 Okay, so we were looking for oxidation, we have already modeled it. The growth models we have created already from dealgrove, we also have seen other kinds of models for oxidation particularly for thenoxides and this was done because the technology was scaling down and the oxide thickness was also scaling down. So we wanted to know what models one should use if the thenoxide comes, however one now knows that SiO2 has already lost race with hafnium oxide and maybe lanthanum oxide for 28 nanometer down. So there is no necessity of gradial model for this because hafnium oxide is not natural oxide of silicon. So obviously this growth model cannot be used, it is a deposition system. So we will see later when we look for depositions, how to deposit metals or oxides or any other thing and which will have a different property and different models. For silicon dioxide 65, some process, some companies still have devices particularly analogue with say silicon dioxide as their insulators, RF circuits are mostly with SiO2 but anything below 45, at least for digital or even 45 digital is hafnium oxide which is most standard Intel process. So we will look into that when it comes but as of now we assume that we should have no oxidation technique anyway, okay. So we did that. Of course even in the whatever node process you will do, you will have some field oxide as we shall see and that will be done by normal oxidation technique. So some model is good enough there for creation of thicker oxide which is maybe 2000 to 3000 Armstrong's. Right now for a 0.5 micron or above process, the oxide thickness was 6000 Armstrong to a micron. Now it will be less than 2000 Armstrong's a field, okay. So there is a thickness variation but still it is thicker oxide enough for Brodyl model to be acceptable. For gate oxide, yes, this may not be now useful sooner or later but they do not think it because there is a research going on to look for some equivalence of silicon oxide now which grown on some materials like there is a material silicon noitred we are trying to see whether we can grow out some thin oxide there. So some other semiconductors may use Brodyl model again, okay. So let us look for oxidation techniques, there are two techniques, one of course is growth that is you must have silicon to create growth out of it, silicon dioxide. The alternate method is deposition in this substrate is unimportant. I can deposit silicon dioxide on any surface, it can be silicon as well but can be any surface, okay. That is called depositions. The growths can be plasma anodization, electrolyte anodization and thermal. This is a process which we looked into way back in 80s, it did not find the acceptance from the industrial community because the industry one of the major criteria is what we call throughput. What is throughput? The number of devices one can create in a single run, okay. So in a furnace if you cannot put 200 wafers it will be very costly for them. So the throughput is a plasma anodization system would be 4 wafers at a time. So how many times I will go and put 200 wafers? So that become very costly but this process can grow even 10 Armstrong's of good oxide which we tried to of my PhD student work for this but somehow of course as I say it is not a industrial process. You can also have a soldier method which means you can deposit in a by electrolyte electrolytes like a cell, you can deposit SiO2. However the most common one as I say is thermal which has furnace we will see today. And there is this process which is called rapid thermal oxidation, RTO rapid thermal oxidation. Actually RTP is the actual name rapid thermal processing, anything can be done in RTP including oxidation. RTP is the process rapid thermal processing. For those who are first time hearing this sentence, normally if you see a furnace temperature rise time versus temperature you ramp this actually we call ramp the furnace. You start with room temperature and go to the temperature of your choice. So typically it is like this and then becomes like this okay. Then when you ramp down it becomes like this okay. Now this takes hell of heat and hell of time okay. So what we do want to do is if you want a very short duration oxidation going on then one can do something like this I may ramp up short time maybe slightly reduce if you wish I can further ramp up very sharp ramps longer maybe ramp down. So any thermal profile in a very short duration can be attempt a can be attempted in rapid thermal processes. This word rapid itself is proven up very sharp rise to improve the thermal conductivity of the system and so that the rises very fast. The rapid thermal processors have halogen lamps around in a parabolic system and there are on-off switches controlled by a microcontroller. One of the small RTP system was created way back by my BTEC student in 1990 or 92. He is currently looking into analog design in Texas Instrument Manager of that. So he made first RTP in India ourselves. So we had a microcontroller design we actually picked up switched on and off. The problem came cooling. So we have a jacket cooling we have a lot of problems. So making a system is a tough job but we made one okay. So this is available now in market. So the problem in RTP is also same number of wafers you can do actually are relatively smaller compared to any furnace kind of processes. So this RTP is still there for specific purposes at least anneals we can do if not the process. So there is a possibility this is no different from furnace all that you are doing is temperature is created in a different way okay. In furnace we can have dry oxidation, we can have wet oxidation and we can also have another one which I will show my results on that pyrogenic. Then we can use nitrous oxide and two oxides. Then we can have high pressure oxidations, we can have low pressure oxidations. And for this we can also during the oxidation we can introduce nitrogen or we can introduce chlorine which is called nitrided oxides and chlorinated oxides. This nitrided oxide was very important for us because this was the way we actually made first India's radiation hard circuits okay some other day. So these are possible thermal processes. If you look for depositions you have two possibilities either it can be physically deposited or chemically deposited. The physical deposition is essentially called using a reactive ion deposition system or sputtering. They are similar but not same okay. In the chemical you can have the CVD which is called chemical vapor deposition, CVDs maybe I should write. The chemical vapor deposition can be done at atmospheric pressure at very low pressures and the most likely these days will do is plasma CVD okay. So let us look at as I said this deposition part will take care when we start the CVD system. So there we will show you how to make so any material can be deposited in fact okay including oxides okay. Right now we are looked into furnace and maybe R2 is same. So we are looked into dry O2 way to O2 models and maybe today we will show you other processes quickly. There is no difference between this N2O plus silicon in SiO2 plus nitrogen is released okay. So that is no different. High pressures, high pressure is called a bomb. So you actually put a water vapours or water solutions and seal the tube okay. And