[Music] [Music] [Music] [Music] [Music] [Music] greetings this is electronic circuits one lecture number three and I am business savvy today we will talk a little more about carrier transport meaning how we move charge in a semiconductor and then we are ready to build our first semiconductor device namely the PN Junction before we do that though let's quickly review what we learned in the last lecture so let me hold this over here what we saw last time was that since the number of free electrons in pure silicon is relatively low about 10 to the 10 per cubic centimeters a pure silicon is not a very good conductor so to increase its conductivity we can introduce impurity atoms into it for example phosphorus as a an atom that has one extra electron that can be donated or boron that has one fewer electron and can create a hole so we said that in n-type semiconductors we doped them with some sort of donor for example phosphorus and because phosphorus has 5 electrons in its outermost shell it ends up with one free electron that is capable of carrying a current and as if the doping level is high enough let's say 10 to the 15 or 16 then the number of free electrons per cubic centimeter is approximately equal to the number of dopant atoms that have been introduced into silicon and that means that number of holes has fallen to an I squared over n D okay we can also create a an a large number of holes in a semiconductor by introducing acceptor atoms such as boron boron has only three electrons in its outermost she´ll so it creates a hole and that hole we have as many holes as many as boron atoms so again if the density of boron is high enough we have a hole density approximately equal to the number of acceptor atoms introduced into silicon and then the number of electrons has fallen considerably to NI squared over an a so these two types of doping help us create majority carriers in the form of electrons or majority carriers in the form of holes and as we will see in a few minutes this is the basis for building a PN Junction now we also started looking at carrier transport meaning how charge moves in semiconductors and we considered a piece of silicon with some amount of doping in it n type or P type and with a width of W and a thickness of H and we saw that we have a two mechanisms one of which is called drift drift simply means we apply voltage across the semiconductor and that creates a current because we have created an electric field inside the semiconductor for semiconductors the velocity of carriers is similar to a parachuters reaches a terminal velocity and is equal to MU times the electric field mu being the mobility of the carriers electrons or holes so we derived an equation for the total current that flows which was given by the velocity of the carriers times WH which is the cross section area of the object we're going through times the density of electrons or holes twines the charge on one electron to give us a total current and we saw that in semiconductor physics we generally would like to express the currents as current densities that means the amount of current that passes through one unit area of the object so one square centimeter for example and that would be Jenny and it's given for both electron flow and hole flow by this expression so here we are assuming that there are some free electrons that carry current and there are also some holes that can carry current now one might be much less than the other but in the general case we need both of these terms multiplied by the electric field all right now I think I forgot one term here we need to add a cue term here so let me make sure that I don't forget that we need to multiply this by the charge of one electron so that the overall expression is in amperes per square centimeters okay so this is one mechanism for current conduction in a semiconductor there's an electric field there's velocity that's correct but there's another mechanism that does not even require a voltage or an electric field and that is called diffusion so today we will talk about diffusion all right so today is a lecture we'll start by talking about diffusion and how we quantify that effect and then that completes our study of current transport and then we go to the first electronic device that we can build the simplest namely the PN Junction so we will study some applications of PN Junction to give us some motivation for why we study this device then we'll talk about the basic structure of this device and try to familiarize ourselves we'll take our time and slowly understand what's going on and then we consider it under one condition which we call equilibrium this device can be considered in different conditions maybe three conditions so we will study only the first one today and then the next a few in the next lecture okay so let's talk about diffusion and see what that means Paris as I said we could have current without voltage strange but true because have volt current without voltage now that goes against everything that we have thought about before that Ohm's law and everything else but just hang on there and we'll hang in there and we'll see how that happens so I would like to show you a quick example of what happens in the in the process of diffusion so here we have a glass of water and I'm going to drop some ink into here so what happens well as you can see the ink molecules are diffusing the ink molecules are going everywhere not just downward because of gravity but also sideways they are going in every direction why is that why do the ink molecules prefer to redistribute themselves well this is because the ink ink molecules have a high concentration where they were injected into the glass writing right here and they would like to equalize their distribution