[Music] [Music] [Music] [Music] [Music] [Music] greetings welcome to electronic circuits one my name is behzod Razavi and i will be your guide on an interesting journey through the world of electronics as you know electronics has affected our lives in many different respects and today we can see it everywhere and our objective in this course is to build the foundation for analysis and design of electronic circuits today what I would like to accomplish is first give you an introduction to electronics and then start with semiconductor physics the devices that we use in electronic design are based on semiconductors and to understand how the devices operate we need to understand semiconductor physics so for that we'll go over some general concepts that are familiar to you from physics and chemistry and then we will look at the concept of doping as one method that we use in semiconductor devices all right so before we go there let's just take a look at what we learned in basic circuit theory and what we are hoping to learn in this course so all right well in basic circuit theory we learned of course circuit theorems KVL and KCl and Norton equivalent dan7 an equivalent etc but we also had a few devices a few components that we could play with resistors capacitors inductors maybe transformers but they were very few in number so we had only resistors capacitors and inductors so this is what we call what we would say basic electric components and with such a small number of components especially only two terminal devices is very difficult to build many useful and exciting circuits so if you recall from your circuit Theory courses they didn't really have that many applications from real life examples of a circuit design another hand in electronics the world is different so in electronics in addition to these basic components we have some other components that suddenly open up the horizons for circuit design we have for example diodes of course we don't know what they are right now and then we have transistors we have two types of transistors we have a bipolar transistors and MOS transistors and then we also have what we call op amps you might have seen them as a black box before so an op amp looks like this is an amplifier with two inputs so with so many devices available suddenly we can build much more complex and sophisticated circuits and that's why electronics is so exciting we every day we come up with new ideas view new ways of connecting these things together you can imagine how many combinations and permutations of these devices can exist and that's why it is interesting to study electronics all right now but because these devices are based on semiconductors we do need to understand semiconductor physics to some extent just the way a an engineer designing an automobile needs to know how the engine operates or the carburetor operates everything else we also need to know how the this device or that device operates internally so for that we start we have to start with semiconductor physics the semiconductor physics that we cover here is not as deep as what you would see in dedicated semiconductors horses but it's just barely enough for this course it's a little boring for the next one or two lectures but you have to bear with me so that you understand this stuff and then you can move on to more exciting circuit examples etc alright so now based on these we can figure out what topics we will cover in this course so the outline of this course is like this we start with semiconductor physics which is the foundation for all of these devices so semi conductors or semiconductor physics at a simple level and once we understand that we can go ahead and build each of these devices so we go ahead and build a diode and understand its inner workings and more importantly find out how we can model this we remember that a resistor satisfies Ohm's law we remember the capacitor satisfies AI is equal to C DV over DT how about a diode what model what mathematical expression should be use for the diode and once we know that we can go and build circuits out of diodes so we learn about diodes and then we go to diode circuits are these useful absolutely you have them everywhere you have them in your charger that charges your cell phone you have them in your laptop everywhere so it's good to know how diode circuits operate our event will repeat this for these other devices so we go to for example bipolar transistors and once we know how they operate on how we can model them we can go ahead and build circuits out of these transistors so you don't bipolar circuits and finally for most devices so we go to mosque transistors and after understanding their operation and they're modeling we can build Maus circuits at the end of this course we will also look at circuits that incorporate our pumps in them and perform interesting functions so at the end of the course we'll also look at what I call often based circuits and this will take us about forty-five hours of lectures okay all right so with this we now have a clear picture as to where we will start and where we will end and we're going to start with semiconductor physics trying to understand how what a semiconductor is what it means and then how we can modify it again we can play with it etc until we can build a diode from that that is the objective as we go along in this course we will also have what I call the frontiers in electronics series the purpose of frontiers in electronics is to give you examples of applications of electronics in daily life this helps us appreciate the beauty of electronic circuits and also see how what we learn in this course becomes useful in everything that we see out there today so we have many examples of electronic devices in our lives for example cell phones and GPS and Wi-Fi etc today we will spend a little bit of time on the cell phone itself and see how it might operate our treatment is very simple and the level of our understanding