heat so the pressure breaks. So you have to guarantee that the pressure is not so excessive that it blasts out okay. So there is a game there and of course the advantage of high pressure oxidation is I already said at high pressure the rate is very high. So very short time you can grow thicker oxides. This is essentially used in some old processes but just to make a point complete I say then there can be a low pressure. So I can evacuate the furnace to a certain vacuum and then pass oxygen to maintain certain amount of gas pressure inside. So I can change partial pressures there and this also has an advantage or disadvantage as may show you one of them okay. During oxidation as I say I can add ammonia so that I can have nitrogen inside in silicon dioxide lattice is called SiOn bond which can be formed there and it is very important in relation hard circuits. Many times we do put chlorine now it is almost given up but there was a time when everyone was trying chlorine at SiO2. The reason was that chlorine is a first group element and as we shall see soon that is a what we call dangling bonds at the SiO2 interface. So chlorine can actually remove those bonds by attaching to them. So it may reduce what we call interface state density. But chlorine itself has a problem it is a larger atom and it has a affinity to silicon so it may form silicon chloride and evaporate and it gives pitting that is why it is called pitting. So we stopped using chlorinated oxides many years back. So we replaced from HCl oxidation to TCA oxidation we tried in my time 70s we have gone through all kinds of chlorinated and nitrided processes. And nowadays except for red hearts nitrided oxides are also not used. So this is typically the techniques available a typical furnace taken from a Google look something like this you have a quartz furnace this is the resistive heaters these are resistive heaters this is called the central zone this is called early zone this is called the end zone. So we can pass the gases through rotameters or through mass flow meters you have a Cl possibility nitrogen oxygen hydrogen whatever you wish you can control the flow rate here and pass the gases inside whenever we start oxidation the first thing we do is to soak the wafers to a given temperature. What is word means soak means when you introduce the wafer from this side they are at room temperature. So when they enter central zone there will be time they will require to actually reach the furnace temperature that is called soaking. So during soaking I do not want oxidation to proceed. So what should I do pass something inert which does not oxidize it. So we pass enough nitrogen it can be as high as 100 liters per minute oxygen nitrogen flow just to allow soaking in the wafers to that temperature. So there is at least 3 to 5 minutes are required for soaking. So you introduce the wafer from this side start nitrogen huge amount so that slowly temperature rises to the wafers quartz rack everything and then this is universal uniform temperature everywhere. Once that happens I first introduce I am doing dry oxidation so I pass oxygen initially whatever amount of oxidation which can fill this and start reducing nitrogen and close the nitrogen. So at whenever I finish nitrogen that is the time when oxidation starts because oxygen is already inside nitrogen was not allowing that oxygen to react. But as I close the nitrogen oxygen oxidant is available for silicon to oxidize the silicon wafers and one can see from here that I can oxidize any number of wafers if I have a central zone thick enough wide enough if you have a large zone what does that mean bigger size furnace huge thermal heating so huge power loss but that is the way you can make. You also as I said coys on the early zones and the end zones this is to maintain the gradient because if this will lose the energy thermal energy so you want to maintain the furnace to a uniform central zone furnace so you must heat both ends okay. So there is a separate coil separate monitor and also there are enough thermocouples to monitor the central zone temperatures. So the oxidation when it finishes before oxygen is switched off you again start nitrogen large amount then no oxidation takes place and then switch off the oxygen. So all processes starts with nitrogen and ends with nitrogen and in between is the time for which a particular process is maintained okay. If you want a seal along with oxidation time so during oxygen you can add 5% a seal vapours okay diluted a seal through a bubbler can mean you can pass a seal inside and you can have chlorinated oxide as we can say or if you want the next process we will see if you can create something using H2 so we can also do hydrogen insertion if we need earlier almost everywhere we had this called rotameters or flow meters for more accuracy now we use mass flow meter for a given gas okay. Typically if you see a rack this silicon vapours are mounted in a quartz rack you can see they go vertically down and they fit it into the slots this is how the rack so larger the rack size larger is the number of vapours one can introduce inside. So any number of vapours you can load depending on the temperature in central temperature zone you have wider or smaller and the rack size you have the rack thickness is a rack slots are essentially for the given vapour size because thicker larger the direct thicker will be vapour so slots will be of thicker this 3 inch why vapours may have say 500 microns of thickness so slot will be 550 so just fits in okay. So depending on the vapour size the slot size is also different okay so is the rack size so is the furnace for example this tube size you can think of it if I am having a 8 inch wafer or 12 inch wafer now so for 12 inch wafer the extra part at least should be 4 more inches so 16 inch tube you can see how big it will be okay and holding those rack coming out coming in it is a game okay but it is all done automatically there is everything is motor controlled so power electronics is heavily used to do this what is called as what rate I should push in what rate I should take out that is possible okay. In other times we had only 4 vapours we cannot afford more than 4 vapours at a time too much cost for us 8 dollars a wafer 3 inch so with available money we could at best put 4 vapours. In normal any process what we call called dummy vapours what we do is some vapours are always kept say one last couple of them and in centre also couple of them and they are never taken out they are oxidized they are always there okay so oxidation keep that actually is adjusting the flow as we say some other day we can. So there are some dummy vapours which are never taken out they are just sitting there all times okay so of course these are not dummy vapours but I am just saying even in the diffusion any process we do there are certain dummies which and some of dummies we can actually take out and monitor also but normally dummies are at least for 4 percent in the whole system yes. From the nitride and oxygen is already present so that the oxidation will start but so do not we pass oxygen from outside into the furnace yeah I mean the tube I have already shown both from the rotameter I will start both gases oxygen is in now but it is not nitrogen being such a heavy amount