equalize their concentration so what they do is they go from the high concentration area to the low concentration areas and that is called diffusion so diffusion is defined as movement movement of charge carriers now of course doesn't have to be charge carriers it can also be ink molecules or anything else you would like but in our case we are interested in charge carriers movement of charge carriers from region a region of high concentration to a region of low concentration okay just the way the ink molecules decided to redistribute themselves so what we see is that if we inject charge if we inject for example electrons into a piece of semiconductor then at the point of injection we have a high concentration and they don't want to stay there they begin to diffuse away into the regions that have a lower concentration and that's how you get a current because the charge is moving from the constantly the high concentration region to the low concentration region and that is current because current is defined as the movement of charge so alright so that means that if I take a piece of semiconductors so let's say n-type or p-type doesn't matter so let's say in tight semiconductors and somehow I inject electrons into here so injection of electrons so if I inject electrons here right around here we have a high concentration so if we plot as a function of distance starting from here at this point we have a high concentration of electrons because we're injecting lots of electrons but electrons don't want to stay here they diffuse away so if we go over here and measure the concentration of electrons let me be lower if we go here we lower and so on so it goes down we don't know exactly what form it goes down but it goes down so we have a high concentration here a low concentration here we say we have a gradient from here to here gradient of concentration and we think of these electrons as rolling down this gradient this like a slope on a hill so they would like to roll down this gradient and go to the other areas where concentration is lower so we have an electron here and electron rolls down this hill because we have a high concentration here and low concentration here and that's a similar effect can occur with holes just keep in mind that if electrons are going from left to right the conventional current which is positive is going from right to left for holes that's fine if holes go from left to right then the conventional current also goes from left to right so these two must be distinguished very well so how can we quantify a current resulting from the field we don't have an electric field we just have different concentration levels well what we are thinking is that the amount of current now we can write I or we can write J will write J we we are thinking that J the current that flows through the semiconductor at any point if I stand there should be proportional to the slope of this concentration you can imagine that if the concentration is constant from here to here let's say there's no injection there is no diffusion right if the you can see that now the ink has completely diffused and there's no more tendency to diffuse any way anymore so if the concentration is constant if the gradient or the slope is zero then there is no more diffusion so it must be proportional to the slope of this concentration so what I'm thinking is that this should be proportional to the slope of the concentration and for electrons P for holes with respect to distance that's what we intuitively expect okay all right so then how do we write this as an equation well we say it has to be equal to DN over DX and then some proportionality factors again to get the unit's right and we call this D sub n D sub n is called the diffusivity of electrons so this is called the de fée you see VT of electrons if it's d sub n this equation is not complete yet why because the current has to be in amperes per square centimeters but this what amperes yet because we don't have any notion of amount of charge that we have charge in coulombs so we put a cue the a DQ meaning charge per electron at the end we multiplied by Q so that this whole thing is now in in the amount of coulombs that pass in one square centimeter in one second and that would be J alright so that is the diffusion current arising from electrons from from the different concentration of electrons if the concentration is not constant now as an exercise you need to prove that even though these are electrons the current the conventional current would still be like this in other words you don't need a negative sign we don't need on it we do not need a negative sign here even though these are electrons so just thought about a thing about it for a few seconds and you will see why this sign is positive not negative all right what if we have both electrons and holes available in a piece of semiconductor and both of them have concentration gradients well a similar effect will occur so we will have DP over DX if there is a concentration gradient for holes and then we will have to multiply it by some diffusivity the diffusivity of electrons is not the same as if you sativa holes so we will call that D sub P and then we just add them up so in general if we have both electron concentration gradients and the hole concentration gradients the total current density is given by starting from electrons we write and derivative of n with respect to X minus DP derivative of holes with respect to X and then the whole thing multiplied by electron charge so again you need to prove to yourself that in this case this sign is positive and the sign is negative when we consider the gradient in hole concentration and the gradient in electron concentration all right so that's a nice little equation