in electronic circuits one we're not pretending that we can design a cell phone or we can even repair a cell phone we're just trying to understand how it generally might operate I'm not for me of a cell phone so we would like to see what exactly is going on inside the cell phone when our voice or data is communicated from one place to another place wirelessly now our treatment is at a simple level so we will just look at the general functionality that we would have in such a system well a cell phone would consist of a transmitter to transmit the data or voice or video of interest and a receiver to receive that processor and retrieve the information okay so what do we need to build a wireless transmitter well first we need an antenna so let's pick an antenna here that's the symbol for an antenna which takes an electrical signal and converts it to an electromagnetic signal so that the waves can propagate through the air and get to the receiver all right now we have let's say my voice which goes to microphone so here's a microphone mic and the microphone generates an electrical signal so if I plot that as a function of time it looks like this so that's what we get at the microphone so the question is can I just connect the microphone output due directly to the antenna and let it convert the to electromagnetic waves and sell them out so can I just short this from here to here now of course you may say well the microphone signal is very weak so you should probably amplify it before you do anything with it so that's true so let's put an amplifier here this is just a very simple audio amplifier to amplify the signal that's generated by these microphones typically these swings that you would see at the output here or on the other of a few millivolts maybe 10 millivolts so we would need to amplify them but can i still can I go ahead and connect this point at this point well no and the reason for that is that for an antenna to be a good antenna meaning a good radiator of electromagnetic energy its dimensions however they are whether is round or rectangular etc its dimensions must be comparable to the wavelength of the signal that we apply to it so for example if you consider this transmitter that is connected to my microphone this transmitter has small antenna inside we don't see it this transmitter operates at I don't know 500 megahertz 600 megahertz the antenna is about this size and somewhere inside or maybe a loop or something all right so we need a frequency here correspond to a wavelength that is reasonable in terms of these antenna dimensions on the other hand the signal that is produced by the microphone the audio signal the voice signal has a frequency range of 20 Hertz to 20 kilohertz and if you do a quick calculation you will see that the wavelength associated with these frequencies is extremely large so there's just no way that we could connect and how do you signal directly to an antenna and hope that antenna with any reasonable dimensions would be able to radiate it would not radiate so what do we do here well what we should think of is start out with a frequency that is friendly to the antenna so maybe one gigahertz two gigahertz whatever we want in cellphones we have 900 megahertz we have 1.8 gigahertz 2 gigahertz 2.2 gigahertz so something like that so we start out with a frequency that is good for the antenna so here's a frequency I will just say 1 gigahertz as an example 1 gigahertz and what you're hoping that is that this information can be somehow combined with this frequency so that this frequency this waveform carries this information for us and then the result is applied to the antenna is the frequency high enough that the internal dimensions will be reasonable and everything is good so we call this waveform the carrier because it will carry the information that we would like to transmit so this is called a carrier all right now how do we combine this information with this in other words how do we impress this information upon this carrier well you can imagine we can change the amplitude according to this information or the frequency etc so there would be some sort of change or modulation as we call it in the properties of this carrier according to the signal that is produced by the microphone so that calls for some box which we call the modulator so here's the modulator and the job of the modulator is to take the information signal that we are producing from the microphone from a camera etc and take this carrier combine these somehow and give us a result that has this information on top of the signal okay all right now this is ready to be transmitted the frequency of the signal is high enough and I say 1 gigahertz that the antenna would be reasonable of visible dimensions but if you are hoping to transmit this information over a long range let's say a mile or two miles or two kilometres etcetera then we might want to apply a large amount of power to this antenna and for that we need another amplifier placed between the modulator and the antenna and this is called a power amplifier so here we have a power amplifier APA it's a cellphone might transmit 500 milliwatts even a watt at this point so that goes a long range alright so we see most of the blocks that we would need some sort of processing of the audio signal a modulator a power amplifier now this carrier has to come from somewhere where does it come from it's a periodic signal so we may think of an oscillator as a circuit that produces a periodic signal it oscillates so it keeps producing a sine or a cosine or a square wave or something so this will come from an oscillator so you may have a 1 gigahertz oscillator or a two kickers oscillator and the signal comes here this is called the carrier signal sometimes we call it the local oscillator and then we somehow impress this information on this maybe modulate this amplitude or its face or its frequency and then we go through the power and when we come out all right