it does not allow oxidation to proceed okay. When you also said that we stop like when you want to stop oxidation means start the nitride nitride. Can we just stop oxygen and. Yeah you have a point if we do this the problem with just no gas system is this silicon dioxide which has the oxygen there actually may dissociate itself at that temperature where there is nothing else to come out stop it process so if you stop nitrogen that additional oxidation process will stop okay so it is essentially to maintain the growth oxide to its own water thickness we did okay also there is a possibility that what is outgassing from this furnace should not go into the furnace okay. So we actually push nitrogen so everything comes out okay you are right and that nitrogen flow is very high so it does not allow anything to happen in fact okay you can also use argons okay any inert gas argon is costly and not easily very high pure argons are available of course they are available but much higher cost then there is a weight oxidation system where ever that H2O2 we are saying there is another tube we can add another flow meter and through this and we can have a heating mantle inside which a quartz this has been put quartz bubbler we put deionized water here past nitrogen slow amount maybe 30 cc 200 cc and since it is heated at 95 degree centigrade water vapors are picked up by this very small amount of nitrogen and pushed into the furnace okay this is called weight oxidation the partial pressure of nitrogen has to be very small compared to water vapors. So we pass then why do you bevel because to come out at a given pressure of water vapors you need something to push so this gas nitrogen allows you to actually push the gas out of water vapors out so that is why it is called bubbler the nitrogen actually bubbles it goes inside and bubbles okay so this weight oxidation is H2O as I said already we have seen the model for H2O same as dioxide then there was an issue many years ago you know the since this water vapour bubblers are outside the diffusion furnace system you can see this is outside the furnace. So what happens that one cannot guarantee the say the water vapour is how much inside and whether it is the purest form because you do not change water every now and then because this is the deionized closed water system and we in those days we figured out which is even now it is figured out that the water quality is not as good water vapour quality is not as good as if would have directly passed the water vapours inside. So to avoid this we suggested a new process which we called as pyrogenic oxidation system way back in 85 in those days patenting was very costly so we could not patent this was our own design and own process but since as I said in 85 the actual work was done in TI for in 82 but published in 85. So we what we did is the following we are this furnace tube and we introduce there is an enveloping this is the bigger tube and through which we can pass either nitrogen or oxygen and at the end from there we seal a small capillary inside from the inside I could put a capillary inside which has a 1 millimeter dia and it is pushed till it reaches a temperature on the end zone or early zone or front zone as it is called to 600 degrees so we actually push the this seal like this that whenever that capillary reaches it has 600 degree to see now from this capillary I introduce hydrogen and I introduce oxygen from the rotor meter this of course also has a flow meter both have flow meters so I can pass some amount of volume of gas of hydrogen some amount of volume of oxygen through this oxygen is so when the oxygen enters it forms envelop around the hydrogen you can see oxygen is coming from outside capillary is inside so when the hydrogen released it finds oxygen surrounding it okay surrounding it so all around is oxygen flow and hydrogen is released in and at this since at 600 degree even at 400 but at least safe is 600 H2 plus half O2 is H2O okay so we create since the gases available to us are ultra high pure so the water which I can create inside a furnace water vapors are relatively far superior than any of the externally added water vapors okay this has many advantages one of course that you get the highly pure water vapors inside the advantage was that if you do little ideal gas laws maybe you I will leave it to you in case you cannot then see my favor we have a partial pressure of water in a total gas system is given by two times the volume of hydrogen these use gas laws okay so many molecules react with so many to give so many to use PV is equal to an Arctic and Katie formulas okay so I can get a partial pressure of two volumes of hydrogen upon two volumes of oxygen plus one volume of hydrogen is called the partial pressure of water vapors in the net gas stream one can see from here if I chose not to have H2 then the partial pressure is 0 so there is no steam obviously so partial pressure is 0 okay there is no water there so only oxidation dry oxidation can take place if complete oxidation takes place and P is we call it one okay so you find out that complete hydrogen is oxidized by oxygen so we get full steam so we save our weight oxidation so by adjusting the oxygen to hydrogen ratio I can adjust from dry oxidation to weight oxidation and in between I can vary from 0.1 0.2 0.5 0.8 different water vapors concentrations is that clear this system has big advantage because if the water vapors are smaller the oxidation rate will be smaller if water vapors are thicker larger than there will be thicker oxides now I can adjust my suitable time I want to do for a give that may I do not want thermal process to go more than this time for diffusion not to change then I adjust my partial pressure for a given time and adjust so that in given time I want I get oxide of my choice okay this was the biggest advantage we got that I can make in a given time desired oxide thickness okay which neither weight or dry can do because in if you want certain thickness dry will take at that temperature this much time or weight will take this much time for this that temperature temperature we do not want to change because furnace ramping will take enough time then so we do not want unless you have RTP we do not do that so this process was first time done 82 when I was working at Tata Institute in Mumbai and we actually measured the oxide thickness at various partial pressures at various temperatures and whatever possible flows and we fitted the curves again okay because we thought everyone will like to use the parabolic rate constant and linear rate constant so we equivalently fit it into the curves and got an expression which looks very funny 2.438 into 10 to power 6 into 2.05 plus P to the PS partial pressure to the power 3 by 4 exponential and this fitted to all all possible partial pressures okay 0 to 1 okay and I can see from here someone was asking now this energy and this pre exponent is my choice I give some variation I allow this only variate here and I allow only this much to vary so I say okay it should not be more than 1 ev should not move less than 0.525 ev now the fit function will try to adjust the pre exponent with this term so that it fits so do not put any physics on it there is no physics on it this is just a fit function okay but for a