 you can follow along with this presentation using printed slides from the nano hub visit www.nano hub.org and download the PDF file containing the slides for this presentation print them out and turn each page when you hear the following sound enjoy the show I'll just begin talking about the interface charges and then pick up the real meat of the discussion in the next class now one thing we realize that this interface between silicon and silicon dioxide that region is a very complicated region you know silicon part you understand diamond lattice do you remember from long back diamond lattice one for the body along the body diagonal and everything silicon is beautiful every electron where they are supposed or every atom where they're supposed to be very nice but as soon as you go to the oxide first of all oxide is amorphous meaning they are in random places so that's what I have shown here that the silicon and oxygen they are sort of randomly configured and then there are also dangling bonds like silicon hydrogen and I explain in a second why they come I have shown on the top how a silicon oxygen bond silicon dioxide actually looks like so the little tetrahedra with four red circles just focus on one element with four circles around this rates are oxygen and little balls inside in so which is a let's say a whitish color that that one is silicon silicon binds with silicon binds with four oxygen right so it binds with four red atoms you see and every red atom every oxygen is sort of bound by between two silicones every rate look at every rate every rate has two silicon atoms the white atoms sort of connecting it up therefore you have silicon dioxide because every silicon connects to four but every oxygen is shared between two so as a result effectively every silicon has four halves right four halves and that gives you silicon dioxide so this is the amorphous structure of silicon dioxide this random networks of tetrahedra this is not diamond lattice diamond that is doesn't look like this this is a tetrahedra but it looks like very different from diamond lattice right so that's silicon dioxide so anytime a oxygen is missing that's a trap that's where all those charges were being trapped before in what I was showing you before and each of the tetrahedra that's what I wanted to make the oxygen is a red and that's being shared between two silicon that's the ash colored ash colored atoms so you can see why this is called a silicon dioxide many times again you will put it on a flat surface because difficult to draw into dimension and draw correspondingly and I have shown you before right how the tetrahedra you pull on tetrahedra out and late flat and this has the four covalent bonds I've shown you before but you realize that the atoms on the surface are unsatisfying because everybody has sort of four nearest neighbors atoms on the surface how many did they have they have sort of three and one of them is sort of dangling and that's not a good thing anytime a bond is unattended that can cause trouble and what happens do you remember that we calculated how many atoms do I have on a surface one zero zero surface one one one surface do you remember and because those bonds are dangling those bonds can capture electrons so those will all come as surface states do you remember the surface state surface recombination velocity and all so this is those from exactly from that diagram so you will have a series of surface states because the crystal is no longer periodic you're stopping it as a result you will have a series of dangling bonds which are not the solution of the periodic Schrodinger equation how many do I have such dangling bonds okay I will you have done this in a homework how many how many could it be number of atoms silicon atoms is on the order of 10 to the power 22 23 right per centimeter cube so if you just make an estimate number per centimeter squared on one zero zero surface would be on the order of 10 to the power 14 per centimeter square per centimeter square and if you didn't do anything that is the defect number of defects you would have had that's the blue line that's the blue line number of defects you would have had 10 to the power 14 per centimeter square that's huge number of defect no hope that a freely exposed silicon will carry any current through its surface no hope every every one of them will be caught by caught by those dangling bonds because it wants another electron wherever it gets it if it's going from source to drain it will catch it and keep it for itself so this is going to be a horrible situation so when you put the silicon dioxide remember that silicon the tetrahedra I just showed you a silicon shared between 4 oxygen and the oxygen being shared between 2 silicon remember the previous picture so that has been laid flat laid flat on the page and that's how it looks so as soon as you bring oxygen a bunch of those dangling bonds are satisfied because they take care of it but the silicon dioxide has a different lattice constant than silicon therefore not all of them are satisfied you can see that the oxygen has taken care of some silicon but a fraction of them are still dangling and therefore when you oxidize it reduces the density to 10 to the power 12 right because many of them have been taken care of the oxygen but still 10 to the power 12 one we did with 10 to the power 12 number of centimeters squared of interface traps so then that is the story of 1960s that they then spend a huge amount of time to pull this push this interface defect density down to 10 to the power 10 nowadays now what is generally done in this case that if you have a lot of dangling bonds on the surface silicon surface then of course the first thing one would do is to bring down the silicon dioxide and this is the flattened version of the silicon dioxide where you see the silicon being sort of nestled between four four atoms oxygen atoms and every oxygen being shared by 2 silicon and that gives you the formula silicon dioxide because silicon half of the four each one gets and that's why it's silicon dioxide now of course what it does is that what you