that's the most basic transmitter that we can build okay now let's go to the receive side and see what should happen there we sort of expect the reverse of all of this to happen right so let's see what what we need to do there okay I will draw the transmitter receiver on this side these waves propagate through the air and are picked up by my receiver antenna so I have an antenna here and I'm trying to build my receiver so here's the receiver so I guess I should call this the transmitters and by the time the waves get to my receiver they are actually quite attenuated so this way will be very little by the time it gets here if it's a long distance and the signal that comes in so is so small that it can't do much with it so that calls for amplification so we need an amplifier right here which we call a low noise amplifier and lnaa and now the signal is a little bigger so we can play with it and then we have to go through some processing maybe demodulation or whatever it takes so that at the end we retrieve this original signal so I'm hoping that now in my receiver I take back that on your signal I can apply to speaker and I can listen to it so there will be some processing here I know this is vague but in the interest of time I won't go through the details of this processing and then here eventually we give the signal to a speaker and that produces the audio signal back for us this is the journey that the voice signal takes has thoughts from this microphone goes through the air is received by the receiver and processed to generate the the voice signal you can imagine that there are many other building blocks in here that we are not talking about in a cell phone today we have a lot a great deal more complexity that than what we see here but this is the bare bone structure at all of our understanding that helps us appreciate what we have here so we see some functions that are very good and necessary we have amplification and the files here here here maybe more down here we have oscillations to build an oscillator we actually need application so we have some sort of amplification that is converted to an oscillator so we need here there are also some interesting functions inside here inside here that we are not covering at this point very well let's begin with semiconductor physics and we start with some general concepts so let's begin with our general concepts okay well we know that atoms consist of a nucleus and some electrons surrounding the atom and of interest to us this is the nucleus and there are electrons in the in these various shells or as we call them orbitals and of interest to us is or the electrons in the last outer shell of the atom so we have some electrons in the last shell or in the last orbital and these electrons play an interesting role in how these atoms interact with other atoms all right so these electrons out here electron they're called valence electrons the ones in the last orbital the outermost shell different atoms have different number of electrons in their valence among their valence electrons so as an example we have sodium sodium has only one electron in the outermost shell and as a result is very reactive it was to get rid of that electron as soon as possible so sodium reacts with everything else very quickly then we have for example neon has eight electrons and that means that this orbital is last orbital is complete so it has no tendency to interact with anything else but we call a noble gas so it has no interaction all right and then we have for example silicon and silicon happens to have four electrons in its outermost shell four electrons so silicon is not as reactive as sodium or as inert as nonreactive as neon is somewhere in between so it could interact with other atoms to some extent and this is the foundation for semiconductors that we study in this course all right so that's silicon atom and let's try to do this let's try to build what we call a crystal of silicon a crystal of silicon is a very regular array of silicon atoms placed very neatly next to each other so here's how it goes do we have the silicon atom here another silicon atom here another one here and so on so you have another one here another one here etc this silicon atom has four electrons available in its outermost shell so what it does it begins to share these electrons with the neighboring atoms so now this silicon but some of the time has eight electrons so it's complete because it has four of its own and then its borrowing for from these four neighboring atoms and so on this continues everywhere these bonds are formed everywhere so you can see that this is a very regular and clean array of atoms very organized and that's what we call the crystal or we call a lattice so silicon has the ability to do this with proper processing of silicon we can create silicon crystal and that's so what we use in semiconductor physics all right so let's say that I have a piece of silicon that I bought and it has the structure in it and I'm wondering if this can conduct electricity so I come along and I apply connected contact here contact here a piece of wire on each side and I connect the battery here with some voltage v1 let's say 1 volt or 2 volts or something and I'm curious to see if there's any current flowing through the semiconductors all right well for the current to flow we need some sort of maybe electron to flow some sort of charge carrier to flow so we need perhaps an electron to start from here and travel all the way this way going from the positive end to the negative end so we need an electron do we have an electron available here that can take off and go around and carry charge it seems that the electrons are all occupied they're all bound to these atoms it seems that no electron is free this electron is shared between these two this electrons are shared between these two etc in fact if we perform this test at Absolute Zero that is exactly true an absolute zero these electrons