simulator how does it matter as long as I give them P as long as I give them T I will get B and B by a and if I get B and B by I know go my growth anyway okay so for me as a simulated person I damn care whether the physics is followed here but the advantage I see in technology is that I have now same thickness of oxide at different times I can adjust by adjusting the partial pressures and that is something very important in actual thermal processes okay is that client point here so this is as I say is ours and nothing we great about it okay before we go of course we have to monitor thicknesses one of the easiest method of finding the outside thickness is to create a slot or a step of course I will come to that little later again but just to show you how do we do it I will do many methods but right now for example on a way for say let us say this is oxide and this is my silicon this is silicon and this is oxide so I create a step by etching then I run something called profiler surface profiler which has a transducer kind of acoustic transducers which is fitted with all kinds of circuitry and it has a traveling system okay so it goes there jumps down so as soon as that transducer jumps down the acoustic sensor finds out that it has traveled vertically down so it displays how much is the thickness however the accuracy of profiler is unless this oxide is sufficiently thick one cannot say it is accurate because it gives you at least 20% errors in actual monitoring firstly you cannot create a step the way oxide will be formed will be some kind of a angle so when the profiler goes it assumes as if it is going vertically but actually it is climbing down okay so the error is inbuilt and there is nothing much but this is very important okay the other method of this is very interesting when the white light shines on the oxides okay you can see depending on the thickness you will see a color on the oxide okay you may see tan you may see for example different thickness of oxide will show you different colors okay so example there is a 7 one cycle will be repeated again blue gray you know white light all blue to red it will keep repeating every now and then as n times you n lambda in optics n time so first cycle is one second cycle is true so the colors will repeat every now and then so but if you know roughly what time you did you know which zone you are okay so if I see the color is tan I say it is 0.05 microns if I see a blue I know it is 0.12 micron okay and this is simple optics okay so by just seeing the wafer I roughly know like a 6000 Armstrong used to be carnation pink so I know as soon as I see a wafer oh it is okay 6000 okay because I know I did one hour or something so it will be around 6000 so if I see a good color of carnation pink I say yeah I have reached 6000 so this first guess we do how much oxide we have grown okay these are only for the overall thing but the actual thickness has to be monitored in many cases and we will see little later what is ellipsometry does that okay ellipsometry okay so profiler color monitoring color monitoring I repeat the intensity of light changes as the thickness of this because light is absorbed there in silicon dioxide so as the color changes I know how much thickness I have okay okay so now having shown you this oxidation this something which you have to learn to do in this exam as well you may need that probably I am not sure but possibly here are the two graphs which I have provided to you this is a 100 wafer silicon please remember four graphs have been given two for 100 and two for 111 if the orientation is not specified it is 100 otherwise it will be specified as 111 please remember in mass technology everyone will use 100 but otherwise if specified then you will have to use 111 is specified okay so I am only using as of right now 100 wafers oriented wafers so this is a for dry case okay this is a die oxidation time and it has been shown at 800 900000 in a and actually you can of course not accurately but you can even extrapolate them okay because it is log of grain so you can extrapolate down to find a different times the thicknesses you can see from here the x axis is in hours please remember x axis is 0.1 hour 1 hour and 10 hour and on this side is the oxidation thickness which is in microns this is 0.01 micron which is 100 Armstrong's 1000 Armstrong's okay unfortunately the current trend is to talk about nanometers but in our time we used to talk Armstrong's so I am more conversant 10 nanometer is 1 Armstrong's okay so 1 nanometer is my 0.1 10 Armstrong is 0.1 nanometer so it 10 to power additional term has nano to 10 it has gone okay so let us say I do a dry oxide for some time maybe I have a ski for the heck of simplicity maybe I do it 1000 degree centigrade for 2 hours okay this is one please remember this is a log scale so this is 2 hours okay so I have got any amount you can do but I am just taking some example I have not done earlier so it is 0.09 is the oxide thickness at 2 hours we may even assume 0.1 but at least it is 0.09 microns so 900 Armstrong's you can see it is slightly lower than 0.1 and by log it is 0.9 okay so it is 900 Armstrong's of oxide is grown off at if I do oxidation dry oxidation for 2 hours I will get 900 Armstrong's of oxide but I followed by a wet oxidation okay for say 30 minutes at same temperature any other temperature so what I do is I did it this oxidation at 1000 and I am doing wet oxidation at say 1100 for 1 hour okay so what I am now do is to find out the new oxide thickness grown already there is an oxide and you are going further so I use this weight graph and first I do it at the weight oxidation temperature I find how much time it would have required to grow 0.09 and microns of oxide that time I calculate that is called my initial time I have not done it weight at that time but equally saying at 1100 I would if I would have done it to grow 0.09 microns how much time I would have taken so let us say this is 0.09 somewhere here so it is you can see it is point roughly 0.09 or 0.05 hours okay so 10 minutes or something 12 minutes of oxidation was required to grow at 1100 0.09 is that point clear to you what is I did I transferred the earlier oxide thickness into the new oxide stream equivalent time I calculate from the oxide thickness I know and the new temperature which I am doing if it is 1000 and then I will have to take this graph okay and then say 0.09 will be somewhere here it will be 0.08 or 0.09 hours so it depends on what temperature you are doing next process you first translate the first process into the new temperature time I operate this find that time so in this case let us say it is a 0.01 then add 30 minutes to it from here ahead is that clear 0.01 is equivalently you have got it plus the new 30 minutes at that time which you are doing weight oxidation you add this time to this this is small change here occur because they have dry oxides are very thin comparatively but in 2 weight cycles if I go through it may happen I have done a weight cycle at 1000 and then at 1100 so I will have enough thickness initially and then I have to translate on the other temperature what time I would have done to do this and add the new time again okay so if I add 30 minutes to this which is roughly half an hour so from here to here it is 