1 00:00:05,120 --> 00:00:05,370 Block 2.4 Charge carrier excitation 2 00:00:05,120 --> 00:00:08,990 How do we make semiconductors conductive? 3 00:00:08,990 --> 00:00:12,510 As discussed so far this week, we need to excite electrons 4 00:00:12,510 --> 00:00:18,099 from the valence band to the conduction band to make semiconductors conductive. 5 00:00:18,099 --> 00:00:21,509 This can be achieved by several different routes. 6 00:00:21,509 --> 00:00:26,259 First, we can excite charge carriers using thermal energy. 7 00:00:26,259 --> 00:00:29,930 Secondly, we can use impurities in the semiconductor material. 8 00:00:29,930 --> 00:00:32,090 This is what we call doping. 9 00:00:32,090 --> 00:00:36,130 The third option, which is very important to solar cells, 10 00:00:36,130 --> 00:00:43,130 is to use the energy in light to excite electrons from the valence band to the conduction band. 11 00:00:43,449 --> 00:00:47,949 Before I will discuss these various routes to excite charge carriers, 12 00:00:47,949 --> 00:00:54,800 I will first discuss the important concept of the Fermi level. 13 00:00:54,800 --> 00:01:00,550 Lets consider a metal. Electrons are filling the electronic band 14 00:01:00,550 --> 00:01:01,870 of a metal. 15 00:01:01,870 --> 00:01:06,360 The electronic band is a band of continuous energy levels. 16 00:01:06,360 --> 00:01:10,520 This band is not fully filled by electrons. 17 00:01:10,520 --> 00:01:15,820 The probability to find an electron is not the same at all energy levels. 18 00:01:15,820 --> 00:01:22,330 At low energy levels you will have a probability of 100% that electrons fill 19 00:01:22,330 --> 00:01:23,590 this level, 20 00:01:23,590 --> 00:01:29,980 while at high levels this probability is close to zero. 21 00:01:29,980 --> 00:01:33,810 The probability to find an electron can be expressed 22 00:01:33,810 --> 00:01:37,670 by the Fermi-Dirac distribution function. 23 00:01:37,670 --> 00:01:46,090 This function reflects the probability that an electron will occupy a state at an energy E. 24 00:01:46,290 --> 00:01:50,700 Low in the valence band this function is equal to 1, 25 00:01:50,700 --> 00:01:55,420 whereas high in the conduction band this function is equal to 0. 26 00:01:55,420 --> 00:02:01,820 Note, that this equation is only valid for a material that is at thermal equilibrium, 27 00:02:01,820 --> 00:02:08,820 which means that no additional energy is coupled into the system by electrical biasing, 28 00:02:09,229 --> 00:02:11,090 light absorption or heat conductivity. 29 00:02:12,090 --> 00:02:20,069 The Fermi level represents the energy level at which the electrons have a 50% change 30 00:02:20,069 --> 00:02:24,579 to occupy the energy level at any given time. 31 00:02:24,579 --> 00:02:30,280 For a metal it easy to see where the Fermi level is positioned. 32 00:02:30,280 --> 00:02:34,349 Physicists use in general the term Fermi level. 33 00:02:34,349 --> 00:02:39,189 Chemists might use a different term, they might call this level the total 34 00:02:39,189 --> 00:02:43,230 chemical potential of an electron. 35 00:02:43,230 --> 00:02:48,840 The shape of the Fermi-Dirac distribution does change with temperature. 36 00:02:48,840 --> 00:02:52,819 At absolute zero, which means a temperature of 0 K 37 00:02:52,819 --> 00:02:59,499 (or minus 273 degree Celsius), the function looks likes a step function. 38 00:02:59,499 --> 00:03:04,099 The probability to occupy a state below the Fermi level is 100%, 39 00:03:04,099 --> 00:03:09,219 whereas the probability above the Fermi level is 0%. 40 00:03:09,219 --> 00:03:15,090 For higher temperatures, this distribution starts to broaden around the Fermi level. 41 00:03:15,090 --> 00:03:21,450 Around the Fermi level the energy is distributed over values between 0 and 1. 42 00:03:21,450 --> 00:03:26,619 The higher the temperature, the broader the distribution around the Fermi level will be. 43 00:03:26,810 --> 00:03:32,129 As you can see, a metal has only one electronic band. 44 00:03:32,129 --> 00:03:36,980 However, for semiconductors this situation is different. 45 00:03:36,980 --> 00:03:41,169 The valence band is almost fully filled with electrons, 46 00:03:41,169 --> 00:03:45,939 whereas the conduction band only has a very few electrons. 47 00:03:45,939 --> 00:03:49,760 The Fermi level is positioned in the forbidden band gap, 48 00:03:49,760 --> 00:03:52,840 between the valence and conduction band. 49 00:03:52,840 --> 00:03:58,579 According to the Fermi-Dirac function electrons have a 50% probability 50 00:03:58,579 --> 00:04:02,489 to occupy the electronic states at the Fermi level. 