that we have for diffusion we don't need electric field we just have different concentrations and different points in a semiconductor ok so let's look at a quick example to see how diffusion actually occurs and what consequences we should expect so I perform an experiment I take a piece of semiconductor so let's draw it like this let's say n-type semiconductor and I inject electrons into here so injection of electrons and we examine the concentration of electrons from here to here so this is distance and we plot the concentration we go in here for some particular device and particular arrangement we measure the concentration as a function of X and what we observe is as follows we see that the concentration goes like this so this is n as a function of X okay it's not a straight line going down it has this behavior alright now what you would like to do is plot the current the diffusion current resulting from this concentration gradient the concentration is not constant here we have the highest because we're injecting the electrons right here and the concentration keeps going down in a nonlinear fashion so what you would like to do is plot the resulting diffusion current okay no problem it's just this DN times DN over DX so the diffusion current density J would be because the derivative is negative the current is negative so the current goes like this here we have a higher slope here we have a lower slope so the current goes like this we have a in magnitude in absolute value we have a large current at the beginning so I can even start from and that the current decreases as we go farther into the material okay so nothing exciting so far but this poses an interesting question we see that at this point we have a high current so let's say at this point we have one milliamp per square centimeter and this current is completely composed of free electrons but then here the current is less in absolute value it might be point two milliamps per square centimeter and again it's only consisting of electrons so something strange is happening here we had lots of electrons here carrying the current but by time we got here we don't have that many electrons left what happened to those electrons when we injected these electrons into here and they started propagating because of the concentration difference they were rolling down this hill why is that they are disappearing as we go here why is that the amount of current is less are the electrons just disappearing in thin air or something happened to the electrons well the answer is that if indeed we observe this behavior it only means one thing it means that the electrons that are propagating in positive x direction must be recombining with the holes that are present in that piece of semiconductor so if we see this behavior the only conclusion the only possibility is that the electrons must be combining with holes as they go this way and that's why we fewer electrons over here than over here so for this behavior we observe that injected electrons recombine because these recombine we can just say combine recombine with holes in the semiconductor okay and that's why the current decreases as we go further in now you may say well I don't this semiconductor with a donor with let's say phosphorus so much that the number of holes available is very very small orders of magnitude smaller so that shouldn't exist this shouldn't happen because we just don't have enough holes they have very very few holes for recombination so if that is the case then the plus will not look like this so let's try to do the plot for the case that the number of holes available the density of holes is so small that just not any significant recombination of the injected electrons with the holes so for that I will change the color of my pen to red and this is what we observed okay so if we work backwards if we know that there is no recombination because we don't have that many holes in the semiconductor then the current in up carried by electrons has to be constant it cannot go like this so the current has to be for example something like this so this is the case of no recombination okay now we work backwards if J is constant like this what should it look like it should be a straight line with a negative slope so n has to be like this so that is the case of no recombination so we see that diffusion still occurs the gradient in concentration still exists but it's a straight line so if if that's the case then the current is constant the current carried primarily by the electrons there are not that many holes in there and everyone is happy on the other hand if the holes are not that small then we will see something like this and we'll see something like that all right very good let's move on and let me just mention a few more concepts here so we saw that the diffusion of carriers is characterized by this equation and we have electron diffusivity and whole diffusivity in there if you're curious about the values let's see if I have those values somewhere here yes so the N is a 34 centimeter squared per volt well so I said centimeter squared per second centimeter squared per second and DP is 12 centimeters squared for a second as you can see I don't remember the units or the values of these constants because I don't use them very often but that's okay we can always look them up and these are the values that we have okay now let's go back to the concept of drift remember for drift this is what we had we said the current carried by drift is given by the mobility times the electric field times the electron charge times the concentration concentration of electrons concentration of holes so that is a drift current that's the diffusion current so in the drift current we have a parameter called mobility to show