0.5 here 0.5 here so at 1100 I actually 0.1, 0.2, 0.4, 0.5 okay so at 0.5 at 1100 degree centigrade somewhere here this is 1100 so this is the oxide thickness I just checked okay so it is very close to 0.28 or something or 0.29 microns okay so this fact has to be understood that when I transfer one temperature cycle to the other to the new for the newer cycle I must get pre-value converted to this one okay let us say again I do something that oxide should go back equivalent time in the newer temperature regime and start the new timing from there is that clear to you this is something that means you may have to move from one graph to other if more than one oxidation cycle is going many a times dry cycles are very short duration so their oxide times thickness is so small so one can assume they are negligible compared to weight oxide times but there can be two weight oxide cycles okay in which case the first weight oxide thickness may be sufficiently large which at the newer regime we have to first transfer okay and then add the additional time to this and find the new oxide is that clear to you this is a very important thing reading the graphs okay let us say I do two weights one at 1000 and then I did at 1100 so let us say I 1000 degree I did it for 30 minutes okay somewhere here 5 so this is around let us say 0.2 okay little less but 0.2 and then I did it at 1100 the next for 30 minutes so for 0.2 I am strong okay you can go back on this side at 1100 degree this time is around 0.3 it is not 0.5 it is 0.3 add this 0.3 over to next 0.5 that means 0.8 hours so you go somewhere here go to 1100 and find the new thickness is that clear so any temperature cycle earlier one should be translated to the new temperature cycle find the time equivalent time there add the new time which are the new this process is asking and find the final result so if you go through n number of cycles n times you have to move from temperature to temperature or dry to weight dry to weight so this is very important because otherwise your thickness monitoring may be absolutely wrong okay they either keep saying most cases dry cycles are so short time so they are equivalent weight cycle time you cannot even it may be less than 0.01 so you say they really I did okay read 0 okay and add just weight cycle but in many cases if it does not happen that you must figure out where is the oxide initial oxide time for the if I change the template please remember I wait for the same way that I showed if I would have done 1000 or even if I let us say at 950 so for 30 minutes of 950 I would have done okay this point something grab this not a thousand this is the time I have done if I do next time thousand I know how much initial time I would have spent to get a thousand degree same thickness so you actually go horizontally for the new temperature find what is the time add the new time now and keep finding as many cycles as you go through as many times you will have to come on graph and re monitor it is that point clear to you this is very important because as I say if you make errors driver cycle normally do not make much errors because weight cycle is much stronger than the dry cycles so this way time cannot be modified too much okay but in cases where two weight cycles go or dry cycle is long enough okay in which case this transfers are important okay so is that point clear so reading from the graph equivalent this is that clear equivalent this from here to here here to here we will have to keep doing if it is more than one cycle of different temperatures and different types of oxidations okay so please remember these two graphs are therefore required just to monitor the exact thickness which is not very exact because at the end from the graph you will read some machines I keep repeating the log graph is initially spaced long space and as you go towards one it becomes compressed okay it is after log numbers log 30 is 0.47 log 40 is 0.6 okay log 50 is 0.7 so obviously when you reach higher values they become smaller and smaller okay so the log graphs are on the top becomes condensed whereas below they are spaced so 0.2 is very here but point it may be 0.5 may be far away but 0.5 to 0.6 is very close okay 50 to 60 is not very different so this log reading I am I am again every year I tell no do not go BB by this is already go actual data given to you this is what we did for different temperature actual outside was measured okay these graphs have shown to you okay time versus thickness when I am traveling if I give you B and B by 8 and use those expression there but if I would not give you BB by any way if I am using normal process I will say okay oxidation was dry oxidation was done for 1 hour at 1000 degree followed by weight oxidation cycle of 950 degree for 1 hour okay so there is no B to know or B by so only you have to find go on the graph get the values please remember the first one should be translated into the second one before you get the actual oxides okay or of course I can do miss I may give a final and then you have to return back and say what first I will have done okay the machine could be like this I may give a final and it is okay then what time I would have done to get this so you may have to find the dioxide time okay the universe problem okay if you can do this problem I can ask you inverse problem okay okay before we do to many other thing I hope especially bossy has already through with you to mass capacitors I trust okay before that I will just show you what characterization I will do I will talk about ellipso-metry I will talk about this is all thickness monitoring either by color technique or profiler or by ellipso-metry either of the three there can be high frequency capacitance voltage characteristics there can be low frequency capacitance voltage characteristics in general we do both HFLF together it is called HFLF CV technique then we will do BTS which is bias temperature stability CV measurements we may do also DLTS which is called deep level transient spectroscopy DLTS deep level transient spectroscopy DLTS of course I will not do detail of anything because I think I may make miss chief for doing I might use devices course here so I do not want to okay and maybe I will do some stress test which is called TDDB time dependent dielectric breakdown I may also show you some secondary current measurements with isochronal timings that is time is same but temperature varies temperature is same time varies we may also do many noise measurement one is called post office noise okay which is very important we also may monitor flicker noise you know what is flicker noise due to dangling bond someone said and that is why this LFCV is required I want to know how many dangling bonds I have it is very funny if I say someone who is working on circuits since someone said it is only low frequency noise okay little below 100 hertz okay so in RF system why are we are so much worried about flicker noise we should not only thermal noise should hurt us but in RF we really worry about flickers okay so why think of it those who are circuit oriented things they know much more think of it flicker noise is below 100 hertz is 7 upon F noise okay as the frequency goes down increases the noise keeps going down where is the issue particularly think of a system which is