are all connected these atoms that have have no way to go but at any finite temperature because of the ambient energy that we have the thermal energy that we have once in a while one of these electrons comes off from that bond and is available to move around so statically speaking at any temperature one electric summer drones are free because they just come off come off of these bonds so this might instead of this we may have an a free electron that becomes available and now yes if we apply voltage some of these free electrons can conduct electricity around this loop also a piece of silicon can conduct electricity at a finite temperature let's say at the room temperature and for that reason we call it a semi conductor is not as good as metals which are very good conductors right and it's not as bad as for example diamond which is a an insulator it doesn't conduct it's somewhere in between it conducts to some extent and that's why we call it a semi conductors very well so that's what we have for the crystal and the silicon the piece of silicon okay so in this study we need to answer a number of questions as we go along understand these principles so let me write these questions here and we will try to answer these questions one by one as we go through the physics of semiconductors so let's add a page here okay so we are dealing with currents and voltages in semiconductors currents are carried when an electron for example moves around or generally a charge carrier moves around so the first question is where do charge carriers come from so let's write that down here where do Sarge carriers come from well I just mentioned that in a piece of silicon we do have electrons charge carriers at a finite temperature because of the thermal energy once in a while the lecture the electron inside the atom inside the valence band has enough energy to come off and become a free electron but is that the only type of charge carrier maybe there are other types of charge carriers that will come along as well so for the second question that we want to answer in our studies is what types of charge carriers do we have the most familiar to us are electrons but are they electrons the only types that can conduct a current through a piece of semiconductor or any other piece of material so we would like to answer that question as well okay so then once we understand these two we need to go and ask the following question how can we modify density of charge carriers intuitively we know that if in a material we have lots of carriers then that material is very conductive if you have very few carriers is not very conductive so that's what we call the density of carriers now if I give you a piece of silicon and it has some number of electrons per cubic centimeters or cubic meter and you're not happy with that number you want to increase it or decrease it how do we exactly do that how do we make sure that this piece of silicon has a higher number of free electrons available for current conduction or a lower number of Korus electrons available so that's what we call modification of carrier densities so we'd like to see how that works and last question that we need to answer in relation to semiconductors is how do charge carriers move that seems the logical question right because we are interested in how current is created in a semiconductor so if I say these electrons are going from here to here by what mechanism are they exactly moving and we need to understand and be able to quantify that mechanism so we will look at that at some point all right so we have partially answered this question we saw that electrons are freed from the bonds inside the silicon crystal but there are other interesting questions that we need to answer so let's go and try them one by one all right so I need to introduce another concept that is necessary for us to understand these questions so let's talk about that concept for a few minutes and then we go back to these questions in the meantime I go to a new color so this is what we call what happened here okay I call it concept of and gap energy now along the lines of what we just discussed about a piece of silicon and some free electrons that we can find there here's what we would expect let's try to plot as a function of absolute temperature the density of free electrons in silicon just very qualitatively so this is density of free electrons in silicon this means that if I go take a piece of silicon either some temperature room temperature for example and I go and look at one cubic centimeter and I count how many free electrons we have that would be any value here all right so as I said at Absolute Zero we have nothing so at Absolute Zero everything is frozen we have no carriers available and generally what we know is that as temperature goes up more electrons have a chance to break free because of the higher available thermal energy in the ambient so in the ambience so we have to have some behavior like this now where there is linear non-linear we don't know at this point but it has some sort of behavior it's if we know that it has to increase with temperature okay so that's fine but something interesting happens if we study two different types of elements for example let's say this is for silicon silicon has 4 electrons in its outermost shell and it has this type of behavior now if I go to the periodic table I can find another element that also has four electrons in its outermost shell and that's germanium so for germanium if I try to construct the same plot I will see something like this so that's germanium both of these are in the same column in the periodic table and they both can be used as semiconductors all right so what is it like this wise germanium density of free electrons a stronger function of temperature than silicon's density okay so we are hoping that maybe there's one equation that can describe both of these and there's only one number in there that depends on silicon or germanium