 Hi, I'm Zor, welcome to Inizor Education. We continue talking about semiconductors. In the previous lecture we were talking about crystalline structure of silicon and using certain impurities like phosphorus or boron, we have achieved this semi-conductivity. Today I would like to explain in more detail about what actually is this crystalline structure, what holds this crystalline structure and why certain elements have this type of structure and why impurities can actually contribute to conductivity in this particular case. Now the reason for all these links between the atoms and molecules is something which is called covalent bonds and today we will talk about covalent bonds between atoms. Okay, now this lecture is part of the course called Physics for Teens. It's presented on Unizor.com website. The website contains the course. It's not just lectures which are not related to each other. I mean you can find this lecture on YouTube for instance and any other lectures actually are there physically but what combines them together is software which is on Unizor.com. So it presents you the menu. It has basically very logical structure so every further material depends on the previous one. It also has exams which you can take. You can take them anonymously. You don't have to sign in. This website is completely free. No strings attached and as I said you don't even have to sign in into the website. I mean there are certain benefits if you sign in but that's completely unrelated to material presented. Now there is a prerequisite course on the same website. It's called Math for Teens and I believe math is extremely important for general understanding of how things are arranged and for physics specifically. So I do suggest you to be familiar at least. I mean you don't have to take the course if you know whatever is in there but the material presented in the Math for Teens course is very important for physics. Okay so covalent bonds. We were talking about silicon and sometimes germanium that's another element which are base for semiconductors so they both make this structure, this crystalline structure which is very important for semiconductor activity. So let me start from something which you definitely know about but I'll put it in a little bit different perspective. The structure of the atom. We actually talked about this many times especially I talked about this when we were talking about using the sunlight to generate electricity, solar power. So the atom as we know contains a nucleus and electrons. Now what I didn't tell before and that's extremely important. The nucleus is in the center and electrons are rotating around it. I mean that's our model. It's not like physically like planets rotating around the sun. It's more like a cloud of electrons and at any particular moment they can be in different places but what's very important and again I didn't talk about this before. The orbits are fixed so to speak. There are certain finite number of orbits where electrons can be located and again orbit is actually like a ring. It has certain thickness if you wish but in any case it's like an energy level. So the electrons which are rotating on a particular radius have certain energy and electrons which are rotating on a further orbit they have their own energy and there is nothing in between so to speak. So this is related to quantum theory, quantum mechanics. The theory which basically has this characteristics of anything being not in some kind of a smooth number of values. It doesn't really fill completely any kind of a segment of energy level from here to here. It can be only on certain distinct positions so if you have an atom, if this is a nucleus, then there is one orbit and there is another orbit and there is a third orbit and these orbits have fixed radius so to speak. I mean you can view this as a fixed radius so electrons cannot be on this radius, can be either this or that or further. So this space between the orbits is not populated by electrons and again it's related to certain quantum approach to structure of the atom and experiments actually confirms that this is much closer to whatever reality is. I mean this quantum model of the atom is much closer to reality it's confirmed by experiments than something which you might actually had in mind when you were just talking about electrons rotating in certain orbits around the atom. So we were not thinking about these distinct levels. It's all related to energy and energy cannot be like divided infinitely down to infinitesimal values. It has certain quantum, whatever the quantum is. Now the second thing which is very important is that electrons as they are rotating around the nucleus, nucleus has protons and neutrons so the protons are positively charged and they are attracting electrons. Now electrons are rotating and again it's in some way equivalent to rotating around the sun. So we have two forces because it's rotating with certain speed if you wish. It's trying basically to get away but the attraction of the protons in the nucleus is not letting it out of the orbit. So that's how it's rotating all the time being attracted to the protons in the nucleus. But at the same time if you have certain fixed orbit, if you have certain number of electrons