called transmitting or receiving system why in a RF transmitter receiving system we are worried also for flickers okay something if you are working with Shalab Gupta or others in RF area madam Shuzhai or someone think of it why flickers are so crucial anyway we will only look into that okay this NIT or DIT is essentially flicker related so these are some measurements so I will come back to it little later before that since he has not done it I actually thought he will not had done it stress is a time dependent dielectric breakdown okay so I apply constant voltage okay for a longer time at a given temperature time dependent so I increase the time and I find after some time the dielectric strength whatever it is at that current starts shooting okay so it is called TDDB time dependent dielectric breakdown is one of the major measurements in thenoxides TDDBs you do not want to read our papers generally but in case anyone is working with in the MOS area even our blue pressurasi myself and pressural have published at least hundred papers in or maybe more including Ram Gopal was one he was our student we have published enough papers of reality what we did in the lab so please see them okay they are not real grower is our models okay and our measurements okay our everything now there is a tendency in they do not even refer the last year your own paper in the next paper as if there is something wrong you know if you as you see it is called cartiline I know this lady and this two people different places she will send all in reference all my papers she will also I will also put every paper so my citation index really that is how the promotions are given tenure ship gets how much citation index here this is our citation index here in the mass capacitor which is a very simple device which we use to characterize oxides okay most electrical properties can be found through this different kinds of CVs so what is a mass capacitor theory so let us start looking at it I have a silicon wafer it can be either P kind or S N kind and then there is a thickness or some oxide thickness of T ox and there is a metal plate which may have a area of a please remember this is two dimensional figure the area term will appear because of this W into L for example if this is L and this is W the area is W into L so there is a metal plate area which is W into L which is sitting on silicon dioxide or if you look at the plan this is this metal plate okay plan this is cross section okay these days drawing is not a compulsory part in IIT no one learns drawing okay so cross section end view. If I apply first thing I can have either initially 0 voltage and afterwards I may apply minus the substrate which is P type or N type right now I chose on P the substrate is not source it is S is name because the VGS is name common in mass transistors so I kept S as substrate but in their case S is the source okay but their substrate is normally connected to source okay so it is okay so it is VGS but not necessarily in most what we call as dynamic threshold devices circuits we do have bulk separate okay. So this advantage with me is that I had done so much circuit so I know where I confuse sometimes whether I should talk about circuits devices materials so okay B substrate I apply minus VGS this is the metal plate and this minus VGS creates a fix a negative charge electronic charge on the metal plate if I apply negative potential you have by law of Gauss there will be a negative charge sitting on the metal plate which I say which has a density per unit area as we call Coulomb's per unit area is QM which is minus since I applied minus charges at the metal and silicon dioxide right now I assume is a very good dielectric and it has no charge inside my presumptions it is a good dielectric and it has no charges inside okay. So if I apply minus QM according to Gauss's law the net charge around the system must be 0 so QM plus QS must be equal to 0 since QM is minus so minus QM must be equal to silicon charge so if I minus QM I must get by induction or what Gauss's law positive charge at the surface if this positive charge has to occur how this positive charges can occur I want I put minus charge equivalently surface should get positive charges because electric field lines must start from positive terminal and go to the negative so equivalent charges must be created okay each starting point must have the end point okay. Now this essentially means that the charges opposite charge will identical equivalent charge will be and my appeal again appeal there are no charges in the oxide as of now okay. If I do that then I find which is the way I can create positive charge this material was P type it has huge number of holes anyway enough but please remember the rest of the part other than surface shown here is charge neutral what does that mean P plus ND is equal to N plus NA this charge neutrality holds there is no electric field here okay so charge neutrality holds is called charge neutral region however the number of holes are enough there okay so some of these holes travels to the surface why because since it is minus VGS the electric field is bottom to upward both across silicon as well as across oxide okay minus potential so electric field is vertically up going up now these holes travel in the direction of electric field okay so holes from the P substrate actually go into the surface now question is then does substrate loses holes no the battery will supply those many so the neutrality still will hold okay do not ask me from where the batteries enough enough charge is available to you so this excess holes which are coming in the P substrate near the surface one can say there were holes initially itself what are you doping you have plus additionally you are created more holes there okay so it is called accumulation so we are accumulating holes okay we are accumulating holes larger the VGS are minus VGS apply more and more holes will appear there and and how many exactly the charge I put on the metal the net charge system must be 0 across the loop okay this is very popular for at least dual degree student will watch or many of you might enjoy this is the charge problem is every year you know this is a very important some circuit they show or some Q1 plus Q2 plus Q3 must be 0 so some funds are always done in all physics papers okay now since this this is charge neutral of course it has small resistance I would not say there is no resistance because after I say silicon but assuming that resistance is 0 or very small this large positive charge here compared to what I apply here you can say what is metal definition of a metal it has large free carriers okay that is what we say either electron or holes both free carriers large free carriers so it has larger the accumulation more metallic it becomes okay so this behaves like a metal insulator metal system okay and the capacitance of this metal insulator metal is the oxide capacitance associated with this oxide thickness which essentially is the way all most people define is C ox is per unit area okay that is because we do not want to talk about area initially when the device finally comes I will multiply with area so the C net oxide is C ox into a where a C ox is epsilon ox by T ox epsilon ox is the dielectric or other permittivity of