can do then is do this anneal it's called a forming gas anneal forming gas many means that once you have grown the silicon dioxide after that you put it in a chamber where you bring in some form of hydrogen some form so there are various ways you can bring in silane on various compounds you can bring in but the bottom line is you bring in that hydrogen molecule or hydrogen molecule which reacts on the surface and then every hydrogen sort of ties up ties up the dangling bonds and you realize it needed one it had one dangling bond hydrogen has one electron one proton and it's a small atom so it can just get through anything and therefore they will come down and essentially passive it all those bonds and now all the silicones are satisfied electrons can grow or go on unimpeded from source to drain without being sort of trapped by the dangling bond off of silicon now this process is very important but before even before that so first of all this will reduce it to a tremendous amount but even before you bring in silane what is done at many times is that this processing of silicon dioxide the growth of silicon dioxide generally has to be done at a very high temperature the temperature you see here in degrees centigrade is 1100 or 1200 degrees C and that will give you a look at the plot it gives you about 2 times 10 to the 11 here you have not yet done this hydrogen or forming guess an eel or the passivation not yet but you still have 10 to the power about 2 times 10 to the power 11 even when you anneal it at 1200 degrees C and it's very important that you keep the anneal temperature very high because if your anneal temperature is low then the number of defects that you have a dangling bonds that you have in the surface can be a very large number one thing I want to point out that this is 111 surface that's where the experimental data is reported from but if it is on 100 surface it will be one third less and this is something you should understand because this is something people often ask you in various interviews and other things that why is silicon is on 100 surface although in many cases 111 surface might have better mobility right it could have better mobility the reason is that when you cut in terms of one zero zero surface the number of bonds you have per centimeter squared is actually less and that they are for the number of dangling bonds are less and as a result you have less strap on one zero zero surface and therefore people prefer to do it and one zero zero surface but here is a 111 surface and you have that certain number the interesting thing is that if you anneal it at a particular temperature and then anneal simply means heating it up just put it in a chamber a piece of silicon and raise the temperature of the furnace like in a microwave you put something in raise the temperature so raise the temperature and if you do that then essentially the number of defects will go down now these are essentially broken silicon bonds which are about to react with oxygen that was coming down but didn't have a chance to so high temperature helps in the reaction process now the best one is of course if you always anneal it in the ambient nitrogen or hydrogen environment rather than pure dry O2 so in that case you can see you can have a flat region even at lower temperature let's say 800 or 9900 degrees because it ties up all the bonds on the on the surface now once you have done it once you have done it then you can see the defect density might go from 10 to the power 12 you can see the blue curve which is ad oxidized and do you see between these two so this is saying that in the mid gap region remember the mid gap regions are the ones that are most interesting we're talking about traps right do you remember Shockley-Ridhall that if you have a lot of traps close to the conduction and valence band doesn't matter the ones that are most effective for Shockley-Ridhall recombination or surface recombination are the ones that are in the middle mid gap region and you can see here that number is on the order of 10 to the power 12 if you do not do any forming as anneal or do not tie it up with hydrogen but as soon as you do so you can see that the number reduces to 10 to the power 10 and this is these today is what you need in order for an operating good MOSFET that you can buy for your Pentium and other processes numbers on the order of 10 to the power 10 number of states per centimeter square now when this defects goes from 10 to the power 12 to 10 to the power 10 after this hydrogen passivation now these defects correspondingly the signature of it that you have been able to reduce the number of defects is also reflected in the CV characteristics you can see here on the bottom right hand side that I have plotted the capacitance as a function of gate voltage now do you see that this capacitance is flipped because the all the capacitances that we had been looking into accumulation was on the negative gate voltage because the substrate was p-type now this particular experiment I have taken it from the book or particular diagram I have taken it from the book in that case the substrate is n-type if it is n-type then you realize that all the voltage polarity required to see accumulation depletion and inversion those will all get the other other way around and you can see that before you have a strange CV curve that goes from it has the accumulation on the right hand side to a particular value do you notice that C divided by C naught is equal to 1 because in accumulation the charge is just sitting next to the oxide so that's why you have it one and then as you go through this threshold of flat band region and gradually go to the accumulation region I'm sorry the inversion region then you can see that on the other side starting from minus 10 volt this is essentially flat and it will lower value of capacitors what frequency is this this is at relatively high frequency right because this is not a higher otherwise it would have gone back and this is a capacitor structure how do you know because in transistor you would have never seen that the flat region well which is