they are filling up, let's say they are filling up the orbit in such a way that there is certain maximum. I mean obviously it depends on the radius of the orbit. But the larger the radius the longer the circumference of this circle and it looks like we can fit more electrons so their repelling of each other is not really strong enough to push something out. But there is a maximum. So certain orbit, certain orbit has certain maximum number of electrons which can fit without pushing each other out from the orbit. If by any chance if you have maximum 8 on this orbit for instance and you have a ninth electrons here it's immediately pushed to upper level to the next one. And if it's already filled up it will be pushed out as well. Maybe not necessarily that particular electron but some electron will be pushed out. So there is a certain number, maximum number of electrons which can fit any orbit. And I can actually tell you which is this number. So the most, the closest orbit around the nucleus has two maximum. The next one 8, the next one 18, the next one 32. Well the next one actually is not continuing this for some reasons which are not to are the part of this lecture. But this is something which we actually can have in mind. So by the way it's 2n square where n is the number of the orbit. 1 square is 1 times 2 is 2. 2 square is 4 times 2 is 8. 3 square is 9 times 2 is 18. And 4 square is 16 times 2 is 32. So this formula for first four orbits actually is held. So these are maximums. Not necessarily completely filled up for anything. I mean obviously the outermost orbit might not actually be completely filled up. You can have 8 and 8, 2 and 8 and then let's say 4. And that's all we have. Because different elements have different number of protons and electrons. Number of protons is equal to number of electrons but it can be 1 for hydrogen. It has one proton and one electron which means the model is this. So this is the nucleus with one proton and this is a first orbit with only one electron. Then the next one is helium where you have 2. And this is already filled up because this is the first orbit. It has 2 maximum. That's it. The next one is 3, 4, etc. I mean we have for I think for any basically number within 100 and something we have certain elements. Some of them are stable. Some of them are not stable but we do have elements. Now what's important in certain cases? I do have examples. So these are two examples. The next example I have is carbon. Carbon has 12 elementary particles inside of a nucleus which is 6 protons, 6 neutrons. If it has 6 protons it has to have 6 electrons. How they are arranged? Well, 2 on the lowest orbit and 4 electrons on the next orbit. So that's the structure of the atom of carbon. And I do have corresponding pictures by the way. On the website every lecture has notes and in the notes I put some pictures. So there are pictures of atoms similar to this one so for carbon. So what's important is that it has completely filled up lower orbit and the next orbit is filled out of 8 possible places 4 electrons are present. Okay, now next one is silicon which is silicon. Silicon is legend. Okay, silicon has 28 particles which is 14 protons plus 14 neutrons. Sorry, not nucleus. Protons and neutrons inside the nucleus. If it has 14 protons it has to have 14 electrons. So 2 goes to the lower orbit. 8 goes to the next one. So that's 10 and we have 4 on the outer orbit. So in this case it looks like this. This is silicon. So 2, 8. Is it 8 here? 1, 2, 3, 4. And 4 on the outer. So there are 3 orbits and we have 4 electrons on the outer orbit. I would like to say right now that what's on the outer orbit is very, very important and we will talk about this. So far I'm just talking about certain examples. Now what's my next example? Titanium. Okay, titanium has 48. So it has 22 protons, 26 neutrons and obviously it has 22 electrons which are broken down to 2 electrons on the first orbit. 8 on the next one. Then we have 10 and 2. Now this is very important and that was quite frankly at some point in the past was a surprise for me. I thought that orbits are supposed to be packed up to the maximum. So maximum is 2. It's filled. Maximum is 8. Next maximum is 18. So we have only 12. So I thought that we will have 12 electrons on the next orbit. Apparently that's not the case. We have many cases when orbits are not really filled up completely. So in this case this orbit it has potentially placed for 18 electrons but only 10 are taken and the next two remaining electrons are going to the outer orbit. The fourth one. Why? I don't know but that's the way how it is. And again what's very important is how many electrons are on the outer orbit because outer orbit is something which actually interacts with other atoms and that's why it's very important how many electrons are on the outer orbit. There is a special name for these electrons which I will talk about. What's my next example? Now titanium is a metal right? We know that. Now again I had an impression that the heavier the nucleus the more protons and neutrons it has inside the heavier element should be. Like if this is a metal then it should be heavy basically. But going behold we have a gas called radon. Radon and it has 222 elemental particles