Intrinsic semiconductors

in this video we're gonna talk about something called intrinsic semiconductors intrinsic and the word intrinsic in the context of semiconductors can be thought of as pure so it means all atoms are identical or all atoms are same so if you're dealing with an intrinsic silicon semiconductor all atoms must be silicon if it's intrinsic germanium semiconductor all atoms must be germanium think of that alright what we'll do is we'll explore the electrical properties of these semiconductors and what we'll find is this you see for metals there are only one thing that's responsible for electric current free electrons right but for semiconductors turns out there are two things responsible for electric current what are the electrons what are the others we'll find out in this video so we'll take a specific example and work with it so let's say we take silicon okay well first look at how the silicon forms a crystal and then we'll look at its electrical properties to do that first let's write down the electronic configuration of silicon so it kind of has 14 electrons so it's electronic configuration would be 1s2 then it will have 2s and 2p they will be completely filled you have 2 & 6 that makes it 10 so will 3s and 3p balls be involved then 3s would be to 3p would be just 2 and you have my you may have already studied in chemistry that atoms love this thing called as octet structure they would like their final energy shell they would like their final orbit to be completely financial to be completely filled with electrons eight electrons octet our silicon only has four electrons in its final shell right so it needs four more how does it get that well if you take a silicon crystal all there all atoms of silicon all atoms are in need of these four electrons so guess what they will do they will end up sharing their electrons and this is called as coil and bond so silicon's end up forming coal and bonds with each other and so if you could see that it might look somewhat like this here it is I'm gonna draw these are the silicon atoms which are covalently bonded with each other all right now don't take this diagram too literally all these lines are just for representation but here's the way to think about look at this silicon for atom for example it has four outermost electrons these are the four electrons we're not showing the innermost electrons and what the silicon is doing is its sharing with four of its neighbors and so as a result notice each silicon atom has now eight electron it's in its vicinity so you have one two three four five six seven eight so this silicon is happy and look at the silicon it's even having even this one has one two three four five six seven eight that one is not shown so all in silicon atoms have eight electrons access to it and as a result of this sharing they're all happy and in fact this is what keeps the entire crystal together okay so now the big question is what about its conducting properties can the Silicon conduct well that really depends upon the temperature it turns out so what we'll do is we'll start with very low temperatures let's go absolutely low let's go to absolute zero if you're at the very low temperature like very close to absolute zero what do you think will the silicon crystal do will it conduct oh it has so many electrons right but the question is can they conduct the answer can only begin by looking at the band diagram of this in previous videos we've spent some time talking about this band structure band theory of solids and if you need more clarity or you need a refresher it would be great idea to go back watch those videos and then come back over here but anyways you would see that for semiconductors the valence band the band which has highest occupied electrons the valence band is completely filled and then you have this gap in the energy which is not allowed for any electrons we call the forbidden energy gap and then you have this next energy band which electrons can occupy all right and I do add absolutely zero tempers elven all the electrons have occupied these states so if you were to look at individual states we just draw that will show that so if you would look at the individual states I'd recall that a band is actually collection of all these states and not showing some of those then each state has two electrons in it remember Pauli's exclusion principle one will be up-spin one will be down spin a third electron can't be over here that next electron will be on the next stair and so on all these electrons are filled in this valence pan and there are no empty states available as a result if we were to put an electric field over here none of these electrons would conduct and the reason for that is if an electron wants to conduct if it wants to accelerate its energy should increase right more kinetic energy and so none of the electrons look so if the energy has to increase well there has to be an energy state available for the electron to go to right but in all the energy states are filled so the electrons energy cannot increase and as a result none of these electrons will conduct and so this whole solid acts like an insulator so at zero Kelvin this whole material acts like an insulator and the reason it acts like an insulator is because well there are no empty energy states available so what happens if we increase the temperature let's say we bring it all the way to room temperature well let's find out I have it ready down over here excellent so imagine we are now we are now at room temperature let's say that's about what that's about 300 Kelvin what will happen now well now at this temperature there's a lot of thermal energies available and as a result some of these electrons can absorb this thermal energy and jump or get excited