at high frequency because in transistor high frequency even at high frequency it goes back to 1 right threshold voltage minus 10 volts here you see that that's where it becomes flat alright now this blue curve corresponds to that very high defect density 10 to the power 12 let's say what happens that after you anneal the effectiveness is reflected by the sharpened by much sharpened the rate rate CV characteristics and you can see it remains flat for more regions the flat band is close to one and the threshold voltage has gone down significantly you see that it's my about minus 2 minus 3 volt and this has happened because all the interface traps that were trapping charges before you know this QF and QIT that was the interface chart those have been taken out therefore your threshold voltage has gone back now this is very important that you understand the physics of this stretch out this is called this blue car this sort of looks like you have stretched the rate curve out so that's why it's called a stretched out CV it gives you a lot of information about the status of the surface remember surface is everything in MOSFET surface is everything and so that gives you a status so we want to understand why this blue curve looks like this why is it stretched out like this so that is what I want to explain to you now this is very important to understand that just like donors is an atom donor is an atom let's say which gives away electron right close to the conduction when gives a electron every trap have very similar characteristics but in this particular case these donor levels the surface levels of course are spread throughout look at the left hand side plot I have plot the conduction and valence band and I have plotted the just close to the interface between silicon dioxide and silicon now the blue and the red these are actually the same surface states now the dotted line is a Fermi level now this is let's assume that these levels are donor like these are not donors these are donor like what it means is that you know when your donor level is below the Fermi level then the donor is full right because it hasn't given away its electron when a donor doesn't give away its electron then it has as many protons as the number of electrons therefore because it hasn't given away anything therefore anything below that dotted line Fermi level is charged zero it has not given away its electrons full donor levels they are first charged zero what about the ones above which are the red dumbbell shape thing what about them those are above Fermi level in above Fermi level typically these are Fermi function is zero therefore they are empty and if the donors are empty then these are positively charged okay look at the so if that that happens if it is donor like if on the other hand look at the middle panel let's assume now that these are not donor like these are accepted like now in this case what does an acceptor do again you see in the middle panel the dotted line being the Fermi level below sorry the the levels above the blue lines small blue blue blue lines in those cases those are empty right above Fermi level they are empty if they are empty that means they have not caught any anymore electrons so in that case what will happen they those will be zero charge because an acceptor until it catches an electron right it is not it's charged neutral okay now on the other hand if it is below then it's full it falls means remember it has one extra place for one extra electron in the outer shell right that's what the acceptor is like boron is an acceptor so it catches one electron it's full as a result everything that is below for acceptors is negative right it takes a minute to think through this but you get the idea now what happens that many times these levels depending on how how the hydrogen bonds are oriented in different direction may either behave like a donor level or an acceptor level so in general order I have seen on the right hand side that generally you have a will have a combination now do you realize the dumbbell shape blue ones these would be positively charged right I'm sorry those would be neutral neutral because below Fermi level donor like and the dumbbell shape red ones those will be positive and similarly what will happen to the ones short red segments on the right these would be below the Fermi level that that means those will be negatively charged because these are acceptors when they have an electron extra electron then they are negatively charged and so from here depending on the Fermi level you can see I can tune how many positive and negative charges I have on the surface right and that will give me different amount of tracial voltage shift so that's what I'm after so let's see what happens now follow with me carefully because this is something the professors like very much and let's see whether I can explain to you what type of substrate I have this is a n type substrate so therefore you can see my CV characteristics is facing to the other side then then what I typically drive typically draw now let me assume that these are donor like all donor like traps now I have bend the band I have applied a positive bias so now the n substrate is in accumulation because it has bought closer to it all the electrons majority carrier now the level the all the different levels are below the Fermi level they are all full if they are all full what is the total amount of charge 0 donor levels all full below the Fermi level 0 charge if it is 0 charge then of course I have whatever my classical standard CV characteristics is no problem if it stayed 0 throughout the voltage swings then I would have this ideal red CV characteristics however however what happens that as you go up by the way on the on the top side I have written alpha VG multiplied by C arc Q ox because this amount of charge depending on the bias will be changing and so alpha the fraction of the total number of defects that contributes to the charge that will be changing depending on the bias there now let's say I'm beginning to go the other way beginning to deplete right so I have to apply a negative