in the nucleus out of those 86 protons and 136 neutrons. And 86 electrons are 2 plus 8 plus 18 plus 32. You see the first four orbits are completely filled up but then I have again 18 and 8. So that's how electrons are distributed among six different orbits. Okay so these are just examples of how different atoms are structured according to the model which we are accepting right now as well the model which describes the world. Is the world really arranged this way? Well let's just put it aside. It's our model and experiments show that whatever the calculations we do using this model etc they correspond to the experiment better than the older model when we did not really take into account the quantum levels of energy. Okay so these are examples of how the atoms are structured and again what's important is what's on the outer orbit. The next important thing is that if you have something which is not filled up on the outer orbit elements have tendency to interact with each other. I mean atoms of elements have this tendency. Now if the outer orbit is completely filled up and completely means two for the first orbit, eight for the next one, eighteen for the next one. So if these orbits are completely filled up then there is no way they can actively interact with other. They are complete. It's like there is nothing there is no holes which other electrons can get into. For instance from other atoms electron cannot just jump into this one because the orbit is already completed. So if it's not filled up this outer layer then there is a possibility of interaction and again the tendency of the atoms is to interact in some way to fill up their outer most layers. So there is certain magic number for each orbit of filling it up basically. These are magic numbers. Now you have something which is called noble gases like argon or helium. They have a complete outer layer. Helium has two and that's the only thing. Then the next one I don't remember has all eight and these are not really actively engaging into any kind of chemical reaction. But something which is some element which is not filling up the outer layer. They are open for interaction. Now what is interaction? Let me just give you a structure of a molecule of the gas made methane. Now methane is CH4. So let's just think about this. C is carbon, H is hydrogen. Carbon has six protons plus six neutrons and six electrons are 2 plus 4. So this is the structure of the atom. This is one orbit and this is another orbit. Now hydrogen has only one proton and only one electron on the orbit. So here is what happens. We have four atoms. We have this atom. We have this atom of hydrogen. We have this atom of hydrogen and we have this atom of hydrogen. You see four electrons and four electrons here and the magic numbers are in this case eight. So what happens is the following. These electrons are shared between both atoms. Now what do I mean share? Well it means they're somehow participating in both orbits. I don't know exactly how it looks from inside but maybe they are rotating not exactly around some kind of a common center of gravity or something like this but in any case they are participating in both orbits. If you can imagine they can actually jump from one orbit to another from one to another all the times and that's and thus most of the time you have two here and correspondingly eight here because these are shared these are shared and these are shared. So these electrons are jumping all the time between these two orbits. They participate they're filling up so nothing else can actually come because at some moment you have two electrons here and they will push out everything else and some moment you have eight electrons here and they will push out so that makes the molecule stable. So I will use this sharing word so these are electrons which are sharing between these two one atom of carbon and four atoms of hydrogen. So that's very important and again I'm not positive about what sharing exactly means but I'm just suggesting you as a model that these electrons can jump either from this orbit to this orbit or backwards and all the time they're like oscillating between these orbits and that what makes this orbit complete with two electrons and this orbit complete with eight electrons four of its own and four borrowed from atoms hydrogen and that's what makes the molecular links stable enough. Now the electrons on the outer orbit of any atom are called balance electrons and these sharing it's called covalent bonds covalent balance electron here and balance electron there they're somehow shared between atoms and that's what actually makes the covalent bond. Now this is true for many molecules and again we can probably go into examples about what kind of molecules exist and what kind of sharing actually exists something like molecules of H2O for instance that's the water same thing we have certain atom of one atom of oxygen and two atoms which are kind of borrowed and that's what makes the whole thing actually working okay now this is about molecules how about crystals well with crystals it's exactly the same thing remember we have silicon it has 28 particles 14 protons and 14 neutrons and 14 electrons are 2 plus 8 plus 4 again 4 by the way carbon has 4 on the outer orbit