how mobile the electrons are in the presence of an electric field in the diffusion we have a parameter called diffusivity that shows how willing electrons or holes are indeed to diffuse in the case of concentration gradients so these are two different parameters and they describe different types of behavior but what's interesting is that there's actually a relationship between mobility and diffusivity which we'll use later on to simplify our equations so that is called Einstein's relation and I stands relation says that D over mu for a given type of carrier electron or hole is equal to KT over Q K is Boltzmann constant T is absolute temperature and Q is the electron charge I usually remember K 1.38 times ten to the minus twenty-three and temperature for example 300 I don't remember the electron charge but what I do remember is this whole quantity this whole quantity actually has a voltage dimension and this whole quantity is equal to 26 millivolts at room temperature as you will see this quantity KT over Q appears in many many types of studies that we do in electronics so it's good to remember this voltage it's good to remember is value this term you know you could remember the expression sometimes this is called the thermal voltage so sometimes we call this the thermal voltage okay so Einstein's relation allows us to simplify things in case we end up with the ratio of diffusivity and mobility we replace it with KT over Q and we carry this on as you will see shortly this appears in some of our equations even today very well let's see where we are okay this concludes our study of charge transport or current transport in semiconductors in summary we have seen two effects drift when we have a voltage and electric field and in response to that electric field we obtain in this type of current and when we have diffusion we obtain this type of current and of course we could have both of these at the same time in sum the semiconductor under some conditions but it's good to remember that these are very different mechanisms and they do different things even though the final result is current conduction and as we will see in electronic devices sometimes we have that sometimes we have this or in some part of the device we have that some part of the device we have this so these are the two mechanisms that we have to remember very well we are now ready to apply the knowledge that we have developed so far to the first electronic device that we can build namely a PN Junction so for that I will add a new page and I will draw a line in the middle okay so we're going to study PN junctions PN Junction all right well the as the name implies there's a junction meaning that two things are connected and presents a PN Junction so maybe we took some P we took some N and we made a junction I mean we we put them together and that's what we call a PN Junction so at a very high level that's exactly what we're doing we have a piece of p-type semiconductor for example silicon doped with boron and a piece of n-type semiconductor for example silicon with phosphorus atoms and we have attached them together to form a junction right here this is a two terminal device and this is one terminal this is the other terminal so it's good because we are used to two terminal devices resistors capacitors inductors the only device that we have seen that had more than two terminals was the transformer but beyond that most of us terminals we have played with have only two terminals voltage sources current sources switches so this device has two terminals it consists of a p-type semiconductor attached to an n-type semiconductor so we call the PN Junction okay so what's the big deal why do we study this device well first let me give you a few examples of where this device is used so in all electronic devices where we have chargers adapters where you take the voltage from the line from the wall under 10 volts or 220 volts and then eventually you bring it and convert it to 3 volts for balls for a cell phone or 12 volts or 18 volts for a laptop and all of these devices all of these chargers all of these adapters we need this type of device a PN Junction a PN Junction is one example of what we call a diode so this device is also called the diode and diodes are essential to building all of these various devices chargers and adapters so chargers and actors any way that you use them you have diodes in them they'll have other interesting applications for example what we call voltage multipliers voltage mob tip voltage multipliers are circuits that increase the voltage for example there are some devices called photo multipliers used in medicine and other applications where we need a supply voltage of 1200 volts okay 1200 volts is a very high voltage so how do we create such a voltage the line voltage that we have is 110 volts or 220 volts so somehow this voltage has to be multiplied up to 1200 volts and that there again we use diodes and capacitors to do something like that so there have many interesting applications in real life okay now this is the first semiconductor device that we study and as such it has it is the simplest because it has only two terminals that's another reason we start with PN junctions or diodes we don't jump into transistors because transistors are more complex so first we have to learn how to walk before we learn how to run and that's the a good entry point for understanding semiconductor devices now let me before studying the details here let me just show you a quick experiment and see what happens so quick experiment all right so I will perform two experiments on this board to show you some interesting effects first experiment let's take a piece of n-type semiconductor and apply a variable voltage to it and measure the