right and in fact that equation exists so we'll try to write an equation for this behavior so his model right will write the density of electrons we denote that by n n is the number of electrons per cubic centimeter and then we'll write ah this is called for an intrinsic piece of silicon we don't know why it's called intrinsic at this point but don't worry butter we'll see that later so intrinsic silicon and N is the density of electrons the number of electrons per cubic centimeter so there's a nice equation for this that gives us this behavior so let me write the equation it's 5.2 times 10 to the 15 times T to the power of three halves times exponential alpha minus EG over 2k t all right so let me walk you through these we have some number times the absolute temperature to the power of three over two multiplied by this exponential this exponential has something here which we call the bandgap energy so this is called deep and gap energy and what it really means is the amount of energy that an electron needs let's say in silicon to break free from the bond inside the atom and become available for current conduction so that's the amount of energy we need and this immediately tells us something it says that in silicon we need a higher energy we need a higher temperature to give the same amount of the same number of electrons per cubic centimeter as germanium so that means that eg is higher for silicon than for germanium now K is Boltzmann's constant both man's constant and its value is good to memorize you'll encounter this many times in electronics is equal to one point three eight times ten to the minus twenty three jewels over Kelvin and T is absolute temperature okay so what we see is that this equation applies to both germanium and silicon the only difference is that eg has different values for different elements so let me write that here eg is approximately equal to one point one two the unit is a little strange you might remember this the unit of energy is electron volts similar to joules but this is more convenient electron volts that Rambo's means the amount of energy that we need to take one electron across one volt of voltage difference and this is for silicon and then for germanium is lower for germanium it is point six seven electron volts or germanium so that tells us why we have a stronger function here for germanium than for silicon all right and then finally if you're curious for example for diamond is 2.5 electron volts for diamond and that's why diamond is such a good insulator as for diamond this would be way down here because of this exponential relationship so diamond has very very low current through it so it's considered a good insulator all right now with this in hand we can go ahead and look at a an example so let me use these equations to just give you an example so here's an example for silicon let's go ahead and calculate an I so at t equals 300 kelvin we have an i equals so we go place 300 here EG is one point one two electron volts we have to worry about these units etc k is this much T is 303 calculations and an eye comes out to be approximately 10 to the 10 electrons per cubic centimeter these are the number of free electrons that we have at the room temperature so if we take a 1 cube 1 1 centimeter by positive it was centimeters the piece of silicon silicon Cristal as I showed you before right so this is one cubic centimeter then inside here we have 10 to the 10 free electrons okay so that gives us a feel for what kind of electron density or conductivity we might have in a piece of silicon at the room temperature or not this number 10 to the 10 electrons per cubic centimeter doesn't have too much significance for us we don't know if this is a large number or small number or what so somehow we have to compare this to something else we don't know if this is a is this considered a really good conductor because we have 10 to the 10 electrons in one cubic centimeter or not well you we have to remember how many atoms of silicon we have in one cubic centimeter and that number is the following so 5 times 10 to the 22 silicon atoms per cubic centimeter so in this little piece here we have this many atoms and of those only this many electrons have been freed so if you look at the ratio of these two we see that a very very small percentage of the atoms of silicon have actually released an electron with this thermal energy that's available all right so that's why we say this is a semiconductor we don't have an abundance of electrons for current conduction the ratio of these two is 10 to the 12 five thousand five times ten to the twelve is a huge number so a very very small fraction of the atoms have released an electron so a piece of silicon as I have described it so far is a roughly poor conductor because we don't have that many electrons available all right so we'll say a poor conductor is still better than diamond to conduct but not as much as we would like it so what I have described so far is called pure silicon or more precisely is called intrinsic silicon so a piece of silicon the way we describe it just a bunch of silicon atoms next to each other is called pure silicon also known as in trinsic silicon okay these have the same meaning if you want to call it pure that's fine it's just pure it's just all silicon atoms in a nice array in the crystal all right so now we need to address or familiarize ourselves with one more concept before all of these come together and that's the concept of holes so a lot let's talk about that this is something that you probably have not seen in any courses before because this is so specific to semiconductors all right so what are holes well let's change the color of our pin and see what we can do okay so let's again take a piece of silicon we the way we have seen it at some finite temperature and observe the following so let's say we had a silicon piece of silicon here lfyou silicon atoms and so on and it just happens that