but the outer orbit was the second one in this case outer orbit is the third one doesn't matter but what matter is that valence electrons are on the outer orbit and they are four valence electrons now the other atoms of silicon also have four so let's just draw it so I will ignore the first and the second orbit I will draw only the third orbit so this is my silicon and the valence electrons are on this third orbit and there are four of them now let's consider the second atom and it also has four electrons now we have similarly here and here and here so what might have happened and it's indeed it happens as our model actually tells us these two electrons are shared which means they're jumping left and right left and right and these electrons are shared and these electrons are shared and these electrons are shared now since they are shared they contribute to both orbits making this 4 plus 4 which is 8 which is a magic number and for these guys we have the same thing actually it continues so these are shared and these are shared and these are shared and these are shared and these and so that's how the whole structure actually is composed now in this case I draw it on the surface of the board like two-dimensional thing in in reality it's a three-dimensional thing in reality four outer electrons are positioned in such a way that they make a tetrider inside you have a nucleus and you have four electrons on four vertices of the triad so in any case this is a structure which is space 3d structure but I can just draw it on the board in this way because again with each electron you have some other electrons in another atom which looks like this um shared electrons shared with this one so that's how we have a crystalline structure diamonds have crystalline structure but not necessarily so look c carbon diamond is made of carbon so it has four electrons so it also has similar kind of a structure but we need a huge temperature and pressure to bring these atoms close enough so these covalent bonds start working because in a naturally occurring carbon that's actually not happening the atoms are so far away from each other that covalent bonds are not really made but under pressure and temperature we are pressing atoms of carbon so strongly that we can actually make artificial diamonds and we do actually it's very expensive but we do and again you will have crystalline structure of the diamond and again the same four electrons on the outer orbit so that's kind of resembles this in a three-dimensional world but in a two-dimensional world it looks like this one carbon instead of silicon and you will have a diamond if the atoms are close enough but in silicon it's already close enough whatever um whatever element we have by the way silicon is occurring naturally sand is co2 it's a dioxide okay so that's how covalent bonds are working they're bringing together atoms and they're filling up the outer most layers energy layers or orbit to some magic number eight is a magic number okay by the way semiconductors are also made not only from silicon but also from germanium now germanium is another element and what's the difference well germanium has how many uh it has uh 32 protons so it's 74 it's 32 protons plus 42 neutrons and 32 protons are 2 plus 8 plus 18 plus 4 so again these three first layers three first orbits are completely filled up and on the outer orbit we also have four and again the similar structure but only germanium atoms will be here and outer orbit has also four electrons and they are making these covalent bonds in exactly the same way um so and again impurities will bring certain new electrons or certain electrons will be lost if it's boring it's lost if it's phosphorus for instance it's extra electrons and it all depends on how many electrons we have on the outer orbit on the phosphorus we have five so this is phosphorus then we have one extra electron which is not paired i mean these are all participating in these covalent bonds and this one is not so it's easy to push it out just bring a little bit energy like heat it up or something like this and it will start moving and it will be a conductor and again if you have a boron for instance if it's a boron then you don't have one electrons which means that neighboring silicon will have a not paired electron which again um would would not actually be um paired with anything so we have a hole here so to speak and so an electron can jump here and the hole will be there and then some electrons will jump here well jump means again it will start sharing but then that would actually means that there is a a hole somewhere else and the holes will be moving in exactly the same way okay that's it that's all i wanted to talk about internal structure of silicon primarily silicon and what makes this crystal very important for semiconductors it's all based on covalent bonds and certain magic numbers of how many electrons can fit into one orbit which makes it stable that's it thank you very much i would suggest you to read all the notes on the lecture go to unizor.com physics 14's course it's electromagnetism and there is a chapter about semiconductors where the theory of semiconductors explained and covalent bonds is one of those lectures thank you very much and good luck