resulting current what should we expect well this is just a resistor remember we calculated the resistance based on mobility and carrier density and so it's just a resistor so if I sweep VX from minus infinity to plus infinity I just have owns log so I know that I X is equal to VX over R R is the resistance of this piece of semiconductor and we just have a nice straight line like so and as you can see the slope of I X as a function of V X is 1 over R so this slope is 1 harsh so nothing dramatic very simple okay well what if I try the same experiment with this beast this PN Junction now we don't know what's going on in the PN Junction yet but I just want to give you a quick preview of what we will see all right so here's a PN Junction so for example we have p on the left and on the right and we perform the same experiment a variable voltage source connected to the two ends V X and we're trying to measure IX so what do we measure let's see so V X PI X okay well if V X is positive we see some current and the current does vary as a function of V X but it does not vary linearly with varies like this that's very strange isn't it also interesting if V X is negative what we see is that IX is almost zero so PI X is on zero so if you compare this with this you see a dramatic difference between what a PN Junction does and what a resistor does the PN Junction does not satisfy Ohm's law anymore it has two types of differences with respect to resistor number one it has different behavior for positive voltages and negative voltages it can tell the difference positive voltages we have current negative voltages we have very little current and the second difference is that when the voltage is positive is not a straight line like a resistor like simple resistor but a strange function in fact it's an exponential function so these two differences can make diodes much more interesting and useful than resistors and that's why they have so many applications as I mentioned before so our objective is to eventually derive these things understand how they come about well by delving into this device and see what's going on with the electrons and holes etc and of course once we have this somehow we would like to create a an electrical model that we can use in analysis and design of circuits using such a device so but step by step we'll take our time all right so let's I would like to raise two questions that we need to answer to understand how a PN Junction operates so let me write the two questions here question number one [Music] when we have a p-type material we have lots of holes very few electrons when we have an n-type material we have lots of electrons very few holes so what happens when we attach them together and write up this interface what exactly happens do they fight each other they don't this slide they don't agree with each other so what exactly happens right so we will ask this question formally how do the charge carriers redistribute themselves after the PN Junction is formed what happens to all these free electrons and holes they are different here from here so when we attach them right at this interface what happens so that's something we need to study very carefully the second question is after we understand that how does the PN Junction behave under three conditions condition number one what is what we call equilibrium equilibrium condition number two is what we call reverse bias and number three for word bias these are all unfamiliar words and expressions don't worry we'll get there but these are two questions that we need to answer so that we understand how the PN Junction behaves and eventually reach this type of characteristic okay so before answering the first question I need to refresh your memory about a few things that we have studied so far so let me change the color of my pen okay so some observations these observations are necessary before we can answer the first question all right so we buy a piece of n-type material and we go in there just by itself without connected without being connected to anything else in the world and try to measure the concentration of electrons and the concentration of holes as a function of distance from here to here so what do we see as a function of distance well we know that we have lots of electrons and very few holes because this is an n-type material so what you will see is that in is up here and P is down here and that is the concentration axis and is very high P is very low how much is in remember the equation we had and was actually about equal to nd the number of donor atoms per cubic centimeter and P was an I squared divided by nd so far so good let's repeat this for a p-type device so here's a p-type device here is that our x-axis some got a p-type device and we are plotting the concentrations in a p-type device we have lots of holes very few electrons so we have lots of holes here that's P and we have very few electrons so that's in and we saw that the number of holes the per cubic centimeter is given by the concentration of acceptor atoms whereas the number of electrons is given by in I squared over an a I hope you can read this on the screen okay so that's just the quick summary of what they have learned before for n-type and p-type doped types of semiconductors now when we try to form a junction of a piece of n and a piece of P right here the notation can be very confusing I have in here I have in here I happy here I happy here so I have to make sure that the all of these parameters don't get confused so we're gonna add some subscripts to distinguish these from each other so let me change the color of my pen so that I can emphasize these subscripts maybe to black so the concentration of electrons in the n-type material would be n sub n sub n