silicon dioxide which is case times epsilon please remember epsilon is a times epsilon 0 epsilon 0 is 8.857810 to power minus 14 per half centimeter per centimeter K is the dielectric constant okay so epsilon given means you should write K ox which is 3.9 for silicon dioxide K is 3.9 and epsilon 0 as I have just now said so that is the epsilon s or epsilon ox okay so this since I know T ox I know the material so I know the capacitance per unit area if I multiply it by the plate area then I get the net capacitance okay. So this is a standard capacitance is call it C ox dash if you wish per if area is multiplied so the capacitance of a negative VJ system is C ox that is it okay oxide capacitance this fact has to be understood because if I have a ceramic capacitor which we use in our circuit lab if I change the polarity of ceramic capacitor it does not matter I can put like this I can put like this it is a same capacitance but in MOS it is not so if the bias put changes the C value is going to change okay and that is it different from normal standard capacitors okay now the next case is I increase the voltage towards positive but increase not big small VGS positive I apply okay so till 0 one can say roughly the oxide capacitance is seen okay as VGS becomes positive that is this maybe if you are written down or you understood fine that if you understood it is better than what you write down you know if you say Vasya will spend enough time on this so more clarification will come there some theories which I have profound here maybe he will prove later wrong and then you can come to me I say no no he in specific case you are right I am also right okay all funds if I apply plus VGS then I am applying positive charge on the metal and by Gauss's law negative charges must appear at the surface interface now how do I create negative charges now the electric field since VGS is positive downwards so holes at the surface actually find the electric field okay so first thing is holes move away from the surface downwards to the ground and as the holes leave semiconductors the acceptors are ionized okay so in this they are ions acceptor ions which are not mobile okay this area is called depletion layer there are no free charges in this region the charge in this must be exactly equal to charge at the metal because Gauss's law is always sank for sank there is another term which we use and if you are done your electrostatics well we also say since silicon and silicon dioxide are two materials the electric field on the two may not be same they will be related to their permittivities and this is called d vector is continuous okay d vector is continuous this is our assumption sometimes if there are charges in oxide this is slightly modified but otherwise you can assume it and the relation we say is epsilon ox into is this capital is fields so epsilon ox into electric field in the oxide must be equal to electric field in semiconductor into permittivity of semiconductor this is sank for sank as long as d is continuous okay this is electrostatic 10 standard or 12th or whatever it is okay electrical engineering is only this much okay so if I positive charge for QM negative charges are due to the depletion layer and if you know the depletion layer the charges and let us say this is my depletion layer thickness called Xd so what is the charge density there Q is the charge associated with carrier negative this Na whatever is the number available into Xd because why I what will be the unit of this Q Na Xd number cha coulombs per unit area so it is called charge density so the depletion charge density is Q Na Xd and if Qm is the charge density on metal then Qm must be equal to opposite of Q Na Xd but Na's are minus so automatically minus charges are appearing to compensate for positive charge at the metal induction law of induction okay one can see since the charge density in depletion layer maybe you can write Q Na Xd minus because it is Na's are minus Xd will derive this or at least show you later K into Psi s upon Q Na Psi s is called surface potential maybe wait for it so as larger the Vgs I apply I will find more charges in the depletion layer larger the voltage I apply larger will be the depletion their thickness and one can see the depletion which is proportional to surface potential and therefore the Vgs and is inversely proportional to root of Na so larger the doping smaller will be Xd smaller the doping larger will be the Xd but the charge density is Q Na Xd and this must be equal to the metal charge which you have applied since there are no free charges at the surface we call this mode as depletion mode of a MOS capacitor okay this is called depletion mode father now there is something which we will discuss little later also in DIT point but just quickly I will say what is happening if you have done your PN junction somewhere well I hope so if there is a depletion layer there is a electric field across by Poisson's equation d by dx is rho by epsilon okay so if there is a space charge here there will be electric field there since semiconductor electric field is will enhance with increase of Xd because roll increase okay larger charges the charge density means larger fields so if I increase Vgs I will have larger electric field in the semiconductors is that clear going down now this electric field what is the purpose of electric field if you have an electron hole sitting here and if I apply electric field holes will travel in the direction of electric field and electrons will opposite to the electric field however when the initial Vgs is positive small positive the electric field in semiconductor is very small because depletion layer is very small okay because it is very small the whole electron please remember in a semiconductor whether it is depletion region or neutral region whole electrons are constantly generated okay their pairs are formed thermally and recombines this is the generation recombination is constant all thermal equilibrium processes but so in the depletion layer also whole electrons are generated here of course there is no electric field please remember below the depletion layer charge neutral no electric field there only in the depletion region there is a electric field so whole electron which are generated in the depletion layer can recombine if this electric field is small because that time constant associates such that whole electron recombine so only depletion region is seen nothing else happens okay whole electrons are generated but they recombine so the depletion layer remains constant you keep increasing Vgs depletion layer will keep on increasing okay but then if Vgs becomes higher and that is the next day so in the case of before that field becomes higher what is the capacitance I see now here is the figure there is a oxide capacitance and in series to that there is a depletion layer capacitance which is called semiconductor capacitance is that okay oxide capacitance and semiconductor capacitance okay so if I see they are in series they are in series combination of CS and C ox so then what is CS the oxide semiconductor current how much it will be the epsilon s by XD whatever is the depletion layer that is the capacitance across the semiconductor however XD is a function of Vgs is that point clear so larger the XD