 00:04:24,960 This implies that under reverse bias, the extreme small current in the block direction 50 00:04:24,960 --> 00:04:29,819 can be represented by electrons moving in the direction of the triangle. 51 00:04:29,819 --> 00:04:35,139 Now, we consider a p-n junction in the dark under forward bias. 52 00:04:35,139 --> 00:04:40,949 The p-n junction generates a significant current in the forward direction of the diode. 53 00:04:40,949 --> 00:04:47,270 As current direction is defined in the direction of the flow of positive charge, it means that 54 00:04:47,270 --> 00:04:53,050 under forward bias the electrons responsible for the current flow in the block direction of the diode. 55 00:04:54,639 --> 00:05:00,240 Note that the current under forward bias is opposite and much higher than under reverse bias. 56 00:05:02,430 --> 00:05:07,459 The relation between the current and voltage of a p-n junction can be illustrated in an so-called 57 00:05:07,459 --> 00:05:08,810 I-V curve. 58 00:05:08,810 --> 00:05:15,120 The vertical axis corresponds to the current of the p-n diode and the horizontal axis represents 59 00:05:15,120 --> 00:05:17,909 the voltage applied over the p-n diode. 60 00:05:17,909 --> 00:05:26,080 A negative voltage, reflected by the grey area in the I-V plot, corresponds to reverse bias voltages. 61 00:05:26,309 --> 00:05:30,569 As we can see the current is close to zero. 62 00:05:30,569 --> 00:05:36,350 Applying a positive voltage, reflected by the light yellow area, corresponds to the forward bias. 63 00:05:36,559 --> 00:05:42,910 Above a certain voltage the current starts to significantly increase with increasing the voltage. 64 00:05:43,419 --> 00:05:50,059 This is a characteristic I-V curve of an ideal silicon p-n junction in the dark. 65 00:05:50,059 --> 00:05:55,689 This I-V curve can be described by a relatively simple expression which shows that the relation 66 00:05:55,689 --> 00:05:59,930 between current and voltage is an exponential function. 67 00:05:59,930 --> 00:06:03,749 The I stands for the current at a given voltage V, 68 00:06:03,749 --> 00:06:08,839 q is the elementary charge of the electron, k_B is the Boltzmann constant 69 00:06:08,839 --> 00:06:12,749 and T is the temperature of the p-n diode. 70 00:06:12,749 --> 00:06:19,279 I_0 is the extreme small current in the block direction under reverse bias conditions. 71 00:06:19,979 --> 00:06:25,219 This current is very often referred to as the leakage current of a p-n junction. 72 00:06:25,219 --> 00:06:30,949 We won't derive why the current and voltage are related by this exponential expression, 73 00:06:30,949 --> 00:06:35,789 you only have to know for the moment that the I-V curve of a p-n junction in the dark 74 00:06:35,789 --> 00:06:39,330 can be described by this expression. 75 00:06:39,330 --> 00:06:44,969 If we put a very large negative voltage into this equation you can easily see 76 00:06:44,969 --> 00:06:50,880 that the exponential term becomes zero and the current is equal to the small leakage current I_0, 77 00:06:50,880 --> 00:06:53,150 close to zero . 78 00:06:53,150 --> 00:06:58,849 If we apply a large positive voltage, we see that we get a large positive current 79 00:06:58,849 --> 00:07:03,979 and the exponential term dominates over the -1 term in the equation. 80 00:07:03,979 --> 00:07:09,839 Note that the current on the vertical axis is positive, if the current flows in the forward 81 00:07:09,839 --> 00:07:16,819 direction of the diode, whereas it is negative if it flows in the block direction of the diode. 82 00:07:17,159 --> 00:07:21,309 Now we will illuminate the p-n junction using light. 83 00:07:21,309 --> 00:07:28,759 It means that we are going to generate a large current, dominated by the drift of the minority charge carriers, 84 00:07:28,759 --> 00:07:33,289 which is opposite to the forward direction of the p-n diode. 