refers to n-type material similarly the concentration of holes in the n-type material will be P sub n so P sub n so the subscript refers to the type of material we have p-type or n-type similarly on the other side if I have a p-type material the concentration of the holes in the p-type material will be denoted by P sub P and the concentration of electrons by n sub P so I hope that this is clear you don't need to be comfortable with this notation because we will use it extensively and then it can become a little confusing very well so that is the situation when I bought a piece of n-type silicon and a piece of p-type silicon and then I'm ready to attach them to form a PN Junction now I should mention that if you do actually that if somehow you go on by a piece of p-type the piece of n-type silicon and try to attach them you will not have a PN Junction because for the PN Junction to behave as I mentioned before this entire device has to be one single crystal and we cannot create a crystal if by just attaching or gluing or melting two pieces of pn n together to form a junction so in reality we start with one piece of silicon here and then we dope these differently to create P and n we cannot just buy them and attach them but assuming that we have a good crystal here and we have some P doping on this slide some n doping on the side we are now ready to study it in detail okay so let me consider the first case okay so the next observation that I would like to make is the following let's consider a piece of n-type silicon just by itself it has an abundance of electrons it has very few holes so the question I ask is what is the net charge in this device what is it at charge well we said we have lots of electrons very few holds so does it mean that the net charge in this piece of silicon is negative no it does not mean that remember that this n-type material just consists of silicon atoms and phosphorous atoms and nothing else we didn't do anything else so we still have charge neutrality because every electron that is present here has one counterpart proton in the nucleus of an atom so if the electron is available from a phosphorus atom that phosphorus atom still has a proton inside the nucleus if the electron came from a silicon atom the silicon atom still has a proton in its nucleus so the total charge in this piece of silicon is zero regardless of the doping level that we have whether is doped or not doped or p-type or n-type so we say we have charge neutrality okay so net charge is zero all right now let's go one step farther and ask in the next question what if I take that piece of n-type material and I happen to take one free electron out of here completely out of the material then what happens well that electron came from somewhere let's say from a from the phosphorus atom right now because we took the electron out of the material we have a positive iron left behind so we will denote that by a circle with a positive in it so if an electron is taken out or extracted the device then we have a net positive charge and that's a result of a positive ion a positive ion is formed okay so like everything else so if you take some charge out of some object some device yes then there's the opposite charge left so if you take an electron out of this we have a positive charge left and that positive charge is associated with one ion so it's important to understand the difference between these two because when we go to the colibri emission we need to remember these very well now with these I think we are ready to embark a pound upon our first study of the PN Junction so let me add one more page all right okay so what we will study now is the PN Junction in equilibrium and pn-junction equilibrium simply means after you form the pn-junction from a single crystal just leave the terminals open don't connect them to anything else in the world so here's our PN Junction [Applause] we have the terminals here on the two sides but they are left open they're not connected to anything else okay this little line here in the case where the doping level changed from P to n and we're assuming this is an abrupt change so it's P and then suddenly it changes to N and now just to make sure that I have these didn't write so at this point I will call the left section N and the right section P so n-type material a p-type material this is the junction interface okay so now what happens well let's remember from the previous page so if I take the previous page for a second remember what happened in N and P before we formed the junction we had n sub n electrons per cubic centimeter on the inside P sub P holes per cubic centimeter on the P side these are the majority carriers and then we have the minority carriers on this side P sub N and L sub P so we're going to form an interface between the P on the end and see what happens so let's go back here and see what we get okay so I need to draw those consultations again so that we remember where we are so we have a high concentration of electrons n sub n ok let me do this more carefully and seven and a low concentration of holes P sub P P sub n then we have a high concentration of holes on this side which we call P sub P and then we have a low concentration of electrons which we call P sub n right that's what we have in the n-type and p-type pieces now when they come together something interesting happens if you look here we have lots of holes you have a high concentration of holes on the right we have a real low concentration of holes on the left so what should happen you should have diffusion because that's how conditions for diffusion are provided they have a high concentration of some particular particle and some low concentration of the same particle so the particles prefer to go to