In this lecture, we'll talk about how we can utilize dope pins or impurities to alter the electrical conductivity of semiconductors. And then we want to look at how temperature influences the electrical conductivity in semiconductors. So we'll start off with our semiconductor. Here's our band structure. Here's our band gap that we have atoms electrons filled all states up to the valence band edge. And then we have our band gap. Then we have our conduction band edge. At 0 Kelvin, we have what we refer to as freeze out. Freeze out we mean there's no thermal agitation, no thermal energy. So everything's perfect. So here we have our states completely filled up to the valence band edge and then our conduction band is completely empty. Now what we're going to do is give a little bit of thermal energy and we're going to excite an electron up into the conduction band. Now once there, notice is sort of free to move to an adjacent site. Now let's give some more energy And excite another electron into the conduction band. And even a little bit more energy. Okay, so now you can see as we increase the amount of thermal energy or the temperature, the number of carriers excited into the conduction band increases. So we can assume that our conductivity is going to increase with thermal energy, not like that of the metal, right? So if we look at our intrinsic element or comp versus a compound semiconductor, our elemental semiconductors typical ones, Silicon, Germania, Tin is another one. Okay, knows that they're just elemental, just Silicon and just Germanium. Now we can have compound semiconductor, probably the most famous gallium arsenide, Indium, Antimonide, Cadmium sulfide and they referred to by the column, okay? Silicon and Germanium are group four, our compound semiconductors either are three five or two six. Again referring from the column from which they come. Now an important aspect when we're looking at the band gap because we'll see it's going to influence a lot of things. That the wider the band gap Is related to a larger difference in the electronegativity. Okay, so if I want to design a smaller band gap, I have a small difference in electronegativity. If I want to design for a wide band gap material, I've looked for large differences in the electronegativity. So conduction, now we gotta define this thing called the hole, okay? Well in Silicon There's all covalent bonds in our valence bond so forth. I can break one of these. Okay, and I can have this missing bond. You can draw there's dash art. There we go. Okay, so that missing bond. Okay, we're going to call that essentially is the hole and it has a + net charge and the net effect is that it appears to move with the electrostatic field. Okay, so now we have our hole and electron. And when we created those earlier, if you recall, there's my conduction band edge, my valence band edge. To create the hole, I had to excite a carrier into the conduction band. So hence for every hole that I create, I should say for every electron I excite into the conduction band, I leave behind a hole. So that turns out to be electron hole pairs. Okay, now we're going to apply electrostatic field. Okay, here's the electrostatic field and this approach, since the field is pointing that away, the holes are going to move in the other way. The electrons are going to move in the opposite direction of the field. Okay, so we create electron hole pairs and in the presence of the electrostatic field, they move in different directions. Now if I want to calculate the conductivity in a semiconductor, I have to keep track of both carrier types, my number of electrons and the number of holes. Electrons and holes will have different mobilities meaning ease at which they move under the presence of electrostatic field. Typically, electrons have a higher mobility, okay? But, it doesn't matter. We keep track of both carrier types. So we have the number of electrons charge in the mobility of the electron. For the holes, the number of holes, the charge and the mobility of the holes. So let's take a moment for inquiry. Okay, in this case we want to look at an elemental semiconductor and if I look closely, we have Germanium. Compound semiconductor Gallium arsenide. Carriers are thermally activated in intrinsic material. And large band gaps in electronegativity will result in large band gaps. Or I should say small differences in electronegativity results in small band gaps.