85 00:07:33,289 --> 00:07:38,259 This is represented in the equivalent circuit by a current source, 86 00:07:38,259 --> 00:07:41,029 which is connected in parallel with the diode. 87 00:07:41,729 --> 00:07:46,650 The electrical symbol of a current source is a circle with an arrow. 88 00:07:46,650 --> 00:07:51,339 The arrow points in the direction of the positive current. 89 00:07:51,339 --> 00:07:55,930 It means that the far majority of electrons in this equivalent circuit 90 00:07:55,930 --> 00:07:59,669 travel through the current source in the opposite direction of the arrow. 91 00:08:00,669 --> 00:08:07,669 The current generated by the light absorption is I_ph, where ph stands for photo. 92 00:08:08,629 --> 00:08:14,919 Note that the photocurrent is in the opposite direction of the forward current of the diode. 93 00:08:14,919 --> 00:08:17,249 Now we look at the I-V curve again. 94 00:08:17,249 --> 00:08:22,789 The red line corresponds to the I-V curve of the diode in the dark. 95 00:08:22,789 --> 00:08:27,719 Adding the photocurrent, the typical I-V curve of the diode shifts down the vertical axis 96 00:08:27,719 --> 00:08:34,190 in the direction of negative currents in reference to the forward bias direction of the diode. 97 00:08:34,190 --> 00:08:37,920 This circuit is the circuit for an ideal solar cell, 98 00:08:37,920 --> 00:08:42,840 this means that we have not included all types of electrical and optical losses. 99 00:08:42,840 --> 00:08:46,150 We will come back to that later this week. 100 00:08:46,150 --> 00:08:51,320 The IV- curve of an ideal solar cell can be described by a simple equation. 101 00:08:51,320 --> 00:08:57,080 The total current generated by an illuminated p-n junction is the photocurrent minus the 102 00:08:57,080 --> 00:09:01,530 current of the p-n diode in the dark. 103 00:09:01,530 --> 00:09:08,530 In the equations so far we have used current I which has the unit ampere. 104 00:09:08,530 --> 00:09:15,240 This is sometimes not the most convenient unit to express the electrical response of a solar cell to light. 105 00:09:15,240 --> 00:09:22,800 If we would increase the area of a solar cell, it means that the total current of the solar cell is increasing as well. 106 00:09:22,870 --> 00:09:26,620 So the current depends on the area. 107 00:09:26,620 --> 00:09:34,260 In the lab, researchers like to use the unit current density J, this is the current generated per area. 108 00:09:34,260 --> 00:09:39,610 The advantage of this unit is that you can compare different solar cell technologies, 109 00:09:39,610 --> 00:09:45,440 as not every technology generates the same amount of current per square meter. 110 00:09:45,440 --> 00:09:51,800 If we assume that A is the area of a solar cell, the current density J is equal 111 00:09:51,800 --> 00:09:55,440 to the current I divided by the area A. 112 00:09:55,440 --> 00:10:03,530 So, the current density is expressed in milliamperes per square centimeter or amperes per square meter. 113 00:10:03,530 --> 00:10:10,140 As you see, the vertical axis of the current-voltage plots are already expressed in current density. 114 00:10:10,140 --> 00:10:17,400 From this point on, we won't talk about I-V curves, but we will talk about J-V curves. 115 00:10:17,400 --> 00:10:20,510 So from now on we will use current density. 116 00:10:20,510 --> 00:10:26,470 Summarized, I have introduced an electrical circuit and simple expression which describes 117 00:10:26,470 --> 00:10:32,470 the behavior of a p-n junction solar cell under voltage biasing and illumination. 118 00:10:32,470 --> 00:10:38,030 This behavior can be represented in a so-called J-V curve. 119 00:10:38,030 --> 00:10:41,970 How does this J-V curve relate to the performance of a solar cell? 120 00:10:41,970 --> 00:10:47,630 Or in other words: the conversion efficiency of light energy into electrical power. 121 00:10:47,630 --> 00:10:50,700 I will answer this question in the next block.