the low concentration area so holes which are majority carriers on the right begin to roll down the gradient and go to the left similarly electrons which are majority carriers in the n-type material begin to roll down this gradient and go to the right so one hole starts from here and goes here one electron starts from here and goes here now remember the charge neutrality principle before we put these together the n-type material was neutral it had as many electrons as many positive negative charges as well as much as positive charge this negative charge is counteracted by some holes and then some protons similarly this guy was neutral but now when I place these together when I form this junction an electron starts from here which has a high concentration and goes here we have taken one electron out of this material if I take one out of a piece of material what happens a positive ion is left behind so for every electron that departs this section and goes to this section we end up with a positive ion a positive ion is an atom that has lost one electron so here it is a positive ion so this continues so we form lots of positive ions on the left side because lots of electrons are leaving the left side to the go to the right side what happens to the right side well lots of holes are going from the right side to the left side every time a hole leaves in fact it is filled by the electron so we form negative ions so we have lots of negative ions here so this continues this continues for a while we have a current consisting of electrons going from here to here we have a current consisting of holes going from here to here so if holes go from here to here the conventional current also goes from right to left okay so we are the current going this way if the electrons go from left to right negative current is going from left to right so positive current still going from right to left so for both of these components we have a current going from right to left so we have a current going this way holes going this way electrons going this way but that's strange isn't it how could we have a current if the terminals are left open that goes against what we intuitively understand well what should happen is that this current may flow for a while but then eventually has to stop and the question is what exactly stops the flow of current well we have these ions that are formed here we have positive charge here negative charge here so in this area here we truly have a charged object charge neutrality does not hold because we have positive ions or negative ions so right around here we have positive charge right around here we have negative charge if we have charge in the net charge we can associate an electric field with that net charge so as we expose that these positive ions on the left and negative ions on the right we create an electric field in this region which way is the field pointing well we just take a positive test charge and put it here and see which way it goes so you put it here the positive charge is pulled this way by these negative guys or push this way by these positive guys so the electric field is pointing from left to right okay all right so that's a lot of information coming through but we saw that we had a diffusion of these currents the diffusion of these holes and electrons which resulted in a current at the same time as these the carriers were moving they were leaving behind ions and these ions formed a charged space charge and that space charge starts creating electric field so we have an electric field going from left to right okay all right so we have an electric field now what does this electric field do well the electric field says if you place a positive charge here I want to push it that way so it doesn't want any positive charge to go this way so if a hole wants to go this way this field opposes it similarly because of these negative ions here the field says if you bring in a negative charge here I want to push it that way so if these three electrons want to diffuse this way the electric field wants to stop them so the electric field that is being created in this region is opposing the diffusion current of the electrons and the hole so you can see now what happens right we have a diffusion of of holes and electrons flowing we have a current flowing but as they flow they leave behind ions the ions create an electric field the electric field opposes that diffusion current and as a result these currents begin to stop so at some point this field is strong enough to stop the de fée hold this way and the diffusion of electrons this way and that's when the junction reaches equilibrium the equilibrium means that the electric field has reached a point to stop the diffusion currents okay and now we call this region this region here where we have only ions the ADI free charge has left has gone to the other side you have only islands this is called the depletion region depletion region it means it's depleted of free charge carriers we don't have any free charge carriers left here because we have only positive ions ions are not able to move around so we don't have any charge we don't have any current conduction all right that's what we call the depletion region and we see that we have an electric field okay so our time is up and we will talk a little more about the equilibrium condition in the next lecture and then we go on to answer the other two questions the other question namely there are two conditions namely what happens when we have reverse bias when we have what happens when we have forward bias and those terms although unfamiliar simply mean what we what do we see here and what do we see here positive voltages and negative voltages across this PN Junction I will see you next time [Music]