this bond loses one electron because of the thermal energy one action came out of here and started moving around so the void that is left behind is called the hole so there's a hole here because there used to be an electron here but it's gone so this bond is missing an electron and that's what we call the hole so this we call the hole all right so because the electron has negative charge when it's taken away this hole has positive charge all right so we associate positive charge two holes in the amount that we associate negative charge two electrons okay but something interesting happens so let's say that I have this piece of silicon and I take a snapshot I take a picture of it at time zero and I see the situation a an electron has just come out of this and a hole has appeared okay all right now a little later I take another picture and this is what I observe so we just take the same piece of silicon we have these atoms sitting here and what I see is that a little lighter so let's say T equals T one maybe a nanosecond later or maybe a second later doesn't really matter for us what I see is that one electron has come out of this bond here and fill this hole here so now the hole is here reiben know that everyone is capable of relinquishing an electron if there's enough thermal energy and just happens that this bond lost an electron and the selection of fell into this hole completed this bond and now we have a hole here okay so we have a hole here now let's take another picture a little later and see what happens so we go to T equals T 2 and try the same thing so again we have these atoms silicon here so they come here and so on and all of these and it just happens that another electron comes out of this bond and fills this hole so we have this complete bond here but then we have a hole here alright so in three consecutive pictures that we took we saw that these electrons were coming off of their bonds and fill in these holes or equivalently what we can say is that there was one hole and that hole moved from left to right it moved from here to here and then to here and because a hole has positive charge associated with it we can say that positive charge has traveled from the left side of the semiconductor to the right side as we look at it at different points in time so we can say a current has crew hasn't has been created as we go from here to here so we say holes are capable of conducting current just the way electrons are and that's a very important concept so when you remember this question that we raised how where the charge carriers come from well we have electrons that we also have holes and these two are two different entities that can simultaneously conduct current electrons can move and conduct current holes can move and conduct current all right if holes go from left to right we have positive current going from left to right if electrons go from left to right we have negative current going from left to right so that's something to remember I also want to emphasize that conduction by holes is not the same as conduction by electrons so let me raise the question here why are poles slower than electrons okay as we will see later when we give properties to electrons and holes we say holes are slower maybe I factor of two why is that well you can see here that the way this hole moved was actually by electrons being is released and trapped one electron was released from here and trapped here then another electron was released from here from here and trapped here so it's not like an electron that just shoots through the lattice and conducts current is the this operation of release and trap release and trap of electrons that equivalently allows a hole to move around and this trap in this release and trap process is slower than just an electron moving on its own without interacting with the other atoms so we say that whole movement of holes is based on release and trap mechanisms and that's why it is slower than the movement of electrons all right so that's what we have so far and now we need to look at a few other interesting concepts remember that I had this equation for the number of free electrons in a piece of silicon at a given temperature how many free holes do I have available as well it's the same number because if you take a piece of silicon for every electron that was released from a bond we have leftover left behind a hole so the number of holes and the number of electrons number of free electrons are the same in the in a pure piece of silicon so we say the density of holes density of holes is the same as density of electrons I'll just say electrons even though we mean free electrons and it's equal to ni for pure silicon okay so that's good to know now from now on we will give you some symbols to these so that we don't have to write them every time so the density of holes will be called lowercase P because P type is positive charge the density of electrons will be called n because it's n-type and these are equal to NI for pure silicon so that's good to remember we also write P times n is equal to n R squared Y well later we will see why we do that but that's what we need to remember okay all right so if I give you a piece of silicon at room temperature you will have 10 to the 10 free electrons per cubic centimeter and 10 to the 10 holes per cubic centimeter that's it right no more no fewer all right but what if you want more what if this poor conductivity is a problem how do we modify the density of free electrons and holes in silicon that is the next question that we need to answer all right so that brings us to what we called doping so let's go and add a page so we need to answer the following question how do we modify the density of charge carriers meaning electrons and holes in semiconductors for example in silicon well right now we're stuck with that 10 to the 10 number because that's what the equation tells us and we know that the number of free electrons and the number