51 00:04:02,489 --> 00:04:07,069 Since no electronic band exists at this level in the forbidden band gap, 52 00:04:07,069 --> 00:04:09,919 no electrons can occupy this level. 53 00:04:09,919 --> 00:04:13,769 So the real distribution of electrons over the two electronic bands 54 00:04:13,769 --> 00:04:16,220 becomes more complicated. 55 00:04:16,220 --> 00:04:21,560 In general the Fermi Dirac function shows that the energy levels in the conduction band 56 00:04:21,560 --> 00:04:27,000 have a low probability to be occupied, while the energy levels in the valence band 57 00:04:27,000 --> 00:04:30,610 have a high probability to be occupied. 58 00:04:30,610 --> 00:04:36,870 At absolute 0, a temperature of 0K (or minus 273 degree Celsius), 59 00:04:36,870 --> 00:04:40,120 all electrons fully occupy the valence band. 60 00:04:40,120 --> 00:04:44,020 The semiconductor material is not conductive. 61 00:04:44,020 --> 00:04:47,830 If we increase the temperature, the shape of the Fermi-Dirac function 62 00:04:47,830 --> 00:04:52,300 broadens around the Fermi level and some electrons have the change 63 00:04:52,300 --> 00:04:55,680 to occupy the conduction band as well. 64 00:04:55,680 --> 00:05:00,930 The higher the temperature, the more electrons can occupy the conduction band. 65 00:05:01,130 --> 00:05:04,099 This demonstrates the physical principle 66 00:05:04,099 --> 00:05:11,069 that if you heat up a semiconductor material, it becomes more conductive. 67 00:05:11,069 --> 00:05:13,849 Using the Fermi Dirac function you can tell something about 68 00:05:13,849 --> 00:05:18,090 the distributions of holes in the conduction band. 69 00:05:18,090 --> 00:05:21,889 The positions in the valence band at which the electrons are missing 70 00:05:21,889 --> 00:05:28,860 are the locations at which the holes are present, indicated by the blue dots again. 71 00:05:28,860 --> 00:05:32,110 So if we remove the fixed electrons in the valence band, 72 00:05:32,110 --> 00:05:39,110 we are left with only the mobile charge carriers, the free electrons and the free holes. 73 00:05:39,819 --> 00:05:44,379 One minus the Fermi Dirac function, shows for a semiconductor the probability 74 00:05:44,379 --> 00:05:49,590 that you will find a hole at certain energy level. 75 00:05:49,590 --> 00:05:54,509 This week we will focus on the behavior of the charge carriers, 76 00:05:54,509 --> 00:05:56,199 electrons and holes in a semiconductor. 77 00:05:56,199 --> 00:06:02,289 We will use the semiconductor material silicon again as an example. 78 00:06:02,289 --> 00:06:06,699 And again I will make a drastic simplification. 79 00:06:06,699 --> 00:06:12,629 The silicon network is a 3-dimensional network as you can see in this animation. 80 00:06:12,629 --> 00:06:18,460 The blue spheres represent the silicon atoms and the red dots represent the valence electrons 81 00:06:18,460 --> 00:06:22,770 in the molecular orbitals which are forming the bonds with the neighboring 82 00:06:22,770 --> 00:06:24,909 atoms. 83 00:06:24,909 --> 00:06:28,830 To illustrate the behavior of charge carriers in the silicon lattice, 84 00:06:28,830 --> 00:06:32,750 I will flatten the material and consider the silicon lattice 85 00:06:32,750 --> 00:06:37,629 to be a 2-dimensional squared lattice. 86 00:06:37,629 --> 00:06:42,689 In this 2-dimensional network, every silicon atom has four bonds 87 00:06:42,689 --> 00:06:47,770 with its neighboring silicon atom, like it has in a 3-dimensional network. 88 00:06:47,770 --> 00:06:53,409 In this schematic silicon network we put some charge carriers. 89 00:06:53,409 --> 00:06:59,460 The animation shows the mobile electrons, which again are indicated with the red dots. 90 00:06:59,460 --> 00:07:03,000 Secondly, we show the holes, which are in this illustration 91 00:07:03,000 --> 00:07:05,490 indicated by the black dots. 92 00:07:05,490 --> 00:07:09,319 They are part of a molecular bond in which one of the two valence electrons 93 00:07:09,319 --> 00:07:10,599 is missing. 94 00:07:10,599 --> 00:07:16,689 Both electrons and holes can move freely around. 95 00:07:16,689 --> 00:07:20,370 So far we have discussed that we can manipulate the density 96 00:07:20,370 --> 00:07:23,419 of the free charge carriers using temperature. 97 00:07:23,419 --> 00:07:26,890 The higher the temperature, the more free electrons and free holes 98 00:07:26,890 --> 00:07:28,500 can be excited. 