from valence band into the conduction band so maybe this electron over here maybe that one absorbs some thermal energy and gets excited and maybe it jumps all the way to this state and maybe that electron let's say is this electron over here and so as a result now if we apply an electric field this electron is free to move why it's free to accelerate because it can increase its energy further now because states are available it couldn't do that before but now it can and so we're gonna say that this now is a free electron and to show that for representation we usually we're gonna put that outside the colon bond saying that it is not stuck over here it is free to move around and it can do that and notice not only did we get a free electron but because that electron now imagine that electron moves away somewhere and because of that notice there is a vacant space available in the valence band this state is now free free for some other electron to come and occupy and because there's a lot of you know thermal agitation maybe this electron goes and occupies that so maybe this electron goes and occupies that and you may be asking like why would the electron do that it's randomness before it couldn't move but now there's an empty state it can no it's a random alright so as a result in the valence band if you look at the band diagram maybe that electron was I don't know maybe it was this electron or maybe this electron so that electron will now go and it has taken this space and as a result the vacant site has moved now that this is the vacant site and maybe another electron maybe this electron now can take up this site alright maybe it's this electron that's the one that's going over there so alright how I'm showing is showing some electrons jumping from one place to another due to thermal thermal randomness and notice as a result can you see that this empty space this vacant space sort of feels like it's moving around does it make sense so instead of saying it's the electrons that are jumping from one place to another what we like to do is we like to think that this vacant space itself is moving freely I know it doesn't make sense because vacant space is not a particle to do that but we like to think of it that way so what we like to do is we like to put a circle over here and we're gonna call that thing as a hole alright we're gonna call that as a hole and the whole idea behind this hole is that we think of hole as a particle and we think of it is freely movable so we're going to assume that it can freely move throughout this entire crystal alright and that's why we get current due to two particles one are the electrons and another one are the holes and guess what these holes act like positive charge carriers and here's why see imagine if you were to put an electric field like this if you put an electric field over here then what is this electron this free electron will accelerate this way right it will accelerate in this direction and similarly this electron well it cannot it's not free but it can go jump from here to here and as a result it seems as if the hole has moved here and then the hole moves here and the moves here so can you see that this hole it's as if the hole if it created as a particle it's as if the hole is moving in the same direction as the electric field it makes sense and that's why we like to think of holes as positively charged particles and so in semiconductors there are two things responsible for current one are the electrons but the other ones are holes a couple of notes to end the video first one is that even though holes are we treat them as positively charged particle don't think that they are going to attract the electrons they don't attract the electrons at all you can think of them there independently moving all right but of course if an electron comes very close to a hole yes it can fall into that hole but don't think they're attracting each other another thing is with the band diagram notice that if you were to carefully draw the electrons in the band diagram we have to be so careful and we cannot put more than two electrons in a horizontal line because you see each level can only have two electrons maximum right with one up spin and one down spin but that makes it so tedious to draw all of this and so you know what we'll do usually usually we forget about all these energy levels and we randomly draw electrons everywhere I know that's not very accurate but that's easier to draw so if we're to show electrons and holes over here from now onwards in future videos I'll just draw them like this I'll just show a few electrons over here all around in reality only two electrons can occupy a particular state but let's relax that now and then I'll show a bunch of a bunch of holes over here and we'll imagine these are all freely moving okay so it's not very accurate I repeat but it's easier to draw that way and it's very easy to represent that alright alright one last thing let's end with an oh gee I like to think of these electrons as water in this water water this empty water bottle is just like conduction band with a lot of space and as a result water can move freely through it and you can think of this valence band which is completely filled with water as a completely filled water bottle like this but the holes then will represent these tiny air bubbles these air bubbles are like waking sites these are the places where the water should have been but it's not there and as a result even now notice these air bubbles seem to move of course in reality it's the water that's actually filling up that place and that vacant site ends up moving but it really feels like this air bubble itself is a particle so that's the idea behind holes and that's why we like to think of holes as a particle