of holes are equal in a piece of pure silicon okay well to get there we go back to the periodic table and look at the small section of it to see if there's any other possibility so let me draw a small piece of the small section of the periodic table I will look at columns that correspond to 4 3 electrons so we know which those are for example we have silicon here and I think we have germanium underneath so germanium we also look at other columns we have a column with 3 electrons in the last orbital all with 5 electrons in that orbital so we have some elements that fall into this category for example boron so that's boron which sure has a symbol of B boron has three electrons in its outermost shell silicon has 4 germanium has for boron has 3 and then 4 5 we have for example phosphorus US Morris whose symbol is P no phosphorus has 5 electrons in its outermost shell all right so these present interesting opportunities for us to go and play with that piece of silicon so far I have said it I have said it's a pure piece of silicon but there's no particular reason why it should be pure what if we go in that crystal of silicon with all those nicely arranged as and try to introduce some other atoms maybe boron atoms or phosphorous atoms what exactly happens something just in me happened right so let's go ahead and do that and see what we get so here's how it goes I'm starting with a piece of silicon so again we have these silicon atoms that are bonded together and sharing their electrons and so on and then I go and in a very controlled manner add for example one phosphorus atom here and then I again have silicon silicon here I come here I come here etc okay so once in a while I add a phosphorus atom so what exactly happens in this case something interesting happens the phosphorus atom has five electrons in its outermost shell now when you start sharing these electrons with the neighboring silicon atoms it shares four of them just like the silicon did before so this phosphorus atom has one electron that is not K is able to share with anyone else right there's nobody else who wants that electron so there's one electron that sort of hanging here because it's an orphan none of these silicon's want it and the phosphorus has that free electron available so that electron now can participate in current conduction that's a relatively free electron that's readily available so we don't have to break an electron out of this bond for it to conduct current we already have an electron from this phosphorus atom that can conduct current so depending on how many phosphorus atoms are introduced into the silicon crystal I can have a larger and larger number of these free electrons so I can make this overall device more conductive by having more phosphorous atoms in it and this process of introducing a an atom of phosphorus or what we call impurity is called doping so doping means we take this piece of silicon and then introduce some non silicon atoms in here for example phosphorus okay so the resulting piece of silicon has a new name this is called extrinsic silicon to distinguish it from intrinsic or pure silicon and that we say silicon is doped or this is an impurity or is extrinsic silicon and then the phosphorus atom itself has a name this is called a donor because it donates an electron to this current conduction so we have introduced donor atoms inside this piece of silicon and now this overall piece of silicon that has extra electrons for conduction will have a new name this is what we call an n-type silicon because it has electrons more free electrons than pure silicon and called an n-type silicon or called extrinsic silicon and so forth all right okay so this tells us that we have a situation like this what's interesting about the situation is that now we can say that if we introduce lots of these phosphorus atoms a typical number is as follows so the density phosphorus atoms is about 10 to the 15 to 10 to the 17 per cubic centimeters so when we dope silicon typically we choose a number in this range depending on what we're trying to do this is considered lightly doped this is called heavily doped but no matter even if you are here and we see that the number of phosphorous atoms that we have introduced is much greater than the number of free electrons or holes that we had in pure silicon in pure silicon this was ten to the ten now we have introduced ten to the fifteen phosphorus atoms many 10 to the 15 free electrons coming from the phosphorus atoms so these electrons coming from phosphorus completely overwhelm the electrons that we had already in pure silicon in other words I can say that the number of or the density of free electrons in this doped piece of silicon and is approximately equal to then density of phosphorous atoms okay because we had some already from the silicon and now we have a lot more from phosphorus this is so much bigger we'll just keep it like that and this density has a name we show that by uppercase n and then lowercase D n is the density of the dopants that we're introducing and D shows that said donor density so we say that n is approximately equal to n D all right and it turns out that also we have n times P is equal to NI squared even this is no longer pure silicon of course we saw that for pure silicon before but even though n has gone up so much and used to be ten to the ten now it's for example in the Dean this product is still equal to NI squared ni that we had before why is that well because P goes down so much the number of holes available in this piece of silicon has gone down why because these free electrons that came out of phosphorus atoms very easily went and filled those holes so the number of holes much smaller and that's why n times P is still equal to NI squared all right so this is what we call an entire piece of silicon which is dr. to give us more electrons alright our time is up I will see you next time 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