99 00:07:29,500 --> 00:07:34,430 Another approach to increase the density of the charge carriers is using doping. 100 00:07:34,430 --> 00:07:41,430 Up to now we have considered pure semiconductor materials without any impurities. 101 00:07:42,629 --> 00:07:46,259 These semiconductor materials are called intrinsic. 102 00:07:46,259 --> 00:07:53,259 It means that the density of mobile electrons and holes are the same in the material. 103 00:07:53,780 --> 00:07:58,449 We can intentionally incorporate impurities in the material. 104 00:07:58,449 --> 00:08:00,539 This is called doping. 105 00:08:00,539 --> 00:08:04,919 Doping can have a significant effect on the charge carrier density. 106 00:08:04,919 --> 00:08:08,740 Which I will explain now. 107 00:08:08,740 --> 00:08:13,099 As example we take again silicon, silicon is a material, 108 00:08:13,099 --> 00:08:15,550 which has four valence electrons. 109 00:08:15,550 --> 00:08:20,639 In the periodic system Silicon is part of the column 110 00:08:20,639 --> 00:08:25,110 with atoms having only four valence electrons. 111 00:08:25,110 --> 00:08:30,530 At the left side of the column with IV-valence elements we see that we have materials 112 00:08:30,530 --> 00:08:37,530 with only three valence electrons, like Boron, Aluminum, and Gallium. 113 00:08:37,579 --> 00:08:40,610 On the right side of silicon in the periodic table 114 00:08:40,610 --> 00:08:46,570 we have atoms which have five valence electrons, like nitrogen and phosphorous. 115 00:08:46,570 --> 00:08:53,570 First, we are going to intentionally put Phosphorous impurities in the silicon network. 116 00:08:54,560 --> 00:08:58,370 Phosphorous has five valence electrons. 117 00:08:58,370 --> 00:09:05,060 The Phosphorous atom will make molecular bonds with its four neighboring silicon atoms. 118 00:09:05,060 --> 00:09:08,260 Since the Phosphorous atom has five valence electrons, 119 00:09:08,260 --> 00:09:11,450 it has one electron left. 120 00:09:11,450 --> 00:09:17,649 This extra electron is easily excited to a free mobile state. 121 00:09:17,649 --> 00:09:20,880 The Phosphorous atom left behind, is not neutral anymore 122 00:09:20,880 --> 00:09:25,649 and becomes a positively charged entity. 123 00:09:25,649 --> 00:09:30,690 This positive charge is fixed to the position where the Phosphorous atom 124 00:09:30,690 --> 00:09:32,769 is residing in the lattice. 125 00:09:33,769 --> 00:09:40,389 The result is that by adding an impurity we have one extra free mobile electron 126 00:09:40,389 --> 00:09:44,089 and a fixed positive charge in the background. 127 00:09:44,089 --> 00:09:46,190 This is called n-doping. 128 00:09:46,190 --> 00:09:51,360 For n-doped semiconductors, the electrons are called the majority charge carriers, 129 00:09:51,360 --> 00:09:55,540 as the density of electrons is much higher than that of the holes. 130 00:09:56,029 --> 00:10:02,290 The holes are called the minority charge carriers in a n-doped semiconductor. 131 00:10:02,290 --> 00:10:07,690 N-doping of silicon can also be illustrated by an electronic band diagram. 132 00:10:07,690 --> 00:10:11,820 The Phophorous atoms are represented as donor states. 133 00:10:11,820 --> 00:10:17,160 These donor states have an energy level within the forbidden band gap of the silicon matrix, 134 00:10:17,160 --> 00:10:20,670 which can be occupied by electrons. 135 00:10:20,670 --> 00:10:26,589 The energy level of the donor states is closer to the conduction band than to the valence band. 136 00:10:26,589 --> 00:10:32,350 This means it requires much less energy for an electron to jump from the donor state 137 00:10:32,350 --> 00:10:37,879 to the conduction band than for an electron from the valence band to the conduction band. 138 00:10:38,279 --> 00:10:43,250 At typical room temperatures many to all of the electrons in the donor states 139 00:10:43,250 --> 00:10:46,589 can be excited to the conduction band. 140 00:10:46,589 --> 00:10:53,589 As a result we have more free mobile electrons than mobile holes in an n-type semiconductor. 141 00:10:53,660 --> 00:11:00,729 We call the states donor states, because they donate an electron to the conduction band. 142 00:11:01,039 --> 00:11:08,110 The electrons are the majority charge carriers, the holes are the minority charge carriers. 143 00:11:08,110 --> 00:11:12,649 As the electrons are the majority charge carriers, the Fermi level will be closer to the 144 00:11:12,649 --> 00:11:14,910 conduction band than to the valence band.