bias because n substrate now am as I am beginning to deplete a fraction of the charges fraction of the defects have moved up the Fermi level do you see that therefore now I have some charge contribution which will change my threshold voltage as a result if this fraction for example if it remain the same throughout for all voltages then I would have a fixed shift in the threshold voltage associated with this amount of charge so I would have this blue curve if this was constant I'm not saying it's constant everywhere but if had it been constant this amount of charge then I would have a fixed shift in the threshold voltage and you can see the blue curve has shifted a little bit more if I now try to invert it invert the substrate all the defects are up above the Fermi level everybody is positive huge change in the threshold voltage so I will have the final curve over there now it's supposed to be first curve was supposed to be magenta and the last one is red hopefully you can see that now of course this is going through this phase is as a function of voltage so as if the threshold voltage keeps changing as you keep pulling the bias as if the threshold voltage keeps changing so the real curve you'll be seeing is not the separate three curves of course what you will be seeing is that there will be transition of this curve among this curve from one to another now do you see you have stressed things out now I have just shown you three discrete points of course it will be a continuum of points and you can see therefore the green will become a continuously stressed out CV characteristics you see that right okay so that is for the donor states on this side on the accumulation I'm sorry the depletion and the inversion side but if you have accepted states that will give you a stretch out on the accumulation side this is how now if it is accepted like then what happens then if you are on the starting from now for this CV characteristics I'm starting from the very right very right because look at the band diagram I've applied a large negative bias close to inversion right is close to inversion now this is accepted like all the states are above for me level as a result they are all empty and if they are all empty empty means accepted means it has not accepted anymore electrons it needs electrons therefore the charge is zero so that CV characteristics is ideal CV characteristics no problem now as you are going the other way because now you are sort of going from the accumulation trying to come the other starting from inversion going to the other way of accumulation then as you move down then of course you have a bunch of acceptors states below the formula level now these are negatively charged because they just accepted an additional electron remember when boron catches an additional electron that is when it becomes NA minus so therefore I will have a some negative charge and when I have negative charge you know correspondingly the threshold voltage if you put the values in it will move to the positive side so now this is will be your threshold voltage you see that and then if you really try to accumulate it go to the other way everything is below formula level all acceptor states full negative impact of full negative the curve has completely shifted to the right again because of these charges you will have this transition going because this is continuous process right so due due to acceptor states therefore you have a corresponding stretch out here and so when you pull them together then you see that you have a continuous if you have a combination of both present donors and acceptor present then you will have this stretch out that will go continuously now there is a I show a discontinuity over there that there will not be any discontinuity because you will sum them you will sum them so therefore the effect will sum up I have shown them individually therefore there is a discontinuity over there and that's what your before before annealing CV characteristics now I'll tell you all about hydrogen passivation and other things two lectures down but for the time being this very important to understand that anytime if you see a stretch out you know your you have to improve your surface and then you go and try out various strategies to improve your surface you know this is has got nothing to do with silicon per se it could be gallium arsenide if you have donor and acceptor like surface states you'll have the same problem it could be graphene or it could be anything and this stretch out simply reflects the fact that there is a voltage dependent charging of the surface states and somehow you have to fix it because otherwise your transistor isn't working and so their strategy will be different here hydrogen passivation works other places there are other things that people have done so to conclude this lecture so we're talking about non-ideal threshold characteristics and obviously obviously it's a very important thing for MOSFET design and this non-ideality arise from wide variety of sources your choice of substrate and the gate gate metal aluminum germanium copper silicon this combination dictates what your work function is going to be and in many cases it's a good thing I'll show you later and trap charges where are this what are these trap charges these are essentially charges that could be sodium moves back and forth this day it doesn't happen because of course even not allowed to get into that room anyway these are robots will essentially say thank you you can stay outside they will do all the handling and they don't have sodium chloride in their hands so therefore you don't have that problem but there are other problems but the interface states a very fundamental problem then these almost there is not too many good ways to handle it hydrogen passivation is one one very big and these are all discovered in 1960s by the way and that made the first Intel transistor possible processor possible in 19 early 1970s all in fair child as I said before and now there are other non-ideal effects due to transistor degradation and I will show you in that two class down how this works