WEBVTT - generated by Videoportal Universität Freiburg 1 00:00:13.400 --> 00:00:18.840 Welcome to the PV online course, in this chapter we will cover how a solar cell works. 2 00:00:19.520 --> 00:00:23.880 In this teaching unit we deal with the transport of charge carriers. 3 00:00:25.280 --> 00:00:27.440 We are looking at a box. 4 00:00:27.440 --> 00:00:32.280 This box has 4 sides that are closed and 2 sides that are open. 5 00:00:33.040 --> 00:00:35.800 In the illustration, these are the right 6 00:00:36.000 --> 00:00:38.080 and left sides respectively. 7 00:00:39.240 --> 00:00:42.480 There are a total of 10 particles in the box, 8 00:00:43.000 --> 00:00:46.440 which can move completely freely and chaotically. 9 00:00:48.320 --> 00:00:50.920 You can imagine the particles as gas. 10 00:00:52.080 --> 00:00:54.360 On average, as many particles 11 00:00:54.360 --> 00:00:57.360 will leave the box to the right side as to the left side. 12 00:00:58.120 --> 00:01:00.000 Of course, this is only a thought experiment. 13 00:01:01.000 --> 00:01:04.000 In reality, the box is a semiconductor crystal 14 00:01:05.000 --> 00:01:07.000 with 10 million free charge carriers. 15 00:01:08.000 --> 00:01:12.000 On average, 5 million would leave the crystal to 16 00:01:12.000 --> 00:01:15.000 one of the two sides. 17 00:01:16.000 --> 00:01:18.000 Now let's look at 5 18 00:01:18.000 --> 00:01:22.000 of these boxes with freely moving particles. 19 00:01:22.000 --> 00:01:24.000 The boxes are connected to each other. 20 00:01:25.000 --> 00:01:28.000 The number of particles in the boxes 21 00:01:28.000 --> 00:01:30.000 decreases from left to right. 22 00:01:31.000 --> 00:01:35.000 The box on the right has 2 particles less than the box on the left. 23 00:01:36.000 --> 00:01:39.000 We now look at the interface between the box 24 00:01:39.000 --> 00:01:43.000 with the 6 and the 4 particles. 25 00:01:43.000 --> 00:01:48.000 From the left box 3 particles will diffuse to the right. 26 00:01:48.000 --> 00:01:51.000 From the right box 2 particles will diffuse to the left. 27 00:01:52.000 --> 00:01:55.000 In sum, 1 particle moves to the right, 28 00:01:56.000 --> 00:01:59.000 so there is a particle flow 29 00:01:59.000 --> 00:02:01.000 of one particle to the right. 30 00:02:01.000 --> 00:02:04.000 This particle flow can be described by the diffusion law: 31 00:02:06.000 --> 00:02:10.000 The number n of particles diffusing through a given area A 32 00:02:10.000 --> 00:02:15.000 is proportional to the particle concentration gradient dn/dx. 33 00:02:17.000 --> 00:02:20.000 D is the 34 00:02:20.000 --> 00:02:23.000 constant of proportionality between the particle flow 35 00:02:23.000 --> 00:02:27.000 and the concentration gradient and is called the diffusion constant. 36 00:02:28.000 --> 00:02:31.000 The particles diffuse to the location 37 00:02:31.000 --> 00:02:33.000 with lower particle density. 38 00:02:34.000 --> 00:02:38.000 The direction of diffusion is therefore opposite to the direction 39 00:02:38.000 --> 00:02:42.000 of the concentration gradient - this is the reason for the minus sign 40 00:02:43.000 --> 00:02:46.000 in front of the diffusion constant. 41 00:02:46.000 --> 00:02:51.000 Diffusion takes place as long as there is a concentration gradient. 42 00:02:53.000 --> 00:02:56.000 The diffusion law is shown here once again. 43 00:02:57.000 --> 00:03:00.000 If the particles are now charged particles, 44 00:03:00.000 --> 00:03:04.000 e.g. electrons, the equation shown is obtained, 45 00:03:05.000 --> 00:03:10.000 in which both sides have been multiplied by e the elementary charge. 46 00:03:10.000 --> 00:03:19.000 But e by A times D_n by dt is an electric current density. 47 00:03:20.000 --> 00:03:25.000 we get the diffusion current density of the electrons. 48 00:03:25.000 --> 00:03:30.000 Analogously, we get the diffusion current density of the holes. 49 00:03:31.000 --> 00:03:34.000 Here there is no "-" in the equation. 50 00:03:34.000 --> 00:03:39.000 However, the equation describes the dependence on dn/dx, i.e. 51 00:03:39.000 --> 00:03:42.000 the concentration gradient of the electrons; 52 00:03:43.000 --> 00:03:46.000 if there were dp by dx, there would also be 53 00:03:46.000 --> 00:03:50.000 a minus sign aswell. 54 00:03:52.000 --> 00:03:53.000 We now come to 55 00:03:53.000 --> 00:03:57.000 another type of charge carrier transport: the field current. 56 00:03:58.000 --> 00:04:00.000 We consider a crystal, to which 57 00:04:00.000 --> 00:04:03.000 an electric voltage U is applied. 58 00:04:04.000 --> 00:04:09.000 Electrons are accelerated in the direction of the positive pole, 59 00:04:09.000 --> 00:04:12.000 but are slowed down by core atoms. 60 00:04:14.000 --> 00:04:17.000 This creates the movement shown. 61 00:04:17.000 --> 00:04:20.000 The strength of the electric field in V/cm 62 00:04:21.000 --> 00:04:26.000 can be determined by the applied voltage and the distance l between the plates. 63 00:04:27.000 --> 00:04:30.000 While the electrons move against the electric field, 64 00:04:31.000 --> 00:04:34.000 the holes move in the direction of the electric field. 65 00:04:36.000 --> 00:04:38.000 The field current density of the electrons 66 00:04:38.000 --> 00:04:42.000 is proportional to the electric field strength. 67 00:04:43.000 --> 00:04:45.000 The proportionality constant 68 00:04:45.000 --> 00:04:48.000 is called electric conductivity. 69 00:04:49.000 --> 00:04:52.000 This can be calculated with the help of the elementary charge, 70 00:04:53.000 --> 00:04:57.000 the concentration of the electrons and again with the mobility of the electrons. 71 00:04:59.000 --> 00:05:02.000 The result is that the field current density 72 00:05:02.000 --> 00:05:06.000 is equal to the elementary charge times the concentration of the electrons times 73 00:05:06.000 --> 00:05:11.000 the mobility of the electrons times the electric field strength. 74 00:05:11.000 --> 00:05:15.000 Analogous to the field 75 00:05:15.000 --> 00:05:18.000 current density of the electrons, we can also calculate 76 00:05:19.000 --> 00:05:21.000 the field current density of the holes. 77 00:05:24.000 --> 00:05:25.000 We conclude: 78 00:05:25.000 --> 00:05:29.000 The movement of charge carriers from higher concentration 79 00:05:29.000 --> 00:05:33.000 to lower concentration generates a diffusion current. 80 00:05:33.000 --> 00:05:38.000 The movement of charge carriers due to an electric field 81 00:05:38.000 --> 00:05:41.000 generates a drift current. 82 00:05:41.000 --> 00:05:44.000 Holes move in the same direction as the electric field, 83 00:05:45.000 --> 00:05:48.000 while electrons move in the opposite direction. 84 00:05:48.000 --> 00:05:50.000 Thank you for your attention.