in this presentation we will study charge densities in a semiconductor let's talk about electrical neutrality first I will explain electrical neutrality with one example and then we will move to charge densities in a semiconductor so first topic today is electrical neutrality electrical neutrality we will try to understand electrical neutrality by one example let's take a copper wire this is our copper wire and as we already know copper is a good conductor and hence there is a generous flow of charge when the potential difference is applied across this wire this is the potential difference of five volt battery and there is a current I in this direction now this copper wire is electrically neutral this wire is not charged but is neutral I can say this because I know the number of electrons entering this copper wire is same as the number of electrons leaving this copper wire for example let's say 100 electrons are entering this copper wire at time T and 100 electrons are also leaving this copper wire at time T which makes this copper wire electrically neutral because no charge is contained in this wire but if it doesn't follows the electrical neutrality then what will happen let's say 100 electrons are entering this copper wire but only 50 electrons are leaving so 50 electrons are still in this copper wire and because of this 50 electrons this copper wire is charged so the electrical neutrality is a very important concept and it is followed in case of conductor as well as in case of semi conductors so electrical neutrality is satisfied by semi conductors also let me write this point down electrical neutrality is satisfied by semi-conductors also let us consider a semiconductor material and consider a situation where this material is doped by both n-type and p-type impurity material so this is our semiconductor material and it is doped by both n-type and p-type impurity materials now we have already seen that electrical neutrality is satisfied by semiconductors also then I can say that I can say that the total the total positive charge is equal to total negative charge this is how we can define electrical neutrality in case of semiconductors if total positive charge is more as compared to the negative charge then this piece of semiconductor material is going to be charged in the same way if total negative charge is more has compared to the total positive charge then also this piece of material will be charged so for electrical neutrality this condition must be followed now we are going to add the impurity materials both n-type and p-type so we have positive donor ions and we have negative donor ions let me draw them quickly okay and let's say and D and subscript D is the concentration of donor atoms and n subscript a is the concentration of acceptor atoms small p is hole concentration and a small end is electron concentration now what is the total positive charge in this semiconductor material it would be it would be + D + small p m-- and subscript D is the concentration of donor atoms and they are positively charged small P is the concentration of holes and in the last presentation we saw holes are similar to the positive charge so the total positive charge is n subscript D plus small P in the same way the total negative charge is n subscript a plus small n so this is a very important relation that we have derived and we are going to use this relation to find out the charge densities in semi conductor now you have a clear idea why we have to study electrical neutrality first before going to the charge density so that we have this relation in our hand let's say this is equation number 1 now we have two cases we have two cases case number one in case number one we will consider an n-type material we will consider and type material we get an n-type material when we dope the pure semiconductor or the intrinsic semiconductor with a pentavalent impurity so in this case only a pentavalent impurity is added to the pure semiconductors note and impurity and hence we have hence we have an A equals to 0 there is no acceptor ion because we have a n-type material now you already know these things and we can put this na equals to 0 in this equation number one so from equation number 1 we can write and subscript D plus small P equals to small n because n a is zero or I can write and subscript D equals to small n minus P we are considering the case of n type material so it is very obvious that the concentration of electrons small n is going to be more as compared to the concentration of holes so we can neglect this P and we will have and subscript D nearly equals to small n so this is what we have derived in case number one and for a better understanding I am going to write this like small end having subscript small n nearly equal to and subscript D this n subscript small n is the electron concentration in n-type material small n is the concentration of electrons and small and having this subscript small n is the concentration of electron in n-type material this is specified for n-type material so this is what you have to remember and now we will use the mass action law that we under I've in the last presentation the mass action law says n P equals to n I square this is what we derived in the last presentation and we will use these two relations to find out the hole concentration in type material so I will write down this mass action law as small n subscript small n small P subscript small N equals to n I Square and this is for n type material that's why I have used small n as subscript for N and P now I will write down n subscript D in place of small n subscript n because we know in case of n type material the electron concentration is approximately equal to the density of donor atoms and D is the density of donor atoms so we can write n subscript D P subscript n equals to n I square and let us divide both the sides by n D and this will give us small P subscript small n equals to NI square by n subscript D so this is the end result for this case number one we will use this in numericals so please remember this now we will move to case number two and in case number two in case number two we will consider we will consider p-type material and the derivation is going to be really simple because we have just derived for n-type material and we are going to use the same concept in case of P type material we add trivalent impurity so we have holes and thus we are going to have and a you will have the acceptor atoms but we don't have the donor atoms so nd is going to be 0 and we will use the equation number 1 and we have 0 plus small P equals to na plus small n or I can write and a equals to P minus n as this is p-type material it is very obvious that the concentration of holes P is going to be greater as compared to the concentration of electrons so we can definitely neglect the concentration of electrons in this case and small P is nearly equal to the concentration of acceptor atoms again I'm going to modify this in order to remember that it is for p-type I'm going to use a subscript P I'm going to use a subscript P here and we will use my section law again to have the concentration of electrons in p-type material mass action law says and subscript P P subscript P is equal to NI square ok this P is for the p-type material and n subscript P we can write P subscript P as na so we have n a so n I square n subscript P is equal to NI square by and a we have divided both the sides by n a to get our and a result so in this presentation the important points to remember are these two results we will use this results in numerical problems and the electrical neutrality the concept of electrical neutrality not only in case of semiconductors but also in case of conductors