capacitance will be smaller in semiconductors in a series capacitance mode what is the way actually we write 1 upon C total is equal to 1 upon C semiconductor plus 1 upon C oxide if C semiconductor is much smaller than it will dominate if C semiconductor is very large C ox will dominate is that correct so if C semiconductor is very large means what that means the Vgs is so small depletion layer is very small so we say the most of the time oxide capacitance is good enough even in small Vgs but as I start increasing Vgs CS starts decreasing because XD start increasing and the net capacitance will start then decreasing because CS 1 upon CS plus 1 upon C ox is 1 upon C CS becoming smaller will actually reduce the net capacitance so initially if I have I will show you this later again it may be C ox but somewhere down the net capacitance let us say apply V versus Vgs so initially it may be C ox smaller Vgs and then it will start dropping to a lower value depending on how much Vgs I apply if I apply Vgs sufficient enough it may go to a very small net capacitance by this simple series formula and obviously it will be much smaller than C ox because net capacitance is decreasing initially it was only oxide capacitance CS is now in series to that so it start dropping however as I just now said if I increase Vgs further okay if I increase Vgs further then the thickness of the depletion layer in semiconductor is large enough so is the electric field is very large relatively now the whole electrons which were generated in this depletion regions which thermally were generated actually experience a force due to electric field what is the force if is the electric ES is the electric field how much is the force on carriers Q times the electric field is the force and we know electrons travel opposite to the direction of electric field and holes in the direction so what we say the additional field now separates whole electrons and they are not allowed to recombine so what happens you write down this later the whole electrons in the depletion layer holes actually are separated from electrons and holes will travel downwards because electric field supports it electrons will go towards surface and since this is a insulator nothing can pass through it electrons start piling up at the interface okay one can see from here that there will be a depletion layer already reached maximum why the reason is once this electron starts separating whatever extra voltage I apply will be there to create this electron separation so the depletion layer then becomes constant though it is an assumption but can assume it is constant okay no more electrons reach to the surface okay so we say we started this p substrate at the surface p doping and now it has become and kind so it is inverted we started with holes there and now it has electrons is there so the surface is now inverted and the region is called inversion channel okay that is the principle of mass transistor so since there is a excess electron channel here at this creation larger the VGS larger will be the electron concentration there so we find since the depletion layer is fixed so of course there is a capacitance associated with a channel also but that we will see later we always say the depletion layer capacitance is constant oxide capacitance is also constant so by this figure which I just now did if this is constant constantly how much is Xd here Xd max before it starts separating whatever is the maximum depletion layer with Q any Xd max is the maximum bulk charge or depletion charge we have okay before inversion sets in okay before inversion sets in so this is constant now this is constant now so the capacitance become net capacitance become constant and here is a figure which shows something initially minus VGS oxide capacitance is Seox small positive VGS it starts dropping down as the depletion layer enhances the capacitance start reducing of semiconductor and therefore the net capacitance start dropping somewhere here the potential VT as the word shown here the electric field is sufficiently high so that whole electrons can be separated the CS becomes constant and therefore the net capacitance become constant this is called high frequency CV now why high and low will see this letter so in high frequency CV the way we monitor that the initially for P substrate or N channel device the Seox for all minus VGS is constant even it is constant little bit inside positive VGS and then it start dropping and at VGS where inversion starts we call that voltage as threshold voltage for the mass capacitor and later as we say in the transistors so the threshold voltage is the threshold of starting inversions okay threshold of starting inversion is called threshold voltage this is not a sharp point the way I shown Professor Vasi will give you many other reasons why it is not so sharp we also have shown another graph but later we will discuss that again if the measurement frequency or if the frequency with which VGS is changing is very low the capacitance comes back to Seox okay that is called low frequency CV for a high frequency CV is this low frequency after inversion sets in the oxide the capacitance returns back to oxide capacitance and this is called low frequency CV okay so what is VT definition when the no no there is a definition we made which is mischievous we say once the electron start coming inversions have come but VT is not defined on that we say when the number of our electron concentration becomes exactly equal to the whole concentration of the substrate then only we say it is an inversion which is essentially called strong inversion so the definition is when the at least same number of electrons must be created as many as the whole sphere but actually inversion starts even much before that once the this crosses in VGS is sufficient it will start inverting so from inversion weak inversion to strong inversion you have an inversion but VT definition says it should be as much as electrons as it was from the initial concentration of holes that is the only difference so there is a mischief we should actually define when the inversion starts okay but we do not define we say any how much as much as this additionally when I show band bending next time this will prove very much why we say inversion is strong inversion is needed so what we say at inversion please I will come back again the for me surface potential by the surface potential we say if I apply VGS part of the potential goes to the oxide like a resistive network plus part goes to semiconductor whatever VGS I apply part goes to semiconductor and part goes to oxide this is a Sanko sign potential divider a resistor or two resistors there is nothing great for VOS I do not know okay and that is what I will find but I will say whenever this surface potential becomes two times the Fermi potential then the inversion sets in so we say VGS is equal to VT when size is this and this V ox can be written as QB by C ox plus minus because it can be P substrate or N substrate QND or Q minus QNA so this is the threshold voltage available to you however assumptions made are the metal work function is same as semiconductor and also there are no oxide charges these will come in and there will be two additional terms may appear okay but you need to know so next time.